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NEW QUESTION: 1
The 10-day VaR of a diversified portfolio is $100m. What is the 20-day VaR of the same portfolio assuming the market shows a trend and the autocorrelation between consecutive periods is 0.2?
A. 141.42
B. 0
C. 1
D. 154.92
Answer: D
Explanation:
Explanation
The square root of time rule cannot be applied here because the returns across the periods are not independent.
(Recall that the square root of time rule requires returns to be iid, independent and identically distributed.) Here there is a 'autocorrelation' in play, which means one period's returns affect the returns of the other period.
VaR is merely a multiple of volatility, or standard deviation, using the factor for the desired confidence level.
VaR across time periods can be combined using the square root of time rule, in fact if returns were independent we could have easily calculated the VaR for the 20-day period as equal to $100m*SQRT(20/10) =
$141.4m
But in this case we need to account for the autocorrelation. We can do this akin to the way we combine the VaR of different assets that have a given correlation. Since we know that:
Variance (A + B) = Variance(A) + Variance(B) + 2*Correlation*StdDev(A)*StdDev(B).
The standard deviation, which the VaR is a multiple of, can be calculated by taking the square root of the variance.
Therefore the combined VaR over the two months will be equal to =SQRT( (100