Consider a portfolio that has equal amounts of $10 invested in two assets. Suppose returns on the two assets are jointly normally distributed. The annual expected returns and variance of returns on the first asset are given by:
u1=.10 o (2/1) = .04
and those for the second asset are given by:
u2 = .05 o (2/2) = .03
Consider three cases:
a: The correlation between the returns is p = 0
b: The correlation between the returns is p= +.50
c: The correlation between the returns is p= -.50
For each case, identify the 99 percent Value at Risk of the portfolio. Explain the pattern of dependence of VaR on the correlation.