├── .DS_Store ├── assets ├── TV.png ├── fw.png └── MRL.png ├── terra-documentation.png ├── white-paper ├── terra-v1.0.pdf ├── terra-v1.1.pdf ├── terra-v0.0.8.pdf ├── terra-v1.1.tex ├── terra-v0.08.tex └── terra-v1.0.tex ├── stability-analysis ├── images │ ├── fig1.png │ ├── fig2.png │ └── fig3.png └── stability-v0.1.tex ├── README.md ├── LICENSE.md └── DISCLAIMER.md /.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/terra-money/documentation/HEAD/.DS_Store -------------------------------------------------------------------------------- /assets/TV.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/terra-money/documentation/HEAD/assets/TV.png -------------------------------------------------------------------------------- /assets/fw.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/terra-money/documentation/HEAD/assets/fw.png -------------------------------------------------------------------------------- /assets/MRL.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/terra-money/documentation/HEAD/assets/MRL.png -------------------------------------------------------------------------------- /terra-documentation.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/terra-money/documentation/HEAD/terra-documentation.png -------------------------------------------------------------------------------- /white-paper/terra-v1.0.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/terra-money/documentation/HEAD/white-paper/terra-v1.0.pdf -------------------------------------------------------------------------------- /white-paper/terra-v1.1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/terra-money/documentation/HEAD/white-paper/terra-v1.1.pdf -------------------------------------------------------------------------------- /white-paper/terra-v0.0.8.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/terra-money/documentation/HEAD/white-paper/terra-v0.0.8.pdf -------------------------------------------------------------------------------- /stability-analysis/images/fig1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/terra-money/documentation/HEAD/stability-analysis/images/fig1.png -------------------------------------------------------------------------------- /stability-analysis/images/fig2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/terra-money/documentation/HEAD/stability-analysis/images/fig2.png -------------------------------------------------------------------------------- /stability-analysis/images/fig3.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/terra-money/documentation/HEAD/stability-analysis/images/fig3.png -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Terra Documentation 2 | ![banner](./terra-documentation.png) 3 | 4 | Contains the white paper, high level directives and specifications for the Terra Protocol. 5 | 6 | ## Status 7 | 8 | White paper 1.0 defines the Terra Protocol as it will be implemented in the [Columbus Mainnet](https://www.github.com/terra-project/core). 9 | 10 | ## Disclaimer 11 | 12 | No Terra documentation contained herein is intended to be investment advice of any kind. Please read the [disclaimer](./DISCLAIMER.md). 13 | 14 | ## Contents 15 | 16 | Terra documentation currently contains the white paper and the stability analysis. 17 | 18 | - [White paper](./white-paper/terra-v1.0.pdf) defines the high level motivation and specs for the Terra Protocol. 19 | - [Stability Analysis](./stability-analysis/stability-v0.1.pdf) publishes our stability analysis of the current Terra Protocol. -------------------------------------------------------------------------------- /LICENSE.md: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2019 Terraform Labs PTE LTD 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /DISCLAIMER.md: -------------------------------------------------------------------------------- 1 | # LEGAL DISCLAIMER 2 | 3 | 4 | The purpose of this Website and White paper is to present Terra Money to the world for academic purposes. It is not to invite investments or time contributions of any kind. 5 | 6 | Nothing in this Website and/or White Paper shall be deemed to constitute a prospectus of any sort of a solicitation for investment, nor does it, in any way, pertain to an offering or a solicitation of an o er to buy any securities in any jurisdiction. The document is not composed in accordance with, and is not subject to, laws or regulations of any jurisdiction which are designed to protect investors. 7 | 8 | Certain statements, estimates, and financial information contained within this Website and/or White Paper constitute forward-looking, or pro-forma statements, and information. Such statements or information involve known and unknown risks and uncertainties which may cause actual events or results to differ materially from the estimates or the results implied or expressed in such forward-looking statements. 9 | 10 | Nothing published by, or republished from, Terraform Labs or any of its subsidiaries should be interpreted as investment advice. Information is provided for educational and amusement purposes only. Terraform Labs is in no way providing trading or investment advice. Please consult with your appropriate licensed professional before making any financial transactions, including any investments related to ideas or opinions expressed, past, present, or future by the aforementioned entities and any future entities that may operate under the parent entities. Terraform Labs does not intend to express financial, legal, tax, or any other advice and any conclusions drawn from statements made by, or on, Terraform Labs shall not be deemed to constitute advice in any jurisdiction. -------------------------------------------------------------------------------- /stability-analysis/stability-v0.1.tex: -------------------------------------------------------------------------------- 1 | \documentclass{article} 2 | \usepackage[utf8]{inputenc} 3 | \usepackage{amsmath} 4 | 5 | \title{Terra Stability Analysis} 6 | \author{\{nick, do\}@terra.money} 7 | \date{\today \\v0.0.1} 8 | 9 | 10 | \usepackage{natbib} 11 | \usepackage{graphicx} 12 | \graphicspath{ {images/} } 13 | \usepackage{pgfplots} 14 | \pgfplotsset{compat=1.15} 15 | 16 | \begin{document} 17 | 18 | \maketitle 19 | 20 | \section{Introduction} 21 | 22 | The purpose of this document is to analyze the stability of the Terra Protocol, in light of two foundational constraints that we are committed to: usability and decentralization. Terra is designed to be first and foremost a transactional currency, and we expect its use as a seamless and stable medium of exchange to dominate the high growth phase. We argue that Terra is best modeled as a decentralized payment network during this period, and that existing payment networks best resemble the dynamics of the Terra economy on its path towards becoming a mainstream currency. We demonstrate that the protocol maintains stability by leveraging Luna, Terra's collateral asset, even in the face of price shocks and precipitous falls in demand. We provide a framework for an additional layer of stability via a centralized fiat reserve during the early days of the protocol, as well as a framework for weaning off of it. Finally we outline areas of ongoing and future research. 23 | 24 | \section{Demand Stickiness of Payment Networks} 25 | 26 | Once consumers lock into a means of payment, they rarely switch to others - becoming “sticky.” The steady growth of payment networks like Visa, Amex and PayPal demonstrate the stickiness of payment networks, and by extension of the transaction volume that goes through them. The volatility of earnings for payment companies is very low, and prices are less volatile than the market benchmark (Figures 1 and 2). More importantly, stickiness and low volatility have significant implications when payment networks are viewed as standalone economies. The transaction volume that goes through a network is roughly proportional to “demand” in the virtual network economy. If the network used its own internal currency, this would directly translate to demand for the currency: higher transaction volume implies higher demand for the currency needed to fuel the economy, assuming roughly constant velocity of money in the network. \textbf{We are thus justified in reasoning about demand in a payments economy via earnings, which are just a proxy for transaction volume.} 27 | 28 | It is clear that Terra functions like a decentralized payment network, and is in fact collateralized by the very shares of the network (Luna), which receive transaction fees as dividends. We expect high transaction/demand stickiness in the Terra economy after some threshold in adoption for all the reasons we mentioned earlier. We discuss ways to measure the threshold in a later section. \textbf{The implications of demand stickiness are low churn, low volatility and consequently high earnings multiples for Luna. We collateralize Terra with an asset that receives a sticky revenue stream and derives its value from the high transactionality of the currency.} We later provide a quantitative version of this argument, demonstrating low volatility by modeling it as a function of churn likelihood. We use those properties in our analysis, making significantly more conservative assumptions compared to existing networks until we have grown in adoption. \textbf{The demand profile of Terra is in stark contrast to demand for speculative assets such as gold and (much more) Bitcoin, the latter two having no intrinsic value, no stickiness and thus being significantly more volatile.} A comparison between the volatility of Visa earnings and of the price of gold illustrates the argument nicely. We consider the volatility of gold a best-case scenario for the volatility of bitcoin long-term (Figure 3). 29 | 30 | Demand stickiness and low volatility have important implications on our stability analysis. They form the basis for valuing Luna, provide a framework for decommissioning the fiat reserve and demonstrate that transaction fees will be consistently low with rare exceptions. 31 | 32 | 33 | 34 | \begin{figure} 35 | \centering 36 | \includegraphics[scale=0.35]{fig1.png} 37 | \caption[] 38 | {VISA/AMEX/Mastercard price compared to SP 500 2008-2018} 39 | \end{figure} 40 | 41 | 42 | \begin{figure} 43 | \centering 44 | \includegraphics[scale=0.35]{fig2.png} 45 | \caption[] 46 | {AMEX, Visa, Mastercard revenues 2008-2018} 47 | \end{figure} 48 | 49 | \begin{figure} 50 | \centering 51 | \includegraphics[scale=0.35]{fig3.png} 52 | \caption[] 53 | {Visa earnings compared to the price of gold 2008-2018} 54 | \end{figure} 55 | 56 | 57 | \newpage 58 | 59 | \section{Guarantee of Solvency} 60 | 61 | Terra remains stable insofar as we are able to sufficiently contract its supply during falls in demand or price shocks, or, in other words, if it remains solvent. We express solvency in the following equation: 62 | 63 | \begin{center} 64 | Luna Reserve + Fiat Reserve ${>=}$ Terra Demand Drop (1) 65 | \end{center} 66 | 67 | Terra Demand Drop may in the worst case be the entirety of Terra's supply. Insofar as this equation holds during the lifetime of Terra, the system remains solvent hence the currency remains stable. 68 | 69 | Recall that the Luna reserve is valued by discounting future transaction fee cash flows. This is described by the following equation: 70 | 71 | $$R_T = \sum_{t=T}^{\infty}\frac{f_tS_t}{(1+r)^t} \hspace{0.2cm} (2)$$ \newline 72 | 73 | An equivalent formulation is via an earnings multiple on present transaction fee payouts: 74 | 75 | $$R_t = f_tT_tV_tm_t \hspace{0.2cm} (3)$$ 76 | 77 | \subsection{No Fiat Reserve} 78 | 79 | We start by analyzing the steady state of our protocol, where there is no Fiat Reserve. After the Terra economy has entered maturity, we fully rely on the Luna Reserve for solvency. We analyze the process of decommissioning the Fiat Reserve in the next section. Recalling our earlier discussion, we note that at this stage comparisons to existing payment networks is legitimate — risk and return may be different, but we expect the risk/return profile to be on the same ballpark. 80 | 81 | Let's explore the worst case for equation (1), where Terra's demand drop is close to 100\%. This is of course an extreme scenario for a relatively stable economy, but a crucial one nonetheless. This could be a coordinated Soros attack or a black swan event. In this case we need the Luna Reserve to be at least as valuable as Terra's supply if we are to stay solvent. Equation (3) simplifies to the following: 82 | 83 | $$f_tV_tm_t >= 1 \hspace{0.2cm} (4)$$ 84 | 85 | To proceed with worst-case analysis in equation (4), we assume an earnings multiple $m_t$ of 5 — this is where Amex traded at the very bottom of the 2008 financial crisis after a calamitous 82\% drop in price (not revenue) in less than 2 years. This is the lowest multiple any of the major payment networks have traded at in their history (Visa, Mastercard, Amex, PayPal). Amex trades at a P/E of more than 100 as of May 2018. We assume a conservative money velocity of 10, this is a historical average for the velocity of the USD's M1 and we consider it a lower bound for Terra given its use in e-commerce which experiences much higher velocities. To satisfy equation (4) under those extreme conditions we need transaction fees of 2\%. This is on-par with the fees major e-commerce companies pay to Visa (e.g. TMON), and in fact approximately break-even for most payment networks given the numerous middlemen their infrastructure involves. 86 | 87 | \textbf{So Terra remains solvent in the most extreme conditions (no fiat reserve, near 100\% drop in demand, rock-bottom Luna earnings multiple) by charging fees on-par with competition.} 88 | 89 | \subsection{Gradually Decreasing Fiat Reserve} 90 | 91 | At genesis we maintain a 100\% fiat reserve that guarantees stability in the very early days during which volatility is expected and natural. As the Terra economy grows and volatility decreases we gradually wean off of the reserve. In what follows we outline the framework for decommissioning the reserve. 92 | 93 | Earlier we argued that demand for payment networks like Terra is very sticky — businesses who start relying on Terra and consumers who develop spending habits tend to stick. We now present a quantitative version of this argument, considering the number of e-commerce companies using Terra, $n$, and the probability that any one company churns over a year, $p$. The number of e-commerce companies using Terra is a good proxy for Terra demand. We demonstrate that as $n$ grows (adoption) and $p$ drops (stickiness) the volatility of Terra demand drops very fast. We further quantify the probability that demand will fall below a given threshold and obtain high-probability bounds for it. 94 | 95 | Observe that the number of companies to churn in a given year follows a Binomial distribution with parameters $n$ and $p$, and is closely approximated by a Normal distribution with mean $np$ and variance $np(1-p)$. The relative volatility of demand (volatility divided by $n$) is therefore $\frac{\sqrt{np(1-p)}}{n}$. As $n$ grows and $p$ decreases this value decreases rapidly. \textbf{Intuitively, all this says is that demand for Terra becomes very stable as adoption grows and churn likelihood decreases.} 96 | 97 | We can easily obtain confidence intervals for demand using this model. To make this concrete let's explore possible scenarios for Terra adoption 1, 3 and 5 years from now, making aggressive assumptions about churn likelihood. To make this analysis statistically significant we consider e-commerce partners to be companies with significant transaction volume (\$1B+ in GMV). 98 | 99 | \begin{center} 100 | \begin{tabular}{ |c|c|c|c|c| } 101 | \hline 102 | Year & Tx vol (\$B) & Churn Prob \% & Max Demand Drop \% & Fiat Ratio \% \\ 103 | \hline \hline 104 | 1 & 10 & 20 & 43 & 100 \\ 105 | \hline 106 | 3 & 60 & 10 & 21 & 20 \\ 107 | \hline 108 | 5 & 140 & 5 & 11 & 10 \\ 109 | \hline 110 | \end{tabular} 111 | \end{center} 112 | 113 | 114 | Note that the maximum drop in demand that we expect decreases as the number of partners increases and churn likelihood decreases. We can expect with high confidence, for example, that after 3 years drops in demand should not exceed 21\%. Some of the assumptions that this model makes will be false, so it will clearly not be fully accurate, but it delivers the main message, which is that demand for Terra is sticky and becomes stable quickly. We will be closely observing how churn probabilities evolve over time and how they impact volatility in Terra demand. 115 | 116 | We set the schedule for decommissioning the fiat reserve in accordance with the volatility of demand for Terra, which we both model and measure historically. From equation (1) from the previous section, the Luna and Fiat Reserves in combination need to be more valuable than any demand drop to maintain solvency. \textbf{The guiding principle for the Fiat Reserve is to provide a buffer for large part of worst-case demand drops in the early years while the economy and markets are immature.} During the first year a 100\% fiat reserve will in fact cover much more than demand drops we expect — this added protection is desirable. In accordance with the estimates above, by year 3 we would maintain a 20\% fiat reserve, and by year 5 at most 10\%. After year 5 we would stop funding the fiat reserve, and would start spending it to fund further growth for Terra. The Foundation may maintain some fiat to provide a liquidity buffer to the Terra market, but that will eventually be a negligible fraction of Terra supply. 117 | 118 | Beyond providing an additional layer of stability, which is all but guaranteed in combination with the Luna Reserve, \textbf{the Fiat Reserve acts as a subsidy to transaction fees up to the point where the Luna Reserve can fund contractions using very low fees.} Say, for example, that there is a Black Swan demand drop of 40\% during year 5, even though our models and historical volatility suggest a drop of more than 10\% is highly unlikely. The Fiat Reserve is only 10\%, so the Luna Reserve is tasked with funding the remaining 30\%. Let's assume an earnings multiple of 5, which is very low given the relative maturity of the Terra economy at this point. From equation (3) above, using a velocity of 10, it follows that transaction fees of 0.6\% are sufficient to fund the demand drop. 119 | 120 | \section{Ongoing and Future Research} 121 | 122 | \begin{itemize} 123 | \item Development of more sophisticated volatility models that will allow us to predict Terra demand volatility more accurately. This will be important in the process of decommissioning the Fiat Reserve. 124 | 125 | \item Further research on the impact of transaction fees on volume. We have argued that volume should see minimal change if transaction fees are lower than traditional payment networks. Are there case studies where high transaction fees in e-commerce hurt volume, or where younger competitors were able to steal volume because of lower fees? 126 | 127 | \item How do we refine our approach to fees and volatility estimation when Terra gains broad adoption outside of e-commerce (eg financial applications like escrow, credit markets etc) 128 | 129 | \item How do we optimize staking incentives for cold deposits depending on market conditions? 130 | 131 | \item Run simulations under a variety of market conditions and stress-test the protocol as much as possible. Vary parameters such as churn probability, earnings multiple and volatility to gauge impact on transaction fees and optimal fiat reserve. 132 | \end{itemize} 133 | 134 | 135 | \section{Conclusion} 136 | 137 | We have demonstrated that the Terra protocol keeps Terra stable, usable and decentralized. In particular we have shown, both by comparison to existing payments networks and quantitatively, that Terra will develop significant demand stickiness as it gains adoption. We have proven that Terra remains solvent under the harshest market conditions with no fiat reserve and with fees on par with competition. We have further provided a framework for a gradually diminishing Fiat Reserve that guarantees very low transaction fees to Terra users throughout the early days of the economy. 138 | 139 | \end{document} 140 | -------------------------------------------------------------------------------- /white-paper/terra-v1.1.tex: -------------------------------------------------------------------------------- 1 | %% LyX 2.3.2 created this file. For more info, see http://www.lyx.org/. 2 | %% Do not edit unless you really know what you are doing. 