How to do Weighted Historical Simulation?

Hi,

I was trying to build a code for Weighted Historical Simulation by altering expected shortfall code from:

https://www.mathworks.com/help/risk/examples/expected-shortfall-estimation-and-backtesting.html

However, this is what I came up with:

% Log Returns calculated
format short;
Returns =tick2ret(UKX_Index_PX_LAST,"method",'continuous');
DateReturns = Date(2:end);
SampleSize = length(Returns);

%Estimation window as 250 days; starts on 1st day of 2007 to end of sample
TestWindowStart = find(year(DateReturns)==2007,1);
TestWindow = TestWindowStart : SampleSize;
EstimationWindowSize = 250;
DatesTest = DateReturns(TestWindow);
ReturnsTest = Returns(TestWindow);

%WHS
VarLevel = 0.95

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

tau = num2cell(sort([1:250],"descend")); 

for t = TestWindow
   
   i = t - TestWindowStart + 1;
   EstimationWindow = t-EstimationWindowSize:t-1;
   
   
   [VaR_Hist(i), VaR_WHSHist(i)] = WHSVar(Returns(EstimationWindow),VarLevel);
   
end

using this new function WHSVar, I am creating:

function [VaR,n_tau] = WHSVar(Sample,VaRLevel)
    N = length(Sample);
    tau = k;
    
    if k <= N
       n_tau = ((eda^(tau-1)*(1-eda)/(1-eda^N));
    else
       c1= ceil(cumsum(n_tau));
       y1 =sortrows([n_tau,w1],"descend");
       y2 = [y1,c1];
       index = find(y2)==VaRLevel;
       WHS_VaR = z(3);
    end
end

The error message is

Error: File: WHSVar.m Line: 10 Column: 48

Invalid expression. When calling a function or indexing a variable, use parentheses.

Otherwise, check for mismatched delimiters.

I attached the data which I am using. How to fix this error? Please I would really appreciate your help as it is for my project in finance.

Kindest Regards,

Clarissa

Answer 1

[Jakob B. Nielsen]

I think you just need to move your parantheses in the function, to contain the entire logic statement.

function [VaR,n_tau] = WHSVar(Sample,VaRLevel)
    N = length(Sample);
    tau = k;
    
    if k <= N
       n_tau = ((eda^(tau-1)*(1-eda)/(1-eda^N));
    else
       c1= ceil(cumsum(n_tau));
       y1 =sortrows([n_tau,w1],"descend");
       y2 = [y1,c1];
       index = find(y2==VaRLevel);  %the logic statement must be inside the parantheses. 
       WHS_VaR = z(3);
    end
end

[C.G. Rodriguez]

Thank you Jakob B. Nielsen.

function [WHS_VaR,n_tau] = WHSVar(Sample,VaRLevel)
   
    N = length(Sample);
    tau = k;
    
    if k <= N
       n_tau = ((eda^(tau-1)*(1-eda)/(1-eda^N));
    else
       c1 = ceil(cumsum(n_tau));
       d1 = [n_tau(:),sample(:)];
       y1 =sortrows(d1,"descend");
       y2 = [y1,c1];
       index = find(y2)==VaRLevel);
       WHS_VaR = z(3);
    end
end

I fixed it and ran the code again. However, this is the error message:

Error: File: WHSVar.m Line: 7 Column: 48

Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters. I am not sure how to fix this error. Please help me. I would greatly appreciate it

[Jakob B. Nielsen]

If you look at the error message, it says something with parentheses and delimiters, so that is where you should look. It also says line 7, so you know its this line:

n_tau = ((eda^(tau-1)*(1-eda)/(1-eda^N));

Count the opening parentheses: there's 5. Now count the closing parentheses - there are only 4.

n_tau = ((eda^(tau-1)*(1-eda) ) /(1-eda^N));   %<-- extra parentheses

also, you still have the parentheses around your index wrong. The full function should look like this:

function [WHS_VaR,n_tau] = WHSVar(Sample,VaRLevel)
   
    N = length(Sample);
    tau = k;
    
    if k <= N
       n_tau = ((eda^(tau-1)*(1-eda))/(1-eda^N));
    else
       c1 = ceil(cumsum(n_tau));
       d1 = [n_tau(:),sample(:)];
       y1 =sortrows(d1,"descend");
       y2 = [y1,c1];
       index = find(y2==VaRLevel);
       WHS_VaR = z(3);
    end
end