https://www.mathworks.com/help/finance/examples/portfolio-optimization-examples-1.html
% https://www.mathworks.com/help/finance/examples/portfolio-optimization-examples-1.html
%% Clear
clc;
clear all;
close all;
%% Set up the Data
load BlueChipStockMoments
mret = MarketMean;
mrsk = sqrt(MarketVar);
cret = CashMean;
crsk = sqrt(CashVar);
%% Create a Portfolio Object
p = Portfolio('AssetList', AssetList, 'RiskFreeRate', CashMean);
p = setAssetMoments(p, AssetMean, AssetCovar);
p = setInitPort(p, 1/p.NumAssets);
[ersk, eret] = estimatePortMoments(p, p.InitPort);
clf;
portfolioexamples_plot('Asset Risks and Returns', ...
{'scatter', mrsk, mret, {'Market'}}, ...
{'scatter', crsk, cret, {'Cash'}}, ...
{'scatter', ersk, eret, {'Equal'}}, ...
{'scatter', sqrt(diag(p.AssetCovar)), p.AssetMean, p.AssetList, '.r'});
%% Set up a Portfolio Optimization Problem
p = setDefaultConstraints(p);
pwgt = estimateFrontier(p, 20);
[prsk, pret] = estimatePortMoments(p, pwgt);
%% Plot efficient frontier
clf;
portfolioexamples_plot('Efficient Frontier', ...
{'line', prsk, pret}, ...
{'scatter', [mrsk, crsk, ersk], [mret, cret, eret], {'Market', 'Cash', 'Equal'}}, ...
{'scatter', sqrt(diag(p.AssetCovar)), p.AssetMean, p.AssetList, '.r'});
%% Illustrate the Tangent Line to the Efficient Frontier
q = setBudget(p, 0, 1);
qwgt = estimateFrontier(q, 20);
[qrsk, qret] = estimatePortMoments(q, qwgt);
%% Plot efficient frontier with tangent line (0 to 1 cash)
clf;
portfolioexamples_plot('Efficient Frontier with Tangent Line', ...
{'line', prsk, pret}, ...
{'line', qrsk, qret, [], [], 1}, ...
{'scatter', [mrsk, crsk, ersk], [mret, cret, eret], {'Market', 'Cash', 'Equal'}}, ...
{'scatter', sqrt(diag(p.AssetCovar)), p.AssetMean, p.AssetList, '.r'});
%% Obtain Range of Risks and Returns
[rsk, ret] = estimatePortMoments(p, estimateFrontierLimits(p));
display(rsk);
display(ret);
%% Find a Portfolio with a Targeted Return and Targeted Risk
TargetReturn = 0.20; % input target annualized return and risk here
TargetRisk = 0.15;
% Obtain portfolios with targeted return and risk
awgt = estimateFrontierByReturn(p, TargetReturn/12);
[arsk, aret] = estimatePortMoments(p, awgt);
bwgt = estimateFrontierByRisk(p, TargetRisk/sqrt(12));
[brsk, bret] = estimatePortMoments(p, bwgt);
% Plot efficient frontier with targeted portfolios
clf;
portfolioexamples_plot('Efficient Frontier with Targeted Portfolios', ...
{'line', prsk, pret}, ...
{'scatter', [mrsk, crsk, ersk], [mret, cret, eret], {'Market', 'Cash', 'Equal'}}, ...
{'scatter', arsk, aret, {sprintf('%g%% Return',100*TargetReturn)}}, ...
{'scatter', brsk, bret, {sprintf('%g%% Risk',100*TargetRisk)}}, ...
{'scatter', sqrt(diag(p.AssetCovar)), p.AssetMean, p.AssetList, '.r'});
%% Blotters
aBlotter = dataset({100*awgt(awgt > 0),'Weight'}, 'obsnames', p.AssetList(awgt > 0));
displayPortfolio(sprintf('Portfolio with %g%% Target Return', 100*TargetReturn), aBlotter, false);
bBlotter = dataset({100*bwgt(bwgt > 0),'Weight'}, 'obsnames', p.AssetList(bwgt > 0));
displayPortfolio(sprintf('Portfolio with %g%% Target Risk', 100*TargetRisk), bBlotter, false);
%% Transactions Costs
BuyCost = 0.0020;
SellCost = 0.0020;
q = setCosts(p, BuyCost, SellCost);
qwgt = estimateFrontier(q, 20);
[qrsk, qret] = estimatePortMoments(q, qwgt);
% Plot efficient frontiers with gross and net returns
clf;
portfolioexamples_plot('Efficient Frontier with and without Transaction Costs', ...
{'line', prsk, pret, {'Gross'}, ':b'}, ...
{'line', qrsk, qret, {'Net'}}, ...
{'scatter', [mrsk, crsk, ersk], [mret, cret, eret], {'Market', 'Cash', 'Equal'}}, ...
