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NEW QUESTION: 1
If A and B be two uncorrelated securities, VaR(A) and VaR(B) be their values-at-risk, then which of the following is true for a portfolio that includes A and B in any proportion. Assume the prices of A and B are log-normally distributed.
A. VaR(A+B) = VaR(A) + VaR(B)
B. The combined VaR cannot be predicted till the correlation is known
C. VaR(A+B) < VaR(A) + VaR(B)
D. VaR(A+B) > VaR(A) + VaR(B)
Answer: C
Explanation:
Explanation
First of all, if prices are lognormally distributed, that implies the returns (which are equal to the log of prices) are normally distributed. To say that prices are lognormally distributed is just another way of saying that returns are normally distributed.
Since the correlation between the two securities is zero, this means their variances can be added. But standard deviations, or volatilities cannot be added (they will be the square root of sum of variances). VaR is nothing but a multiple of standard deviation, and therefore it is not additive if correlations are anything other than 1 (ie perfect positive, which would imply we are dealing with the same asset). Therefore VaR(A+B)=SQRT(VaR(A)