3 | \documentclass[11pt]{article} 4 | \usepackage[LGR,T1]{fontenc} 5 | \usepackage[latin9]{inputenc} 6 | \usepackage{geometry} 7 | \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} 8 | \usepackage{color} 9 | \usepackage{amsmath} 10 | \usepackage{amssymb} 11 | \usepackage{graphicx} 12 | \usepackage{setspace} 13 | \doublespacing 14 | \usepackage[unicode=true, 15 | bookmarks=false, 16 | breaklinks=false,pdfborder={0 0 1},backref=section,colorlinks=true] 17 | {hyperref} 18 | \hypersetup{pdftitle={Terra Money White Paper}, 19 | linkcolor=black,citecolor=blue,filecolor=magenta,urlcolor=blue} 20 | 21 | \makeatletter 22 | 23 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands. 24 | \DeclareRobustCommand{\greektext}{% 25 | \fontencoding{LGR}\selectfont\def\encodingdefault{LGR}} 26 | \DeclareRobustCommand{\textgreek}[1]{\leavevmode{\greektext #1}} 27 | \ProvideTextCommand{\~}{LGR}[1]{\char126#1} 28 | 29 | 30 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands. 31 | \usepackage{xcolor} 32 | \usepackage{adjustbox} 33 | \usepackage{titling}\usepackage{titlesec}\usepackage{eurosym} 34 | \usepackage{harvard}\usepackage{amsfonts} 35 | \usepackage{pdflscape}\usepackage{chicago}\setcounter{MaxMatrixCols}{30} 36 | \usepackage[bottom]{footmisc} 37 | 38 | 39 | % This shrinks the space before and after display formulas 40 | \usepackage{etoolbox} 41 | \apptocmd\normalsize{% 42 | \abovedisplayskip=5pt 43 | %\abovedisplayshortskip=6pt % plus 3pt 44 | \belowdisplayskip=6pt 45 | %\belowdisplayshortskip=7pt plus 3pt 46 | }{}{} 47 | 48 | % slim white space before title, section/subsection headers 49 | \setlength{\droptitle}{-.75in} 50 | \titlespacing*{\section}{0pt}{.2cm}{0pt} 51 | \titlespacing*{\subsection}{0pt}{.2cm}{0pt} 52 | \definecolor{mygray}{gray}{0.95} 53 | 54 | \makeatother 55 | 56 | \usepackage{listings} 57 | \lstset{language=C, 58 | basicstyle={\ttfamily}, 59 | backgroundcolor={\color{mygray}}, 60 | keywordstyle={\color{black}\bfseries}, 61 | frame=tlrb} 62 | \begin{document} 63 | \title{Terra Money:\\ 64 | Stability and Adoption} 65 | \author{Evan Kereiakes, Do Kwon, Marco Di Maggio, Nicholas Platias} 66 | \date{April 2019} 67 | 68 | \maketitle 69 | 70 | \begin{center} 71 | {\large{}{}\vspace{-1.5cm} 72 | }{\large\par} 73 | \par\end{center} 74 | 75 | \begin{center} 76 | 77 | \par\end{center} 78 | \begin{abstract} 79 | \begin{singlespace} 80 | While many see the benefits of a price-stable cryptocurrency that 81 | combines the best of both fiat and Bitcoin, not many have a clear 82 | plan for the adoption of such a currency. Since the value of a currency 83 | as a medium of exchange is mainly driven by its network effects, a 84 | successful new digital currency needs to maximize adoption in order 85 | to become useful. We propose a cryptocurrency, Terra, which is both 86 | price-stable and growth-driven. It achieves price-stability via an 87 | elastic money supply, enabled by stable mining incentives. It also 88 | uses seigniorage created by its minting operations as transaction 89 | stimulus, thereby facilitating adoption. There is demand for a decentralized, 90 | price-stable money protocol in both fiat and blockchain economies. 91 | If such a protocol succeeds, then it will have a significant impact 92 | as the best use case for cryptocurrencies. 93 | \end{singlespace} 94 | \end{abstract} 95 | \thispagestyle{empty} 96 | 97 | \newpage\setcounter{page}{1} 98 | 99 | \section{Introduction} 100 | 101 | The price-volatility of cryptocurrencies is a well-studied problem 102 | by both academics and market observers (see for instance, Liu and 103 | Tsyvinski, 2018, Makarov and Schoar, 2018). Most cryptocurrencies, 104 | including Bitcoin, have a predetermined issuance schedule that, together 105 | with a strong speculative demand, contributes to wild fluctuations 106 | in price. Bitcoin's extreme price volatility is a major roadblock 107 | towards its adoption as a medium of exchange or store of value. Intuitively, 108 | nobody wants to pay with a currency that has the potential to double 109 | in value in a few days, or wants to be paid in a currency if its value 110 | can significantly decline before the transaction is settled. The problems 111 | are aggravated when the transaction requires more time, e.g. for deferred 112 | payments such as mortgages or employment contracts, as volatility 113 | would severely disadvantage one side of the contract, making the usage 114 | of existing digital currencies in these settings prohibitively expensive. 115 | 116 | At the core of how the Terra Protocol solves these issues is the idea 117 | that a cryptocurrency with an elastic monetary policy would maintain 118 | a stable price, retaining all the censorship resistance of Bitcoin, 119 | and making it viable for use in everyday transactions. However, price-stability 120 | is not sufficient for the wide adoption of a currency. Currencies 121 | inherently have strong network effects: a customer is unlikely to 122 | switch over to a new currency unless a critical mass of merchants 123 | are ready to accept it, but at the same time, merchants have no reason 124 | to invest resources and educate staff to accept a new currency unless 125 | there is significant customer demand for it. For this reason, Bitcoin's 126 | adoption in the payments space has been limited to small businesses 127 | whose owners are personally invested in cryptocurrencies. Our belief 128 | is that while an elastic monetary policy is the solution to the stability 129 | problem, an efficient fiscal policy can drive adoption. In addition, 130 | the Terra Protocol offers strong incentives for users to join the 131 | network with an efficient fiscal spending regime, managed by a Treasury, 132 | where multiple stimulus programs compete for financing. That is, proposals 133 | from community participants will be vetted by the rest of the ecosystem 134 | and, when approved, they will be financed with the objective to increase 135 | adoption and expand the potential use cases. The Terra Protocol with 136 | its balance between fostering stability and adoption represents a 137 | meaningful complement to fiat currencies as a means of payment and 138 | store of value. 139 | 140 | The rest of the paper is organized as follows. We first discuss the 141 | protocol and how stability is achieved and maintained, through the 142 | calibration of miners' demand and the use of the native mining Luna 143 | token. We then dig deeper into how stable mining incentives are adopted 144 | to smooth out economic fluctuations. Lastly, we discuss how Terra's 145 | fiscal policy can be used as an efficient stimulus to drive adoption. 146 | 147 | \section{Multi-fiat peg monetary policy } 148 | 149 | A stable-coin mechanism must answer three key questions: 150 | \begin{itemize} 151 | \item \textbf{How is price-stability defined?} Stability is a relative concept; 152 | which asset should a stable-coin be pegged to in order to appeal to 153 | the broadest possible audience? 154 | \item \textbf{How is price-stability measured?} Coin price is exogenous 155 | to the Terra blockchain, and an efficient, corruption-resistant price 156 | feed is necessary for the system to function properly. 157 | \item \textbf{How is price-stability achieved?} When coin price has deviated 158 | from the target, the system needs a way to apply pressures to the 159 | market to bring price back to the target. 160 | \end{itemize} 161 | This section will specify Terra's answers to the above questions 162 | in detail. 163 | 164 | \subsection{Defining stability against regional fiat currencies } 165 | 166 | The existential objective of a stable-coin is to retain its purchasing 167 | power. Given that most goods and services are consumed domestically, 168 | it is important to create crypto-currencies that track the value of 169 | local fiat currencies. Though the US Dollar dominates international 170 | trade and forex operations, to the average consumer the dollar exhibits 171 | unacceptable volatility against their choice unit of account. 172 | 173 | Recognizing strong regionalities in money, Terra aims to be a family 174 | of cryptocurrencies that are each pegged to the world's major currencies. 175 | Close to genesis, the protocol will issue Terra currencies pegged 176 | to USD, EUR, CNY, JPY, GBP, KRW, and the IMF SDR. Over time, more 177 | currencies will be added to the list by user voting. TerraSDR will 178 | be the flagship currency of this family, given that it exhibits the 179 | lowest volatility against any one fiat currency (Kereiakes, 2018). 180 | TerraSDR is the currency in which transaction fees, miner rewards 181 | and stimulus grants will be denominated. 182 | 183 | It is important, however, for Terra currencies to have access to shared 184 | liquidity. For this reason, the system supports atomic swaps among 185 | Terra currencies at their market exchange rates. A user can swap TerraKRW 186 | for TerraUSD instantly at the effective KRW/USD exchange rate. This 187 | allows all Terra currencies to share liquidity and macroeconomic fluctuations; 188 | a fall in demand by one currency can quickly be absorbed by the others. 189 | We can therefore reason about the stability of Terra currencies in 190 | a group; we will be referring to Terra loosely as a single currency 191 | for the remainder of this paper. As Terra's ecosystem adds more currencies, 192 | its atomic swap functionality can be an instant solution to cross 193 | border transactions and international trade settlements. 194 | 195 | \subsection{Measuring stability with miner oracles } 196 | 197 | Since the price of Terra currencies in secondary markets is exogenous 198 | to the blockchain, the system must rely on a decentralized price oracle 199 | to estimate the true exchange rate. We define the mechanism for the 200 | price oracle as the following: 201 | \begin{itemize} 202 | \item For any Terra sub-currency in the set of currencies C = {TerraKRW, 203 | TerraUSD, TerraSDR... } miners submit a vote for what they believe 204 | to be the current exchange rate in the target fiat asset. 205 | \item Every n blocks the vote is tallied by taking the weighted medians 206 | as the true rates. 207 | \item Some amount of Terra is rewarded to those who voted within 1 standard 208 | deviation of the elected median. Those who voted outside may be punished 209 | via slashing of their stakes. The ratio of those that are punished 210 | and rewarded may be calibrated by the system every vote to ensure 211 | that a sufficiently large portion of the miners vote. 212 | \end{itemize} 213 | Several issues have been raised in implementing decentralized oracles, 214 | but chief among them is the possibility for voters to profit by coordinating 215 | on a false price vote. Limiting the vote to a specific subset of users 216 | with strong vested interest in the system, the miners, can vastly 217 | decrease the odds of such a coordination. A successful coordination 218 | event on the price oracle would result in a much higher loss in the 219 | value of the miner stakes than any potential gains, as Luna stakes 220 | are time-locked to the system. 221 | 222 | The oracle can also play a role in adding and deprecating Terra currencies. 223 | The protocol may start supporting a new Terra currency when oracle 224 | votes for it satisfies a submission threshold. Similarly, the failure 225 | to receive a sufficient number of oracle votes for several periods 226 | could trigger the deprecation of a Terra currency. 227 | 228 | \subsection{Achieving stability with consistent mining rewards} 229 | 230 | Once the system has detected that the price of a Terra currency has 231 | deviated from its peg, it must apply pressures to normalize the price. 232 | Like any other market, the Terra money market follows the simple rules 233 | of supply and demand for a pegged currency. That is: 234 | \begin{itemize} 235 | \item Contracting money supply, all conditions held equal, will result in 236 | higher relative currency price levels. That is, when price levels 237 | are falling below the target, reducing money supply sufficiently will 238 | return price levels to normalcy. 239 | \item Expanding money supply, all conditions held equal, will result in 240 | lower relative currency price levels. That is, when price levels are 241 | rising above the target, increasing money supply sufficiently will 242 | return price levels to normalcy. 243 | \end{itemize} 244 | Of course, contracting the supply of money isn't free; like any other 245 | asset, money needs to be bought from the market. Central banks and 246 | governments shoulder contractionary costs for pegged fiat systems 247 | through a variety of mechanisms including intervention, the issuance 248 | of bonds and short-term instruments thus incurring interest expenses, 249 | and hiking of money market rates and reserve ratio requirements thus 250 | losing revenue. Put in a different way, central banks and governments 251 | absorb the volatility of the pegged currencies they issue. 252 | 253 | Analogously, Terra miners absorb volatility in Terra supply. 254 | \begin{itemize} 255 | \item \textbf{In the short term, miners absorb Terra contraction costs} 256 | through mining power dilution. During a contraction, the system mints 257 | and auctions more mining power to buy back and burn Terra. This contracts 258 | the supply of Terra until its price has returned to the peg, and temporarily 259 | results in mining power dilution. 260 | \item \textbf{In the mid to long term, miners are compensated with increased 261 | mining rewards}. First, the system continues to buy back mining power 262 | until a fixed target supply is reached, thereby creating long-run 263 | dependability on available mining power. Second, the system increases 264 | mining rewards, which will be explained in more detail in a later 265 | section. 266 | \end{itemize} 267 | In summary, miners bear the costs of Terra volatility in the short 268 | term, while being compensated for it in the long-term. Compared to 269 | ordinary users, miners have a long-term vested interest in the stability 270 | of the system, with invested infrastructure, trained staff and business 271 | models with high switching cost. The remainder of this section will 272 | discuss how the system absorbs short-term volatility and creates stable 273 | long-term incentives for Terra miners. 274 | 275 | \subsection{Miners absorb short-term Terra volatility } 276 | 277 | The Terra Protocol runs on a Proof of Stake (PoS) blockchain, where 278 | miners need to stake a native cryptocurrency Luna to mine Terra transactions. 279 | At every block period, the protocol elects a block producer from the 280 | set of staked miners, which is entrusted with the work required to 281 | produce the next block by aggregating transactions, achieving consensus 282 | among miners, and ensuring that messages are distributed properly 283 | in a short timeframe with high fault tolerance. 284 | 285 | The block producer election is weighted by the size of the active 286 | miner's Luna stake. Therefore, \textbf{Luna represents mining power 287 | in the Terra network.} Similar to how a Bitcoin miner's hash power 288 | represents a pro-rata odds of generating Bitcoin blocks, the Luna 289 | stake represents pro-rata odds of generating Terra blocks. 290 | 291 | Luna also serves as the most immediate defense against Terra price 292 | fluctuations. The system uses Luna to make the price for Terra by 293 | agreeing to be counter-party to anyone looking to swap Terra and Luna 294 | at Terra's target exchange rate. More concretely: 295 | \begin{itemize} 296 | \item When TerraSDR's price < 1 SDR, users and arbitragers can send 1 TerraSDR 297 | to the system and receive 1 SDR's worth of Luna. 298 | \item When TerraSDR's price > 1 SDR, users and arbitragers can send 1 SDR's 299 | worth of Luna to the system and receive 1 TerraSDR. 300 | \end{itemize} 301 | The system's willingness to respect the target exchange rate irrespective 302 | of market conditions keeps the market exchange rate of Terra at a 303 | tight band around the target exchange rate. An arbitrageur can extract 304 | risk-free profit when 1 TerraSDR = 0.9 SDR by trading TerraSDR for 305 | 1 SDR's worth of Luna from the system, as opposed to 0.9 SDR's worth 306 | of assets she could get from the open market. Similarly, she can also 307 | extract risk-free profit when 1 TerraSDR = 1.1 SDR by trading in 1 308 | SDR worth of Luna to the system to get 1.1 SDR worth of TerraSDR, 309 | once again beating the price of the open market. 310 | 311 | The system finances Terra price making via Luna: 312 | \begin{itemize} 313 | \item To buy 1 TerraSDR, the protocol mints and sells Luna worth 1 SDR 314 | \item By selling 1 TerraSDR, the protocol earns Luna worth 1 SDR 315 | \end{itemize} 316 | As Luna is minted to match Terra offers, volatility is moved from 317 | Terra price to Luna supply. If unmitigated, this Luna dilution presents 318 | a problem for miners; their Luna stakes are worth a smaller portion 319 | of total available mining power post-contraction. The system burns 320 | a portion of the Luna it has earned during expansions until Luna supply 321 | has reached its 1 billion equilibrium issuance. Therefore, Luna can 322 | have steady demand as a token with pro-rata rights to Terra mining 323 | over the long term. The next section discusses how the system offers 324 | stable mining incentives to keep the market for mining and demand 325 | for Luna long-term stable through volatile macroeconomic cycles. 326 | 327 | \subsection{Miners are compensated with long-term stable rewards} 328 | 329 | Miners play a foundational role in the security and stability of Terra. 330 | They provide the former by participating in PoS consensus. They provide 331 | the latter by absorbing short-term volatility in Terra demand. \textbf{Stable 332 | demand for mining is a core requirement for both security and stability.} 333 | To achieve this, the protocol aims to offer stable and predictable 334 | rewards in all economic conditions, booms and busts alike. The network 335 | is best off when it can consistently compensate those that protect 336 | it. 337 | 338 | The protocol has two ways of rewarding miners for their work: 339 | \begin{itemize} 340 | \item \textbf{Transaction fees}: All Terra transactions pay a small fee 341 | to miners. Fees default to 0.1\% and are capped at 1\%, meaning that 342 | transacting with Terra in e-commerce will be much cheaper than transacting 343 | with traditional payment options such as credit cards\footnote{The fee per transaction is capped at 1SDR (1.39 USD at the time of 344 | writing), meaning that larger transactions also pay considerably less 345 | than traditional wire transfers}. 346 | \item \textbf{Seigniorage (Luna burn)}: When demand for Terra increases, 347 | the system mints Terra and earns Luna in return. This is called seigniorage 348 | --- the value of newly minted currency minus the cost of issuance 349 | (which in this case is zero). The system burns a portion of earned 350 | Luna, which makes mining power scarcer. The remaining portion of seigniorage 351 | goes to the Treasury to fund fiscal stimulus. 352 | \end{itemize} 353 | To understand rewards from the perspective of a miner, we look at 354 | the basic calculus one has to go through to determine the viability 355 | of a long-term commitment to mining on the Terra network. After fixed 356 | costs, the profit (or loss) from a mining operation for a single unit 357 | of mining power (1 Luna) comes down to rewards minus cost of work 358 | for that unit. A bit more formally, during a future work period $t$, 359 | profit or loss for a unit of mining power equals 360 | \[ 361 | P(t)=\frac{TotalRewards(t)}{LunaSupply(t)}-UnitMiningCost(t) 362 | \] 363 | 364 | Frequent alternations between profit and loss -- positive and negative 365 | $P(t)$ -- would create highly unstable mining demand. The goal of 366 | the protocol is to make this calculus easier and more predictable. 367 | With that in mind, most of the uncertainty in $P(t)$ comes down to 368 | the first term, ie \emph{unit mining rewards.} As a consequence, unit 369 | mining rewards are the primary consideration for making a long-term 370 | commitment to the network. Stable unit mining rewards produce stable 371 | demand for mining, while volatile unit mining rewards produce the 372 | opposite. 373 | 374 | By default, there is uncertainty both in total rewards (from fees) 375 | and in the supply of Luna, so both terms contribute to the volatility 376 | in unit rewards. First, rewards from fees tend to increase when the 377 | economy grows and tend to decrease when the economy shrinks. Second, 378 | Luna supply tends to decrease when the economy grows (because Luna 379 | is burned from seigniorage), and it tends to increase when the economy 380 | shrinks (because new Luna is issued to buy back Terra). The implication 381 | is that unit mining rewards have a tendency to move strongly in the 382 | direction of the economy, either up or down.\textbf{ }By extention 383 | this also applies to mining demand. 384 | 385 | So in order to create mining demand that is long-term stable,\textbf{ 386 | the protocol creates predictable rewards in all economic conditions. 387 | }To achieve this, the protocol uses transaction fees and the rate 388 | of Luna burn as levers to \emph{oppose} changes in unit mining rewards. 389 | Transaction fees affect total rewards, while the rate of Luna burn 390 | affects Luna supply -- the two determinants of \emph{unit} mining 391 | rewards. The basic logic is the following: 392 | \begin{itemize} 393 | \item if unit mining rewards are \emph{increasing}: 394 | \begin{itemize} 395 | \item \emph{decrease}\textbf{ }fees 396 | \item \emph{decrease} Luna burn 397 | \end{itemize} 398 | \item if unit mining rewards are \emph{decreasing}: 399 | \begin{itemize} 400 | \item \emph{increase} fees 401 | \item \emph{increase} Luna burn 402 | \end{itemize} 403 | \end{itemize} 404 | While working to smooth out fluctuations in miner compensation, the 405 | protocol also targets stable growth in line with the long-term growth 406 | of the Terra economy. This is a natural reward for their long-term 407 | commitment to serving the network. 408 | 409 | To formalize those ideas, we discuss the mechanism to smooth out unit 410 | mining rewards in more detail \footnote{The mechanism we present is slightly simplified. We omit a few details, 411 | eg the protocol uses moving averages in mining rewards for robustness 412 | and ensures consistent contribution of buybacks relative to fees in 413 | all situations.}. Fees and the rate of Luna burn -- the ``stability levers'' -- 414 | are adjusted every week in response to changes in unit mining rewards. 415 | We define the rate of Luna burn as follows: what portion (\%) of seigniorage 416 | does the protocol use to buy back and burn Luna, as opposed to depositing 417 | to the Treasury? Let $f_{t}$, $b_{t}$ and $R_{t}$ be transaction 418 | fees, the rate of Luna burn and \emph{unit} mining rewards at time 419 | $t$ respectively. Then the rule for adjusting the values of $f$ 420 | and $b$ is the following: 421 | 422 | \[ 423 | f_{t+1}=(1+g)\cdot\frac{R_{t-1}}{R_{t}}\cdot f_{t} 424 | \] 425 | 426 | \[ 427 | b_{t+1}=(1+g)\cdot\frac{R_{t-1}}{R_{t}}\cdot b_{t} 428 | \] 429 | 430 | The update rules should now make clear what we mean when we say that 431 | fees (and Luna burn rate) \emph{oppose} changes in unit mining rewards: 432 | the current value, $f_{t}$, is multiplied by the \emph{inverse change 433 | }in unit mining rewards, $\frac{R_{t-1}}{R_{t}}$. For example, if 434 | unit mining rewards were cut in half then fees would double in response, 435 | and conversely if unit mining rewards were to double fees would be 436 | cut in half in response. The result is scaled by a small growth factor, 437 | $1+g$, that permits gradual growth in unit mining rewards commensurate 438 | with the \emph{long-term} growth rate of the economy. 