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FIN5100: Revision on Risk and Return

Risk and Return

1. Ripken Iron Works faces the following probability distribution:

  State of Probability of Stock’s Expected Return

the Economy State Occurring   if this State Occurs   

Boom 0.25 25%

Normal 0.50 15  

Recession 0.25 5  

What is the coefficient of variation on the company's stock?  (Assume that the standard deviation is calculated using the probability statistic.)

2. An analyst has estimated how a particular stock’s return will vary depending on what will happen to the economy:

  State of Probability of Stock’s Expected Return

the Economy State Occurring   if this State Occurs   

Recession 0.10 -60%

Below Average 0.20 -10  

Average 0.40 15  

Above Average 0.20 40  

Boom 0.10 90  

What is the coefficient of variation on the company’s stock?  (Use the population standard deviation to calculate the coefficient of variation.)

3. Calculate the required rate of return for Mercury Inc., assuming that investors expect a 5 percent rate of inflation in the future.  The real risk-free rate is equal to 3 percent and the market risk premium is 5 percent.  Mercury has a beta of 2.0, and its realized rate of return has averaged 15 percent over the last 5 years

4. You hold a diversified portfolio consisting of a $10,000 investment in each of 20 different common stocks (i.e., your total investment is $200,000).  The portfolio beta is equal to 1.2.  You have decided to sell one of your stocks which has a beta equal to 0.7 for $10,000.  You plan to use the proceeds to purchase another stock which has a beta equal to 1.4.  What will be the beta of the new portfolio?

5. You recently purchased a stock that is expected to earn 19 percent in a booming economy, 12 percent in a normal economy, and lose 8 percent in a recessionary economy. The probability of a boom economy is 16 percent while the probability of a normal economy is 78 percent. What is your expected rate of return on this stock?

6. The common stock of Manchester & Moore is expected to earn 14 percent in a recession, 7 percent in a normal economy, and lose 4 percent in a booming economy. The probability of a boom is 15 percent while the probability of a recession is 5 percent. What is the expected rate of return on this stock?

7. The returns on the common stock of New Image Products are quite cyclical. In a boom economy, the stock is expected to return 23 percent in comparison to 14 percent in a normal economy and a negative 18 percent in a recessionary period. The probability of a recession is 18 percent while the probability of a boom is 22 percent. What is the standard deviation of the returns on this stock?

8. What is the expected return and standard deviation for the following stock?

9. You are comparing Stock A to Stock B. Given the following information, what is the difference in the expected returns of these two securities?

10. You own the following portfolio of stocks. What is the portfolio weight of Stock C?

Question 11.

Part I

 ANA  Corporation has collected information on the following three investments:

(i) Find the expected return for each stock) 

(ii) Find the standard deviation for each stock) 

(iii) Based on your result (i) and (ii), which stock is the most favorable and why?)

Part II

Mamat as portfolio manager is holding  the following investments in his portfolio:)

Stock                Amount Invested Beta

1 RM 150 mil 0.7

2 RM 100 mil 1.0

 3 RM 250 mil 1.6

 (The risk-free rate, k_rf, is 5 percent and the portfolio has required return of 11.655 percent. Khaleef is thinking about selling all of his holdings of Stock 3, and investing the money in Stock 4, which has a beta of 0.9.)

(i) Calculate the beta of original portfolio? 

(ii) By using CAPM method, find the market risk ?

(iii) Calculate the beta of new portfolio?

(iv) What would be the new portfolio’s return?  

Question 12

a) You are being offered to invest in a portfolio which consists of three stocks. Based on the capital asset pricing model (CAPM), and the portfolio information as shown in the table, will you invest in this portfolio? Show your calculations.)

 (The market’s required rate of return is 11%, and the risk-free rate is 3.2%.)

b) You are allocating RM 200,000 to a portfolio comprising two investments below. Estimate the portfolio’s return and standard deviation  if you allocate RM 120,000 in Investment X and the remaining fund in Investment Y.