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VALUE AT RISK: HISTORICAL SIMULATION, MONTE CARLO SIMULATION AND

VARIANCE COVARIANCE METHODS IN MATLAB

By JOHN MUTEBA MWAMBA

DEPARTMENT OF ECONOMICS AND ECONOMETRICS

UNIVERSITY OF JOHANNESBURG

Value at risk in Matlab

Historical Simulation: The alpha quantile

x=retALSI %returns of your asset

mu=mean(x)

sigma=std(x)

VaR.hist=quantile(x,alpha); where alpha is 95,97,99%,..

VaR.hist=quantile(x,[0.950 0.975 0.990 0.999]) , % for historical simulation

%X is a vector of returns. To generate for instance 10000 returns point in Matlab us this code

%returns=normrnd(0.2,1,1,10000);

Monte Carlo Simulation: Simulation from normal distribution

mydata=normrnd(mu,sigma,1,5000); sigma and mu are empirical value of historical returns

%then use VaR.hist to compute the VaR

VAR=quantile(mydata,[0.950 0.975 0.990 0.999])

Variance covariance method in Matlab

%For one asset VaR=[mu+Z*sigma]

% Different values of Z

0.95 0.975 0.99 0.999Z 1.645 1.960 2.326 3.090

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Z=[1.645 1.96 2.326 3.090]

VaRCov=[mu+Z*sigma]

%For a portfolio of more than one asset; use function portvrisk (in financial toolbox)

%import your data in Matlab as a matrixportfo is the name of your dataset

PortReturn=mean(mean(portfo)); % expected return of portfolio i.e. mean of portfolio returns

PortRisk=mean(std(portfo));% stdv of portfolio I.e. stdev of portfolio returns

RiskThreshold=[0.05;0.025;0.01;0.001]; %default alpha is 0.05

VaRvc=portvrisk(PortReturn,PortRisk,RiskThreshold)