439 | 440 | How well does the mechanism work in practice? We have run extensive 441 | simulations to stress-test and refine it under a breadth of assumptions. 442 | In what follows we share and discuss a representative example that 443 | applies significant stress to the mechanism and sheds light on how 444 | it achieves its objective. We consider a simulated 10 year period 445 | during which the Terra economy experiences both rapid growth and severe 446 | turbulence. We demonstrate how the protocol adjusts its stability 447 | levers in response to economic conditions, and how those adjustments 448 | in turn shape unit mining rewards. 449 | 450 | \pagebreak{} 451 | 452 | \begin{adjustbox}{center} 453 | 454 | \includegraphics[scale=0.57]{/Users/nicholas/Dropbox/terra/graphs/mining_rewards_graphs/WP/TV} 455 | 456 | \end{adjustbox} 457 | 458 | \begin{adjustbox}{center} 459 | 460 | \includegraphics[scale=0.57]{/Users/nicholas/Dropbox/terra/graphs/mining_rewards_graphs/WP/fw} 461 | 462 | \end{adjustbox} 463 | 464 | \begin{adjustbox}{center} 465 | 466 | \includegraphics[scale=0.57]{/Users/nicholas/Dropbox/terra/graphs/mining_rewards_graphs/WP/MRL} 467 | 468 | \end{adjustbox} 469 | 470 | The first graph shows simulated weekly \textbf{transaction volume} 471 | and its annual moving average. Transaction volume can be thought of 472 | as the GDP of the Terra economy. The economy experiences rapid growth 473 | followed by a severe multi-year recession that wipes out 93\% of GDP 474 | over 3 years and requires 6 years for full recovery. This scenario 475 | is a stern test -- if it were describing the price of Bitcoin it 476 | would be by far the longest bear market in its history and tied for 477 | worst in terms of drawdown (equal to the 93\% drop between June and 478 | November 2011). While we think that Terra's adoption-driven demand 479 | will be far more stable than Bitcoin's speculation-driven demand, 480 | the stability mechanism has been designed to confidently withstand 481 | Bitcoin-level volatility. 482 | 483 | The second graph shows \textbf{transaction fees and the Luna burn 484 | rate}, the two levers used by the protocol to smooth out fluctuations 485 | in unit mining rewards. We observe that both move \emph{opposite} 486 | to the direction of the economy (which is also the default direction 487 | of unit mining rewards). 488 | 489 | The third graph shows the annual moving average of \textbf{unit mining 490 | rewards. }The growth target we have set in this example is 15\% annually. 491 | As was designed, unit mining rewards experience steady growth with 492 | low volatility, unpurturbed by the cycles in Terra's GDP. The adjustments 493 | in fees and the Luna burn rate have successfully absorbed the expected 494 | volatility in unit mining rewards and created predictable growth. 495 | This is achieved with fees that average less than 0.5\% (with a momentary 496 | peak at the 1\% maximum) and a Luna burn rate that averages roughly 497 | 50\% (meaning that on average 50\% of seigniorage is granted to the 498 | Treasury). 499 | 500 | Stable demand for mining is a core requirement for the security and 501 | stability of Terra. Unit mining rewards are the primary consideration 502 | and the biggest source of risk for miners. They are by default highly 503 | cyclical, hence highly uncertain. Reducing that uncertainty in the 504 | face of volatile conditions is the key to stable mining demand. We 505 | have outlined a simple mechanism that uses transaction fees and Luna 506 | burn as levers to achieve this, and demonstrated its effectiveness 507 | in the most severe economic conditions. 508 | 509 | \section{Growth-driven fiscal policy} 510 | 511 | Despite their enormous potential, smart contracts have faced roadblocks 512 | in adoption due to the price volatility of their underlying currency. 513 | Price volatility makes smart contracts unusable for most mainstream 514 | financial applications, as most users are accustomed to valuing determinate 515 | payouts in insurance, credit, mortgage, and payroll. Terra will offer 516 | a stable dApp platform oriented to building financial applications 517 | that use Terra as their underlying currency, thus allowing smart contracts 518 | to mature into a useful infrastructure for mainstream businesses. 519 | Terra Platform DApps will help to drive growth and stabilize the Terra 520 | family of currencies by diversifying its use cases. In this section 521 | we discuss how the protocol subsidizes the growth of the more successful 522 | applications through its growth-driven fiscal policy. 523 | 524 | National governments use expansionary fiscal spending with the objective 525 | of stimulating growth. The hope of fiscal spending is that the economic 526 | activity instigated by the original spending results in a feedback 527 | loop that grows the economy more than the amount of money spent in 528 | the initial stimulus. This concept is captured by the spending multiplier 529 | --- how many dollars of economic activity does one dollar of fiscal 530 | spending generate? The spending multiplier increases with the marginal 531 | propensity to consume, meaning that the effectiveness of the expansionary 532 | stimulus is directly related to how likely economic agents are to 533 | increase their spending. 534 | 535 | In a previous section, we discussed how Terra seigniorage is directed 536 | to both miner rewards and the Treasury. At this point, it is worth 537 | describing how exactly the Treasury implements Terra's fiscal spending 538 | policy, with its core mandate being to stimulate Terra's growth while 539 | ensuring its stability. In this manner, Terra achieves greater efficiency 540 | by returning seigniorage not allocated for stability back to its users. 541 | 542 | The Treasury's main focus is the allocation of resources derived from 543 | seigniorage to decentralized applications (dApp). To receive seigniorage 544 | from the Treasury, a dApp needs to register for consideration as an 545 | entity that operates on the Terra network. dApps are eligible for 546 | funding depending on their economic activity and use of funding. 547 | 548 | The funding procedure for a dApp works as follows: 549 | \begin{itemize} 550 | \item A dApp applies for an account with the Treasury; the application includes 551 | metadata such as the Title, a url leading to a detailed page regarding 552 | the use of funding, the wallet address of the applicant, as well as 553 | auditing and governance procedures. 554 | \item At regular voting intervals, Luna validators vote to accept or reject 555 | new dApp applications for Treasury accounts. The net number of votes 556 | (yes votes minus no votes) needs to exceed 1/3 of total available 557 | validator power for an application to be accepted. 558 | \item Luna validators can exercise control over which dApps may open accounts 559 | with the Treasury. The funding itself is determined by validator voting 560 | for each funding period in accordance with a weight that is assigned 561 | to each dApp. This allows the Treasury to prioritize dApps that earn 562 | the most funding. 563 | \item At each voting session, Luna validators have the right to request 564 | that a dApp be blacklisted, for example because it behaves dishonestly 565 | or fails to account for its use of Treasury funds. Again, the net 566 | number of votes (yes votes minus no votes) needs to exceed 1/3 of 567 | total available validator power for the blacklist to be enforced. 568 | A blacklisted dApp loses access to its Treasury account and is no 569 | longer eligible for funding. 570 | \end{itemize} 571 | The motivation behind assigning funding weights to dApps is to maximize 572 | the impact of the stimulus on the economy by rewarding the dApps that 573 | are more likely to have a positive effect on the economy. The Treasury 574 | uses two criteria to determine spending allocations: (1) \textbf{robust 575 | economic activity} and (2) \textbf{efficient use of funding}. dApps 576 | with a strong track record of adoption receive support for their continued 577 | success, and dApps that have grown relative to their funding are rewarded 578 | with more seigniorage, as they have a successful track record of efficiently 579 | using their resources. 580 | 581 | Those two criteria are combined into a single weight which determines 582 | the relative funding that dApps receive from the aggregate funding 583 | pool. For instance, a dApp with a weight of 2 would receive twice 584 | the amount of funding of a dApp with a weight of 1. 585 | 586 | We lay out the funding weight equation, followed by a detailed explanation 587 | of all the parts: For a time period t, let $TV_{t}$ be a dApp's transaction 588 | volume and $F_{t}$ be the Treasury funding received. Then, the protocol 589 | determines the funding weight $w_{t}$ for the period as follows: 590 | 591 | \[ 592 | w_{t}=\left(1-\lambda\right)TV_{t}^{*}+\lambda\frac{\Delta TV_{t}^{*}}{F_{t-1}^{*}} 593 | \] 594 | 595 | The notation {*} denotes a moving average, so $TV_{t}^{*}$ would 596 | be the moving average of transaction volume leading up to time period 597 | t, while $\Delta TV_{t}^{*}$ would be a difference of moving averages 598 | of different lengths leading up to time period t. One might make the 599 | averaging window quarterly for example. Finally, the funding weights 600 | among all dApps are scaled to sum to 1. 601 | \begin{itemize} 602 | \item \textbf{The first term} is proportional to $TV_{t}^{*}$, the average 603 | transaction volume generated by the dApp in the recent past. This 604 | is an indicator of the dApp's \textbf{economic activity}, or more 605 | simply the size of its micro-economy. 606 | \item \textbf{The second term} is proportional to $\Delta TV*_{t}/F*_{t}-1$. 607 | The numerator describes the trend in transaction volume --- it is 608 | the difference between a more and a less recent average. When positive, 609 | it means that the transaction volume is following an upward trajectory 610 | and vice versa. The denominator is the average funding amount received 611 | by the dApp in the recent past, up to and including the previous period. 612 | So the second term describes how economic activity is changing relative 613 | to past funding. Overall, larger values of this ratio capture instances 614 | where the dApp is fast-growing for each dollar of funding it has received. 615 | This is in fact the spending multiplier of the funding program, a 616 | prime indicator of \textbf{funding efficiency}. 617 | \item The parameter \textgreek{l} is used to determine the relative importance 618 | of economic activity and funding efficiency. If it is set equal to 619 | 1/2 then the two terms would have equal contribution. By decreasing 620 | the value of \textgreek{l}, the protocol can favor more heavily dApps 621 | with larger economies. Conversely, by increasing the value of \textgreek{l} 622 | the protocol can favor dApps that are using funding with high efficiency, 623 | for example by growing fast with little funding, even if they are 624 | smaller in size. 625 | \end{itemize} 626 | An important advantage of distributing funding in a programmatic way 627 | is that it is simpler, objective, transparent and streamlined compared 628 | to open-ended voting systems. In fact, compared to decentralized voting 629 | systems, it is more predictable, because the inputs used to compute 630 | the funding weights are transparent and slow moving. Furthermore, 631 | this system requires less trust in Luna validators, given that the 632 | only authority they are vested with is determining whether or not 633 | a dApp is honest and makes legitimate use of funding. 634 | 635 | Overall, the objective of Terra governance is simple: fund the organizations 636 | and proposals with the highest net impact on the economy. This will 637 | include dApps solving real problems for users, increasing Terra's 638 | adoption and as a result increasing the GDP of the Terra economy. 639 | 640 | \section{Conclusion} 641 | 642 | We have presented Terra, a stable digital currency that is designed 643 | to complement both existing fiat and cryptocurrencies as a way to 644 | transact and store value. The protocol adjusts the supply of Terra 645 | in response to changes in demand to keep its price stable. This is 646 | achieved using Luna, the mining token whose stable rewards are designed 647 | to absorb volatility from changing economic cycles. Terra also achieves 648 | efficient adoption by returning seigniorage not invested in stability 649 | back to its users. Its transparent and democratic distribution mechanism 650 | gives dApps the power to attract and retain users by tapping into 651 | Terra's economic growth. 652 | 653 | If Bitcoin's contribution to cryptocurrency was immutability, and 654 | Ethereum expressivity, our value-add will be usability. The potential 655 | applications of Terra are immense. Immediately, we foresee Terra being 656 | used as a medium-of-exchange in online payments, allowing people to 657 | transact freely at a fraction of the fees charged by other payment 658 | methods. As the world starts to become more and more decentralized, 659 | we see Terra being used as a dApp platform where price-stable token 660 | economies are built on Terra. Terra is looking to become the first 661 | usable currency and stability platform on the blockchain, unlocking 662 | the power of decentralization for mainstream users, merchants, and 663 | developers. 664 | 665 | \noindent {\small{}{}\newpage}\textbf{\small{}{}References }{\small\par} 666 | 667 | \noindent {\small{}{}Liu, Yukun and Tsyvinski, Aleh, Risks and Returns 668 | of Cryptocurrency (August 2018). NBER Working Paper No. w24877. Available 669 | at https://ssrn.com/abstract=3226806. }{\small\par} 670 | 671 | \noindent {\small{}{}Makarov, Igor and Schoar, Antoinette, Trading 672 | and Arbitrage in Cryptocurrency Markets (April 30, 2018). Available 673 | at SSRN: https://ssrn.com/abstract=3171204. }{\small\par} 674 | 675 | \noindent {\small{}{}Kereiakes, Evan, Rationale for Including Multiple 676 | Fiat Currencies in Terra's Peg (November 2018). Available at https://medium.com/terra-money/rationale-for-including-multiple-fiat-currencies-in-terras-peg-1ea9eae9de2a }{\small\par} 677 | 678 | \noindent {\small{}{}Taylor, John B. (1993). \textquotedbl Discretion 679 | versus Policy Rules in Practice.\textquotedbl{} Carnegie-Rochester 680 | Conference Series on Public Policy. 39: 195--214. }{\small\par} 681 | 682 | 683 | \end{document} 684 | -------------------------------------------------------------------------------- /white-paper/terra-v0.08.tex: -------------------------------------------------------------------------------- 1 | \documentclass{article} 2 | \usepackage[utf8]{inputenc} 3 | \usepackage{amsmath} 4 | 5 | \title{Terra: A price-stable and democratic money-as-protocol} 6 | \author{\{do, nick\}@terra.money} 7 | \date{\today \\v0.0.8} 8 | 9 | 10 | \usepackage{natbib} 11 | \usepackage{graphicx} 12 | \usepackage{pgfplots} 13 | \pgfplotsset{compat=1.15} 14 | 15 | \begin{document} 16 | 17 | \maketitle 18 | 19 | \begin{abstract} 20 | A price stable cryptocurrency would allow for more mass adoption outside of mere trading and speculation. Bitcoin has provided part of the solution, but it has become more of a commodity akin to gold rather than a medium of exchange or unit of account. We propose Terra, an alternative to Bitcoin which expands and contracts in supply to stabilize unit price. Similar to how fiat currencies are supported by sovereign taxation, Terra is supported by taxation on the value created on its network. Superior to fiat currencies, Terra operates under a decentralized guarantee of solvency, eliminating risks of currency failures and Soros attacks. Finally, Terra engages in decentralized fiscal spending, ensuring that economic growth is distributed equitably via democratic consensus rather than via a politicized system of elected delegates. 21 | 22 | The need for a decentralized, price-stable protocol of money is massive in both fiat and blockchain economies. If such a protocol succeeds, then it will have an enormous impact and prove to be the best use case for cryptocurrencies in the real world. 23 | 24 | \end{abstract} 25 | 26 | \pagebreak 27 | \tableofcontents 28 | \pagebreak 29 | 30 | \section{Introduction} 31 | 32 | Short-term price-stability is a central component of any mainstream currency. Without it, currency cannot be relied on as a store of value, as the value of one's savings could plummet overnight. Price volatility is also unacceptable for mediums-of-exchange for a similar reason, as it introduces risk of appreciation on the part of the purchaser and risk of depreciation on the part of the merchant. Finally, price volatile currencies cannot be used as a unit of account, as the purchasing power implied by contractual obligations and balance sheets would roller-coaster over time. 33 | 34 | With the explosion of the decentralized economy, dApps are starting to discover the importance of price stability as well. For utility token projects, it is difficult to build an economy on tokens that are inherently subject to price speculation, as it is difficult to build a medium-of-exchange paradigm on such tokens. Imagine deciding to become a storage service provider on Filecoin, only to have your revenues fluctuate massively due to its price-volatility. People often forget that cryptocurrencies must first function effectively as currencies before the utility of their technologies can be proven. 35 | 36 | Many people correctly see the development of a price-stable cryptocurrency, a "stable-coin," as a massive opportunity. But not many yet understand that the responsibility involved is commensurately large. Currency regimes have a responsibility to equitably distribute economic growth. Today, fiat fiscal spending suffers from centralization risk in its elected delegates, which are influenced by political variables and corporate lobbies. This leads to inefficient and inequitable allocation of capital. Bitcoin has not done much better, as its inflexible scarcity has vastly enriched early investors and alienated late-comers. A mainstream, truly global cryptocurrency will ensure that growth in the system is distributed equitably by the decentralized consensus of its constituents. 37 | 38 | In this white paper, we propose a new cryptocurrency \textit{Terra} that is as stable as the earth and global in ambition. We will first formalize the problem requirements of price-stabilizing a decentralized currency. Secondly, we will define a protocol that holds the requisite solution properties, and show why it is sufficiently robust. Lastly, we will also show how this protocol can be extended as a platform for price-stability that allows third-party decentralized assets to achieve price-stability. 39 | 40 | \section{The Price Stabilization Problem} 41 | 42 | In this section, we look at how fiat currencies achieve short-term price-stability, and how such mechanisms can be replicated on a decentralized protocol. 43 | 44 | \subsection{The quantity theory of money} 45 | 46 | If we look past the bells and whistles of currency markets, we can see that money is just an expression of the value in an economic system. Simplistically stated, this means that should someone somehow happen to own all the money supply in an economy, he should be able to purchase all the value contained therein. Therefore, each unit of money is value-equivalent to a share of the economy's value, divided by the number of money units in circulation. 47 | 48 | A couple of corollaries is evident. 49 | 50 | \begin{itemize} 51 | \item In the same economic system, should the money supply suddenly double, there would be twice as much currency to describe an equal amount of value. Therefore, the value of each unit of currency would be halved. Conversely, should the opposite were to occur, the unit value of currency would double. 52 | \item Similarly, should the value in the economy suddenly double with the same number of currency units, each currency unit would double in value. It's trivial to see that should economic output suddenly drop by half, each currency unit would also halve. 53 | \end{itemize} 54 | 55 | This insight is formalized in the Quantity Theory of Money, which states that the general price level of goods and services, denoted by the unit value of currency, is directly proportional to the money supply. QTM forms the foundation of monetary policies used by central banks, which expand the money supply when price levels are too high, and contract the money supply when price levels are too low. A decentralized protocol can rely on similar mechanisms to stabilize the unit price of its own cryptocurrency. 56 | 57 | \subsection{Guarantee of solvency through taxation} 58 | 59 | Fiat currencies derive value from the solvency of their governments, which is estimated by contrasting the cash inflow from taxation to the cash outflow from fiscal spending. Governments which vastly outspent their income from taxes through an unrestrained mint have suffered sovereign debt crises and currency failures. Governments that exercised fiscal prudence, “living within their means,” have managed to defend the value of their currencies. 60 | 61 | Formulated in a different way, fiat currencies are propped up by a centralized reserve value-defined by income from taxes. For a currency to retain its value, this reserve must be reasonably solvent. To formalize, the short-term purchasing power of a currency holds if the following inequality holds: 62 | 63 | $$A_t + D_t < R_t + L_t$$ 64 | 65 | Where $A_t$ , $D_t$, $R_t$, and $L_t$ are the resources available to the attackers, the defectors, the reserve and the loyalists at time $t$. Governments with a strong currency have generally kept $R_t$ prohibitively large to be shorted by speculators. 