{'scatter', sqrt(diag(p.AssetCovar)), p.AssetMean, p.AssetList, '.r'});
%% Turnover Constraint
BuyCost = 0.0020;
SellCost = 0.0020;
Turnover = 0.2;
q = setCosts(p, BuyCost, SellCost);
q = setTurnover(q, Turnover);
[qwgt, qbuy, qsell] = estimateFrontier(q, 20);
[qrsk, qret] = estimatePortMoments(q, qwgt);
% Plot efficient frontier with turnover constraint
clf;
portfolioexamples_plot('Efficient Frontier with Turnover Constraint', ...
{'line', prsk, pret, {'Unconstrained'}, ':b'}, ...
{'line', qrsk, qret, {sprintf('%g%% Turnover', 100*Turnover)}}, ...
{'scatter', [mrsk, crsk, ersk], [mret, cret, eret], {'Market', 'Cash', 'Equal'}}, ...
{'scatter', sqrt(diag(p.AssetCovar)), p.AssetMean, p.AssetList, '.r'});
displaySumOfTransactions(Turnover, qbuy, qsell)
%% Tracking-Error Constraint
ii = [15, 16, 20, 21, 23, 25, 27, 29, 30]; % indexes of assets to include in tracking portfolio
TrackingError = 0.05/sqrt(12);
TrackingPort = zeros(30, 1);
TrackingPort(ii) = 1;
TrackingPort = (1/sum(TrackingPort))*TrackingPort;
% ERROR steTracckingError
q = setTrackingError(p, TrackingError, TrackingPort);
qwgt = estimateFrontier(q, 20);
[qrsk, qret] = estimatePortMoments(q, qwgt);
[trsk, tret] = estimatePortMoments(q, TrackingPort);
% Plot efficient frontier with tracking-error constraint
clf;
portfolioexamples_plot('Efficient Frontier with 5% Tracking-Error Constraint', ...
{'line', prsk, pret, {'Unconstrained'}, ':b'}, ...
{'line', qrsk, qret, {'Tracking'}}, ...
{'scatter', [mrsk, crsk], [mret, cret], {'Market', 'Cash'}}, ...
{'scatter', trsk, tret, {'Tracking'}, 'r'});
%% Combined Turnover and Tracking-Error Constraints
Turnover = 0.3;
InitPort = (1/q.NumAssets)*ones(q.NumAssets, 1);
ii = [15, 16, 20, 21, 23, 25, 27, 29, 30]; % indexes of assets to include in tracking portfolio
TrackingError = 0.05/sqrt(12);
TrackingPort = zeros(30, 1);
TrackingPort(ii) = 1;
TrackingPort = (1/sum(TrackingPort))*TrackingPort;
q = setTurnover(q, Turnover, InitPort);
qwgt = estimateFrontier(q, 20);
[qrsk, qret] = estimatePortMoments(q, qwgt);
[trsk, tret] = estimatePortMoments(q, TrackingPort);
[ersk, eret] = estimatePortMoments(q, InitPort);
% Plot efficient frontier with combined turnover and tracking-error constraint
clf;
portfolioexamples_plot('Efficient Frontier with Turnover and Tracking-Error Constraint', ...
{'line', prsk, pret, {'Unconstrained'}, ':b'}, ...
{'line', qrsk, qret, {'Turnover & Tracking'}}, ...
{'scatter', [mrsk, crsk], [mret, cret], {'Market', 'Cash'}}, ...
{'scatter', trsk, tret, {'Tracking'}, 'r'}, ...
{'scatter', ersk, eret, {'Initial'}, 'b'});
%% Maximize the Sharpe Ratio
p = setInitPort(p, 0);
swgt = estimateMaxSharpeRatio(p);
[srsk, sret] = estimatePortMoments(p, swgt);
% Plot efficient frontier with portfolio that attains maximum Sharpe ratio
clf;
portfolioexamples_plot('Efficient Frontier with Maximum Sharpe Ratio Portfolio', ...
{'line', prsk, pret}, ...
{'scatter', srsk, sret, {'Sharpe'}}, ...
{'scatter', [mrsk, crsk, ersk], [mret, cret, eret], {'Market', 'Cash', 'Equal'}}, ...
{'scatter', sqrt(diag(p.AssetCovar)), p.AssetMean, p.AssetList, '.r'});
% Set up a dataset object that contains the portfolio that maximizes the Sharpe ratio
Blotter = dataset({100*swgt(swgt > 0),'Weight'}, 'obsnames', AssetList(swgt > 0));
displayPortfolio('Portfolio with Maximum Sharpe Ratio', Blotter, false);
%% Confirm that Maximum Sharpe Ratio is a Maximum
psratio = (pret - p.RiskFreeRate) ./ prsk;
ssratio = (sret - p.RiskFreeRate) / srsk;
clf;
subplot(2,1,1);
plot(prsk, pret, 'LineWidth', 2);
hold on
scatter(srsk, sret, 'g', 'filled');
title('\bfEfficient Frontier');
xlabel('Portfolio Risk');
ylabel('Portfolio Return');
hold off
subplot(2,1,2);
plot(prsk, psratio, 'LineWidth', 2);
hold on
scatter(srsk, ssratio, 'g', 'filled');
title('\bfSharpe Ratio');
xlabel('Portfolio Risk');
ylabel('Sharpe Ratio');
hold off
%% Illustrate that Sharpe is the Tangent Portfolio
q = setBudget(p, 0, 1);
qwgt = estimateFrontier(q, 20);
[qrsk, qret] = estimatePortMoments(q, qwgt);
% Plot that shows Sharpe ratio portfolio is the tangency portfolio
clf;
portfolioexamples_plot('Efficient Frontier with Maximum Sharpe Ratio Portfolio', ...
