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probability of the state of

economic

Rate of return

STOCK A

if states

STOCK B

occurs

STOCK C
boom 0,2 0,4 -0,04 0,12
good 0,3 0,2 0,05 0,08
poor 0,4 0,04 0,1 0,02
burst 0,1 -0,06 0,14 0

a. Calculate the expected return of each stock.
b. Calculate the variance and standard deviation of each stock.
c. Calculate the expected return of the portfolio (Portfolio1) consisting 40% of stock A,
40% of stock B and 20% of stock C.
d. Calculate the variance and standard deviation of this portfolio.
e. Consider an alternative portfolio (Portfolio2) 40% of stock A, 20% of stock B, 10% of
stock C and 30% in the risk-free asset. Risk-free asset expected return is 2%. What is
this portfolio’s expected return, variance and standard deviation?
f. Based on CAPM calculate each stock beta if market risk premium is 5%.
g. Which stock has the lowest systematic risk? Which stock has the lowest total risk?
Which stock is “safest”? Explain.
h. What is the beta of the Portfolio1 and Portfolio?

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Hubert Koch
Hubert KochLv2
28 Sep 2019

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Related questions

Evaluating risk and return Stock X has a 10.0% expected return, a beta coefficient of 0.9, and a 40% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. Calculate each stock's coefficient of variation. Round your answers to two decimal places.

a. CVx = CVy =

b. Calculate each stock's required rate of return. Round your answers to two decimal places.
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c. Calculate the required return of a portfolio that has $4,500 invested in Stock X and $2,500 invested in Stock Y. Round your answer to two decimal places.
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Problem 11-25 Portfolio Returns and Deviations [LO 2]

Consider the following information on a portfolio of three stocks:
State of
Economy		 Probability of
State of Economy		 Stock A
Rate of Return		 Stock B
Rate of Return		 Stock C
Rate of Return
Boom .13 .02 .32 .50
Normal .55 .10 .22 .20
Bust .32 .16 –.21 –.35
Required:
(a)

If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio’s expected return, the variance, and the standard deviation? (Do not round intermediate calculations. Round your variance answer to 5 decimal places (e.g., 32.16161) and input your other answers as a percentage rounded to 2 decimal places (e.g., 32.16).)
Expected return %
Variance
Standard deviation %
(b)

If the expected T-bill rate is 4.25 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
Expected risk premium %

Evaluating risk and return

Stock X has a 9.5% expected return, a beta coefficient of 0.8, and a 40% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%.

Calculate each stock's coefficient of variation. Round your answers to two decimal places. Do not round intermediate calculations.
CVx =
CVy =

Which stock is riskier for a diversified investor?

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X.

For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the higher standard deviation of expected returns is more risky. Stock X has the higher standard deviation so it is more risky than Stock Y.

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the lower beta is more risky. Stock X has the lower beta so it is more risky than Stock Y.

For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the lower standard deviation of expected returns is more risky. Stock Y has the lower standard deviation so it is more risky than Stock X.

For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is less risky. Stock Y has the higher beta so it is less risky than Stock X.


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If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?
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