Reference no: EM133121521

Question 1: Below are the monthly returns for the stocks ABL and HHT as well as the returns on the market. ABL's returns: (7.6%, 3.3%, -3.3%, 8.5%, 0.5%, 1.3%, -1.4%, 1.9%, 21.3%, -3.7%, -1.8%, 2.4%). HHT's returns: (4.5%, -4.9%, 4.7%, 4.4%, -0.8%, -4.5%, 0.1%, 3.7%, -6.2%, -1.2%, 1%, 18.4%). The market returns were: (1%, -6.8%, 1.2%, 7.5%, -0.1%, -1%, 3.6%, -6.2%, -1.4%, 1.8%, 2.5%, 9.2%).

Using the information above, perform each of the following tasks:

a) Compute the first four moments (mean, standard deviation, skew, kurtosis) for the returns for ABL [use stdev/skew/kurt in excel]

b) Compute the geo-metric average return for HHT

c) Compute the correlation between the returns of ABL and HTT

d) Compute the standard deviation and Sharpe ratio for a portfolio that has 40% of funds invested in ABL and the remainder in HHT if the risk-free rate is 0.18% per year.

e) Find the beta for ABL and HHT. Which stock of the two is more defensive?

Question 2: John has a utility function given by the expression U(x) = E(r) - ½A(s²). Where E(r) is the expected return on an asset and s is the standard deviation of returns on that asset. John has the opportunity to purchase the XJK security that returns 26.9% with 23% probability and returns 9% the remainder of the time. The security has a price of $33 and A=4

a) What is the risk-neutral valuation of the XJK security? Recall the risk-neutral value is simply the expected value.

b) Using the utility function above, find John's risk-averse valuation of XJK security. Hint: Find John's certainty equivalent (CEQ) for this security's payoff.

c) If the expected annual return on the market is 3.615%, the standard deviation of the market return is 6.2% and the risk-free rate for the next year is 1.29% then what is John's optimal percent of funds that he'll invest in the market?

d) Use the rates given in part c to answer this question. If a stock had a Beta of 1.87 what would be the expected return for that stock in the coming year?