For an equity portfolio valued at V whose beta is β, the value at risk at a 99% level of confidence is represented by which of the following expressions? Assume σ represents the market volatility.
For the PRM exam, it is important to remember the z-multiples for both 99% and 95% confidence levels (these are 2.33 and 1.64 respectively).
The value at risk for an equity portfolio is its standard deviation multiplied by the appropriate z factor for the given confidence level. If we knew the standard deviation, VaR would be easy to calculate. The standard deviation can be derived using a correlation matrix for all the stocks in the portfolio, which is not a trivial task. So we simplify the calculation using the CAPM and essentially say that the standard deviation of the portfolio is equal to the beta of the portfolio multiplied by the standard deviation of the market.
Therefore VaR in this case is equal to Beta x Mkt Std Dev x Value x z-factor, and therefore Choice 'a' is the correct answer.
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