Question

A junior analyst in a bank calculates the 1-day VaR of a portfolio, and then simply calculates the 5-day VaR to be £4m based on the 1-day VaR without taking into account the possible autocorrelations. Her supervisor then mentions to her that she cannot assume the autocorrelation to be 0, and that she needs to recalculate the 5-day VaR by taking into account the first-order correlation of 0.15 for the daily changes in the portfolio value. What would the 5-day VaR be using the correct method?A junior analyst in a bank calculates the 1-day VaR of a portfolio, and then simply calculates the 5-day VaR to be £4m based on the 1-day VaR without taking into account the possible autocorrelations. Her supervisor then mentions to her that she cannot assume the autocorrelation to be 0, and that she needs to recalculate the 5-day VaR by taking into account the first-order correlation of 0.15 for the daily changes in the portfolio value. What would the 5-day VaR be using the correct method?

Answer 1

Soln : Given : 5 day VaR = 4million

based on the 1 day VaR given. Now, it was assumed initialy that that autocorrelation is 0 that will simply give

5 day VaR = 1day VaR *(5)^0.5 , So, 1 day VaR = 4/(5)^0.5 = 1.79 mn

Now, we need to consider that autocorrelation = 0.15 instead of 0.

Hence the 5 day VaR = 1 day VaR * sqrt(5 +5*autocorrelation) = 1.79* (5+5*.15)^0.5 = 1.79*(5.75)^0.5 = 4.29 million

5 day VaR in this case should be 4.29 million instead of 4 million.