An investor has $2,000 invested in stock A and $5,000 in stock B. The daily volatilities of A and B are 1.5% and 1% respectively and the coefficient of correlation is 0.8

What is the one day 99% VaR? Assume that returns are multivariate normal (Note that N(-2.326)=0.01)
A. $177
B. $135
C. $215
D. $331

A

The standard deviation of the change in the stock A position in one day is 2,000×0.015= $30 . The standard deviation of the change in the value of the stock B position in one day is 5,000×0.01 = $50 . The variance of the combined position is 302+502+2×0.8×30×50 = 5,800 . The standard deviation is the square root of this or 76.16 and the 99% VaR is therefore 2.326 times 76.16 this or about $177 .