66 | 67 | In order for a currency operated by a decentralized protocol to be viable, it must too provision a reserve with taxes collected from its network. We can do this by charging transaction fees from the blockchain network, since taxes are just transaction fees (weighted by politics) on a national payment network. Unlike fiat currency schemes, however, a protocol currency scheme must maintain a full-reserve populated with decentralized assets. 68 | 69 | \begin{enumerate} 70 | \item \textbf{Full reserve}: Protocol currencies are not backed by sovereign enforcement, and must therefore ensure full parity for every unit ever issued. It cannot issue bonds or get loans in good faith, since its only possibility of paying it back is the unfounded optimism of believers and loyalists. In such a scheme, the currency peg holds to the extent the belief of loyalists exceed the belief of defectors; any sustained recession or determined Soros attack can bring it to its knees. Therefore, it is not sufficient for a protocol currency to maintain a reasonably high value of $R_t$, but rather to keep the reserve ratio $>$ 1 by guaranteeing $R_t > A_t + D_t$. 71 | 72 | \item \textbf{Decentralized assets}: The reserve must be constructed from decentralized assets, as centralized assets carry significant custodial risk. For one, real assets are governed by the goodwill of the foundation rather than transparent rules of the blockchain, creating short-term defection incentives for the foundation. There is also risk of seizures, regulatory scrutiny, bankruptcy or natural disaster. 73 | \end{enumerate} 74 | 75 | Through maintenance of a decentralized full-reserve, the system can operate via a guarantee of solvency that is capable of fully funding contractions. 76 | 77 | 78 | \section{The Terra Protocol} 79 | 80 | Terra is a cryptocurrency price-pegged to a basket of currencies much like the IMF's SDR. At genesis, the composition of the basket will exactly mirror the composition of the SDR \footnote{Currently U.S. dollar 41.73\%, Euro 30.93\%, Renminbi 10.92\%, Japanese yen 8.33\%, British pound 8.09\%. Source: International Monetary Fund.}, but the basket will, over time, include basic goods and services with worldwide usage and appeal such as gold, corn, and timber. This approach frees Terra from the monetary policies of any one government, and eventually allows it to transition to a completely fiat-independent monetary policy regime. 81 | 82 | In the interest of simplicity, however, we will write as if Terra is pegged to a fiat currency such as the USD for the remainder of this paper. 83 | 84 | 85 | \subsection{Overview} 86 | 87 | We outline the basic mechanism of the Terra Protocol. The protocol is guaranteed to be solvent by a full-reserve, which retains its value from the transaction fees collected from the network. The protocol operates via a guarantee of solvency, ensuring that the market value of the reserve is greater than the value of Terra in circulation. The stability of such a system is not maintained by blind faith and optimism of loyalists but a guarantee that the system can fully contract the money supply if need be. 88 | 89 | Every pre-determined time period, the protocol engages in the following mechanisms to stabilize Terra's price: 90 | 91 | \begin{itemize} 92 | 93 | \item \textbf{Price estimation via deposit holder vote}: The protocol estimates the current price for Terra relative to the asset it is pegged to by taking votes weighted-by-stake of the deposit holders in the Stability Reserve. 94 | 95 | \item \textbf{Maintenance of full reserve}: The protocol maintains a “stability reserve” made up of user deposits with rewards varied to ensure the system is over-reserved. 96 | \begin{itemize} 97 | 98 | \item \textbf{Luna tokens}: The protocol defines Luna, a token with fixed supply that generates rewards from Terra transactions, paid out for contributions to the system's price-stability and equity. 99 | \item \textbf{Reserve deposits}: Users are incentivized to deposit Luna into the Reserve, as deposits yield income from transaction fees collected from the network. 100 | \item \textbf{Variable transaction fees}: The protocol levies a small fee from Terra transactions, calibrated to guarantee that the market value of the Stability Reserve exceeds Terra's circulating supply. 101 | \end{itemize} 102 | 103 | \item \textbf{Price stabilization by expansion and contraction of the money supply}: The protocol expands and contracts the supply of Terra tokens to calibrate the exchange rate with the peg, leveraging the Quantity Theory of Money intuition money supply = price level. 104 | \begin{itemize} 105 | 106 | \item \textbf{Contraction by reserve}: When exchange rate of Terra $<$ price peg, the reserve buys up Terra from the market and burns it, contracting the money supply such that price level = money supply. 107 | \item \textbf{Expansion through fiscal spending}: When exchange rate of Terra $>$ price peg, the system mints new Terra and takes proposals / votes from Luna stakeholders to engage in decentralized fiscal spending for the betterment of the system. 108 | \end{itemize} 109 | \end{itemize} 110 | 111 | 112 | \subsection{Price estimation via deposit holder vote} 113 | 114 | Since the price of Terra in secondary markets is exogenous to the blockchain, the system must rely on a decentralized price oracle to estimate the true exchange rate. We define the mechanism for the price oracle as the following: 115 | 116 | \begin{itemize} 117 | 118 | \item The system defines “stability providers,” users with a significant stake in cold deposits in the stability reserve of the system. 119 | \item Every $n$ blocks, stability providers cast their vote on what they think the exchange rate for Terra was. These votes are all cast on the same block, and the votes that exceed the block size are disregarded. 120 | \item The weighted median of the votes is taken as the true exchange rate. A part of the stake of the voters who voted outside 1 standard deviation is taken, and rewarded to voters who voted within. The punishments / rewards are calibrated by the system every vote to ensure that a sufficiently large portion of the stakeholders vote. 121 | \end{itemize} 122 | 123 | Unlike generic stakeholders, stability providers have a large incentive to defend the stability of the system, since price-volatility may lead to erosion or total loss of their deposits. Furthermore, by forcing votes to be made on the same block, the system avoids signaling risk, as voters are not aware of others' votes before the poll has closed. 124 | 125 | This stake-weighted consensus-based selection algorithm guarantees the authenticity of price estimates as long as there is no collusion of more than fifty percent of the cold deposit holders. Note that the guarantee made here is similar to Bitcoin's regarding transaction validity, creating a price-oracle made secure by decentralized consensus. 126 | 127 | 128 | \subsection{Full stability reserve} 129 | 130 | Most central banks maintain reserves directly via foreign currency and gold bullion holdings, as well as indirectly via fractional reserve requirements in licensed commercial banks. Similarly, Terra maintains a Stability Reserve that finances contraction of the Terra money supply whenever necessary. Given that Terra is not backed by a sovereign government, whose authority, monopoly of force and taxation provide solid backing to fiat currencies, the robustness of its Reserve is essential to stability. 131 | 132 | The operating mandate of the Stability Reserve is to maintain a market value that is equal to or in excess of the value of Terra in circulation. If we define the Reserve Ratio to be the ratio between the value of the Stability Reserve and the value of circulating Terra, this is equivalent to saying that the mandate of the Stability Reserve is to maintain a Reserve Ratio of at least 1. The protocol achieves this by relying on the defining feature of Terra: transactional value. 133 | 134 | \subsubsection{Luna token} 135 | The protocol relies on Luna for the price stability of Terra. Luna has a fixed supply, which is decided at genesis. Fees from Terra transactions are used to reward users who participate in the system's democratic process, which requires staking Luna in the Stability Reserve. Insofar as real transactions are taking place in the Terra economy, Luna tokenholders can expect steady rewards for their efforts. This property gives Luna tangible, non-speculative value. This is particularly important, as it will soon be clear that Luna also collateralizes the Terra economy. 136 | 137 | \subsubsection{Deposits} 138 | Users are incentivized to deposit Luna into the Reserve, as it is required to engage in activities that accrue rewards from transaction fees collected from the network. This is akin to variable interest being paid out to deposits in a bank. There are two types of Luna deposits: 139 | 140 | \begin{itemize} 141 | \item Hot deposits: Withdrawable subject to a 24h withdrawal notice. 142 | \item Cold deposits: Locked up for 100 days, withdrawable immediately thereafter. 143 | \end{itemize} 144 | 145 | Transaction fees are paid out to depositors on a pro-rata basis, weighted by the deposit type: payouts to cold deposits are weighted by a factor $w > 1$. The value of $w$ is initialized at 2, after which it is dynamically calibrated by the protocol based on the following: 146 | 147 | \begin{itemize} 148 | \item Cold deposit ratio: the protocol aims to maintain a healthy ratio of Cold deposits in the Reserve, and will make Cold deposits more attractive if the ratio is low. 149 | \item Terra price volatility: the protocol strongly incentivizes Cold over Hot deposits when the price of Terra is volatile. Volatility in the price of Terra increases the likelihood that the Reserve will be used to finance contraction of the Terra supply. Long-term commitments to the Reserve are needed more than ever during periods of volatility and imminent contraction. 150 | \end{itemize} 151 | 152 | \subsubsection{Reserve ratio band} 153 | 154 | The protocol establishes a minimum buffer above the guaranteed Reserve Ratio of 1 to ensure that it has the time and bandwidth to respond to drops in value. The Reserve Ratio it targets lies above that buffer, allowing for volatility in the value of the Reserve without the need to take action. The protocol also sets a ceiling for the Reserve Ratio, above which it is inefficient to be maintained. 155 | 156 | Formally, the protocol defines a band for the Reserve Ratio $(r_{min}, r_{max})$ and a target ratio $r*$, where $1 < r_{min} < r* < r_{max}$. The protocol restricts the Reserve Ratio within the band and targets $r*$. The definition of the band relies on the maximum drawdown in the price of Luna over the past $100$ days, which we call $d$. 157 | 158 | \begin{itemize} 159 | \item $r_{min}$ is set to the fixed value 1.2 160 | \item $r*$ is defined as $r_{min}/(1-d)$. Equivalently, $r*$ is defined so that a drawdown of $d$ in the Reserve Ratio would result in $r_{min}$. E.g. if $d = 1/2$ then $r* = 2r_{min}$ 161 | \item $r_{max}$ is defined as $2{r*} - r_{min}$, i.e. it is defined so that $r*$ is the average of $r_{min}$ and $r_{max}$ 162 | \end{itemize} 163 | 164 | 165 | The protocol determines the target Reserve Ratio $r*$ based on the recently experienced volatility in the price of Luna. Given that the Reserve Ratio must remain consistently above 1, the target increases when the price of Luna is likely to experience big drops. As such, the band within which the Reserve Ratio is restricted is fat when the price of Luna is volatile/experiences major drawdowns, and shrinks when the price of Luna is stable or it experiences steady growth. The protocol thus shields the Reserve Ratio commensurately to the volatility it is being exposed to. 166 | 167 | \subsubsection{Iterative transaction fee calibration} 168 | 169 | Transaction fees are the primary lever that the protocol uses to calibrate the Reserve Ratio when it drifts outside of the desired band. When the Reserve Ratio drops below $r_{min}$, the protocol increases transaction fees to bring it back up. Conversely, when the Reserve Ratio grows above $r_{max}$, the protocol decreases transaction fees to lower it. Intuitively, transaction fees control the cash flows that accrue to Luna holders. For example, an increase in transaction fees increases the expected cash flow that Luna holders receive. As such it increases the price of Luna, and consequently the value of the Reserve. 170 | 171 | To this end, the protocol implements a novel algorithm, Dynamic Multiplication / Milestone-based Decrement (DMMD), which calibrates transaction fees iteratively to keep the Reserve Ratio within bounds. Transaction fees are calculated proportionally to the value of each transaction, and are initialized at 0.1 percent. Fees are dynamically increased when the protocol determines that the Reserve Ratio needs to increase, and decreased when the Reserve Ratio is favorable and the Terra economy experiences sustainable growth. DMMD takes inspiration from the AIMD algorithm used by TCP for congestion control. 172 | 173 | DMMD takes the following steps: 174 | 175 | \begin{itemize} 176 | \item \textbf{Dynamic multiplication of fees}: When the Reserve Ratio drops below $r_{min}$, the protocol multiplies transaction fees by $m = {r*}/r_{min}$. Let $f$ be the previous transaction fees; then $f' = mf$. 177 | 178 | \item \textbf{Milestone}: The new transaction fees remain in effect until the supply of Terra has experienced net growth percentage of at least $m$. E.g. if transaction fees were increased by 50 percent, the increase will remain in effect until the supply of Terra has experienced net growth of at least 50 percent. 179 | 180 | \item \textbf{Milestone-based decrement of fees}: After the growth milestone has been reached, transaction fees are subject to a decrement schedule of 0.02 percent every 10 days. Fees are also decremented by 0.02 percent for every consecutive 24h period during which the Reserve Ratio lies above $r_{max}$. 181 | \end{itemize} 182 | 183 | DMMD hikes up fees when the Reserve Ratio drops out of the band. The fee hike targets a Reserve Ratio of $r*$. This is done by multiplying fees by the factor the Reserve Ratio needs to grow by to reach $r*$. For example, if the Reserve Ratio needs to grow by 10\% to reach its target, the protocol increases fees by 10\%. The fee increase produces a surplus in fee revenue, driving up the value of the Reserve. In the Stability Analysis section we demonstrate that this procedure achieves the target Reserve Ratio $r*$. The protocol maintains the increased fee regime until the Terra economy has grown sufficiently to cover the fee surplus it provides. In the earlier example, as soon as the Terra supply has grown by 10\% transaction fees can return to previous levels while maintaining in absolute value the fee surplus that has been achieved. In other words, after the growth milestone has been hit, the protocol can iteratively decrement fees. If the Reserve Ratio grows beyond the ceiling $r_{max}$, transaction fees can be safely decremented. 184 | 185 | Under situations of extreme duress, multiple fee increases may need to take place before the Reserve Ratio sits comfortably within the band. Since fee increases are calibrated based on the maximum Luna price drawdown recently experienced, each subsequent fee increase will be more aggressive than the previous one during a period of such high volatility. This limits the need for subsequent fee increases to truly extreme conditions. Fee increases can take place at most once every 24h. This is an additional layer of protection to prevent sharp fee increases when the price of Luna experiences volatility that is significantly higher than previously observed. 186 | 187 | The value of transactions is calculated under the assumption that Terra is on par with its pegged asset. If that is not the case, the effective transaction fee may be higher/lower. For example, if the price of Terra has drifted 5 percent below its peg, the transaction fee levied will be approximately 5 percent higher to compensate for the drop. This adjustment allows the protocol to shield transaction fees from short-term volatility in the price of Terra. 188 | 189 | 190 | 191 | \subsection{Contraction by leveraging deposits} 192 | 193 | When the price of Terra drifts below its peg, the protocol borrows Luna from the Stability Reserve and uses it to purchase Terra from the open market and burn it. Luna is borrowed from all deposits on a pro-rata basis. As explained in the "full stability reserve" section, transaction fees are calibrated to keep the reserve ratio always greater than the size of the Terra economy. 194 | 195 | \subsection{Expansion by decentralized fiscal spending} 196 | 197 | Most stable-coins have a multi-coin structure where new money supply in expansionary cycles is rewarded or used to increase the value of collateral tokens. While this may seem to be positive for stabilization, in reality it creates a speculative dependency between the strength of the reserve and uncertain expectations for future growth. Growth-dependent reserves / collateral schemes are inherently downward failure prone, as sharp recessions dampen future growth outlook and collapse the value of the backing assets. 198 | 199 | Luna deposits accrue interest rate from Terra transaction fees instead of new money supply. Not only is this approach less speculative, as the issuance of transaction fees are not dependent on a binary outcome of growth, but it gives the system a control lever, the rate of fees, to counter market volatility to stabilize the value of the reserve. During contractions, the system can increase transaction fees, increasing expected cash flow for deposit holders and thereby the valuation of the reserve. During expansions the system can decrease transaction fees, reducing the value of the reserve and resulting in more favorable costs of capital. 200 | 201 | So how does the Terra protocol spend its newly minted money supply? Recall that governments not only have a responsibility to keep prices stable, but also to distribute wealth toward socially responsible areas. Fiscal spending in key areas such as infrastructure, community housing, and subsidies are essential to ensuring financial inclusion for people disenfranchised from the system. However, resource allocation in governments today are incredibly inefficient because of centralization costs, such as corruption, regional self-interest, and corporate lobbies. Decentralized fiscal spending has the power to make sure resource allocation can be achieved through consensus, such that more people can take part in fiscal governance to decide what can best enhance the ecosystem. 202 | 203 | The system defines the following variables: 204 | \begin{itemize} 205 | \item \textbf{Delegates}: users with more than 1000 Luna in cold deposits in the stability reserve. The system assumes these nodes to have significant loyalty in the system, given the size of their deposits. Each delegate proposes and votes for funding proposals in the decentralized legislature, their vote weighted by their own stake and the stakes of other deposit holders who stake with them. Each delegate is assigned a uid. 206 | 207 | \item \textbf{Decentralized legislature}: Terra convenes a decentralized legislature, which operates over a session of n blocks, spanning over several weeks. The legislature's mandate is to reach a consensus on how Terra's economic growth should be spent. 208 | 209 | \item \textbf{Funding proposals}: Each delegate can submit and vote on funding proposals. A funding proposal is a tuple containing the size of the funding request, the destination wallet address, the uid of the delegate, and a WWW url link describing the proposal. 210 | \end{itemize} 211 | 212 | 213 | Every 15 minutes, when Terra's exchange rate $>$ peg, the system issues $\frac{P{'} Q{'}}{P} - Q$ new Terra, and sells it in open market operations for Ethereum. After settling its debts accrued from contractions to deposit holders, the Ethereum is deposited in a special smart contract wallet. 214 | 215 | The system defines a session for the decentralized legislature, which spans over $n$ blocks, roughly equivalent to 1 month. At the beginning of every session, the legislature considers how to use the Ethereum gains from the previous session. 216 | 217 | \begin{itemize} 218 | \item At the beginning of each session, stakers have a chance to examine the voting histories / proposals of each delegate and shuffle allegiances. Stakers can also choose to abstain from supporting a candidate without losing their rewards. 219 | 220 | \item During the session, each delegate can submit and vote on funding proposals. Delegates can also vote against funding proposals. 221 | 222 | \item At the end of the session, funding proposals are arranged in a queue, ordered by vote balance (votes for stakes - votes against stakes). Each proposal is dequeued in a FIFO order, until all the Ethereum from the previous session is expended. Funding proposals with negative vote balances are removed from the queue. 223 | 224 | \item If there are Ethereum funds remaining from the session, they are moved to the next session of the legislature. 225 | 226 | \item Participants in the legislative process are rewarded with the transaction fees collected in the previous session proportional to the size of their stake. This way, the reward given is proportional to their democratic efforts. 227 | 228 | \end{itemize} 229 | 230 | 231 | This decentralized governance of fiscal spending returns control of money back to its users, and affords greater room for financial inclusion than the state-operated models today. 232 | 233 | \subsection{Genesis fiat reserve} 234 | 235 | Although we expect the Stability Reserve and the Terra Protocol to be effective in maintaining the full reserve guarantee in the long run, special safeguards need to be put in place in the early days after network launch. First, the market will need time to adjust to the Protocol before rational valuations can be made. Secondly, the network may be vulnerable to low-liquidity trading and low transaction volume at genesis, which will result in volatile transaction volumes and therefore uncertain rewards for Luna stakers. 