├── screen_shot.PNG ├── example_run.m ├── util ├── randfixedsum_license.txt ├── calculate_metrics.m ├── randfixedsum.m ├── getInputs.m └── extract_portfolio.m ├── README.md ├── portfolio_sortino_ratio.m └── LICENSE /screen_shot.PNG: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/elayden/portfolio_sortino_ratio/HEAD/screen_shot.PNG -------------------------------------------------------------------------------- /example_run.m: -------------------------------------------------------------------------------- 1 | script_path = 'portfolio_sortino_ratio'; % insert path to folder 'portfolio_sortino_ratio' 2 | addpath(script_path) 3 | 4 | csv_dir = fullfile(script_path,'sample_portfolio'); 5 | 6 | % [Sortino ratio, Sharpe ratio, total return, Downside Risk, SD, Drawdown] 7 | outcomeWeights = [1,0,1,.09,0,1.5]; 8 | 9 | nRandom = 1000; 10 | minWeight = .05; maxWeight = 1; limitTickers = 10; 11 | plotScatter = true; plotCorrs = true; 12 | useParallel = false; 13 | 14 | % Run optimization: 15 | results = portfolio_sortino_ratio(csv_dir, 'nRandom', nRandom, ... 16 | 'outcomeWeights', outcomeWeights, 'minWeight', minWeight, ... 17 | 'maxWeight', maxWeight,'limitTickers', limitTickers, ... 18 | 'plotScatter', plotScatter, 'plotCorrs', plotCorrs,'parallel',useParallel) %#ok 19 | 20 | % View optimized weights: 21 | results.weights 22 | 23 | % View average stats across years: 24 | results.stats 25 | 26 | % View returns for optimized portfolio compared to individual assets across 27 | % years: 28 | results.returns -------------------------------------------------------------------------------- /util/randfixedsum_license.txt: -------------------------------------------------------------------------------- 1 | Copyright (c) 2015, John D'Errico 2 | All rights reserved. 3 | 4 | Redistribution and use in source and binary forms, with or without 5 | modification, are permitted provided that the following conditions are 6 | met: 7 | 8 | * Redistributions of source code must retain the above copyright 9 | notice, this list of conditions and the following disclaimer. 10 | * Redistributions in binary form must reproduce the above copyright 11 | notice, this list of conditions and the following disclaimer in 12 | the documentation and/or other materials provided with the distribution 13 | 14 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 15 | AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16 | IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17 | ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 18 | LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 19 | CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 20 | SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 21 | INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 22 | CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 23 | ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 24 | POSSIBILITY OF SUCH DAMAGE. 25 | -------------------------------------------------------------------------------- /util/calculate_metrics.m: -------------------------------------------------------------------------------- 1 | function [sharpe, sortino, totalReturn, portfolioSD, downsideRisk] = calculate_metrics(returns, weights, riskFreeReturn) 2 | 3 | useRiskAdjustedSortino = false; % if so, uses same risk adjustment as for Sharpe, rather than 0 4 | [nRows, nCols] = size(returns); 5 | 6 | % Geometric Sharpe Ratio: https://quant.stackexchange.com/questions/3607/should-i-use-an-arithmetic-or-a-geometric-calculation-for-the-sharpe-ratio 7 | % average exp(mean(log(1+returns))) - 1 is equiv. to geomean(returns) 8 | riskAdjustedReturns = returns - repmat(riskFreeReturn,1,nCols); 9 | compoundedAdjustedReturns = sum(repmat(weights,nRows,1).*log(1+riskAdjustedReturns),2); 10 | sharpe = mean(compoundedAdjustedReturns) ./ sum(weights.*std(log(1+riskAdjustedReturns))) .* sqrt(252); 11 | 12 | % Arithmetic: 13 | % SD = std(returns); sharpe = mean(riskAdjustedReturns) ./ SD .* sqrt(252); SD = SD .* sqrt(252); % annualized SD's 14 | 15 | % Expected Portfolio Return: https://quant.stackexchange.com/questions/25371/geometric-means-standard-deviation-and-sharpe-ratios 16 | logReturns = log(1+returns); 17 | totalReturn = (exp(mean(logReturns))).^nRows - 1; 18 | totalReturn = sum(totalReturn.*weights); 19 | 20 | % Portfolio SD: 21 | SD = std(logReturns).*sqrt(252); % annualized SD's 22 | wSD = weights .* SD; 23 | portfolioSD = sqrt(wSD * corr(logReturns) * wSD'); 24 | 25 | % Sortino Ratio 26 | if useRiskAdjustedSortino 27 | downsideRisk = sum(weights .* sqrt( sum( min(0,log(1+riskAdjustedReturns)).^2 ) / nRows )); 28 | sortino = mean(compoundedAdjustedReturns) / downsideRisk * sqrt(252); 29 | else 30 | downsideRisk = sum(weights .* sqrt( sum( min(0,log(1+returns)).^2 ) / nRows )); 31 | sortino = mean(sum(repmat(weights,nRows,1).*log(1+returns),2)) / downsideRisk * sqrt(252); 32 | end 33 | end -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Portfolio Sortino Ratio 2 | 3 |

4 | 5 | ## Info: 6 | This function optimizes portfolio weights based on a user-specified 7 | weighted linear combination of the Sortino ratio, Sharpe ratio, average 8 | total return, average downside risk, average standard deviation of 9 | returns, and max drawdown. The basic idea is to provide a directory as 10 | input 'csv_dir'. This folder should contain .csv files of historical 11 | data for each ticker desired to comprise part of a portfolio. The 12 | function will then return an optimized weighting scheme based on user's 13 | criteria. It will also output historical performance data for the 14 | portfolio, an alternative equally-weighted portfolio, and for each 15 | individual ticker. Furthermore, you can choose to plot a matrix showing 16 | correlations among the individual assets, as well as a 3D point cloud 17 | showing where the optimized portfolio falls among other randomly 18 | generated portfolios on the highest-weighted dimensions. The function 19 | was designed using data from Yahoo Finance (https://finance.yahoo.com/) 20 | but should work with other data sources provided the formatting is 21 | similar. Try optimizing the sample portfolio included (with data from 22 | 2006-2018) to gain a better understanding of use cases. (See example 23 | below.) 