A) A portfolio's daily losses have a mean of $1.5 million and a standard deviation of

$18 million. Calculate the 1-day and 10-day 97% VaR and ES (expected shortfall).

For the 10-day VaR and ES, please use both the precise and the approximate

formulas. Suppose now the daily losses in the portfolio's value have a first-order

serial correlation of 0.35. Calculate the 5-day, 98% VaR and ES using both the

precise and approximate formulas. Re-do the calculations (without showing the

interim steps) for the 5-day, 98% VaR and ES using the precise formula when the

serial correlation is 0.15, 0.55 and 0.75. What can you conclude?

B) A portfolio consists of options on three stocks, A, B and C. The details are as

follows:

StockA StockB StockC

Option delta 0.6645 -0.5546 -0.6725

Number of options 210 125 118

Stock Price(S) 55.25 32.75 66.14

Daily Volatility 0.018 0.012 0.026

The correlations in returns among the three stocks are:

AB = 0.35, AC= 0.66, and BC = 0.48.

Please calculate the 10-day, 98% VaR for the three option positions separately and

for the portfolio as a whole. How much is the diversification benefit?