VaR of an Equity Portfolio

[harry_summy]

Hello David

Here I have developed an spreadsheet (see attachment) which calculates VaR of an equity Portfolio based on the CAPM model. Here we are making several assumption. My question is what is the standard practice followed by financial institutions world over while calculating VaR of the Equity Portfolio.

Regards,
Harish Kumar

 

[David Harper CFA FRM]

Hi Harish,

Your XLS looks good to me, a faithful implement of CAPM. I agree it makes several assumptions. I think the most important "violation" is to omit specific risk. In other words, technically speaking, I do not think the CAPM can be used but rather the single-index model. That is:

CAPM: E[return] = riskfree + (beta)(ERP)
Single index = alpha + market return * (beta; i.e., market factor) + specific return

(The FRM 2008 assigned Noel Amenc text is highly recommended for review of the difference between CAPM and single index. At a superficial level, the difference is the merely the specific return. But it is important, even if the E[idiosyncratic return] = 0 this in no way implies that it has a 0 dispersion. The variance of the specific return is what Basel calls the "specific risk").

The variance of CAPM is just as your XLS: VaR = beta^2*[variance of market return] so that CAPM volatilty is:
volatility = SQRT[beta^2*[variance of market factor]] = beta*volatility of market factor; i.e., what you have in your XLS.

But this unrealistically omits specific risk. So, the more practical approaches would take variance of single index; e.g., applying variance rule directly:

Var [single index expected return] = variance [beta*market factor] + variance [specific return] + 2*beta*covariance(market factor, specific return).

So, at this point I would recommend Carol Alexander's Volume IV of Market Risk Analysis. (it is a deep topic) There are different ways to go. The simplest is to assume no correlation between market factor and specific return. But, to get to your question, I *think* that all approaches require including the specific risk. Basel II standardized market risk "building block" approach charges at least 4% of gross equity exposure (long + short) for the specific risk. So, to my knowledge all banks must incorporate the specific risk (and the correlation between specific and market risk).

I hope that helps, David