24 | 25 | ## Note on risk free rate data (IRX): 26 | You must keep util/^IRX.csv (13 week treasury bill rates) up-to-date for risk free rate data. Download historical data at 27 | . If other data in 28 | your portfolio is more recent than ^IRX.csv, that additional data will 29 | be discarded automatically. Also, statistics will only go back as far 30 | as the most recent oldest data across all tickers. 31 | 32 | ## Cautionary note: 33 | Your results may be skewed if your data does not go 34 | back sufficiently far and includes only one portion of a market cycle 35 | (e.g., all bull market, no recessions). To gain insight into 36 | performance over the whole market cycle, try to include data going back 37 | to 2008 or 2000, if not longer. When this is not possible, note that 38 | assets with high volatility and high annual returns during a bull 39 | market will often be the same assets that sustain the largest losses 40 | during major market corrections. In the case of major recessions these 41 | losses can sometimes exceed -40% in a calendar year. 42 | 43 | ## Disclaimer: 44 | This open-source research tool is not intended to provide 45 | investment advice. It is intended only for informational purposes, and 46 | the user is not recommended to use the tool to make actual investment 47 | decisions. Seek a duly licensed professional for investment advice. 48 | 49 | ## 50 | If you find portfolio_sortino_ratio useful and would like to support its continued development, feel free to send a cup of coffee! :)

51 | [![paypal](https://www.paypalobjects.com/en_US/i/btn/btn_donateCC_LG.gif)](https://paypal.me/ElliotLayden?locale.x=en_US) 52 | -------------------------------------------------------------------------------- /util/randfixedsum.m: -------------------------------------------------------------------------------- 1 | function [x,v] = randfixedsum(n,m,s,a,b) 2 | 3 | % [x,v] = randfixedsum(n,m,s,a,b) 4 | % 5 | % This generates an n by m array x, each of whose m columns 6 | % contains n random values lying in the interval [a,b], but 7 | % subject to the condition that their sum be equal to s. The 8 | % scalar value s must accordingly satisfy n*a <= s <= n*b. The 9 | % distribution of values is uniform in the sense that it has the 10 | % conditional probability distribution of a uniform distribution 11 | % over the whole n-cube, given that the sum of the x's is s. 12 | % 13 | % The scalar v, if requested, returns with the total 14 | % n-1 dimensional volume (content) of the subset satisfying 15 | % this condition. Consequently if v, considered as a function 16 | % of s and divided by sqrt(n), is integrated with respect to s 17 | % from s = a to s = b, the result would necessarily be the 18 | % n-dimensional volume of the whole cube, namely (b-a)^n. 19 | % 20 | % This algorithm does no "rejecting" on the sets of x's it 21 | % obtains. It is designed to generate only those that satisfy all 22 | % the above conditions and to do so with a uniform distribution. 23 | % It accomplishes this by decomposing the space of all possible x 24 | % sets (columns) into n-1 dimensional simplexes. (Line segments, 25 | % triangles, and tetrahedra, are one-, two-, and three-dimensional 26 | % examples of simplexes, respectively.) It makes use of three 27 | % different sets of 'rand' variables, one to locate values 28 | % uniformly within each type of simplex, another to randomly 29 | % select representatives of each different type of simplex in 30 | % proportion to their volume, and a third to perform random 31 | % permutations to provide an even distribution of simplex choices 32 | % among like types. For example, with n equal to 3 and s set at, 33 | % say, 40% of the way from a towards b, there will be 2 different 34 | % types of simplex, in this case triangles, each with its own 35 | % area, and 6 different versions of each from permutations, for 36 | % a total of 12 triangles, and these all fit together to form a 37 | % particular planar non-regular hexagon in 3 dimensions, with v 38 | % returned set equal to the hexagon's area. 39 | % 40 | % Roger Stafford - Jan. 19, 2006 41 | 42 | % Check the arguments. 43 | if (m~=round(m))|(n~=round(n))|(m<0)|(n<1) 44 | error('n must be a whole number and m a non-negative integer.') 45 | elseif (sn*b)|(a>=b) 46 | error('Inequalities n*a <= s <= n*b and a < b must hold.') 47 | end 48 | 49 | % Rescale to a unit cube: 0 <= x(i) <= 1 50 | s = (s-n*a)/(b-a); 51 | 52 | % Construct the transition probability table, t. 53 | % t(i,j) will be utilized only in the region where j <= i + 1. 54 | k = max(min(floor(s),n-1),0); % Must have 0 <= k <= n-1 55 | s = max(min(s,k+1),k); % Must have k <= s <= k+1 56 | s1 = s - [k:-1:k-n+1]; % s1 & s2 will never be negative 57 | s2 = [k+n:-1:k+1] - s; 58 | w = zeros(n,n+1); w(1,2) = realmax; % Scale for full 'double' range 59 | t = zeros(n-1,n); 60 | tiny = 2^(-1074); % The smallest positive matlab 'double' no. 61 | for i = 2:n 62 | tmp1 = w(i-1,2:i+1).*s1(1:i)/i; 63 | tmp2 = w(i-1,1:i).*s2(n-i+1:n)/i; 64 | w(i,2:i+1) = tmp1 + tmp2; 65 | tmp3 = w(i,2:i+1) + tiny; % In case tmp1 & tmp2 are both 0, 66 | tmp4 = (s2(n-i+1:n) > s1(1:i)); % then t is 0 on left & 1 on right 67 | t(i-1,1:i) = (tmp2./tmp3).*tmp4 + (1-tmp1./tmp3).*(~tmp4); 68 | end 69 | 70 | % Derive the polytope volume v from the appropriate 71 | % element in the bottom row of w. 72 | v = n^(3/2)*(w(n,k+2)/realmax)*(b-a)^(n-1); 73 | 74 | % Now compute the matrix x. 75 | x = zeros(n,m); 76 | if m == 0, return, end % If m is zero, quit with x = [] 77 | rt = rand(n-1,m); % For random selection of simplex type 78 | rs = rand(n-1,m); % For random location within a simplex 79 | s = repmat(s,1,m); 80 | j = repmat(k+1,1,m); % For indexing in the t table 81 | sm = zeros(1,m); pr = ones(1,m); % Start with sum zero & product 1 82 | for i = n-1:-1:1 % Work backwards in the t table 83 | e = (rt(n-i,:)<=t(i,j)); % Use rt to choose a transition 84 | sx = rs(n-i,:).