# Using MATLAB to Develop Portfolio Optimization Models

### Bob Taylor (view profile)

29 Sep 2005 (Updated )

Scripts to create time-evolving efficient frontiers and to backtest results.

BCSdrawdown.m
```%BCSDRAWDOWN BlueChipStock drawdown analysis

RefIndex = 45;

[NumMonths, NumAssets] = size(RetHistory);
NumStocks = NumAssets - 3;

NumPortfolios = 40;
Periodicity = 12;

NumPeriods = floor(NumMonths/Periodicity);
StartIndex = NumMonths - NumPeriods * Periodicity;
if StartIndex < 1
NumPeriods = NumPeriods - 1;
StartIndex = StartIndex + Periodicity;
end
EndIndex = NumMonths;

iend = StartIndex;

PortRet = ones(NumPortfolios, NumPeriods);
IndexRet = ones(1,NumPeriods);

for k = 1:NumPeriods
istart = iend;
iend = istart + Periodicity;

% calculate asset returns at specified periodicity

A = ones(NumAssets,1);
for i = (istart+1):iend
for j = 1:NumAssets;
A(j) = A(j) * (1.0 + RetHistory(i,j));
end
end

for j = 1:NumAssets
if isnan(A(j))
A(j) = 0.0;
end
end

% calculate portfolio returns at specified periodicity

H = PortHistory{istart};
P = H * A(1:NumStocks);

if (k > 1)
for i = 1:NumPortfolios
PortRet(i,k) = PortRet(i,k - 1) * P(i);
end
IndexRet(k) = IndexRet(k - 1) * A(RefIndex);
end
end

MaxDD = maxdrawdown(PortRet');
IDD = maxdrawdown(IndexRet');
IDD = repmat(IDD,1,NumPortfolios);

figure(1);
plot(MaxDD);
hold all
plot(IDD)
set(gca,'ylim',[-1 0]);
ylabel('\bfMaximum Drawdown');
xlabel('\bfPortfolio Number on Efficient Frontier');
title('\bfDrawdown of Portfolio Sequence');
hold off
```