1) DW Co. stock has an annual return mean and standard deviation of 12 percent and 33 percent, respectively. What is the smallest expected loss in the coming year with a probability of 5 percent?
2) A stock has an annual return of 11.8 percent and a standard deviation of 48 percent. What is the smallest expected gain over the next year with a probability of 1 percent?
3) Tyler Trucks stock has an annual return mean and standard deviation of 8 percent and 27 percent, respectively. Michael Moped Manufacturing stock has an annual return mean and standard deviation of 19 percent and 63 percent, respectively. Your portfolio allocates equal funds to Tyler Trucks stock and Michael Moped Manufacturing stock. The return correlation between Tyler Trucks and Michael Moped Manufacturing is .5. What is the smallest expected loss for your portfolio in the coming month with a probability of 1 percent?
4) You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 8 percent and 13 percent, respectively. The standard deviations of the assets are 30 percent and 38 percent, respectively. The correlation between the two assets is 0.43 and the risk-free rate is 5.6 percent. What is the optimal Sharpe ratio in a portfolio of the two assets? What is the smallest expected loss for this portfolio over the coming year with a probability of 5 percent?