^(1/i); % Use rs to compute next simplex coord. 85 | sm = sm + (1-sx).*pr.*s/(i+1); % Update sum 86 | pr = sx.*pr; % Update product 87 | x(n-i,:) = sm + pr.*e; % Calculate x using simplex coords. 88 | s = s - e; j = j - e; % Transition adjustment 89 | end 90 | x(n,:) = sm + pr.*s; % Compute the last x 91 | 92 | % Randomly permute the order in the columns of x and rescale. 93 | [~,p] = sort(rand(n,m)); % The values placed in ig are ignored 94 | x = (b-a)*x(p+repmat([0:n:n*(m-1)],n,1))+a; % Permute & rescale x 95 | 96 | return -------------------------------------------------------------------------------- /util/getInputs.m: -------------------------------------------------------------------------------- 1 | function parsed_inputs = getInputs(inputs,parsed_inputs,input_types) 2 | 3 | inputNames = fieldnames(parsed_inputs); 4 | N_inputs = length(inputNames); 5 | 6 | if nargin==3 && iscell(input_types) % check if permissable data types are provided 7 | for i = 1:N_inputs 8 | j = find(strcmp(inputNames{i},inputs)); 9 | if ~isempty(j) 10 | this_input = inputs{j+1}; 11 | % Check "OR" first: 12 | useOr = 0; 13 | for k = 1:size(input_types{i},1) 14 | switch input_types{i}{k,1} 15 | case 'char' 16 | if ischar(this_input) 17 | useOr = k; 18 | break; 19 | end 20 | case 'struct' 21 | if isstruct(this_input) 22 | useOr = k; 23 | break; 24 | end 25 | case 'logical' 26 | if islogical(this_input) 27 | useOr = k; 28 | break; 29 | end 30 | case 'numeric' 31 | if isnumeric(this_input) 32 | useOr = k; 33 | break; 34 | end 35 | case 'cell' 36 | if iscell(this_input) 37 | useOr = k; 38 | break; 39 | end 40 | case 'axes' 41 | if isgraphics(this_input,'axes') 42 | useOr = k; 43 | break; 44 | end 45 | case 'file' 46 | if exist(this_input,'file')==2 47 | useOr = k; 48 | break; 49 | end 50 | case 'vector' 51 | if isvector(this_input) 52 | useOr = k; 53 | break; 54 | end 55 | end 56 | end 57 | % Next, check "AND": 58 | failedAnd = 0; 59 | for k = 1:size(input_types{i},2) 60 | switch input_types{i}{useOr,k} 61 | case 'char' 62 | if ~ischar(this_input) 63 | failedAnd = k; 64 | break; 65 | end 66 | case 'struct' 67 | if ~isstruct(this_input) 68 | failedAnd = k; 69 | break; 70 | end 71 | case 'logical' 72 | if ~islogical(this_input) 73 | failedAnd = k; 74 | break; 75 | end 76 | case 'numeric' 77 | if ~isnumeric(this_input) 78 | failedAnd = k; 79 | break; 80 | end 81 | case 'cell' 82 | if ~iscell(this_input) 83 | failedAnd = k; 84 | break; 85 | end 86 | case 'axes' 87 | if ~isgraphics(this_input,'axes') 88 | failedAnd = k; 89 | break; 90 | end 91 | case 'file' 92 | if ~exist(this_input,'file')==2 93 | failedAnd = k; 94 | break; 95 | end 96 | case '' 97 | break; 98 | end 99 | end 100 | if failedAnd 101 | error(['Invalid input for ''',inputs{j},'''.']) 102 | else 103 | parsed_inputs.(inputNames{i}) = inputs{j+1}; 104 | end 105 | end 106 | end 107 | else % ignore input data types 108 | for i = 1:N_inputs 109 | j = find(strcmp(inputNames{i},inputs)); 110 | parsed_inputs.(inputNames{i}) = inputs{j+1}; 111 | end 112 | end 113 | 114 | end -------------------------------------------------------------------------------- /util/extract_portfolio.m: -------------------------------------------------------------------------------- 1 | function [out] = extract_portfolio(csv_dir) 2 | % Find files: 3 | listing = dir(fullfile(csv_dir,'*.csv')); 4 | if isempty(listing) 5 | listing = dir(fullfile(csv_dir,'*.xlsx')); 6 | end 7 | % Extract tables: 8 | data = cell(1,length(listing)); 9 | for i = 1:length(listing) 10 | dataTable = readtable(fullfile(csv_dir,listing(i).name)); 11 | data{i} = dataTable; 12 | end 13 | % Get Ticker Names: 14 | tickers = cell(1,length(listing)); 15 | for i = 1:length(listing) 16 | tickers{i} = listing(i).name(1:end-4); 17 | end 18 | % Check for presence of Close or AdjClose fields: 19 | for i = 1:length(data) 20 | colNames = data{i}.Properties.VariableNames; 21 | if sum(strcmpi(colNames,'AdjClose'))==0 && sum(strcmpi(colNames,'Close'))==0 22 | error(['ERROR: Ticker ',tickers{i},' has no field ''AdjClose'' or ''Close''.']) 23 | end 24 | end 25 | % Check format of columnNames: 26 | for i = 1:length(data) 27 | colNames = data{i}.Properties.VariableNames; 28 | if sum(strcmpi(colNames,'Date')) 29 | data{i}.Properties.VariableNames{strcmpi(colNames,'Date')} = 'Date'; 30 | end 31 | if strcmpi(colNames,'AdjClose') 32 | data{i}.Properties.VariableNames{strcmpi(colNames,'AdjClose')} = 'AdjClose'; 33 | end 34 | if strcmpi(colNames,'Close') 35 | data{i}.Properties.VariableNames{strcmpi(colNames,'Close')} = 'Close'; 36 | end 37 | if strcmpi(colNames,'volume') 38 | data{i}.Properties.VariableNames{strcmpi(colNames,'volume')} = 'volume'; 39 | end 40 | end 41 | % Eliminate unused columns: 42 | for i = 1:length(data) 43 | colNames = data{i}.Properties.VariableNames; 44 | if sum(strcmpi(colNames,'AdjClose'))>0 45 | delInd = (strcmpi(colNames,'AdjClose') + strcmpi(colNames,'Date') + strcmpi(colNames,'volume'))==0; 46 | data{i}(:,delInd) = []; 47 | data{i} = data{i}(:,[find(strcmpi(data{i}.Properties.VariableNames,'Date')),... 48 | find(strcmpi(data{i}.Properties.VariableNames,'AdjClose')),... 49 | find(strcmpi(data{i}.Properties.VariableNames,'Volume'))]); 50 | data{i}.Properties.VariableNames{strcmpi(data{i}.Properties.VariableNames,'AdjClose')} = 'Close'; 51 | elseif sum(strcmpi(colNames,'Close'))>0 52 | delInd = (strcmpi(colNames,'Close') + strcmpi(colNames,'Date') + strcmpi(colNames,'volume'))==0; 53 | data{i}(:,delInd) = []; 54 | data{i} = data{i}(:,[find(strcmpi(data{i}.Properties.VariableNames,'Date')),... 55 | find(strcmpi(data{i}.Properties.VariableNames,'Close')),... 