Any ideas about how to compute VaR

[Jet Cheng]

Hey guys, I have a problem about estimating Value-at -risk for a portfolio consisting equity investment and bonds. I have the historical return data for the portfolio for like 2000 days . so it is easy to estimate its VaR using historical values. But I want to ask how to use Monte Carlo simulation to compute VaR ? any idea how insurance company conducting VaR on their portfolio ?

many thanks.

 

[moretodo]

VaR essentially is a cumulative probability of a particular event. If you knew i.e. have a mathematical expression for the stochastic volatility varying in time, you could technically come up with an expression for the CDF/PDF of your portfolio gain/loss which could be then used to estimate VaR.

Alternatively you may use MC but while using simple MC, your making the undesirable assumption that all macroeconomic factors affecting the portfolio have had the exact same effect over the course of the 2000 days of data which isnt true. Perhaps a weighted MC would be more prudent but have no idea how you could calculate the weights as a proxy for changing macroeconomic factors.

 

[Jet Cheng]

VaR essentially is a cumulative probability of a particular event. If you knew i.e. have a mathematical expression for the stochastic volatility varying in time, you could technically come up with an expression for the CDF/PDF of your portfolio gain/loss which could be then used to estimate VaR.

Alternatively you may use MC but while using simple MC, your making the undesirable assumption that all macroeconomic factors affecting the portfolio have had the exact same effect over the course of the 2000 days of data which isnt true. Perhaps a weighted MC would be more prudent but have no idea how you could calculate the weights as a proxy for changing macroeconomic factors.

thanks for your reply...to make things easier, i would confine the discussion to stock investment, so i can ignore covariance....i agree with you the a simple MC is not convincing. Currently the method i am thinking about is to seperate the time interval into different periods, estimating ARMA-QGARCH and generating the simulated data in different period of time. but i donot quite understand about the weighted MC.

will you please shed more light on that?

 

[moretodo]

firstly, stocks do have co-variances between them so I'm not sure if you can ignore it.

Weighted MC basically means assigning a higher weight to simulations that are more realistic to that of today and less to the ones seem less likely. Its basically adding another layer of probabilistic abstraction to the MC process. These weights are based upon the relevance and the similarity of historical data to that of the present time. Typically, most empirical studies of this kind or MCs make the assumption that financial performance is very cyclical for most asset classes and thats were weighted MC comes in.

 

[Jet Cheng]

firstly, stocks do have co-variances between them so I'm not sure if you can ignore it.

Weighted MC basically means assigning a higher weight to simulations that are more realistic to that of today and less to the ones seem less likely. Its basically adding another layer of probabilistic abstraction to the MC process. These weights are based upon the relevance and the similarity of historical data to that of the present time. Typically, most empirical studies of this kind or MCs make the assumption that financial performance is very cyclical for most asset classes and thats were weighted MC comes in.

thanks for your reply... actually concerning focusing on stock markets, what i want to say is to focus on one markte and ignore the covariance between bonds and stocks.
what you mentioned about weighted MC is quite illuminating and it seems the weights is a measure of the similarity of data patterns in different time period.