Portf Optimization

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));