56 | find(strcmpi(data{i}.Properties.VariableNames,'volume'))]); 57 | end 58 | if sum(strcmpi(data{i}.Properties.VariableNames,'volume')) 59 | data{i}.Properties.VariableNames{strcmpi(data{i}.Properties.VariableNames,'volume')} = 'volume'; 60 | end 61 | end 62 | % Convert all dates to datenum's (i.e., number of days from January 0, 0000) (works irrespective of date format): 63 | sizes = zeros(1,length(data)); 64 | for i = 1:length(data) 65 | data{i}.Date = datenum(data{i}.Date); 66 | sizes(i) = size(data{i},1); 67 | end 68 | % Find most limited data: 69 | latestStartingDate = 0; 70 | for i = 1:length(data) 71 | if min(data{i}.Date) > latestStartingDate 72 | latestStartingDate = min(data{i}.Date); 73 | end 74 | end 75 | % Eliminate data prior to this value for others: 76 | for i = 1:length(data) 77 | data{i}(data{i}.Date < latestStartingDate,:) = []; 78 | end 79 | % Find most limited data: 80 | earliestEndingDate = 9999999; 81 | for i = 1:length(data) 82 | if max(data{i}.Date) < earliestEndingDate 83 | earliestEndingDate = max(data{i}.Date); 84 | end 85 | end 86 | % Eliminate data prior to this value for others: 87 | for i = 1:length(data) 88 | data{i}(data{i}.Date > earliestEndingDate,:) = []; 89 | end 90 | % Check Rows for same dates: 91 | sizes = zeros(1,length(data)); 92 | for i = 1:length(data) 93 | sizes(i) = size(data{i},1); 94 | end 95 | if ~all(sizes==mode(sizes)) 96 | ixDifferent = find(sizes~=mode(sizes)); 97 | warnStr = 'Some tickers ('; 98 | for i = 1:length(ixDifferent) 99 | warnStr = [warnStr, tickers{i}, ', ']; %#ok 100 | end 101 | warnStr(end-1:end) = []; 102 | warnStr = [warnStr, ') do not have the same dates recorded. Trying interpolation.']; 103 | warning(warnStr); 104 | % If some dates different, try interpolating: 105 | ixUse = find(sizes==mode(sizes),1); 106 | for i = ixDifferent 107 | pp = csape(data{i}.Date, data{i}.Close, 'variational'); 108 | pred = ppval(pp, data{ixUse}.Date); % evaluate PP at xx 109 | tempTable = data{ixUse}(:,1); tempTable.Close = pred; 110 | if isfield(data{i},'Volume') 111 | pp2 = csape(data{i}.Date, data{i}.Volume, 'variational'); 112 | pred2 = ppval(pp2, data{ixUse}.Date); % evaluate PP at xx 113 | tempTable.volume = pred2; 114 | end 115 | data{i} = tempTable; 116 | end 117 | end 118 | % Convert cell2double, if any: 119 | for i = 1:length(data) 120 | if iscell(data{i}.Close) 121 | data{i}.Close = str2double(data{i}.Close); 122 | end 123 | if sum(strcmpi(data{i}.Properties.VariableNames,'volume')) && iscell(data{i}.volume) 124 | data{i}.volume = str2double(data{i}.volume); 125 | end 126 | end 127 | % Prepare output structure: 128 | out = struct('ticker',cell(1,length(data)),'date',cell(1,length(data)),... 129 | 'raw',cell(1,length(data)),'return',cell(1,length(data)),'volume',... 130 | cell(1,length(data))); 131 | % Convert to return (daily percent change): 132 | for i = 1:length(data) 133 | returns = data{i}.Close(2:end,:) ./ data{i}.Close(1:end-1,:) - 1; 134 | out(i).ticker = tickers{i}; 135 | out(i).date = data{i}.Date(2:end); 136 | out(i).raw = data{i}.Close(2:end); 137 | out(i).return = returns; 138 | if sum(strcmpi(data{i}.Properties.VariableNames,'volume')) 139 | out(i).volume = data{i}.volume(2:end); 140 | end 141 | end 142 | end -------------------------------------------------------------------------------- /portfolio_sortino_ratio.m: -------------------------------------------------------------------------------- 1 | function [results] = portfolio_sortino_ratio(csv_dir, varargin) 2 | % RESULTS = PORTFOLIO_SORTINO_RATIO(CSV_DIR, varargin) 3 | % 4 | % *Info: 5 | % This function optimizes portfolio weights based on a user-specified 6 | % weighted linear combination of the Sortino ratio, Sharpe ratio, average 7 | % total return, average downside risk, average standard deviation of 8 | % returns, and max drawdown. The basic idea is to provide a directory as 9 | % input 'csv_dir'. This folder should contain .csv files of historical 10 | % data for each ticker desired to comprise part of a portfolio. The 11 | % function will then return an optimized weighting scheme based on user's 12 | % criteria. It will also output historical performance data for the 13 | % portfolio, an alternative equally-weighted portfolio, and for each 14 | % individual ticker. Furthermore, you can choose to plot a matrix showing 15 | % correlations among the individual assets, as well as a 3D point cloud 16 | % showing where the optimized portfolio falls among other randomly 17 | % generated portfolios on the highest-weighted dimensions. The function 18 | % was designed using data from Yahoo Finance (https://finance.yahoo.com/) 19 | % but should work with other data sources provided the formatting is 20 | % similar. Try optimizing the sample portfolio included (with data from 21 | % 2006-2018) to gain a better understanding of use cases. (See example 22 | % below.) 23 | % 24 | % *Note: you must keep ^IRX.csv (13 week treasury bill rates) in the util 25 | % folder up-to-date for risk free rate data. Download historical data at 26 | % . If other data in 27 | % your portfolio is more recent than ^IRX.csv, that additional data will 28 | % be discarded automatically. Also, statistics will only go back as far 29 | % as the most recent oldest data across all tickers. 30 | % 31 | % *Cautionary note: your results may be skewed if your data does not go 32 | % back sufficiently far and includes only one portion of a market cycle 33 | % (e.g., all bull market, no recessions). To gain insight into 34 | % performance over the whole market cycle, try to include data going back 35 | % to 2008 or 2000, if not longer. When this is not possible, note that 36 | % assets with high volatility and high annual returns during a bull 37 | % market will often be the same assets that sustain the largest losses 38 | % during major market corrections. In the case of major recessions these 39 | % losses can sometimes exceed -40% in a calendar year. 40 | % 41 | % *Disclaimer: This open-source research tool is not intended to provide 42 | % investment advice. It is intended only for informational purposes, and 43 | % the user is not recommended to use the tool to make actual investment 44 | % decisions. Seek a duly licensed professional for investment advice. 