Using Expected Shortfall Estimation and Backtesting Code

Hi All,

I use the following coding and would like to test it against the portfolio I have created. Unfortunately I get the same error every time:Array indices must be positive integers or logical values.

H = readtable('CAPM2.csv');

symbol = {'PBIT'};

nAsset = numel(symbol);

Convert prices to returns

Returns = (H{:,symbol});

Select assets into portfolio

symbol2 = {'Datum'};

Datum = (H{:,symbol2});

DateReturns = Datum(1:end);

SampleSize = length(Returns);

TestWindowStart = find(year(DateReturns)==2015,1);

TestWindowEnd = find(year(DateReturns)==2019,1,'last');

TestWindow = TestWindowStart:TestWindowEnd;

EstimationWindowSize = 250;

DatesTest = DateReturns(TestWindow);

ReturnsTest = Returns(TestWindow);

VaRLevel = 0.975;

VaR_Hist = zeros(length(TestWindow),1);

ES_Hist = zeros(length(TestWindow),1);

for t = TestWindow

i = t - TestWindowStart + 1;

EstimationWindow = t-EstimationWindowSize:t-1;

[VaR_Hist(i),ES_Hist(i)] = hHistoricalVaRES(Returns(EstimationWindow),VaRLevel);

end

Array indices must be positive integers or logical values.

The problem arises when creating the EstimationWindow. The result is always negative. Unfortunately I have already tried to convert it to positive, unfortunately without success.

[Sai Sri Pathuri]

Can you attach the file 'CAPM2.csv'?

[jens pauwels]

Sure

Answer 1

[Sai Sri Pathuri]

I am assuming that you want to declare EstimationWindow as first 250 indices for t = 1 and shift it by 1 for every loop. The window you declared is,

EstimationWindow = t-EstimationWindowSize:t-1;

For t = 1, this EstimationWindow will take the values -249 to 0. But, in MATLAB, the indices start from 1. Hence, the error is being thrown. You may declare the EstimationWindow as

EstimationWindow = t:EstimationWindowSize-t+1; 

[jens pauwels]

thanks that took me a step further, unfortunately he gives me the next error in the next line

VaR_Hist = zeros(length(TestWindow),1);

ES_Hist = zeros(length(TestWindow),1);

for t = TestWindow

i = t - TestWindowStart + 1;

EstimationWindow = t:EstimationWindowSize-t+1;

[VaR_Hist(i),ES_Hist(i)] = hHistoricalVaRES(Returns(EstimationWindow),VaRLevel);

end

Operator '.*' is not supported for operands of type 'cell'.

Error in ExpectedShortfallBacktestingExample2>hHistoricalVaRES (line 249)

ES = ((k - N*VaRLevel).*z(k) + sum(z(k+1:N)))/(N.*(1 - VaRLevel));

Local Functions

function [VaR,ES] = hHistoricalVaRES(Sample,VaRLevel)

% Compute historical VaR and ES

% See [5] for technical details

% Convert to losses

Sample = Sample;

N = length(Sample);

k = ceil(N*VaRLevel);

z = sort(Sample);

VaR = z(k);

if k < N

ES = ((k - N*VaRLevel)*z(k) + sum(z(k+1:N)))/(N*(1 - VaRLevel));

else

ES = z(k);

end

end

function [VaR,ES] = hNormalVaRES(Mu,Sigma,VaRLevel)

% Compute VaR and ES for normal distribution

% See [4] for technical details

VaR = -1*(Mu-Sigma*norminv(VaRLevel));

ES = -1*(Mu-Sigma*normpdf(norminv(VaRLevel))./(1-VaRLevel));

end

function [VaR,ES] = hTVaRES(DoF,Mu,Sigma,VaRLevel)

% Compute VaR and ES for t location-scale distribution

% See [4] for technical details

VaR = -1*(Mu-Sigma*tinv(VaRLevel,DoF));

ES_StandardT = (tpdf(tinv(VaRLevel,DoF),DoF).*(DoF+tinv(VaRLevel,DoF).^2)./((1-VaRLevel).*(DoF-1)));

ES = -1*(Mu-Sigma*ES_StandardT);

end

[jens pauwels]

I was able to solve this problem but instead i recieve the next error

Array indices must be positive integers or logical values.


Error in ExpectedShortfallBacktestingExample2>hHistoricalVaRES (line 246)
 VaR = z(k);

but k i positive

function [VaR,ES] = hHistoricalVaRES(Sample,VaRLevel)
    % Compute historical VaR and ES
    % See [5] for technical details

    % Convert to losses
    Sample = -Sample;
    
    N = length(Sample);
    k = ceil(N*VaRLevel);
    
    z = sort(Sample);
    
    VaR = z(k);
    
    if k < N
       ES = ((k - N*VaRLevel)*z(k) + sum(z(k+1:N)))/(N*(1 - VaRLevel));
    else
       ES = z(k);
    end