MANAGERIAL STATISTICS QUESTION: PLEASE PROVIDE WORK AND FORMULAS PER QUESTION

Value at Risk. Financial analysts commonly use an approach called value at reisk to compare the risk of stocks or portfolios. The analyst tries to estimate a low percentile (such as the 5th or 10th percentile) of the forecasted range of possible returns for a given stock or portfolio and that percentile is used as a rough measure of the worst-case senario for that investment. Suppose an analyst is trying to compare two investments: Investment A has a forecasted average return of $10 million with a standard deviation of $3 million, and Investment B has a forecasted average return of $12 million with a standard deviation of $5 million. The analyst wants to avoid risk and invest in the one that has a larger 5 percentile for the return distribution. Which investment should he/she make?