236 | 237 | Therefore, at genesis, the Foundation will use its votes it to direct new money supply to a fiat reserve. This fiat reserve will act as a guarantor of last resort, buying up Terra during extreme market downturns and providing an additional layer of safety to the Protocol. Given that keeping the price-stability of the peg is a need most early participants realize, the Foundation will likely succeed in winning over sufficient votes such that most new money supply will go to the fiat reserve, maintaining near 1:1 parity between the Terra economy and the fiat reserve. 238 | 239 | With the maturation of the Terra economy, other stabilizing forces will start to appear. Third party decentralized apps being built on the Terra protocol will both grow the size of the economy and diversify its assets to make it more vulnerable to external price shocks. The Protocol's stabilizing mechanisms will grow more effective, with the market growing more sensitive to its signals. When such a time comes, Terra will have to be weaned slowly from the fiat reserve and operate as a completely decentralized currency. 240 | 241 | The beauty of the decentralized legislative model is that it allows for such critical decisions to be made via democratic consensus. As the community starts to gain more faith in the ability of the Protocol to operate independently, it will start to vote for other funding proposals unrelated to the fiat reserve. Thus, Terra can be protected by a robust fiat reserve at genesis and organically outgrow its protection through its decentralized legislative system. 242 | 243 | 244 | \section{Stability Analysis} 245 | 246 | The protocol guarantees the stability of Terra via the Stability Reserve, whose mandate is to be consistently more valuable than the supply of Terra in circulation. If the Reserve is able to maintain a Reserve Ratio of at least 1, it is capable of contracting Terra supply to whatever extent necessary in order to maintain its peg. In this section we argue the following: 247 | 248 | \begin{itemize} 249 | \item The DMMD algorithm restricts the Reserve Ratio within its band in almost all situations 250 | 251 | \item The DMMD algorithm achieves this while enforcing low and sustainable transaction fees 252 | \end{itemize} 253 | 254 | We further review the two significant threats to stability that the Reserve is tasked to defend against and demonstrate DMMD's effectiveness in doing so: price shocks and prolonged recessions. 255 | 256 | Before arguing for the effectiveness of DMMD, we present a valuation model for Luna that will be useful for our analysis. Luna can be thought of as a non-dilutive share in future transaction fees accrued by the Terra network. As such, we value the Reserve as the NPV of future transaction fees. Formally: 257 | 258 | $$R_T = \sum_{t=T}^{\infty}\frac{f_tS_t}{(1+r)^t}$$ \newline 259 | 260 | Where $R_T$ is the value of the Reserve at time $T$, $f_t$ is the transaction fee at time period $t$, $S_t$ is the Terra transaction volume at time period t and r is the discount rate. 261 | 262 | An equivalent formulation which will be illustrative later on is the following: 263 | $$R_t = f_tT_tV_tm_t$$ 264 | 265 | Where $R_t$ is the value of the Reserve, $f_t$ is the transaction fee, $T_t$ is the Terra supply, $V_t$ is the velocity of money and $m_t$ is an earnings multiple for Luna, all at time $t$. If $t$ is annual, $f_tT_tV_t$ represents the transaction fee earnings accrued to the Reserve during year $t$ (recall that the total value of transactions during some period is equal to the money supply multiplied by its average velocity during that period). 266 | 267 | \subsection{Enforcement of reserve ratio band} 268 | 269 | We claim the following: 270 | The Reserve Ratio is guaranteed to stay within its band under DMMD, barring short periods ($<$24h) of extreme unforeseen volatility or wildly irrational markets. This is a consequence of the following: 271 | 272 | 273 | \begin{itemize} 274 | \item If the Reserve Ratio drifts below the lower end of its band, DMMD will bring it close to the target ratio $r*$. 275 | 276 | We claim that fee multiplication enforced by DMMD subject to the algorithm's subsequent Milestone and fee Decrement schedules will have an approximately linear effect on the Reserve Ratio under rational markets, thus bringing it close to the target ratio $r*$. We argue this based on the Luna valuation model laid out earlier. Observe that each discounted transaction fee cash flow is linear in the transaction fee charged during that period, holding transaction volume fixed. Let $m$ be the multiplication factor applied to fees by DMMD, and let $P$ be the number of periods elapsed before Terra supply grows by a factor of $m$. Multiplying the transaction fee by $m$ similarly multiplies cash flows by $m$ for the $P$ time periods that follow. The scaling of cash flows by a factor of $m$ for the first $P$ terms of the NPV calculation results in an approximately linear scaling of the entire sum, keeping in mind the exponentially growing discount as time periods increase. We further note that the fee growth rate applied thereafter is likely to be higher seeing as the Terra economy is experiencing growth following the $P$ time periods discussed. \footnote{The above analysis assumes roughly constant Terra velocity, and that small fee increases have negligible impact on transaction volume (which is a reasonable assumption given fees charged will be significantly less than those charged by traditional card processors).} 277 | 278 | \item If the Reserve Ratio drifts above the upper end of its band, DMMD will bring it close to the target ratio $r*$. 279 | 280 | The mechanism that enforces this is simple: DMMD decrements the transaction fee by a fixed amount whenever the Reserve Ratio remains above $r_{max}$ for a small amount of time. Once the growth milestone has been hit, DMMD will iteratively decrement transaction fees to further reduce the Reserve Ratio. 281 | 282 | \end{itemize} 283 | 284 | \subsection{Transaction fee sustainability} 285 | 286 | We claim that the transaction fees enforced by the DMMD algorithm can be kept sustainably low compared to traditional card processors. We review the evolution of transaction fees during periods of growth and recession. 287 | 288 | 289 | \begin{itemize} 290 | \item Transaction fees in a period of growth 291 | 292 | Observe that during a period of growth of the Terra supply, the expected growth rate and the discount rate in assessing future cash flows are likely to increase/decrease respectively. As such, the transaction fees required to sustain a Reserve Ratio within the band are lower, even as the supply of Terra increases. DMMD will iteratively decrease transaction fees during this period. 293 | 294 | \item Transaction fees in a recession 295 | 296 | We begin by observing that a transaction fee hike occurs when the Reserve Ratio drops below $r_{min}$, the lower end of the band. The target Reserve Ratio $r*$ targeted by the previous fee increase was determined so that any drawdown in the price of Luna not larger than what had been experienced in the past 100 days would keep the Reserve Ratio within the band. As such, a transaction fee hike takes place only when Luna experiences a significant price drop. The hike is proportional to $1-d$, where $d$ is the maximum drawdown during the past 100 day period. This implies that in aggregate, a 90 percent total decline in the price of Luna would result in a transaction fee hike of at most 10x. Considering the initial transaction fee is 0.1 percent, a 10x hike is still sustainable until growth recommences. 297 | \end{itemize} 298 | 299 | To ground the sustainability of the transaction fee schedule implemented by DMMD, we confirm with realistic numbers that a Reserve Ratio of 1 is easily achievable. Consider the latter formulation of the price of the Luna supply, At an annual money velocity of 10, which is the velocity of USD's M1, and a conservative earnings multiple of 40, which Visa is currently priced at, a transaction fee of 0.25 percent is sufficient for a Reserve Ratio of 1. At a maximum drawdown of 50 percent, which is very high, the target Reserve Ratio would be 2.4, implying a transaction fee of 0.6 percent under similar assumptions. In practice, we expect velocity of Terra to be much higher than that of M1 of the USD, given that the primary use case for the stable-coin in the early days will be as a medium of exchange in a payment network system rather than a store of value. This means that we will likely be able to charge even more competitive transaction fees, and leverage transaction fees even more aggressively during time of duress. 300 | Finally, we review the Reserve's resilience against two significant threats to stability. 301 | 302 | \subsection{Price shocks} 303 | 304 | Arguably the most lethal risk to the survival of a stable-coin is a sudden price shock. This may come in many forms, such as a Black Swan event or a shorting attack. The defining characteristic of a price shock is a big and sudden selloff with high volume, usually coupled with a sudden loss of faith in the system. Shocks are hard to defend against because they typically compromise the value of speculative collateral, or if there is no collateral the market's support for the currency. In the case of a shorting attack, a well-resourced attacker can eat through fat reserves if they do not offer full collateralization. Stable-coins that appear to be perfectly healthy can get wiped out like this. 305 | 306 | As argued in the earlier sections, the Stability Reserve is guaranteed to maintain a Reserve Ratio of at least 1 almost consistently. A price shock would trigger a strong transaction fee hike that would offer significantly increased cash flow to Luna holders for a predictable period of time. This guarantee is strengthened by the nature of Terra's collateral. The reliance of Terra on an endogenous non-speculative revenue-generating asset, Luna, makes the protocol immune to such shocks. Luna is backed by the transactional value of Terra. Insofar as Terra is a useful currency that people choose to transact with, Luna will retain its value by virtue of the Terra cash flows it generates. 307 | 308 | \subsection{Prolonged recessions} 309 | 310 | A prolonged recession is a possibility all stable-coins need to defend against. It is a particularly hard scenario to design for, as all private currencies to some extent rely on demand for their stability. Most currencies enter a death spiral they can't get out of when a prolonged recession starts to take place. 311 | 312 | The Terra protocol guarantees that the Stability Reserve remains adequately funded during recessions, and that it gracefully contracts while steadfastly maintaining the stability of Terra. We demonstrated the mechanism by which the Reserve Ratio stays afloat during prolonged recessions in the previous section: transaction fees gradually increase to counter the decrease in the supply of Terra and the price of Luna. Intermittent growth brings fees back down to make the fee schedule more sustainable. The DMMD algorithm allows graceful contraction with sustainable transaction fees by design. We further note that incentives for Cold deposits significantly strengthen during recessions, as the payout weight in favor of Cold deposits increases. This ensures that there is sufficient incentive for depositors to sustain the Reserve during the recession. 313 | 314 | 315 | \section{A Look at Other Stable-coins} 316 | 317 | We discussed earlier why a stable-coin scheme is robust if and only if it maintains a full reserve of decentralized assets. To the best of our knowledge, Terra is the first stable-coin project to attempt this; previous implementations forfeit either the full reserve or the decentralization of their backing assets. 318 | 319 | \subsection{Real asset backed model} 320 | 321 | There are a number of coins claiming to be backed 1:1 by fiat (Tether), gold (Digix) or some other real world asset. The construction involves a centralized reserve holding the collateral, such as a bank account or a safe, and a legal framework to support the mapping between the tokens and the reserve. 322 | 323 | It is easy to see there is significant centralization risk in this model. The reserve could be seized by regulators. The foundation supporting the reserve could steal the reserve. The holding bank could be robbed / go bankrupt. Trust is required of centralized custodians and natural circumstances. Centralized models also incur custodian costs. The foundation maintaining the reserve has to pay for operational overhead; legal fees to deter regulatory challenges, software infrastructure, and staffing costs. Recent uncertainty around Tether, from SEC's regulatory attention, the Foundation's lack of transparency, to troubled banking relations with the company's banking founders all indicate that real-asset collateralization has significant long term risks due to centralization. 324 | 325 | \subsection{Margin call model} 326 | 327 | Instead of real-world assets, some coins choose to be backed with volatile crypto assets, such as Ethereum. Over-collateralization is required to protect the stable-coin from the underlying asset's own price-volatility. Shocks in the value of the collateral will either propagate to the value of the coin, or will trigger a margin call which destroys the coin and returns the collateral to the owner unless more collateral is posted. This is anything but stability: even if the market value of the coin avoids the shock, the only way to keep using it is by further increasing (over)exposure to a volatile asset that just suffered a price shock! 328 | 329 | \subsection{Bond model} 330 | 331 | Some stable-coins choose not to be backed by anything at all, instead electing to issue bonds. We discussed earlier why protocol currencies cannot issue bonds in good faith. The scheme can potentially be extremely unstable, succeeding only so far as there are more believers of the system as there are defectors. Even if loyalists are better resourced for a time, through an extremely well funded foundation or etc, such a scheme is bound to fail if a similarly well-leveraged attacker were to emerge, or if the economy were to enter a sustained recession (as they do from time to time). 332 | 333 | \section{The Terra Platform} 334 | 335 | Although a global, transactional currency is the most obvious application for Terra, many other decentralized applications can also benefit from its price-stability. Every token economy needs its currency to be a price-stable store-of-value and medium-of-exchange. This need has led each token project to implement its own rudimentary stable-coin scheme, creating hundreds of separate monetary policies and thousands of potential Soroses. The introduction of a stable cryptocurrency application platform will allow dApp developers to delegate monetary policy to Terra and focus on their core competencies. 336 | 337 | In this section, we show how the Terra Protocol can be extended to provide price-stability as a platform for third party dApps. We outline the broad mechanisms that allow price-stable assets to be built on the Terra Protocol. Code-level specifications and implementation details of this platform are outside of the scope of this document. 338 | 339 | \subsection{The mechanism} 340 | 341 | Terra is collateralized by the transaction fees collected from its network. The basic mechanism of the Terra platform is similarly straightforward; the system collateralizes the dApp token economy from the transaction fees collected from it. We describe the mechanism of the Terra platform, by showing how it stabilizes the price of a fictional dApp token called ABC. 342 | 343 | For the purposes of this section, let $X$ note the transaction fees collected, $P$ the price, $Q$ the money supply, and $R$ the size of the Stability Reserve. 344 | 345 | \begin{itemize} 346 | \item \textbf{Genesis contract}: At network genesis, the developer fixes the genesis supply of ABC. 347 | 348 | \item \textbf{Learning period}: In the beginning of the learning period, the system allows the price of ABC to float. While doing so, it collects transaction fees from the ABC economy, until the total amount of fees collected is at least $ P^{ABC}_{t}Q^{ABC}_{t} \frac{r_{min}}{2}$. During the learning period, the system may choose to levy a higher tx fee on the ABC economy than the rest of the Terra ecosystem to speed up the transition to the next phase. 349 | 350 | \item \textbf{Stability period}: As the system switches over from the learning period to the stability period, it fixes the current exchange rate between Terra and the new token to be the peg. The Terra platform expands and contracts the supply of the new token, to keep the exchange rate of the token around the peg. 351 | 352 | \begin{itemize} 353 | \item The token economy maintains an allegiance ratio, which is defined by the function: 354 | 355 | $$\frac{ 356 | min(R_t \frac{X^{ABC}_t}{X^{total}_t}, \sum_{t} X^{ABC}_t) 357 | }{ 358 | P^{ABC}_{t}Q^{ABC}_{t} 359 | }$$ 360 | 361 | This means that the Terra protocol will collateralize the token economy to the extent of its contribution to the ecosystem, quantified in transaction fees. 362 | 363 | \item The Terra platform does not obey a hard peg, but rather chooses to use a fluctuating band around the target exchange rate. The width of the band is inversely proportional to the allegiance ratio, such that it is thin when a lot of tx fees are being collected from the network, and thick when few tx fees are being collected from the network. The system contracts the supply of the new token when the exchange rate $<$ band floor, and expands the supply when the exchange rate $>$ band ceiling. 364 | 365 | \item The developer defines a callback \texttt{mint(int numNewTokens)} that is called whenever new tokens are minted during expansionary cycles. 366 | 367 | \end{itemize} 368 | \end{itemize} 369 | 370 | 371 | 372 | 373 | \subsection{Observations} 374 | 375 | \begin{itemize} 376 | \item \textbf{Stabilization mechanism is blunt when transaction fees are low.} Token economies have an incentive to pay transaction fees honestly, as the stability mechanism is calibrated to favor economies that pay more tx fees. Such a scheme will likely favor token economies that are structured to be more transaction heavy. In order to level the playing field, we can introduce a holding fee in the form of inflation, and account for it in the allegiance ratio. 377 | 378 | \item \textbf{Bad developers can't bankrupt the reserve.} Note that the stability reserve never expends more than the total amount of transaction fees collected from the token economy in trying to stabilize it, meaning Terra's trade balance with the token economy is always positive. This deters any bad actors looking to profit from the Stability Reserve by creating ghost tokens. 379 | \end{itemize} 380 | 381 | \subsection{An alliance of currencies} 382 | 383 | Through the mechanism outlined above, the Terra platform manages to create an alliance of currencies that collaborate with each other to stabilize the price. Each new token economy built on the Terra platform help to diversify the economic alliance, as transaction fee decreases in one token economy may be hedged by an increase in another. Furthermore, the ecosystem benefits from the sheer scale of multiple economies working together, increasing the cost of Soros attacks and decreasing vulnerabilities from external price shocks. 384 | 385 | 386 | \section{Conclusion} 387 | 388 | Terra is the first price-stable cryptocurrency that can make a guarantee of solvency with a reserve made up of decentralized assets. The price-stability of such a regime cannot be taken away by centralized actors nor attacked by speculators. Terra is an improvement on both fiat currencies and Bitcoin, since it is safe from both speculative volatility and political pollution of its monetary policy. 389 | 390 | If Bitcoin's contribution to cryptocurrency was immutability, and Ethereum expressivity, our value-add will be usability. The potential applications of Terra is immense. Immediately, we foresee Terra being used as a medium-of-exchange in online payments, allowing people to transact freely at a fraction of fees charged by Visa and Mastercard. As the world starts to become more and more decentralized, we see Terra being used as a dApp platform where price-stable token economies are built on Terra. Terra is looking to become the first usable currency and stability platform on the blockchain, unlocking the power of decentralization for mainstream users, merchants, and developers. 391 | 392 | 393 | % \bibliographystyle{plain} 394 | % \bibliography{references} 395 | 396 | % \nocite{*} 397 | 398 | \end{document} 399 | -------------------------------------------------------------------------------- /white-paper/terra-v1.0.tex: -------------------------------------------------------------------------------- 1 | %% LyX 2.3.1-1 created this file. For more info, see http://www.lyx.org/. 2 | %% Do not edit unless you really know what you are doing. 