45 | % 46 | % Inputs: 47 | % 48 | % 'csv_dir', a full path which contains .csv files of financial 49 | % data; files should be titled using the ETF/stock 50 | % ticker name 51 | % 52 | % Optional Name-Value Pair Arguments: 53 | % 54 | % 'nRandom', "optimization" uses the simple method of iterating 55 | % over a large number of random portfolio weights and 56 | % then selecting the best based on given criteria. The 57 | % larger this number, the better the selection that 58 | % will likely be made. (default: 10,000) 59 | % 60 | % 'outcomeWeights', a 1x6 vector containing weights which 61 | % correspond to optimization preferences for 62 | % [Sortino ratio, Sharpe ratio, total return, 63 | % Downside Risk, SD, Drawdown] (i.e., setting this 64 | % parameter allows one to gear the portfolio 65 | % optimization toward a more aggressive or conservative 66 | % portfolio strategy; weights need not sum to 1 67 | % (default: [1,0,1,0,0,1]) 68 | % 69 | % 'minWeight', numeric value (range: 0-1) specifying the minimum 70 | % weight that any ticker may receive (default: 0) 71 | % 72 | % 'maxWeight', numeric value (range: 0-1) specifying the maximum 73 | % weight that any ticker may receive (default: 1) 74 | % 75 | % 'limitTickers', numeric value (range: 0 to nTickers) specifying the 76 | % number of tickers to include in the optimized 77 | % portfolio (i.e., can be a subset of the max number 78 | % possible) (default: include all tickers) 79 | % 80 | % 'plotScatter', boolean denoting whether to plot a 3D scatter plot 81 | % showing the optimized portfolio among 82 | % randomly permuted portfolios in terms of the most 83 | % highly weighted dimensions (default: true) 84 | % 85 | % 'plotCorrs', boolean denoting whether to plot an imagesc plot 86 | % showing the correlations between the returns of each 87 | % ticker across all years (default: true) 88 | % 89 | % 'parallel', boolean denoting whether to use parallel processing 90 | % (default: false) 91 | % 92 | % Outputs: 93 | % 94 | % 'results', a structure containing: 95 | % 96 | % 'results.weights' 97 | % a table showing tickers with optimized weights 98 | % 99 | % 'results.stats' 100 | % a table of average Sortino, Sharpe, total return, 101 | % downsideRisk, SD, and max drawdown across years for 102 | % the optimized portfolio, an equal weights portfolio, 103 | % and ranges across permutations for each measure 104 | % 105 | % 'results.sortino' 106 | % a table displaying Sortino ratio by year for both 107 | % the optimized portfolio, an equally weighted 108 | % portfolio, and for each individual ticker; tickers 109 | % are sorted in descending order of average Sortino 110 | % 111 | % 'results.sharpe' 112 | % a table displaying Sharpe ratio by year for both 113 | % the optimized portfolio, an equally weighted 114 | % portfolio, and for each individual ticker; tickers 115 | % are sorted in descending order of average Sharpe 116 | % 117 | % 'results.returns' 118 | % the same as (.sharpe) but for total return; tickers 119 | % are sorted in descending order of average returns 120 | % 121 | % 'results.downsideRisk' 122 | % the same as (.sharpe) but for downside risk; tickers 123 | % are sorted in ascending order of average downside 124 | % risk 125 | % 126 | % 'results.SD' 127 | % the same as (.sharpe) but for SD; tickers are 128 | % sorted in ascending order of average SD 129 | % 130 | % Example function call: 131 | % 132 | % results = portfolio_sharpe_ratio(folderPath,... 133 | % 'nRandom',10000,'outcomeWeights',[.3,0,.3,0,0,.4],... 134 | % 'minWeight',.01,'maxWeight',.9,'limitTickers',10,'plotScatter',1,... 135 | % 'plotCorrs',0,'parallel',true); 136 | % 137 | % -this will use 10,000 randomly permuted portfolio weights 138 | % -weights minimizing drawdown as a more important evaluation criterion 139 | % than maximizing Sortino ratio or total return (both are weighted .3) 140 | % -will not weight any portfolio asset less than 1% 141 | % -will not weight any portfolio asset more than 90% 142 | % -will limit the number of assets in the optimized portfolio to 10 143 | % -will plot the 3D scatter plot but not the corrlation matrix 144 | % -will use parallel processing 145 | % 146 | % Author: Elliot Layden, 2018 147 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 148 | 149 | hWait1 = waitbar(.5,'Please wait...'); 150 | 151 | % Identify Function Path and Add Helper Scripts: 152 | script_fullpath = mfilename('fullpath'); 153 | [script_path,~,~] = fileparts(script_fullpath); 154 | addpath(genpath(script_path)) 155 | 156 | % Get Inputs: 157 | inputs = varargin; 158 | parsed = struct('nRandom', 10000, 'outcomeWeights', [1,0,1,0,0,1], ... 159 | 'minWeight', 0, 'maxWeight', 1,'limitTickers', 0, 'plotScatter', true,... 160 | 'plotCorrs', true,'parallel',false); 161 | % Column of internal cells == OR, Row of internal cells == AND 162 | input_types = {{'numeric'},{'vector'},{'numeric'},{'numeric'},{'numeric'},... 163 | {'logical';'numeric'},{'logical';'numeric'},{'logical';'numeric'}}; 164 | parsed = getInputs(inputs, parsed, input_types); 165 | nRandom = parsed.nRandom; outcomeWeights = parsed.outcomeWeights; 166 | limitTickers = parsed.limitTickers; 167 | minWeight = parsed.minWeight; maxWeight = parsed.maxWeight; 168 | plotScatter = parsed.plotScatter; plotCorrs = parsed.plotCorrs; 169 | useParallel = parsed.parallel; 170 | if nRandom <=0; nRandom = 10000; end 171 | if length(outcomeWeights)~=6 172 | warning('''outcomeWeights'' should be a 1x6 vector. Please check your inputs.') 173 | outcomeWeights = [1,0,1,0,0,1]; 174 | end 175 | outcomeWeights = outcomeWeights./sum(outcomeWeights); 176 | 177 | % Initialize Results: 178 | results = struct('weights',[],'stats',[],'sortino',[],'sharpe',[],... 