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• Syeda Umaima

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Financial Management and Policy/Financial Management Lecture#3 and 4

Risk and Return on investment

Q No. 1 Two stock prices for six days are given below. Price A 25 29 33 29 26 29

Price B 55 60 61 63 61 60

Calculate: 1. 2. 3. 4. 5.

Average return of both stock Standard deviation of each stock Coefficient of Variation of each stock Which stock is less risky based on Standard deviation? Which stock you will select based on Coefficient of variation?

Q2. Consider the following scenario analysis:

Scenario Recession Normal Economy Boom

Probability 0.30 0.30 0.40

Stocks -6 % +14 +26

Bonds +15% +7 +5

a) Calculate the expected rate of return and standard deviation for each investment? b) Which investment would you prefer? Q3. Use the data in the previous problem and consider a portfolio with weights of 0.70 in stocks and 0.30 in bonds. a) What is the rate of return on the portfolio in each scenario? b) What is the expected rate of return and standard deviation of the portfolio? c) Would you prefer to invest in the portfolio, in stocks only, or in bonds only?

Q4. (Student Practice) Use the data in the previous problem and consider a portfolio with weights of 0.60 in stocks and 0.40 in bonds. a) What is the rate of return on the portfolio in each scenario? b) What is the expected rate of return and standard deviation of the portfolio? c) Would you prefer to invest in the portfolio, in stocks only, or in bonds only, give reason?

Q5. a) A share of stock with a beta of .80 now sells for $45. Investors expect the stock to pay a year-end dividend of $1.80. The T-bill rate is 4.5 percent, and the market risk premium is 7 percent. If the stock is perceived to be fairly priced today, what must be investors’ expectations of the price of the stock at the end of the year?

b) The following table shows betas for several companies. Calculate each stock’s expected rate of return using CAPM. Assume the risk free rate of interest is 9 percent. Use a 6 Percent risk premium for the market portfolio.

Company

Beta

Cisco CitiGroup Merck Walt Disney

2.03 1.63 0.50 0.74

c) If the expected rate of return on the market portfolio is 14 percent and T- bills yield is 6 percent, what must be the beta of a stock that investors expect to return 10 percent? d) You have equal investment in all four stocks given in part (b) of this question. What would be your portfolio beta? e) Student practice: Suppose you have investment as follows: Cisco CitiGroup Merck Walt Disney

20% 20% 30% 30%

Take the Beta as given above and calculate your portfolio beta.

Q No.6 Suppose kRF = 5%, kM = 10% and kA = 12%. a. Calculate Stock A’s beta. b. If Stock A’s beta were 2.0, what would be A’s new required rate of return? Q No.7 Suppose kRF = 9%, kM = 14%, and bi = 1.3. a. What is ki, the required rate of return on stock i? b. Now suppose kRF (1) increases to 10 percent or (2) decreases to 8 percent. The slope of the SML remains constant. How would this affect kM and ki?

Q No.8 Suppose you hold a diversified portfolio consisting of a $7500 investment in each of 20 different common stocks. The portfolio beta is equal to 1.12. Now suppose you have decided to sell one of the stocks in your portfolio with a beta equal to 1.0 for $7500 and to use these proceeds to buy another stock for your portfolio. Assume the new stock’s beta is equal to 1.75. Calculate your portfolio’s new beta. Q No.9: Student Practice Market rate of return is 18%, risk free rate of return 8% and beta is 1.2 Calculate required rate of return Calculate risk premium Q No.10: Student Practice Market rate of return is 14%, beta is 1.5 and required rate of return is 18.5%. What is risk free rate of return? Q No.11: Student Practice Here are stock market and Treasury bill returns between 1997 and 2001 Year 1997 1998 1999 2000 2001

Stock return 31.29 23.43 23.56 -10.89 -10.97

T-Bill return 5.26 4.86 4.68 5.89 3.83

a.What was the risk premium on common stock in each year? b. What was the average risk premium? c.What was the standard deviation of the risk premium?

Q No. 12: Student Practice ECRI Corporation is a holding company with four main subsidiaries. The percentage of its business coming from each subsidiaries, and their respective betas, are as follows: Subsidiary Electric utility Cable company Real estate International/special projects

% of Business 60% 25 10 5

Beta 0.70 0.90 1.30 1.50

a. What is the holding company’s beta? b. Assume that the risk-free rate is 6 percent and the market risk premium is 5 percent. What is the holding company’s required rate of return?