3 | \documentclass[11pt]{article} 4 | \usepackage[LGR,T1]{fontenc} 5 | \usepackage[latin9]{inputenc} 6 | \usepackage{geometry} 7 | \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} 8 | \usepackage{color} 9 | \usepackage{amsmath} 10 | \usepackage{amssymb} 11 | \usepackage{graphicx} 12 | \usepackage{pgfplots} 13 | \usepackage{setspace} 14 | \doublespacing 15 | \usepackage[unicode=true, 16 | bookmarks=false, 17 | breaklinks=false,pdfborder={0 0 1},backref=section,colorlinks=true] 18 | {hyperref} 19 | \hypersetup{pdftitle={Terra Money White Paper}, 20 | linkcolor=black,citecolor=blue,filecolor=magenta,urlcolor=blue} 21 | 22 | \makeatletter 23 | 24 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands. 25 | \DeclareRobustCommand{\greektext}{% 26 | \fontencoding{LGR}\selectfont\def\encodingdefault{LGR}} 27 | \DeclareRobustCommand{\textgreek}[1]{\leavevmode{\greektext #1}} 28 | \ProvideTextCommand{\~}{LGR}[1]{\char126#1} 29 | 30 | 31 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands. 32 | \usepackage{color,titling,titlesec} 33 | \usepackage{eurosym} 34 | \usepackage{harvard}\usepackage{amsfonts} 35 | \usepackage{graphicx,pdflscape} 36 | \usepackage{chicago}\setcounter{MaxMatrixCols}{30} 37 | \usepackage[bottom]{footmisc} 38 | 39 | % This shrinks the space before and after display formulas 40 | \usepackage{etoolbox} 41 | \apptocmd\normalsize{% 42 | \abovedisplayskip=5pt 43 | %\abovedisplayshortskip=6pt % plus 3pt 44 | \belowdisplayskip=6pt 45 | %\belowdisplayshortskip=7pt plus 3pt 46 | }{}{} 47 | 48 | % slim white space before title, section/subsection headers 49 | \setlength{\droptitle}{-.75in} 50 | \titlespacing*{\section}{0pt}{.2cm}{0pt} 51 | \titlespacing*{\subsection}{0pt}{.2cm}{0pt} 52 | 53 | \makeatother 54 | 55 | \begin{document} 56 | \title{Terra Money:\\ 57 | Stability and Adoption} 58 | \author{Evan Kereiakes, Do Kwon, 59 | Marco Di Maggio, Nicholas Platias} 60 | \date{February 2019} 61 | \maketitle 62 | \begin{center} 63 | {\large{}\vspace{-1.5cm} 64 | }{\large\par} 65 | \par\end{center} 66 | \begin{abstract} 67 | \begin{singlespace} 68 | While many see the benefits of a price-stable cryptocurrency that 69 | combines the best of both fiat and Bitcoin, not many have a clear 70 | plan to get such a currency adopted. Since the value of a currency 71 | as medium of exchange is mainly driven by its network effects, a successful 72 | new digital currency needs to maximize adoption in order to become 73 | useful. We propose a cryptocurrency, Terra, which is both price-stable 74 | and growth-driven. It achieves price-stability via an elastic money 75 | supply enabled by countercyclical mining incentives and transaction 76 | fees. It also uses seigniorage created by its minting operations as 77 | transaction stimulus, thereby facilitating adoption. There is demand 78 | for a decentralized, price-stable money protocol in both fiat and 79 | blockchain economies. If such a protocol succeeds, then it will have 80 | a significant impact as the best use case for cryptocurrencies. 81 | \end{singlespace} 82 | \end{abstract} 83 | \thispagestyle{empty} 84 | 85 | \newpage\setcounter{page}{1} 86 | 87 | \section{Introduction} 88 | 89 | The price-volatility of cryptocurrencies is a well-studied problem 90 | by both academics and market observers (see for instance, Liu and 91 | Tsyvinski, 2018, Makarov and Schoar, 2018). Most cryptocurrencies, 92 | including Bitcoin, have a predetermined issuance schedule that, together 93 | with a strong speculative demand, contributes to wild fluctuations 94 | in price. Bitcoin\textquoteright s extreme price volatility is a major 95 | roadblock towards its adoption as a medium of exchange or store of 96 | value. Intuitively, nobody wants to pay with a currency that has the 97 | potential to double in value in a few days, or wants to be paid in 98 | the currency if its value can significantly decline before the transaction 99 | is settled. The problems are aggravated when the transaction requires 100 | more time, e.g. for deferred payments such as mortgages or employment 101 | contracts, as volatility would severely disadvantage one side of the 102 | contract, making the usage of existing digital currencies in these 103 | settings prohibitively expensive. 104 | 105 | At the core of how the Terra Protocol 106 | solves these issues is the idea that a cryptocurrency with an elastic 107 | monetary policy would stabilize its price, retaining all the censorship 108 | resistance of Bitcoin, and making it viable for use in everyday transactions. However, price-stability is not sufficient to get a new currency widely adopted. Currencies are inherently characterized by strong network 109 | effects: a customer is unlikely to switch over to a new currency unless 110 | a critical mass of merchants are ready to accept it, but at the same 111 | time, merchants have no reason to invest resources and educate staff 112 | to accept a new currency unless there is significant customer demand 113 | for it. For this reason, Bitcoin\textquoteright s adoption in the 114 | payments space has been limited to small businesses whose owners are 115 | personally invested in cryptocurrencies. Our belief is that while 116 | an elastic monetary policy is the solution to the stability problem, 117 | an efficient fiscal policy can drive adoption. Then, the Terra Protocol 118 | also offers strong incentives for users to join the network with an 119 | efficient fiscal spending regime, managed by a Treasury, where multiple 120 | stimulus programs compete for financing. That is, proposals from community 121 | participants will be vetted by the rest of the ecosystem and, when 122 | approved, they will be financed with the objective to increase adoption 123 | and expand the potential use cases. 124 | 125 | The Terra Protocol with its balance 126 | between fostering stability and adoption represents a meaningful complement 127 | to fiat currencies as means of payment, and store of value. The rest 128 | of the paper is organized as follows. We first discuss the protocol 129 | and how stability is achieved and maintained, through the calibration 130 | of miners\textquoteright{} demand and the use of the native mining 131 | Luna token. We then dig deeper in how countercyclical incentives and 132 | fees are adopted to smooth fluctuations. Second, we discuss how Terra\textquoteright s 133 | fiscal policy can be used as an efficient stimulus to drive adoption. 134 | 135 | \section{Multi-fiat peg monetary policy } 136 | 137 | A stable-coin mechanism must answer three key questions: 138 | \begin{itemize} 139 | \item \textbf{How is price-stability defined?} Stability is a relative concept; 140 | which asset should a stable-coin be pegged to in order to appeal to 141 | the broadest possible audience? 142 | \item \textbf{How is price-stability measured?} Coin price is exogenous 143 | to the Terra blockchain, and an efficient, corruption-resistant price 144 | feed is necessary for the system to function properly. 145 | \item \textbf{How is price-stability achieved?} When coin price has deviated 146 | from the target, the system needs a way to apply pressures to the 147 | market to bring price back to the target. 148 | \end{itemize} 149 | This section will specify Terra\textquoteright s answers to the above 150 | questions in detail. 151 | 152 | \subsection{Defining stability against regional fiat currencies } 153 | 154 | The existential objective of a stable-coin is to retain its purchasing 155 | power. Given that most goods and services are consumed domestically, 156 | it is important to create crypto-currencies that track the value of 157 | local fiat currencies. Though the US Dollar dominates international 158 | trade and forex operations, to the average consumer the dollar exhibits 159 | unacceptable volatility against her choice unit of account. 160 | 161 | Recognizing strong regionalities in money, Terra aims to be a family of cryptocurrencies that are each pegged to the world's major currencies. Close to genesis, the protocol will issue Terra currencies pegged to USD, EUR, CNY, JPY, GBP, KRW, and the IMF SDR. Over time, more currencies will be added to the list by user voting. TerraSDR will be the flagship currency of this family, given that it exhibits the lowest volatility against any one fiat currency (Kereiakes, 2018). TerraSDR be the currency in which transaction fees, miner rewards and stimulus grants will be denominated. 162 | 163 | It is important, however, for Terra currencies to have access to shared liquidity. For this reason, the system supports atomic swaps among Terra currencies at their market exchange rates. A user can swap TerraKRW for TerraUSD instantly at the effective KRW/USD exchange rate. This allows all Terra currencies to share liquidity and macroeconomic fluctuations; a fall in demand by one currency can quickly be absorbed by the others. We can therefore reason about the stability of Terra currencies in a group; we will be referring to Terra loosely as a single currency for the remainder of this paper. As Terra's ecosystem adds more currencies, its atomic swap functionality can be an instant solution to cross border transactions, international trade settlements and usurious capital controls. 164 | 165 | 166 | 167 | 168 | \subsection{Measuring stability with miner oracles } 169 | 170 | Since the price of Terra currencies in secondary markets is exogenous to the blockchain, the system must rely on a decentralized price oracle to estimate the true exchange rate. We define the mechanism for the price oracle as the following: 171 | 172 | \begin{itemize} 173 | \item For any Terra sub-currency in the set of currencies C = {TerraKRW, TerraUSD, TerraSDR... } miners submit a vote for what they believe to be the current exchange rate in the target fiat asset. 174 | \item Every n blocks the vote is tallied by taking the weighted medians as the true rates. 175 | \item Some amount of Terra is rewarded to those who voted within 1 standard deviation of the elected median. Those who voted outside may be punished via slashing of their stakes. The ratio of those that are punished and rewarded may be calibrated by the system every vote to ensure that a sufficiently large portion of the miners vote. 176 | \end{itemize} 177 | 178 | Several issues have been raised in implementing decentralized oracles, but chief among them is the possibility for voters to profit by coordinating on a false price vote. Limiting the vote to a specific subset of users with strong vested interest in the system, the miners, can vastly decrease the odds of such a coordination. A successful coordination event on the price oracle would result in a much higher loss in the value of the miner stakes than any potential gains, as Luna stakes are time-bound to the system. 179 | 180 | The oracle can also play a role in adding and deprecating Terra currencies. The protocol may start supporting a new Terra currency when oracle votes for it satisfies a submission threshold. Similarly, the failure to receive a sufficient number of oracle votes for several periods could trigger the deprecation of a Terra currency. 181 | 182 | 183 | \subsection{Achieving stability through countercyclical mining } 184 | 185 | Once the system has detected that the price of a Terra currency has 186 | deviated from its peg, it must apply pressures to normalize the price. 187 | Like any other market, the Terra money market follows simple rules 188 | of supply and demand for a pegged currency. That is: 189 | \begin{itemize} 190 | \item Contracting money supply, all conditions held equal, will result in 191 | higher relative price levels. That is, when price levels are falling 192 | below the target, reducing money supply sufficiently will return price 193 | levels to normalcy. 194 | \item Expanding money supply, all conditions held equal, will result in 195 | lower relative price levels. That is, when price levels are rising 196 | above the target, increasing money supply sufficiently will return 197 | price levels to normalcy. 198 | \end{itemize} 199 | Of course, contracting the supply of money isn\textquoteright t free; 200 | like any other asset, money needs to be bought from the market. Central 201 | banks and governments shoulder contractionary costs for pegged fiat 202 | systems through a variety of mechanisms including intervention, the 203 | issuance of bonds and short-term instruments thus incurring costs 204 | of interest, and hiking of money market rates and reserve ratio requirements 205 | thus losing revenue. Put in a different way, central banks and governments 206 | absorb the volatility of the pegged currencies they issue. 207 | 208 | Analogously, Terra miners absorb volatility in Terra supply. 209 | \begin{itemize} 210 | \item \textbf{In the short term, miners absorb Terra contraction costs} 211 | through mining power dilution. During a contraction, the system mints 212 | and auctions more mining power to buy back and burn Terra. This effectively 213 | contracts the supply of Terra until its price has returned to the 214 | peg, and temporarily results in mining power dilution. 215 | \item \textbf{In the mid to long term, miners are compensated with increased 216 | mining rewards}. First, the system continues to buy back mining power 217 | until a fixed target supply is reached, thereby creating long-run 218 | dependability in available mining power. Second, the system increases 219 | mining rewards, which will be explained in more detail in a later 220 | section. 221 | \end{itemize} 222 | In summary, miners bear the costs of Terra volatility in the short 223 | term, while being compensated for it in the long-term. Compared to 224 | ordinary users, miners have a long-term vested interest in the stability 225 | of the system, with invested infrastructure, trained staff and business 226 | models with high switching cost. The remainder of this section will 227 | discuss how the system forwards short-term volatility and creates 228 | long-term incentives for Terra miners. 229 | 230 | \subsection{Miners absorb short-term Terra volatility } 231 | 232 | The Terra Protocol runs on a Proof of Stake (PoS) blockchain, where 233 | miners need to stake a native cryptocurrency Luna to mine Terra transactions. 234 | At every block period, the protocol elects among the set of staked 235 | miners a block producer, which is entrusted with the work required 236 | to produce the next block by aggregating transactions, achieving consensus 237 | among miners, and ensuring that messages are distributed properly 238 | in a short timeframe with high fault tolerance. 239 | 240 | The block producer election is weighted by the size of the active 241 | miner\textquoteright s Luna stake. Therefore, \textbf{Luna represents 242 | mining power in the Terra network.} Similar to how a Bitcoin miner\textquoteright s 243 | hash power represents a pro-rata odds of generating Bitcoin blocks, 244 | the Luna stake represents pro-rata odds of generating Terra blocks. 245 | 246 | Luna also serves as the most immediate defense against Terra price 247 | fluctuations. The system uses Luna to make the price for Terra by 248 | agreeing to be counter-party to anyone looking to swap Terra and Luna 249 | at Terra's target exchange rate. More concretely: 250 | \begin{itemize} 251 | \item When TerraSDR's price < 1 SDR, users and arbitragers can send 1 TerraSDR 252 | to the system and receive 1 SDR's worth of Luna. 253 | \item When TerraSDR's price > 1 SDR, users and arbitragers can send 1 SDR's 254 | worth of Luna to the system and receive 1 TerraSDR. 255 | \end{itemize} 256 | 257 | The system's willingness to respect the target exchange rate irrespective 258 | of market conditions keeps the market exchange rate of Terra at a 259 | tight band around the target exchange rate. An arbitrager can benefit when 1 TerraSDR = 0.9 SDR by trading TerraSDR for 1 SDR's worth of Luna from the system, as opposed to 0.9 SDR's worth of assets she could get from the open market. Similarly, she can also benefit when 1 TerraSDR = 1.1 SDR by trading in 1 SDR’s worth of Luna to the system to get 1.1 SDR’s worth of TerraSDR, once again beating the price of the open market. 260 | 261 | The system finances Terra price making via Luna: 262 | \begin{itemize} 263 | \item To buy 1 TerraSDR, the protocol mints and sells Luna worth 1 SDR 264 | \item By selling 1 TerraSDR, the protocol earns Luna worth 1 SDR 265 | \end{itemize} 266 | As Luna is minted to match Terra offers, volatility is moved from 267 | Terra price to Luna supply. If unmitigated, this Luna dilution presents 268 | a problem for miners; their Luna stakes are worth a smaller portion 269 | of total available mining power post-contraction. The system 270 | burns a portion of the Luna it has earned during expansions until 271 | Luna supply has reached its 1 billion equilibrium issuance. Therefore, 272 | Luna can have steady demand as a token with pro-rata rights to Terra 273 | mining over the long term. The next section discusses how the system 274 | offers countercyclical mining incentives to keep the market for mining 275 | and demand for Luna long-term stable through volatile macroeconomic 276 | cycles. 277 | 278 | \subsection{Countercyclical Mining Rewards } 279 | 280 | Our objective is to counteract fluctuations in the value of mining 281 | Terra by calibrating mining rewards to be countercyclical. The main 282 | intuition behind a countercyclical policy is that it attempts to counteract 283 | economic cycles by increasing mining rewards during recessions and 284 | decreasing mining rewards during booms. The protocol has two levers 285 | at its disposal to calibrate mining rewards: transaction fees, and 286 | the proportion of seigniorage that gets allocated to miners. 287 | \begin{itemize} 288 | \item Transaction fees: The protocol levies a small fee from every Terra 289 | transaction to reward miners. Fees default to 0.1\% but may vary over 290 | time to smooth out mining rewards. If mining rewards are declining, 291 | an increase in fees can reverse that trend. Conversely, high mining 292 | rewards give the protocol leeway to bring fees down. Fees are capped 293 | at 2\%, so they are restricted to a range that does not exceed the 294 | fees paid to traditional payment processors. 295 | \item Seigniorage: Users can mint Terra by paying the system Luna. This 296 | Luna earned by the system is seigniorage, the value of newly minted 297 | currency minus the cost of issuance. The system burns a portion of 298 | seigniorage, which makes mining power scarcer and reduces mining competition. 299 | The remaining portion of seigniorage goes to the Treasury to finance 300 | fiscal stimulus. The system can calibrate the allocation of seigniorage 301 | between those two destinations to impact mining reward profiles. 302 | \end{itemize} 303 | We use two key macroeconomic indicators as inputs for controlling 304 | mining rewards: money supply and transaction volume. Those two indicators 305 | are important signals for the performance of the economy. Looking 306 | at the equation for mining rewards: when the economy underperforms 307 | relative to recent history (money supply and transaction volume have 308 | decreased) a higher proportion of seigniorage is allocated to mining 309 | rewards, and transaction fees increase; conversely, when the economy 310 | outperforms recent history (money supply and transaction volume have 311 | increased) a lower proportion of seigniorage is allocated to mining 312 | rewards, and transaction fees decrease. 313 | 314 | Phrasing the above more formally, both the proportion of seigniorage 315 | that gets allocated to mining rewards $w_t$ and the adjustment in transaction 316 | fees $f_t$ are controlled over time as follows: 317 | 318 | \[ 319 | w_{t+1}=w_{t}+\beta\left(\frac{M_{t}}{M_{t}^{*}}-1\right)+\gamma\left(\frac{TV_{t}}{TV_{t}^{*}}-1\right) 320 | \] 321 | 322 | \[ 323 | f_{t+1}=f_{t}+\kappa\left(\frac{M_{t}}{M_{t}^{*}}-1\right)+\lambda\left(\frac{TV_{t}}{TV_{t}^{*}}-1\right) 324 | \] 325 | 326 | In the above $M_{t}$ is Terra money supply at time $t$, $M_{t}^{*}$ 327 | is the historical moving average of money supply over the previous 328 | quarter, $TV_{t}$ is Terra transaction volume at time $t$ and $TV_{t}^{*}$ 329 | is correspondingly the historical moving average of transaction volume 330 | over the previous quarter. The parameters \textgreek{b}, \textgreek{g}, 331 | \textgreek{k} and \textgreek{l} are all negative real numbers in the 332 | range {[}-1, 0) and will be calibrated to produce responses that are 333 | gradual but effective. Indicative values that have worked well in 334 | our simulations are between -0.5 and -1 for \textgreek{b}, \textgreek{g} 335 | and between -0.005 and -0.01 for \textgreek{k}, \textgreek{l} respectively. 336 | Both $w_t$ and $f_t$ are restricted within the range imposed by the protocol 337 | (between 10\% and 90\% for $w_t$, and between 0.1\% and 2\% for $f_t$). 338 | 339 | To see how this might work in practice: say that money supply is 10\% 340 | higher than quarterly average and transaction volume is 20\% higher 341 | than quarterly average. Let \textgreek{b}, \textgreek{g} be -0.5 and 342 | \textgreek{k}, \textgreek{l} be -0.01 respectively. The seigniorage 343 | allocation weight to mining rewards would decrease by 15\% and transaction 344 | fees would decrease by 0.3\% (both on an absolute basis). These are 345 | reasonable adjustments that allocate proportionally more capital to 346 | the Treasury and ease the fee burden on users in response to strong 347 | performance of the economy. 348 | \begin{center} 349 | \includegraphics[scale=0.42]{graph_tvgap} 350 | \par\end{center} 351 | 352 | Alternatively, as the graph shows, when the gap widens, i.e. as the 353 | economy shrinks, the fees will increase from the example starting 354 | point of 0.1\% to the maximum of 2\% that will still make Terra more 355 | convenient than Visa and Mastercard. 356 | 357 | The rule we have outlined for making mining rewards countercyclical 358 | is simple, intuitive and easily programmable. It takes inspiration 359 | from Taylor\textquoteright s Rule (Taylor, 1993), utilized by monetary 360 | authorities banks to help frame the level of nominal interest rates 361 | as a function of inflation and output. Similarly, exactly as a central 362 | bank, the protocol observes the health of the economy, in our case 363 | the money supply and transaction volume, and adjusts its main levers 364 | to ensure the sustainability of the economy. 365 | 366 | 367 | \section{Terra Platform} 368 | Smart contracts have enormous potential, but their use cases are limited by the price volatility of their underlying currency. The canonical function of a smart contract is to hold an escrow of tokens to be distributed when some set of conditions are triggered. Such a scheme is quite simply a futures contract, where all involved parties are forced to speculate on the price movement of the funds held by the contract. Price volatility makes smart contracts unusable for most mainstream financial applications, as most users are used to value determinate payouts in insurance, credit, mortgage, and payroll. 