Return and Measures of Risk



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  1. Return and Measures of Risk. Stocks A and B have the following probability distributions of possible future returns:



Probability (pi)




(ri1) A (%)




B (%)


0.1




-15




-20

0.2




0




10

0.4




5




20

0.2




10




30

0.1




25




50

(a) Calculate the expected rate of return for each stock and the standard deviation of returns for each stock,

= (-15)(0,1) + (0)(0,2) + (5)(0,4) + (10)(0,2) + (25)(0,1) = 5

= (-20)(0,1) + (10)(0,2) + (20)(0,4) + (30)(0,2) + (50)(0,1) = 19

(b) Calculate the coefficient of variation,


A B


Expected return 5% 19%

Standard Deviation 9,49% 17%

(c) Which stock is less risky? Explain.

Stock A which is 68 percent of probability that the actual return will be in the range of 5% plus or minus 9,49% or from minus 4,49% to 14,49%. Since the range is bigger than stock B, so the stock A is more risky than B.



  1. Absolute and Relative Risk. Ken Parker must decide which of two securities is best for him. By using probability estimates, he computed the following statistics:



Statistic

Security X

Security Y

Expected return (ŕ)

12%

8%

Standard deviation ()

20%

10%

(a) Compute the coefficient of variation for each security, and (b) explain why the standard deviation and coefficient of variation give different rankings of risk. Which method is superior and why?

  1. Diversification Effects. The securities of firms A and B have the expected return and standard deviations given below; the expected correlation between the two stocks (AB) is 0.1.






ŕ




A

14%

20%

B

9%

30%

Compute the return and risk for each of the following portfolios: (a) 100 percent A; (b) 100 percent B; (c) 60 percent A – 40 percent B; and (d ) 50 percent A–50 percent B.

  1. Diversification Effects. Use the same facts as for Problem 7.4, except for this problem assume the expected correlation between the two stocks (ρAB) = -1.0.



  1. Portfolio Risk. What is the standard deviation of the following two-stock portfolio?






Weighting


Standard

Deviation




Correlation





Stock A

60%

11%

0.7

Stock B

40%

14%




(CFM adapted.)

  1. CAPM. If Treasury bills yield 10 percent, and Alpha Company’s expected return for next year is 18 percent and its beta is 2, what is the market’s expected return for next year? Assume the capital asset pricing model (CAPM) applies and everything is in equilibrium.



  2. CAPM. Assume the following: the risk-free rate is 8 percent, and the market portfolio expected return is 12 percent.



Portfolio

Beta


A

0.6

B

1.0

C

1.4

(a) Calculate for each of the three portfolios the expected return consistent with the capital asset pricing model. (b) Show graphically the expected portfolio returns in (a). (c) Indicate what would happen to the capital market line if the expected return on the market portfolio were 10 percent (CFA, adapted.)
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