1. Assume that Fund X has an expected return of 19% and a standard deviation of 30%. The risk-free rate is 7%. Your client's degree of risk aversion is A=2

a. Calculate the Sharpe ratio on Fund X b. Your goal is to maximize your client's level utility. What fraction of your client's portfolio should be allocated to Fund X (W_x) and what fraction should be allocated to the risk-free security (W_f)? c. Using the portfolio weights found in b, calculate the Sharpe ratio on your client's optimized portfolio d. Another client has a coefficient of risk aversion (A=4). Which client is more risk averse

2.

Investment	Expected return	Standard Deviation
V	12%	35%
W	10%	15%
X	14%	29%
Y	5%	10%
Z	8%	21%

a. On the chart above, plot approximately the indifference curves of a risk-averse investor. Based on these indifference curves, which investment woul dbe most preferred (assume one again that you can invest in only one security)?

3.

Portfolio	Expected (mean) return	standard deviation
Buffs Investment Group	14%	18%
Ducks Capital Investment	7%	20%

a. Assume that your coefficient of risk aversion is A=3. Calculate your utility from investment int he risk-free security b. Assume that your coefficient of risk aversion is A=3. Calculate your utility from investing in the Ducks fund c. What is the expected return on a portfolio with a weight of 0.70 in the Buffs fund and a weight of 0.30 in the Ducks fund? d. Assume the correlation between Buffs and Ducks funds is 0.2. What is the standard deviation of a portfolio with a weight of 0.7 in the Buffs fund and a weight of 0.3 in the Ducks fund? e. Imagine now that you will invest only in the Buffs fund and the risk-free security and that you require a portfolio with an expected return of 10%. Determine the portfolio weights in the Buffs fund(W_B ) and the risk-free security (W_f) on your preferred portfolio.