179 | 'returns',[],'downsideRisk',[],'SD',[]); 180 | 181 | % Extract portfolio data: 182 | warning('off','all'); data = extract_portfolio(csv_dir); warning('on','all') 183 | 184 | % Get risk-free rates (10-year treasury rates): 185 | warning('off','all') 186 | riskFreeData = readtable(fullfile(script_path,'util','^IRX.csv')); 187 | warning('on','all') 188 | riskFreeData.Date = datenum(riskFreeData.Date); 189 | [~,ixUse,ixRiskFree] = intersect(data(1).date,riskFreeData.Date); 190 | riskFreeData = riskFreeData(ixRiskFree,:); 191 | annualized = str2double(riskFreeData.Close); 192 | riskFree = (( 1 + annualized/100 ).^(1/252)-1); % data starts as whole-number percentages 193 | ixDelete = isnan(riskFree); riskFree(ixDelete) = []; 194 | dates = year(riskFreeData.Date); dates(ixDelete) = []; 195 | years = unique(dates); nYears = length(years); 196 | 197 | % Limit portfolio data to what's available for riskFree data: 198 | for ix = 1:length(data) 199 | data(ix).date = data(ix).date(ixUse); 200 | data(ix).raw = data(ix).raw(ixUse); 201 | data(ix).return = data(ix).return(ixUse); 202 | data(ix).volume = data(ix).volume(ixUse); 203 | data(ix).date(ixDelete) = []; 204 | data(ix).raw(ixDelete) = []; 205 | data(ix).return(ixDelete) = []; 206 | data(ix).volume(ixDelete) = []; 207 | end 208 | 209 | % Extract all tickers: 210 | nRows = size(data(1).return,1); nTickers = length(data); 211 | returns = zeros(nRows,nTickers); raw = returns; tickers = cell(1, nTickers); 212 | for ix = 1:nTickers 213 | returns(:,ix) = data(ix).return; 214 | raw(:,ix) = data(ix).raw; 215 | tickers{ix} = data(ix).ticker; 216 | end 217 | 218 | % Input Checking: 219 | if limitTickers >= nTickers; limitTickers = 0; end 220 | if minWeight < 0; minWeight = 0; end 221 | if maxWeight > 1; maxWeight = 1; end 222 | 223 | axesLabels = {'Sortino','Sharpe','Return','DownsideRisk','SD','Drawdown'}; 224 | 225 | % Permuted weights: 226 | delete(hWait1); 227 | if useParallel 228 | hCheck = gcp('nocreate'); 229 | if isempty(hCheck) || ~hCheck.Connected 230 | hPool = parpool; 231 | end 232 | else 233 | hWait = waitbar(0,'Processing...'); 234 | end 235 | if limitTickers > 0 236 | weights = randfixedsum(limitTickers,nRandom,1,minWeight,maxWeight)'; 237 | useTickers = zeros(nRandom, limitTickers); 238 | else 239 | weights = randfixedsum(nTickers,nRandom,1,minWeight,maxWeight)'; 240 | useTickers = repmat((1:nTickers), nRandom, 1); 241 | end 242 | 243 | meanSharpe = zeros(nRandom,1); meanSortino = zeros(nRandom,1); 244 | meanReturn = zeros(nRandom,1); meanSD = zeros(nRandom,1); 245 | maxDrawdown = zeros(nRandom,1); meanDownsideRisk = zeros(nRandom,1); 246 | if useParallel 247 | fprintf('Parallel computing progress:\n'); 248 | fprintf(['\n' repmat('.',1,nRandom/1000) '\n\n']); 249 | end 250 | if useParallel 251 | parfor perm = 1:nRandom 252 | if rem(perm,1000)==0 253 | fprintf('\b|\n'); % prints a tick at start of each parallel iteration 254 | end 255 | if limitTickers > 0 256 | useTickers(perm,:) = randperm(nTickers, limitTickers); 257 | end 258 | sharpe = zeros(1,nYears); sortino = sharpe; yearlyReturns = sharpe; SD = sharpe; downsideRisk = sharpe; 259 | for ix = 1:nYears 260 | [sharpe(ix), sortino(ix), yearlyReturns(ix), SD(ix), downsideRisk(ix)] = calculate_metrics(... 261 | returns(dates==years(ix),useTickers(perm,:)), ... 262 | weights(perm,:), riskFree(dates==years(ix))); %#ok 263 | end 264 | meanSortino(perm) = geomean(sortino +10); 265 | meanSortino(perm) = meanSortino(perm) -10; 266 | meanSharpe(perm) = geomean(sharpe +10); 267 | meanSharpe(perm) = meanSharpe(perm) -10; 268 | meanReturn(perm) = geomean(yearlyReturns + 10); 269 | meanReturn(perm) = meanReturn(perm) -10; 270 | meanSD(perm) = geomean(SD); 271 | meanDownsideRisk(perm) = geomean(downsideRisk); 272 | maxDrawdown(perm) = min(yearlyReturns); 273 | end 274 | else 275 | for perm = 1:nRandom 276 | if rem(perm,1000)==0 277 | waitbar(perm/nRandom, hWait); 278 | end 279 | if limitTickers > 0 280 | useTickers(perm,:) = randperm(nTickers, limitTickers); 281 | end 282 | sharpe = zeros(1,nYears); sortino = sharpe; yearlyReturns = sharpe; SD = sharpe; downsideRisk = sharpe; 283 | for ix = 1:nYears 284 | [sharpe(ix), sortino(ix), yearlyReturns(ix), SD(ix), downsideRisk(ix)] = calculate_metrics(... 285 | returns(dates==years(ix),useTickers(perm,:)), ... 286 | weights(perm,:), riskFree(dates==years(ix))); 287 | end 288 | meanSortino(perm) = geomean(sortino +10); 289 | meanSortino(perm) = meanSortino(perm) -10; 290 | meanSharpe(perm) = geomean(sharpe +10); 291 | meanSharpe(perm) = meanSharpe(perm) -10; 292 | meanReturn(perm) = geomean(yearlyReturns + 10); 293 | meanReturn(perm) = meanReturn(perm) -10; 294 | meanSD(perm) = geomean(SD); 295 | meanDownsideRisk(perm) = geomean(downsideRisk); 296 | maxDrawdown(perm) = min(yearlyReturns); 297 | end 298 | end 299 | if useParallel && (isempty(hCheck) || ~hCheck.Connected) 300 | delete(hPool) 301 | else 302 | delete(hWait) 303 | end 304 | 305 | % Calculate Mahalanobis Distance of each permuted portfolio to ideal: 306 | permData = [meanSortino, meanSharpe, meanReturn, meanDownsideRisk, meanSD, maxDrawdown]; 307 | permDataZ = zscore(permData); 308 | permDataZ = permDataZ - repmat(min(permDataZ),nRandom,1); 309 | permDataZ = permDataZ ./ repmat(max(permDataZ),nRandom,1); 310 | % best = repmat([max(permDataZ(:,1)), min(permDataZ(:,2)), max(permDataZ(:,3))],nRandom,1); 311 | % dist = sqrt(sum(repmat(outcomeWeights.*[1,-1,1],nRandom,1).*(permDataZ - repmat(best,nRandom,1)).^2,2)); 312 | dist = sqrt(sum(repmat(outcomeWeights,nRandom,1).*(permDataZ - repmat([1,1,1,0,0,1],nRandom,1)).^2,2)); 313 | [~, ix_best] = min(dist); % find min. distance 314 | 315 | compute_results(ix_best); 316 | 317 | function compute_results(ix_best) 318 | 319 | bestWeights = weights(ix_best,:); % find best weights 320 | [bestWeights_sort, ixWeights] = sort(bestWeights,'descend'); 321 | 322 | % Add to results struct: 323 | results.weights = cell2table(num2cell(round(bestWeights_sort*100,3))); 324 | tickers1 = tickers(useTickers(ix_best,:)); tickers1 = tickers1(ixWeights); 325 | results.weights.Properties.VariableNames = tickers1; 326 | results.weights.Properties.RowNames = {'% weight:'}; 327 | 328 | % Calculate yearly for optimized weights: 329 | sharpe_opt = zeros(1,nYears); sortino_opt = sharpe_opt; 330 | yearlyReturns_opt = sharpe_opt; SD_opt = sharpe_opt; downsideRisk_opt = sharpe_opt; 331 | for i = 1:nYears 332 | [sharpe_opt(i), sortino_opt(i), yearlyReturns_opt(i), SD_opt(i), downsideRisk_opt(i)] = calculate_metrics(... 