Let r denote the continuously compounded monthly return on Microsoft stock and let W0 denote initial wealth to be invested over the month. Assume that r iid N(0:05;(0:12)2 ) and that W0 = $100,000.

Determine the 1% and 5% value-at-risk (VaR) over the month on the investment. That is, determine the loss in investment value that may occur over the next month with 1% probability and with 5% probability. (Hint: compute the 1% and 5% quantile from the Normal distribution for r and then convert continuously compounded return quantile to a simple return quantile using the transformation R = e r 1: )

Determine the 1% and 5% expected shortfall (ES) over the month on the investment.

Determine the 1% and 5% value-at-risk (VaR) over the year on the investment. (Hint: to answer this question, you must determine the normal distribution that applies to the annual (12 month) continuously compounded return.)

Determine the 1% and 5% expected shortfall (ES) over the year on the investment.