Expected Return and Risks
1. Suppose you purchase an asset with a face value of $1000 when the risk-free rate is 4%. Further, you anticipate 4 market conditions with the following probabilities: Excellent state, 0.20; Good state, 0.45, Poor state, 0.25; and a state of a crash, 0.10. If the end of year prices that are associated with the market conditions are $1,030, $1,015, $890, and $500, respectively, and the projected dividends are 5,4,3, and2 respectively:
(a) What is the holding period return for each state? (b) what is the expected mean of holding period return? (c) What is the standard deviation of the HPR? (d) What is the risk premium that is associated with the excess return? (e) What is the Sharpe ratio? [see pp.127 &133]
2. Suppose the risk-free rate is 4%, the expected rate of return is 8% and the variance of a portfolio is estimated as 500%. What is the slope of the Capital Allocation Line? Interpret the meaning of your estimation of the slope. [see p.168 of your text]
3. Imagine that the expected returns that are associated with an investment are 0.06, 0.08, 0.094, 0.12 and 0.134. If the standard deviations that are associated with the returns are 0, 0.022, 0.066, 0.154, and 0.176 respectively, what is the investor’s utility function? [see p. 159, pp.170-171 of your text]
Plot the utility function of the investor on a scale of 0, 0.1, 0.2, 0.3, and 0.4 for additional credit.