333 | returns(dates==years(i),useTickers(ix_best,:)), bestWeights, riskFree(dates==years(i))); 334 | end 335 | % Calculate for equal weighting: 336 | equalWeights = ones(1,nTickers)./nTickers; 337 | sharpe_eq = zeros(1,nYears); sortino_eq = sharpe_eq; 338 | yearlyReturns_eq = sharpe_eq; SD_eq = sharpe_eq; downsideRisk_eq = sharpe_eq; 339 | for i = 1:nYears 340 | [sharpe_eq(i), sortino_eq(i), yearlyReturns_eq(i), SD_eq(i), downsideRisk_eq(i)] = calculate_metrics(... 341 | returns(dates==years(i),:), equalWeights, riskFree(dates==years(i))); 342 | end 343 | % Calculate stats for individual tickers: 344 | sharpe_ind = zeros(nTickers, nYears); sortino_ind = sharpe_ind; 345 | yearlyReturns_ind = sharpe_ind; SD_ind = sharpe_ind; downsideRisk_ind = sharpe_ind; 346 | for i = 1:nTickers 347 | for j = 1:nYears 348 | [sharpe_ind(i,j), sortino_ind(i,j), yearlyReturns_ind(i,j), SD_ind(i,j), downsideRisk_ind(i,j)] = calculate_metrics(... 349 | returns(dates==years(j),i), 1, riskFree(dates==years(j))); 350 | end 351 | end 352 | 353 | % Save table output 'stats': 354 | results.stats = cell2table(num2cell(round([... 355 | geomean(sortino_opt + 10), geomean(sharpe_opt +10), ... 356 | geomean(yearlyReturns_opt + 10), geomean(downsideRisk_opt), ... 357 | geomean(SD_opt) min(yearlyReturns_opt);... 358 | geomean(sortino_eq + 10), geomean(sharpe_eq +10), ... 359 | geomean(yearlyReturns_eq +10), geomean(downsideRisk_eq), ... 360 | geomean(SD_eq), min(yearlyReturns_eq);... 361 | max(meanSortino), max(meanSharpe), max(meanReturn), ... 362 | min(meanDownsideRisk), min(meanSD), max(maxDrawdown);... 363 | min(meanSortino), min(meanSharpe), min(meanReturn), ... 364 | max(meanDownsideRisk), max(meanSD), min(maxDrawdown)],3))); 365 | results.stats.Var1(1:2) = results.stats.Var1(1:2) - 10; 366 | results.stats.Var2(1:2) = results.stats.Var2(1:2) - 10; 367 | results.stats.Var3(1:2) = results.stats.Var3(1:2) - 10; 368 | results.stats.Properties.VariableNames = axesLabels; 369 | results.stats.Properties.RowNames = {'Optimized','EqualWeights','Best','Worst'}; 370 | 371 | yearLabels = sprintfc('%d',years); 372 | for i = 1:length(yearLabels) 373 | yearLabels{i} = ['y',yearLabels{i}]; 374 | end 375 | rowLabels = [{'Optimized','EqualWeights'},tickers]; 376 | 377 | % Save table output 'sortino': 378 | sortinoMat = [sortino_opt; sortino_eq; sortino_ind]; 379 | [~, sortinoMat_ix] = sort(geomean(sortinoMat + 10,2),'descend'); 380 | results.sortino = cell2table(num2cell(round(sortinoMat(sortinoMat_ix,:),3))); 381 | results.sortino.Properties.VariableNames = yearLabels; 382 | results.sortino.Properties.RowNames = rowLabels(sortinoMat_ix); 383 | 384 | % Save table output 'sharpe': 385 | sharpeMat = [sharpe_opt; sharpe_eq; sharpe_ind]; 386 | [~, sharpeMat_ix] = sort(geomean(sharpeMat + 10,2),'descend'); 387 | results.sharpe = cell2table(num2cell(round(sharpeMat(sharpeMat_ix,:),3))); 388 | results.sharpe.Properties.VariableNames = yearLabels; 389 | results.sharpe.Properties.RowNames = rowLabels(sharpeMat_ix); 390 | 391 | % Save table output 'returns': 392 | yearlyReturnsMat = [yearlyReturns_opt; yearlyReturns_eq; yearlyReturns_ind]; 393 | [~, yearlyReturns_ix] = sort(geomean(yearlyReturnsMat + 10,2),'descend'); 394 | results.returns = cell2table(num2cell(round(yearlyReturnsMat(yearlyReturns_ix,:),3))); 395 | results.returns.Properties.VariableNames = yearLabels; 396 | results.returns.Properties.RowNames = rowLabels(yearlyReturns_ix); 397 | 398 | % Save table output 'DownsideRisk': 399 | DownsideRiskMat = [downsideRisk_opt; downsideRisk_eq; downsideRisk_ind]; 400 | [~, downsideRisk_ix] = sort(geomean(DownsideRiskMat,2),'ascend'); 401 | results.downsideRisk = cell2table(num2cell(round(DownsideRiskMat(downsideRisk_ix,:),3))); 402 | results.downsideRisk.Properties.VariableNames = yearLabels; 403 | results.downsideRisk.Properties.RowNames = rowLabels(downsideRisk_ix); 404 | 405 | % Save table output 'SD': 406 | SDMat = [SD_opt; SD_eq; SD_ind]; 407 | [~, SD_ix] = sort(geomean(SDMat,2),'ascend'); 408 | results.SD = cell2table(num2cell(round(SDMat(SD_ix,:),3))); 409 | results.SD.Properties.VariableNames = yearLabels; 410 | results.SD.Properties.RowNames = rowLabels(SD_ix); 411 | 412 | assignin('base','results',results) 413 | end 414 | 415 | % Plot Sharpe x Return x SD 416 | rotate_on = true; zoom_on = false; crosshair_on = false; 417 | targetSize = 200; 418 | if plotScatter 419 | if nRandom > 10000 420 | sparseIx = randperm(nRandom,10000); 421 | else 422 | sparseIx = 1:nRandom; 423 | end 424 | [~,ix_axes] = sort(outcomeWeights,'descend'); 425 | fig_title = [axesLabels{ix_axes(1)},' x ', axesLabels{ix_axes(2)},' x ',... 426 | axesLabels{ix_axes(3)},' x ',axesLabels{ix_axes(4)},' x ',axesLabels{ix_axes(5)}]; 427 | hfig = figure('Name',fig_title,'units','norm','Color',[1,1,1],'Position',... 428 | [.061,.116,.861,.806],'NumberTitle','off','MenuBar','none'); 429 | tool_menu = uimenu(hfig,'Label','Tools'); 430 | h_tools(1) = uimenu(tool_menu,'Label','Rotate','Checked','on','Callback',{@change_tool,1}); 431 | h_tools(2) = uimenu(tool_menu,'Label','Zoom','Callback',{@change_tool,2}); 432 | h_tools(3) = uimenu(tool_menu,'Label','Select New','Callback',{@change_tool,3}); 433 | hScatter = scatter3(permData(sparseIx,ix_axes(1)),permData(sparseIx,ix_axes(2)),... 434 | permData(sparseIx,ix_axes(3)),20,'o','fill'); hold on; 435 | mainAx = gca; set(mainAx,'FontSize',14) 436 | % Set point colors to outcomeWeights #4: 437 | cMax = max(permData(sparseIx,ix_axes(4))); cMin = min(permData(sparseIx,ix_axes(4))); 438 | useColors = round((permData(sparseIx,ix_axes(4))-cMin) ./ (cMax - cMin) .