1. The following table reports the year-end stock prices and the dividends paid in that year by Dufresne Zihuatanejo Resorts, Inc. (DZR) for the past four years.
|
Year
|
Price
|
Dividend
|
HPR
|
|
2014
|
42
|
3
|
|
|
2013
|
36
|
3
|
|
|
2012
|
30
|
2
|
|
|
2011
|
33
|
2
|
|
(a). Calculate the holding period returns for 2012, 2013 and 2014.
(b). Calculate the arithmetic average annual return.
(c). Calculate the geometric average annual return.
(d). Calculate the sample standard deviation of the returns.
2. Using historical data, you calculate the beta and standard deviation of two stocks: Warden Norton Outsourcing Inc. (WNO) and Red's Parcel Service (RPS). Your findings are summarized in the table below.
|
Stock
|
Beta
|
Std Dev
|
|
WNO
|
1.2
|
20%
|
|
RPS
|
0.8
|
22%
|
In addition, you find that the covariance between the returns of the two stocks is 0.011, and the risk-free rate at which investors can borrow or lend is 2%.
(a). Which stock has more firm-specific risk? Fully explain how you know.
(b). Which stock is riskier to a well-diversified investor? How do you know?
(c). Calculate the correlation between the two stocks.
(d). Assume the CAPM framework. The expected return of WNO is 8%. Calculate the expected return of RPS.
(e). Based on your answer to the previous question, does either stock dominate the other? If so, which is dominated?
(f). Of all the combinations of these two stocks, the portfolio with the smallest standard deviation (i.e., the MVP) has weights of 56% in WNOand 44% in RPS. Calculate the standard deviation of the MVP.
(g). Calculate the beta of the MVP described above.
(h). You wish to find the optimal risky portfolio (i.e., the ORP) of these two stocks. Describe how you would do this.
(i). Following the procedure described above, you find that the ORP has an expected return of 7.46% and a standard deviation of 17.08%. Calculate the portfolio weights in WNO and RPS in the ORP.
(j). You wish to show that a portfolio on the tangency line can dominate any portfolio on the two-stock IOS other than the ORP described above. As proof, you construct a portfolio on the tangency line that has the same expected return as WNO. What will be the portfolio weight in the risk-free asset in this portfolio?
(k). Show that the portfolio formed in the previous question does dominate WNO by calculating its standard deviation.
3. For the year that just ended, Brooks Hatlen Bookstores (BHB) is reporting EPS of $1.50 and ROE of 11%. The company is about to pay an annual dividend in the amount of $0.90. The market expects the company's payout ratio and ROE to remain constant. The required rate of return on the company's equity is 9%.
(a). Calculate the expected growth rate of BHB's earnings.
(b). Using a constant growth dividend discount model, find the intrinsic value of a share of BHB.
(c). BHB's CFO is considering lowering the company's payout ratio.
i. Explain the two ways that this decision would affect the future dividends of BHB. (Hint: they have contrasting effects on the intrinsic value of the stock.)
ii. Will the CFO's decision cause the stock price to increase, decrease or remain unchanged? How do you know?
(d). You project more rapid growth for BHB in upcoming years. Specifically, you believe that dividends will grow at 20% for the next 2 years, at 10% for the four years after that, and then at the rate you found in part (a) forever. Find the intrinsic value of a share of the stock under this scenario.
(e). Your formula sheet states that PVGO=P_(with growth)-P_(no growth). In class we saw a simple formula for P_(no growth). What was the formula? Give a detailed explanation of how we arrive at this formula.
4. The following table gives the expected return and standard deviation of several portfolios that lie on the efficient frontier.
|
Expected Return
|
Standard Deviation
|
|
0.1524
|
0.1541
|
|
0.1392
|
0.1346
|
|
0.1260
|
0.1163
|
|
0.1128
|
0.0998
|
|
0.0996
|
0.0864
|
The risk-free rate of return is 3%. Of the five portfolios in the table, which one could be the optimal risky portfolio? How do you know? (You should not use a graph to answer this question.)