369 | 370 | The introduction of a stable dApp platform will allow smart contracts to mature into a useful infrastructure for mainstream businesses. Though most dApps today issue native tokens with custom token economics, for vast majority of cases such tokens have limited use cases and fragments the overall user experience, as users today needs to sell tokens A and buy tokens B and C to interact with dApps. Instead, the Terra Platform will be oriented to building financial applications that use Terra as their underlying currency. 371 | 372 | Terra Platform DApps will help to drive growth and stabilize the Terra by diversifying its use cases. The protocol may therefore subsidize the growth of the more successful applications through its growth-driven fiscal policy, and we talk about this in the next section. 373 | 374 | 375 | \section{Growth-driven fiscal policy} 376 | 377 | National governments use expansionary fiscal spending with the objective 378 | of stimulating growth. On the balance, the hope of fiscal spending 379 | is that the economic activity instigated by the original spending 380 | results in a feedback loop that grows the economy more than the amount 381 | of money spent in the initial stimulus. This concept is captured by 382 | the spending multiplier \textemdash{} how many dollars of economic 383 | activity does one dollar of fiscal spending generate? The spending 384 | multiplier increases with the marginal propensity to consume, meaning 385 | that the effectiveness of the expansionary stimulus is directly related 386 | to how likely economic agents are to increase their spending. 387 | 388 | In a previous section, we discussed how Terra seigniorage is directed 389 | to both miner rewards and the Treasury. At this point, it is worth 390 | describing how exactly the Treasury implements Terra's fiscal spending 391 | policy, with its core mandate being stimulating Terra's growth while 392 | ensuring its stability. In this manner, Terra achieves greater efficiency 393 | by returning seigniorage not allocated for stability back to its users. 394 | 395 | The Treasury's main focus is the allocation of resources derived from 396 | seigniorage to decentralized application (dApp). To receive seigniorage 397 | from the Treasury, a dApp needs to register for consideration as an 398 | entity that operates on the Terra network. dApps are eligible for 399 | funding depending on their economic activity and use of funding. A 400 | dApp registers a wallet with the network that is used to track economic 401 | activity. Transactions that go through the wallet count towards the 402 | dApp's transaction volume. 403 | 404 | The funding procedure for a dApp works as follows: 405 | \begin{itemize} 406 | \item A dApp applies for an account with the Treasury; the application includes 407 | metadata such as the Title, a url leading to a detailed page regarding 408 | the use of funding, the wallet address of the applicant, as well as 409 | auditing and governance procedures. 410 | \item At regular voting intervals, Luna validators vote to accept or reject 411 | new dApp applications for Treasury accounts. The net number of votes 412 | (yes votes minus no votes) needs to exceed 1/3 of total available 413 | validator power for an application to be accepted. 414 | \item Luna validators may only exercise control over which dApps can open 415 | accounts with the Treasury. The funding itself is determined programmatically 416 | for each funding period by a weight that is assigned to each dApp. 417 | This allows the Treasury to prioritize dApps that earn the most funding. 418 | \item At each voting session, Luna validators have the right to request 419 | that a dApp be blacklisted, for example because it behaves dishonestly 420 | or fails to account for its use of Treasury funds. Again, the net 421 | number of votes (yes votes minus no votes) needs to exceed 1/3 of 422 | total available validator power for the blacklist to be enforced. 423 | A blacklisted dApp loses access to its Treasury account and is no 424 | longer eligible for funding. 425 | \end{itemize} 426 | The motivation behind assigning funding weights to dApps is to maximize 427 | the impact of the stimulus on the economy by rewarding the dApps that 428 | are more likely to have a positive effect on the economy. The Treasury 429 | uses two criteria for allocating spending: (1) \textbf{robust economic 430 | activity} and (2) \textbf{efficient use of funding}. dApps with a 431 | strong track record of adoption receive support for their continued 432 | success, and dApps that have grown relative to their funding are rewarded 433 | with more seigniorage, as they have a successful track record of efficiently 434 | using their resources. 435 | 436 | Those two criteria are combined into a single weight which determines 437 | the relative funding that dApps receive from the aggregate funding 438 | pool. For instance, a dApp with a weight of 2 would receive twice 439 | the amount of funding of a dApp with a weight of 1. 440 | 441 | We lay out the funding weight equation, followed by a detailed explanation 442 | of all the parts: For a time period t, let TV\_t be a dApp's transaction 443 | volume and F\_t be the Treasury funding received. Then we determine 444 | the funding weight $w_{t}$ for the period as follows: 445 | 446 | \[ 447 | w_{t}=\left(1-\lambda\right)TV_{t}^{*}+\lambda\frac{\Delta TV_{t}^{*}}{F_{t-1}^{*}} 448 | \] 449 | 450 | The notation {*} denotes a moving average, so TV{*}\_t would be the 451 | moving average of transaction volume leading up to time period t, 452 | while \textgreek{D}TV{*}\_t would be a difference of moving averages 453 | of different lengths leading up to time period t. One might make the 454 | averaging window quarterly for example. Finally, the funding weights among 455 | all dApps are scaled to sum to 1. 456 | \begin{itemize} 457 | \item \textbf{The first term} is proportional to $TV_{t}^{*}$, the average 458 | transaction volume generated by the dApp in the recent past. This 459 | is an indicator of the dApp's \textbf{economic activity}, or more 460 | simply the size of its micro-economy. 461 | \item \textbf{The second term} is proportional to $\Delta TV*_{t}/F*_{t}-1$. 462 | The numerator describes the trend in transaction volume \textemdash{} 463 | it is the difference between a more and a less recent average. When 464 | positive, it means that the transaction volume is following an upward 465 | trajectory and vice versa. The denominator is the average funding 466 | amount received by the dApp in the recent past, up to and including 467 | the previous period. So the second term describes how economic activity 468 | is changing relative to past funding. Overall, larger values of this 469 | ratio capture instances where the dApp is fast-growing for each dollar 470 | of funding it has received. This is in fact the spending multiplier 471 | of the funding program, a prime indicator of \textbf{funding efficiency}. 472 | \item The parameter \textgreek{l} is used to determine the relative importance 473 | of economic activity and funding efficiency. If it isset equal to 474 | 1/2 then the two terms would have equal contribution. By decreasing 475 | the value of \textgreek{l}, the protocol can favor more heavily dApps 476 | with larger economies. Conversely, by increasing the value of \textgreek{l} 477 | the protocol can favor dApps that are using funding with high efficiency, 478 | for example by growing fast with little funding, even if they are 479 | smaller in size. 480 | \end{itemize} 481 | The votes on registering and blacklisting a dApp serve to minimize 482 | the risk that the above system is gamed during its infancy. It is 483 | the responsibility of Luna validators to hold dApps accountable for 484 | dishonest behavior and blacklist them if necessary. As the economy 485 | grows and becomes more decentralized, the bar to register and blacklist 486 | an App can be adjusted. 487 | 488 | An important advantage of distributing funding in a programmatic way 489 | is that it is simpler, objective, transparent and streamlined compared 490 | to open-ended voting systems. In fact, compared to decentralized voting 491 | systems, it is more predictable, because the inputs used to compute 492 | the funding weights are transparent and slow moving. Furthermore, 493 | this system requires less trust in Luna validators, given that the 494 | only authority they are vested with is determining whether or not 495 | a dApp is honest and makes legitimate use of funding. 496 | 497 | Overall, the objective of Terra governance is simple: fund the organizations 498 | and proposals with the highest net impact on the economy. This will 499 | include dApps solving real problems for users, increasing Terra's 500 | adoption and as a result increasing the GDP of the Terra economy. 501 | 502 | \section{Conclusion} 503 | 504 | We have presented Terra, a stable digital currency that is designed 505 | to complement both existing fiat and cryptocurrencies as a way to 506 | transact and store value. The protocol adjusts the supply of Terra 507 | in response to changes in demand to keep its price stable. This is 508 | achieved using Luna, the mining token whose countercyclical rewards 509 | are designed to absorb volatility from changing economic cycles. Terra 510 | also achieves efficient adoption by returning seigniorage not invested 511 | in stability back to its users. Its transparent and democratic distribution 512 | mechanism gives dApps the power to attract and retain users by tapping 513 | into Terra's economic growth. 514 | 515 | If Bitcoin\textquoteright s contribution to cryptocurrency was immutability, 516 | and Ethereum expressivity, our value-add will be usability. The potential 517 | applications of Terra are immense. Immediately, we foresee Terra being 518 | used as a medium-of-exchange in online payments, allowing people to 519 | transact freely at a fraction of the fees charged by other payment 520 | methods. As the world starts to become more and more decentralized, 521 | we see Terra being used as a dApp platform where price-stable token 522 | economies are built on Terra. Terra is looking to become the first 523 | usable currency and stability platform on the blockchain, unlocking 524 | the power of decentralization for mainstream users, merchants, and 525 | developers. 526 | 527 | \noindent {\small{}\newpage}\textbf{\small{}References }{\small\par} 528 | 529 | \noindent {\small{}Liu, Yukun and Tsyvinski, Aleh, Risks and Returns 530 | of Cryptocurrency (August 2018). NBER Working Paper No. w24877. Available 531 | at https://ssrn.com/abstract=3226806. }{\small\par} 532 | 533 | \noindent {\small{}Makarov, Igor and Schoar, Antoinette, Trading and 534 | Arbitrage in Cryptocurrency Markets (April 30, 2018). Available at 535 | SSRN: https://ssrn.com/abstract=3171204. }{\small\par} 536 | 537 | \noindent {\small{}Kereiakes, Evan, Rationale for Including Multiple 538 | Fiat Currencies in Terra\textquoteright s Peg (November 2018). Available 539 | at https://medium.com/terra-money/rationale-for-including-multiple-fiat-currencies-in-terras-peg-1ea9eae9de2a }{\small\par} 540 | 541 | \noindent {\small{}Taylor, John B. (1993). \textquotedbl Discretion 542 | versus Policy Rules in Practice.\textquotedbl{} Carnegie-Rochester 543 | Conference Series on Public Policy. 39: 195\textendash 214. }{\small\par} 544 | \end{document} 545 | %% LyX 2.3.1-1 created this file. For more info, see http://www.lyx.org/. 546 | %% Do not edit unless you really know what you are doing. 547 | \documentclass[12pt]{article} 548 | \usepackage[LGR,T1]{fontenc} 549 | \usepackage[latin9]{inputenc} 550 | \usepackage{geometry} 551 | \geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in} 552 | \usepackage{color} 553 | \usepackage{amsmath} 554 | \usepackage{amssymb} 555 | \usepackage{graphicx} 556 | \usepackage{setspace} 557 | \doublespacing 558 | \usepackage[unicode=true, 559 | bookmarks=false, 560 | breaklinks=false,pdfborder={0 0 1},backref=section,colorlinks=true] 561 | {hyperref} 562 | \hypersetup{pdftitle={How QE Works: Evidence on the Refinancing Channel}, 563 | linkcolor=black,citecolor=blue,filecolor=magenta,urlcolor=blue} 564 | 565 | \makeatletter 566 | 567 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands. 568 | \DeclareRobustCommand{\greektext}{% 569 | \fontencoding{LGR}\selectfont\def\encodingdefault{LGR}} 570 | \DeclareRobustCommand{\textgreek}[1]{\leavevmode{\greektext #1}} 571 | \ProvideTextCommand{\~}{LGR}[1]{\char126#1} 572 | 573 | 574 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands. 575 | \usepackage{color,titling,titlesec} 576 | \usepackage{eurosym} 577 | \usepackage{harvard}\usepackage{amsfonts} 578 | \usepackage{graphicx,pdflscape} 579 | \usepackage{chicago}\setcounter{MaxMatrixCols}{30} 580 | \usepackage[bottom]{footmisc} 581 | 582 | % This shrinks the space before and after display formulas 583 | \usepackage{etoolbox} 584 | \apptocmd\normalsize{% 585 | \abovedisplayskip=5pt 586 | %\abovedisplayshortskip=6pt % plus 3pt 587 | \belowdisplayskip=6pt 588 | %\belowdisplayshortskip=7pt plus 3pt 589 | }{}{} 590 | 591 | % slim white space before title, section/subsection headers 592 | \setlength{\droptitle}{-.75in} 593 | \titlespacing*{\section}{0pt}{.2cm}{0pt} 594 | \titlespacing*{\subsection}{0pt}{.2cm}{0pt} 595 | 596 | \makeatother 597 | 598 | \begin{document} 599 | \title{Terra Money:\\ 600 | Stability and Adoption} 601 | \author{Evan Kereiakes (evan@terra.money) \and Do Kwon (do@terra.money) \and 602 | Marco Di Maggio (marco@terra.money) \and Nicholas Platias (nick@terra.money)} 603 | \date{February 2019} 604 | \maketitle 605 | \begin{center} 606 | {\large{}\vspace{-1.5cm} 607 | }{\large\par} 608 | \par\end{center} 609 | \begin{abstract} 610 | \begin{singlespace} 611 | While many see the benefits of a price-stable cryptocurrency that 612 | combines the best of both fiat and Bitcoin, not many have a clear 613 | plan to get such a currency adopted. Since the value of a currency 614 | as medium of exchange is mainly driven by its network effects, a successful 615 | new digital currency needs to maximize adoption in order to become 616 | useful. We propose a cryptocurrency, Terra, which is both price-stable 617 | and growth-driven. It achieves price-stability via an elastic money 618 | supply enabled by countercyclical mining incentives and transaction 619 | fees. It also uses seigniorage created by its minting operations as 620 | transaction stimulus, thereby facilitating adoption. There is demand 621 | for a decentralized, price-stable money protocol in both fiat and 622 | blockchain economies. If such a protocol succeeds, then it will have 623 | a significant impact as the best use case for cryptocurrencies. 624 | \end{singlespace} 625 | \end{abstract} 626 | \thispagestyle{empty} 627 | 628 | \newpage\setcounter{page}{1} 629 | 630 | \section{Introduction} 631 | 632 | The price-volatility of cryptocurrencies is a well-studied problem 633 | by both academics and market observers (see for instance, Liu and 634 | Tsyvinski, 2018, Makarov and Schoar, 2018). Most cryptocurrencies, 635 | including Bitcoin, have a predetermined issuance schedule that, together 636 | with a strong speculative demand, contributes to wild fluctuations 637 | in price. Bitcoin\textquoteright s extreme price volatility is a major 638 | roadblock towards its adoption as a medium of exchange or store of 639 | value. Intuitively, nobody wants to pay with a currency that has the 640 | potential to double in value in a few days, or wants to be paid in 641 | the currency if its value can significantly decline before the transaction 642 | is settled. The problems are aggravated when the transaction requires 643 | more time, e.g. for deferred payments such as mortgages or employment 644 | contracts, as volatility would severely disadvantage one side of the 645 | contract, making the usage of existing digital currencies in these 646 | settings prohibitively expensive. At the core of how the Terra Protocol 647 | solves these issues is the idea that a cryptocurrency with an elastic 648 | monetary policy would stabilize its price, retaining all the censorship 649 | resistance of Bitcoin, and making it viable for use in everyday transactions. 650 | However, price-stability is not sufficient to get a new currency widely 651 | adopted. Currencies are inherently characterized by strong network 652 | effects: a customer is unlikely to switch over to a new currency unless 653 | a critical mass of merchants are ready to accept it, but at the same 654 | time, merchants have no reason to invest resources and educate staff 655 | to accept a new currency unless there is significant customer demand 656 | for it. For this reason, Bitcoin\textquoteright s adoption in the 657 | payments space has been limited to small businesses whose owners are 658 | personally invested in cryptocurrencies. Our belief is that while 659 | an elastic monetary policy is the solution to the stability problem, 660 | an efficient fiscal policy can drive adoption. Then, the Terra Protocol 661 | also offers strong incentives for users to join the network with an 662 | efficient fiscal spending regime, managed by a Treasury, where multiple 663 | stimulus programs compete for financing. That is, proposals from community 664 | participants will be vetted by the rest of the ecosystem and, when 665 | approved, they will be financed with the objective to increase adoption 666 | and expand the potential use cases. The Terra Protocol with its balance 667 | between fostering stability and adoption represents a meaningful complement 668 | to fiat currencies as means of payment, and store of value. The rest 669 | of the paper is organized as follows. We first discuss the protocol 670 | and how stability is achieved and maintained, through the calibration 671 | of miners\textquoteright{} demand and the use of the native mining 672 | Luna token. We then dig deeper in how countercyclical incentives and 673 | fees are adopted to smooth fluctuations. Second, we discuss how Terra\textquoteright s 674 | fiscal policy can be used as an efficient stimulus to drive adoption. 675 | 676 | \section{Multi-fiat peg monetary policy } 677 | 678 | A stable-coin mechanism must answer three key questions: 679 | \begin{itemize} 680 | \item \textbf{How is price-stability defined?} Stability is a relative concept; 681 | which asset should a stable-coin be pegged to in order to appeal to 682 | the broadest possible audience? 683 | \item \textbf{How is price-stability measured?} Coin price is exogenous 684 | to the Terra blockchain, and an efficient, corruption-resistant price 685 | feed is necessary for the system to function properly. 686 | \item \textbf{How is price-stability achieved?} When coin price has deviated 687 | from the target, the system needs a way to apply pressures to the 688 | market to bring price back to the target. 689 | \end{itemize} 690 | This section will specify Terra\textquoteright s answers to the above 691 | questions in detail. 692 | 693 | \subsection{Defining stability against regional fiat currencies } 694 | 695 | The existential objective of a stable-coin is to retain its purchasing 696 | power. Given that most goods and services are consumed domestically, 697 | it is important to create crypto-currencies that track the value of 698 | local fiat currencies. Though the US Dollar dominates international 699 | trade and forex operations, to the average consumer the dollar exhibits 700 | unacceptable volatility against her choice unit of account. 701 | 702 | Recognizing strong regionalities in money, Terra aims to be a family 703 | of cryptocurrencies that are each pegged to the world's major currencies. 704 | Close to genesis, the protocol will issue Terra currencies pegged 705 | to USD, EUR, CNY, JPY, GBP, KRW, and the IMF SDR. Over time, more 706 | currencies will be added to the list by user voting. TerraSDR will 707 | be the flagship currency of this family, given that it exhibits the 708 | lowest volatility against any one fiat currency (Kereiakes, 2018). 709 | TerraSDR be the currency in which payment of transaction fees, disbursements 710 | of miner rewards and fiscal spending will be denominated. 711 | 712 | \subsection{Measuring stability with miner oracles } 713 | 714 | Since the price of Terra currencies in secondary markets is exogenous 715 | to the blockchain, the system must rely on a decentralized price oracle 716 | to estimate the true exchange rate. We define the mechanism for the 717 | price oracle as the following: 718 | \begin{itemize} 719 | \item For any Terra sub-currency in the set of currencies C = \{TerraKRW, 720 | TerraUSD, TerraSDR... \} miners submit a vote for what they believe 721 | to be the current exchange rate between the sub-currency and its target 722 | fiat asset. To prevent front-running, voters submit a hash of the 723 | price value instead of the price itself. 724 | \item Every n blocks the vote is tallied by having voters submit a solution 725 | to the vote hash. The weighted median of the votes is taken for both 726 | the target and observed exchange rates as the true rates. 727 | \item Some amount of Terra is rewarded to those who voted within 1 standard 728 | deviation of the elected median. Those who voted outside may be punished 729 | via slashing of their stakes. The ratio of those that are punished 730 | and rewarded may be calibrated by the system every vote to ensure 731 | that a sufficiently large portion of the miners vote. 732 | \end{itemize} 733 | Several issues have been raised in implementing decentralized oracles, 734 | but chief among them is the possibility for voters to profit by coordinating 735 | on a false price vote. Limiting the vote to a specific subset of users 736 | with strong vested interest in the system, the miners, can vastly 737 | decrease the odds of such a coordination. A successful coordination 738 | event on the price oracle would result in a much higher loss in the 739 | value of the miner stakes than any potential gains of a successful 740 | coordination. 