* 359)+1; 439 | colorMat = jet(360); colormap(colorMat); 440 | hScatter.CData = colorMat(useColors,:); set(gca,'clim',[cMin,cMax]) 441 | hColor = colorbar; title(hColor,axesLabels{ix_axes(4)},'FontSize',12,'FontWeight','normal'); 442 | % Add optimized portfolio: 443 | hCurrPoint1 = scatter3(permData(ix_best,ix_axes(1)), ... 444 | permData(ix_best,ix_axes(2)), permData(ix_best,ix_axes(3)),... 445 | targetSize,'x','k'); 446 | hCurrPoint2 = scatter3(permData(ix_best,ix_axes(1)), ... 447 | permData(ix_best,ix_axes(2)), permData(ix_best,ix_axes(3)),... 448 | targetSize,'o','k'); 449 | xlabel(axesLabels{ix_axes(1)}); ylabel(axesLabels{ix_axes(2)}); zlabel(axesLabels{ix_axes(3)}); rotate3d 450 | % Set sizes to outcomeWeights #5: 451 | minSize = 5; maxSize = 60; 452 | sizes = permData(sparseIx,ix_axes(5)) - min(permData(sparseIx,ix_axes(5))); 453 | sizes = (sizes./range(sizes)).*(maxSize-minSize) + minSize; 454 | hScatter.SizeData = sizes; 455 | leg_ax = axes('Parent',hfig,'Visible','off'); hold(leg_ax,'on'); h_leg = zeros(1,2); 456 | for ix = 1:2; h_leg(ix) = scatter(1,1,1,'filled','MarkerFaceColor','b','Parent',leg_ax); end 457 | 458 | % [h_legend, icons] = legend(mainAx, h_leg, 'Location','northwest','Labels',... 459 | % {num2str(round(min(permData(sparseIx,ix_axes(5))),4)), ... 460 | % num2str(round(max(permData(sparseIx,ix_axes(5))),4))},'FontName','Arial','FontSize',14); 461 | 462 | axes(mainAx) 463 | [h_legend, icons] = legend(h_leg, {num2str(round(min(permData(sparseIx,ix_axes(5))),4)), ... 464 | num2str(round(max(permData(sparseIx,ix_axes(5))),4))}, 'Location','northwest',... 465 | 'FontName','Arial','FontSize',14); 466 | 467 | icons(3).Children.MarkerSize = 2; icons(4).Children.MarkerSize = 8; 468 | axes(mainAx) 469 | set(get(h_legend,'title'),'String',axesLabels{ix_axes(5)},... 470 | 'FontSize',12,'FontWeight','normal','Visible','on') 471 | h_legend.Title.NodeChildren.Position= [0.5 1.5 0]; 472 | set(leg_ax,'Visible','off'); 473 | end 474 | 475 | % Plot ticker correlation matrix: 476 | if plotCorrs 477 | nTickers = length(data); r = corr(returns); r(eye(nTickers)==1) = 0; 478 | fig_title = 'Ticker Correlation Matrix'; 479 | figure('Name',fig_title,'units','norm','Color',[1,1,1],'Position',... 480 | [.236,.106,.554,.806],'NumberTitle','off','MenuBar','none'); 481 | imagesc(r); 482 | set(gca,'XTick',1:nTickers,'XTickLabels',tickers,'YTick',1:nTickers,... 483 | 'YTickLabels',tickers,'XTickLabelRotation',90,'FontSize',12) 484 | colormap('jet'); colorbar; 485 | end 486 | 487 | %% Callbacks: 488 | function change_tool(~, ~, which_tool) 489 | switch which_tool 490 | case 1 % Rotate 491 | if ~rotate_on 492 | zoom off; rotate3d on; 493 | rotate_on = true; zoom_on = false; crosshair_on = false; 494 | for ixx = 1:3; h_tools(ixx).Checked = 'off'; end 495 | h_tools(1).Checked = 'on'; 496 | else 497 | rotate3d off; rotate_on = false; h_tools(1).Checked = 'off'; 498 | end 499 | 500 | case 2 % Zoom 501 | if ~zoom_on 502 | zoom on; rotate3d off; 503 | zoom_on = true; rotate_on = false; crosshair_on = false; 504 | for ixx = 1:3; h_tools(ixx).Checked = 'off'; end 505 | h_tools(2).Checked = 'on'; 506 | else 507 | zoom off; zoom_on = false; h_tools(2).Checked = 'off'; 508 | end 509 | case 3 % Cross-hair 510 | if ~crosshair_on 511 | zoom off; rotate3d off; 512 | zoom_on = false; rotate_on = false; crosshair_on = true; 513 | for ixx = 1:3; h_tools(ixx).Checked = 'off'; end 514 | h_tools(3).Checked = 'on'; 515 | set(hfig,'WindowButtonDownFcn',@cursor_click_callback,'pointer','crosshair'); 516 | else 517 | crosshair_on = false; h_tools(3).Checked = 'off'; 518 | set(hfig,'WindowButtonDownFcn',[],'pointer','arrow'); 519 | end 520 | end 521 | end 522 | 523 | function cursor_click_callback(~,~,~) 524 | if crosshair_on 525 | % Find clicked point (Inspired by Click3dPoint by Babak Taati 526 | % (https://www.mathworks.com/matlabcentral/fileexchange/7594-click3dpoint)): 527 | pt = get(mainAx,'CurrentPoint'); % Get mouse location 528 | camPos = get(mainAx, 'CameraPosition'); % camera position 529 | camTgt = get(mainAx, 'CameraTarget'); % where the camera is pointing to 530 | camDir = camPos - camTgt; % camera direction 531 | camUpVect = get(mainAx, 'CameraUpVector'); % camera 'up' vector 532 | % Build an orthonormal frame based on the viewing direction and the up vector (the "view frame") 533 | zAxis = camDir/norm(camDir); 534 | upAxis = camUpVect/norm(camUpVect); 535 | xAxis = cross(upAxis, zAxis); 536 | yAxis = cross(zAxis, xAxis); 537 | rot = [xAxis; yAxis; zAxis]; % view rotation 538 | % the point cloud represented in the view frame 539 | rotatedPointCloud = rot * permData(:,ix_axes(1:3))'; 540 | % the clicked point represented in the view frame 541 | rotatedPointFront = rot * pt' ; 542 | % find the nearest neighbour to the clicked point 543 | ix_best = dsearchn(rotatedPointCloud(1:2,:)',rotatedPointFront(1:2)); 544 | selectedPoint = round(permData(ix_best,ix_axes),4); 545 | 546 | % Recompute results & adjust plot for selectedPoint: 547 | compute_results(ix_best); 548 | delete(hCurrPoint1); delete(hCurrPoint2); 549 | hCurrPoint1 = scatter3(permData(ix_best,ix_axes(1)), ... 550 | permData(ix_best,ix_axes(2)), permData(ix_best,ix_axes(3)), ... 551 | targetSize,'x','k'); 552 | hCurrPoint2 = scatter3(permData(ix_best,ix_axes(1)), ... 553 | permData(ix_best,ix_axes(2)), permData(ix_best,ix_axes(3)), ... 554 | targetSize,'o','k'); 555 | disp(['Results successfully recalculated for selected portfolio: ',... 556 | axesLabels{ix_axes(1)},': ',num2str(selectedPoint(1)),'; ',... 557 | axesLabels{ix_axes(2)},': ',num2str(selectedPoint(2)),'; ',... 558 | axesLabels{ix_axes(3)},': ',num2str(selectedPoint(3)),'; ',... 559 | axesLabels{ix_axes(4)},': ',num2str(selectedPoint(4)),'; ',... 560 | axesLabels{ix_axes(5)},': ',num2str(selectedPoint(5))]) 561 | end 562 | end 563 | 564 | end -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------