{'line', prsk, pret}, ...
{'line', qrsk, qret, [], [], 1}, ...
{'scatter', srsk, sret, {'Sharpe'}}, ...
{'scatter', [mrsk, crsk, ersk], [mret, cret, eret], {'Market', 'Cash', 'Equal'}}, ...
{'scatter', sqrt(diag(p.AssetCovar)), p.AssetMean, p.AssetList, '.r'});
%% Dollar-Neutral Hedge-Fund Structure 130 -30
Exposure = 1;
q = setBounds(p, -Exposure, Exposure);
q = setBudget(q, 0, 0);
q = setOneWayTurnover(q, Exposure, Exposure, 0);
[qwgt, qlong, qshort] = estimateFrontier(q, 20);
[qrsk, qret] = estimatePortMoments(q, qwgt);
[qswgt, qslong, qsshort] = estimateMaxSharpeRatio(q);
[qsrsk, qsret] = estimatePortMoments(q, qswgt);
% Plot efficient frontier for a dollar-neutral fund structure with tangency portfolio
clf;
portfolioexamples_plot('Efficient Frontier with Dollar-Neutral Portfolio', ...
{'line', prsk, pret, {'Standard'}, 'b:'}, ...
{'line', qrsk, qret, {'Dollar-Neutral'}, 'b'}, ...
{'scatter', qsrsk, qsret, {'Sharpe'}}, ...
{'scatter', [mrsk, crsk, ersk], [mret, cret, eret], {'Market', 'Cash', 'Equal'}}, ...
{'scatter', sqrt(diag(p.AssetCovar)), p.AssetMean, p.AssetList, '.r'});
% Set up a dataset object that contains the portfolio that maximizes the Sharpe ratio
Blotter = dataset({100*qswgt(abs(qswgt) > 1.0e-4), 'Weight'}, ...
{100*qslong(abs(qswgt) > 1.0e-4), 'Long'}, ...
{100*qsshort(abs(qswgt) > 1.0e-4), 'Short'}, ...
'obsnames', AssetList(abs(qswgt) > 1.0e-4));
displayPortfolio('Dollar-Neutral Portfolio with Maximum Sharpe Ratio', Blotter, true, 'Dollar-Neutral');
%% 130/30 Fund Structure
Leverage = 0.3;
q = setBounds(p, -Leverage, 1 + Leverage);
q = setBudget(q, 1, 1);
q = setOneWayTurnover(q, 1 + Leverage, Leverage);
[qwgt, qbuy, qsell] = estimateFrontier(q, 20);
[qrsk, qret] = estimatePortMoments(q, qwgt);
[qswgt, qslong, qsshort] = estimateMaxSharpeRatio(q);
[qsrsk, qsret] = estimatePortMoments(q, qswgt);
% Plot efficient frontier for a 130-30 fund structure with tangency portfolio
clf;
portfolioexamples_plot(sprintf('Efficient Frontier with %g-%g Portfolio', ...
100*(1 + Leverage),100*Leverage), ...
{'line', prsk, pret, {'Standard'}, 'b:'}, ...
{'line', qrsk, qret, {'130-30'}, 'b'}, ...
{'scatter', qsrsk, qsret, {'Sharpe'}}, ...
{'scatter', [mrsk, crsk, ersk], [mret, cret, eret], {'Market', 'Cash', 'Equal'}}, ...
{'scatter', sqrt(diag(p.AssetCovar)), p.AssetMean, p.AssetList, '.r'});
% Set up a dataset object that contains the portfolio that maximizes the Sharpe ratio
Blotter = dataset({100*qswgt(abs(qswgt) > 1.0e-4), 'Weight'}, ...
{100*qslong(abs(qswgt) > 1.0e-4), 'Long'}, ...
{100*qsshort(abs(qswgt) > 1.0e-4), 'Short'}, ...
'obsnames', AssetList(abs(qswgt) > 1.0e-4));
displayPortfolio(sprintf('%g-%g Portfolio with Maximum Sharpe Ratio', 100*(1 + Leverage), 100*Leverage), Blotter, true, sprintf('%g-%g', 100*(1 + Leverage), 100*Leverage));