741 | 742 | \subsection{Achieving stability through countercyclical mining } 743 | 744 | Once the system has detected that the price of a Terra currency has 745 | deviated from its peg, it must apply pressures to normalize the price. 746 | Like any other market, the Terra money market follows simple rules 747 | of supply and demand for a pegged currency. That is: 748 | \begin{itemize} 749 | \item Contracting money supply, all conditions held equal, will result in 750 | higher relative price levels. That is, when price levels are falling 751 | below the target, reducing money supply sufficiently will return price 752 | levels to normalcy. 753 | \item Expanding money supply, all conditions held equal, will result in 754 | lower relative price levels. That is, when price levels are rising 755 | above the target, increasing money supply sufficiently will return 756 | price levels to normalcy. 757 | \end{itemize} 758 | Of course, contracting the supply of money isn\textquoteright t free; 759 | like any other asset, money needs to be bought from the market. Central 760 | banks and governments shoulder contractionary costs for pegged fiat 761 | systems through a variety of mechanisms including intervention, the 762 | issuance of bonds and short-term instruments thus incurring costs 763 | of interest, and hiking of money market rates and reserve ratio requirements 764 | thus losing revenue. Put in a different way, central banks and governments 765 | absorb the volatility of the pegged currencies they issue. 766 | 767 | Analogously, Terra miners absorb volatility in Terra supply. 768 | \begin{itemize} 769 | \item \textbf{In the short term, miners absorb Terra contraction costs} 770 | through mining power dilution. During a contraction, the system mints 771 | and auctions more mining power to buy back and burn Terra. This effectively 772 | contracts the supply of Terra until its price has returned to the 773 | peg, and temporarily results in mining power dilution. 774 | \item \textbf{In the mid to long term, miners are compensated with increased 775 | mining rewards}. First, the system continues to buy back mining power 776 | until a fixed target supply is reached, thereby creating long-run 777 | dependability in available mining power. Second, the system increases 778 | mining rewards, which will be explained in more detail in a later 779 | section. 780 | \end{itemize} 781 | In summary, miners bear the costs of Terra volatility in the short 782 | term, while being compensated for it in the long-term. Compared to 783 | ordinary users, miners have a long-term vested interest in the stability 784 | of the system, with invested infrastructure, trained staff and business 785 | models with high switching cost. The remainder of this section will 786 | discuss how the system forwards short-term volatility and creates 787 | long-term incentives for Terra miners. 788 | 789 | \subsection{Miners absorb short-term Terra volatility } 790 | 791 | The Terra Protocol runs on a Proof of Stake (PoS) blockchain, where 792 | miners need to stake a native cryptocurrency Luna to mine Terra transactions. 793 | At every block period, the protocol elects among the set of staked 794 | miners a block producer, which is entrusted with the work required 795 | to produce the next block by aggregating transactions, achieving consensus 796 | among miners, and ensuring that messages are distributed properly 797 | in a short timeframe with high fault tolerance. 798 | 799 | The block producer election is weighted by the size of the active 800 | miner\textquoteright s Luna stake. Therefore, \textbf{Luna represents 801 | mining power in the Terra network.} Similar to how a Bitcoin miner\textquoteright s 802 | hash power represents a pro-rata odds of generating Bitcoin blocks, 803 | the Luna stake represents pro-rata odds of generating Terra blocks. 804 | 805 | Luna also serves as the most immediate defense against Terra price 806 | fluctuations. The system uses Luna to make the price for Terra by 807 | agreeing to be counter-party to anyone looking to swap Terra and Luna 808 | at Terra's target exchange rate. More concretely: 809 | \begin{itemize} 810 | \item When TerraSDR's price < 1 SDR, users and arbitragers can send 1 TerraSDR 811 | to the system and receive 1 SDR's worth of Luna. 812 | \item When TerraSDR's price > 1 SDR, users and arbitragers can send 1 SDR's 813 | worth of Luna to the system and receive 1 TerraSDR. 814 | \end{itemize} 815 | The system's willingness to respect the target exchange rate irrespective 816 | of market conditions keeps the market exchange rate of Terra at a 817 | tight band around the target exchange rate. 818 | 819 | The system finances Terra price making via Luna: 820 | \begin{itemize} 821 | \item To buy 1 TerraSDR, the protocol mints and sells Luna worth 1 SDR 822 | \item By selling 1 TerraSDR, the protocol earns Luna worth 1 SDR 823 | \end{itemize} 824 | As Luna is minted to match Terra offers, volatility is moved from 825 | Terra price to Luna supply. If unmitigated, this Luna dilution presents 826 | a problem for miners; their Luna stakes are worth a smaller portion 827 | of total available mining power post-contraction. Therefore, the system 828 | burns a portion of the Luna it has earned during expansions until 829 | Luna supply has reached its 1 billion equilibrium issuance. Therefore, 830 | Luna can have steady demand as a token with pro-rata rights to Terra 831 | mining over the long term. The next section discusses how the system 832 | offers countercyclical mining incentives to keep the market for mining 833 | and demand for Luna long-term stable through volatile macroeconomic 834 | cycles. 835 | 836 | \subsection{Countercyclical Mining Rewards } 837 | 838 | Our objective is to counteract fluctuations in the value of mining 839 | Terra by calibrating mining rewards to be countercyclical. The main 840 | intuition behind a countercyclical policy is that it attempts to counteract 841 | economic cycles by increasing mining rewards during recessions and 842 | decreasing mining rewards during booms. The protocol has two levers 843 | at its disposal to calibrate mining rewards: transaction fees, and 844 | the proportion of seigniorage that gets allocated to miners. 845 | \begin{itemize} 846 | \item Transaction fees: The protocol levies a small fee from every Terra 847 | transaction to reward miners. Fees default to 0.1\% but may vary over 848 | time to smooth out mining rewards. If mining rewards are declining, 849 | an increase in fees can reverse that trend. Conversely, high mining 850 | rewards give the protocol leeway to bring fees down. Fees are capped 851 | at 2\%, so they are restricted to a range that does not exceed the 852 | fees paid to traditional payment processors. 853 | \item Seigniorage: Users can mint Terra by paying the system Luna. This 854 | Luna earned by the system is seigniorage, the value of newly minted 855 | currency minus the cost of issuance. The system burns a portion of 856 | seigniorage, which makes mining power scarcer and reduces mining competition. 857 | The remaining portion of seigniorage goes to the Treasury to finance 858 | fiscal stimulus. The system can calibrate the allocation of seigniorage 859 | between those two destinations to impact mining reward profiles. 860 | \end{itemize} 861 | We use two key macroeconomic indicators as inputs for controlling 862 | mining rewards: money supply and transaction volume. Those two indicators 863 | are important signals for the performance of the economy. Looking 864 | at the equation for mining rewards: when the economy underperforms 865 | relative to recent history (money supply and transaction volume have 866 | decreased) a higher proportion of seigniorage is allocated to mining 867 | rewards, and transaction fees increase; conversely, when the economy 868 | outperforms recent history (money supply and transaction volume have 869 | increased) a lower proportion of seigniorage is allocated to mining 870 | rewards, and transaction fees decrease. 871 | 872 | Phrasing the above more formally, both the proportion of seigniorage 873 | that gets allocated to mining rewards wt and the adjustment in transaction 874 | fees ft are controlled over time as follows: 875 | 876 | \[ 877 | w_{t+1}=w_{t}+\beta\left(\frac{M_{t}}{M_{t}^{*}}-1\right)+\gamma\left(\frac{TV_{t}}{TV_{t}^{*}}-1\right) 878 | \] 879 | 880 | \[ 881 | f_{t+1}=f_{t}+\kappa\left(\frac{M_{t}}{M_{t}^{*}}-1\right)+\lambda\left(\frac{TV_{t}}{TV_{t}^{*}}-1\right) 882 | \] 883 | 884 | In the above $M_{t}$ is Terra money supply at time $t$, $M_{t}^{*}$ 885 | is the historical moving average of money supply over the previous 886 | quarter, $TV_{t}$ is Terra transaction volume at time $t$ and $TV_{t}^{*}$ 887 | is correspondingly the historical moving average of transaction volume 888 | over the previous quarter. The parameters \textgreek{b}, \textgreek{g}, 889 | \textgreek{k} and \textgreek{l} are all negative real numbers in the 890 | range {[}-1, 0) and will be calibrated to produce responses that are 891 | gradual but effective. Indicative values that have worked well in 892 | our simulations are between -0.5 and -1 for \textgreek{b}, \textgreek{g} 893 | and between -0.005 and -0.01 for \textgreek{k}, \textgreek{l} respectively. 894 | Both wt and ft are restricted within the range imposed by the protocol 895 | (between 0\% and 90\% for wt, and between 0.01\% and 2\% for ft). 896 | 897 | To see how this might work in practice: say that money supply is 10\% 898 | higher than quarterly average and transaction volume is 20\% higher 899 | than quarterly average. Let \textgreek{b}, \textgreek{g} be -0.5 and 900 | \textgreek{k}, \textgreek{l} be -0.01 respectively. The seigniorage 901 | allocation weight to mining rewards would decrease by 15\% and transaction 902 | fees would decrease by 0.3\% (both on an absolute basis). These are 903 | reasonable adjustments that allocate proportionally more capital to 904 | the Treasury and ease the fee burden on users in response to strong 905 | performance of the economy. 906 | \begin{center} 907 | \includegraphics[scale=1.25]{graph_tvgap} 908 | \par\end{center} 909 | 910 | Alternatively, as the graph shows, when the gap widens, i.e. as the 911 | economy shrinks, the fees will increase from the example starting 912 | point of 0.1\% to the maximum of 2\% that will still make Terra more 913 | convenient than Visa and Mastercard. 914 | 915 | The rule we have outlined for making mining rewards countercyclical 916 | is simple, intuitive and easily programmable. It takes inspiration 917 | from Taylor\textquoteright s Rule (Taylor, 1993), utilized by monetary 918 | authorities banks to help frame the level of nominal interest rates 919 | as a function of inflation and output. Similarly, exactly as a central 920 | bank, the protocol observes the health of the economy, in our case 921 | the money supply and transaction volume, and adjusts its main levers 922 | to ensure the sustainability of the economy. 923 | 924 | \section{Growth-driven fiscal policy} 925 | 926 | National governments use expansionary fiscal spending with the objective 927 | of stimulating growth. On the balance, the hope of fiscal spending 928 | is that the economic activity instigated by the original spending 929 | results in a feedback loop that grows the economy more than the amount 930 | of money spent in the initial stimulus. This concept is captured by 931 | the spending multiplier \textemdash{} how many dollars of economic 932 | activity does one dollar of fiscal spending generate? The spending 933 | multiplier increases with the marginal propensity to consume, meaning 934 | that the effectiveness of the expansionary stimulus is directly related 935 | to how likely economic agents are to increase their spending. 936 | 937 | In a previous section, we discussed how Terra seigniorage is directed 938 | to both miner rewards and the Treasury. At this point, it is worth 939 | describing how exactly the Treasury implements Terra's fiscal spending 940 | policy, with its core mandate being stimulating Terra's growth while 941 | ensuring its stability. In this manner, Terra achieves greater efficiency 942 | by returning seigniorage not allocated for stability back to its users. 943 | 944 | The Treasury main focus is the allocation of resources derived from 945 | seigniorage to decentralized application (dApp). To receive seigniorage 946 | from the Treasury, a dApp needs to register for consideration as an 947 | entity that operates on the Terra network. dApps are eligible for 948 | funding depending on their economic activity and use of funding. A 949 | dApp registers a wallet with the network that is used to track economic 950 | activity. Transactions that go through the wallet count towards the 951 | dApp's transaction volume. 952 | 953 | The funding procedure for a dApp works as follows: 954 | \begin{itemize} 955 | \item A dApp applies for an account with the Treasury; the application includes 956 | metadata such as the Title, a url leading to a detailed page regarding 957 | the use of funding, the wallet address of the applicant, as well as 958 | auditing and governance procedures. 959 | \item At regular voting intervals, Luna validators vote to accept or reject 960 | new dApp applications for Treasury accounts. The net number of votes 961 | (yes votes minus no votes) needs to exceed 1/3 of total available 962 | validator power for an application to be accepted. 963 | \item Luna validators may only exercise control over which dApps can open 964 | accounts with the Treasury. The funding itself is determined programmatically 965 | for each funding period by a weight that is assigned to each dApp. 966 | This allows the Treasury to prioritize dApps that earn the most funding. 967 | \item At each voting session, Luna validators have the right to request 968 | that a dApp be blacklisted, for example because it behaves dishonestly 969 | or fails to account for its use of Treasury funds. Again, the net 970 | number of votes (yes votes minus no votes) needs to exceed 1/3 of 971 | total available validator power for the blacklist to be enforced. 972 | A blacklisted dApp loses access to its Treasury account and is no 973 | longer eligible for funding. 974 | \end{itemize} 975 | The motivation behind assigning funding weights to dApps is to maximize 976 | the impact of the stimulus on the economy by rewarding the dApps that 977 | are more likely to have a positive effect on the economy. The Treasury 978 | uses two criteria for allocating spending: (1) \textbf{robust economic 979 | activity} and (2) \textbf{efficient use of funding}. dApps with a 980 | strong track record of adoption receive support for their continued 981 | success, and dApps that have grown relative to their funding are rewarded 982 | with more seigniorage, as they have a successful track record of efficiently 983 | using their resources. 984 | 985 | Those two criteria are combined into a single weight which determines 986 | the relative funding that dApps receive from the aggregate funding 987 | pool. For instance, a dApp with a weight of 2 would receive twice 988 | the amount of funding of a dApp with a weight of 1. 989 | 990 | We lay out the funding weight equation, followed by a detailed explanation 991 | of all the parts: For a time period t, let TV\_t be a dApp's transaction 992 | volume and F\_t be the Treasury funding received. Then we determine 993 | the funding weight $w_{t}$ for the period as follows: 994 | 995 | \[ 996 | w_{t}=\left(1-\lambda\right)TV_{t}^{*}+\lambda\frac{\Delta TV_{t}^{*}}{F_{t-1}^{*}} 997 | \] 998 | 999 | The notation {*} denotes a moving average, so TV{*}\_t would be the 1000 | moving average of transaction volume leading up to time period t, 1001 | while \textgreek{D}TV{*}\_t would be a difference of moving averages 1002 | of different lengths leading up to time period t. One might make the 1003 | averaging window quarterly for example. The parameters \textgreek{k}, 1004 | \textgreek{l} are between 0 and 1 and determine the relative importance 1005 | of the two terms being summed. Finally, the funding weights among 1006 | all dApps are scaled to sum to 1. 1007 | \begin{itemize} 1008 | \item \textbf{The first term} is proportional to $TV_{t}^{*}$, the average 1009 | transaction volume generated by the dApp in the recent past. This 1010 | is an indicator of the dApp's \textbf{economic activity}, or more 1011 | simply the size of its micro-economy. 1012 | \item \textbf{The second term} is proportional to $\Delta TV*_{t}/F*_{t}-1$. 1013 | The numerator describes the trend in transaction volume \textemdash{} 1014 | it is the difference between a more and a less recent average. When 1015 | positive, it means that the transaction volume is following an upward 1016 | trajectory and vice versa. The denominator is the average funding 1017 | amount received by the dApp in the recent past, up to and including 1018 | the previous period. So the second term describes how economic activity 1019 | is changing relative to past funding. Overall, larger values of this 1020 | ratio capture instances where the dApp is fast-growing for each dollar 1021 | of funding it has received. This is in fact the spending multiplier 1022 | of the funding program, a prime indicator of \textbf{funding efficiency}. 1023 | \item The parameter \textgreek{l} is used to determine the relative importance 1024 | of economic activity and funding efficiency. If it isset equal to 1025 | 1/2 then the two terms would have equal contribution. By decreasing 1026 | the value of \textgreek{l}, the protocol can favor more heavily dApps 1027 | with larger economies. Conversely, by increasing the value of \textgreek{l} 1028 | the protocol can favor dApps that are using funding with high efficiency, 1029 | for example by growing fast with little funding, even if they are 1030 | smaller in size. 1031 | \end{itemize} 1032 | The votes on registering and blacklisting a dApp serve to minimize 1033 | the risk that the above system is gamed during its infancy. It is 1034 | the responsibility of Luna validators to hold dApps accountable for 1035 | dishonest behavior and blacklist them if necessary. As the economy 1036 | grows and becomes more decentralized, the bar to register and blacklist 1037 | an App can be adjusted. 1038 | 1039 | An important advantage of distributing funding in a programmatic way 1040 | is that it is simpler, objective, transparent and streamlined compared 1041 | to open-ended voting systems. In fact, compared to decentralized voting 1042 | systems, it is more predictable, because the inputs used to compute 1043 | the funding weights are transparent and slow moving. Furthermore, 1044 | this system requires less trust in Luna validators, given that the 1045 | only authority they are vested with is determining whether or not 1046 | a dApp is honest and makes legitimate use of funding. 1047 | 1048 | Overall, the objective of Terra governance is simple: fund the organizations 1049 | and proposals with the highest net impact on the economy. This will 1050 | include dApps solving real problems for users, increasing Terra's 1051 | adoption and as a result increasing the GDP of the Terra economy. 1052 | 1053 | \section{Conclusion} 1054 | 1055 | We have presented Terra, a stable digital currency that is designed 1056 | to complement both existing fiat and cryptocurrencies as a way to 1057 | transact and store value. The protocol adjusts the supply of Terra 1058 | in response to changes in demand to keep its price stable. This is 1059 | achieved using Luna, the mining token whose countercyclical rewards 1060 | are designed to absorb volatility from changing economic cycles. Terra 1061 | also achieves efficient adoption by returning seigniorage not invested 1062 | in stability back to its users. Its transparent and democratic distribution 1063 | mechanism gives dApps the power to attract and retain users by tapping 1064 | into Terra's economic growth. 1065 | 1066 | If Bitcoin\textquoteright s contribution to cryptocurrency was immutability, 1067 | and Ethereum expressivity, our value-add will be usability. The potential 1068 | applications of Terra are immense. Immediately, we foresee Terra being 1069 | used as a medium-of-exchange in online payments, allowing people to 1070 | transact freely at a fraction of the fees charged by other payment 1071 | methods. As the world starts to become more and more decentralized, 1072 | we see Terra being used as a dApp platform where price-stable token 1073 | economies are built on Terra. Terra is looking to become the first 1074 | usable currency and stability platform on the blockchain, unlocking 1075 | the power of decentralization for mainstream users, merchants, and 1076 | developers. 1077 | 1078 | \noindent {\small{}\newpage}\textbf{\small{}References }{\small\par} 1079 | 1080 | \noindent {\small{}Liu, Yukun and Tsyvinski, Aleh, Risks and Returns 1081 | of Cryptocurrency (August 2018). NBER Working Paper No. w24877. Available 1082 | at https://ssrn.com/abstract=3226806. }{\small\par} 1083 | 1084 | \noindent {\small{}Makarov, Igor and Schoar, Antoinette, Trading and 1085 | Arbitrage in Cryptocurrency Markets (April 30, 2018). Available at 1086 | SSRN: https://ssrn.com/abstract=3171204. }{\small\par} 1087 | 1088 | \noindent {\small{}Kereiakes, Evan, Rationale for Including Multiple 1089 | Fiat Currencies in Terra\textquoteright s Peg (November 2018). Available 1090 | at https://medium.com/terra-money/rationale-for-including-multiple-fiat-currencies-in-terras-peg-1ea9eae9de2a }{\small\par} 1091 | 1092 | \noindent {\small{}Taylor, John B. (1993). \textquotedbl Discretion 1093 | versus Policy Rules in Practice.\textquotedbl{} Carnegie-Rochester 1094 | Conference Series on Public Policy. 39: 195\textendash 214. }{\small\par} 1095 | \end{document} 1096 | --------------------------------------------------------------------------------