Mapping Equity Positions

Equity positions are a bit more tricky compared to the FX positions. The main problem arises while dealing with the correlations between the different equity positions. As the number of positions in the equity portfolio increases, the correlation matrix can become substantially large and almost impossible to handle.

In case of equity positions, the number of risk factors are reduced by modeling the individual stock returns using a factor model. The simplest way to do so is to use the CAPM model under which the returns from a security can be represented using the equity market returns.

ri = α + βrm + ε

Where,

α represents the firm-specific constant

ε is a zero-mean specific constant

β is the stock’s beta

rm is the market return.

If we assume that the equity portfolio of a bank is sufficiently diversified, then the α of different stocks will offset each other and the returns of the portfolio can be simply written as

rp = βprm + ε

Where:

βp is the portfolio beta

rm is the market return

Let’s take a simple example to understand how we can use this to calculate the portfolio VaR.

Let’s say we have a portfolio of $100 million invested in three stocks, namely A, B, and C. Also assume that the related stock market index is the S&P500 index.

The details are provided below: