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Risk-Return Problems

7. Calculating Returns and DeviationsBased on the followinginformation, calculate the expected return and standard deviationfor the two stocks. Find covariance and correlation between thetwo stocks.

Answer: AB= 0.0103

AB= 0.9953

State of Economy Probability of State Stock A Return Stock B Return

Recession 0.15 0.02 -0.15

Normal 0.60 0.09 0.18

Boom 0.25 0.18 0.50

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Risk-Return Problems

10.Returns and DeviationsConsider the following information:

a. Your portfolio is invested 30 percent in A and C, and 40 percent

in B. What is the portfolio expected return?

b. What is the variance of this portfolio? The standard deviation?

Answer:E(kP)= 0.08765

2P= 0.008338

P= 0.091

State of Economy Probability of State Stock A Return Stock B Return Stock C Return

Boom 0.20 0.10 0.20 0.35

Good 0.50 0.07 0.10 0.15

Poor 0.25 0.04 0.00 -0.05Bust 0.05 0.00 -0.08 -0.40

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Risk-Return Problems

30. Portfolio Returns and DeviationsGiven the following information on aportfolio of three stocks:

a. If your portfolio is invested 30 percent in A and B and 40 percent

in C, what is the portfolio expected return? The variance? The

standard deviation?

b. If the expected T-bill rate is 5.25 percent, what is the expected risk

premium on the portfolio?

c. If the expected inflation rate is 5 percent, what is the expected real

return on the portfolio? What is the expected real risk premium on

the portfolio?Answer: a) expected return=0.1875 standard deviation=0.2426

b)premium=0.135

c)portfolio expected real return=0.13095 real premium=0.12857

State of Economy Probability of State Stock A Return Stock B Return Stock C Return

Boom 0.20 0.20 0.30 1.00

Normal 0.70 0.10 0.05 0.30

Bust 0.10 0.00 -0.20 -0.80

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Risk-Return Problems

32. Analyzing a PortfolioYou have $100,000 to invest in either

Stock D, Stock F, or a risk-free asset. You must invest all of your

money. Your goal is to create a portfolio that has an expected

return of 10 percent and is only 60 percent as risky as the overall

market. If D has an expected return of 20 percent and a beta of

1.5, F has an expected return of 15 percent and a beta of 1.15 and

the risk-free rate is 5 percent, how much money will you invest in F?

Answer: $66,667 investment in F

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Risk-Return Problems

33. Systematic versus Unsystematic RiskGiven the followinginformation on stocks A and B:

The market risk premium is 8 percent and the risk-free rate is 6

percent. Which stock has the most systematic risk? Which one hasthe most unsystematic risk? Which stock is riskier? Explain.

Answer: A has more systematic risk

B has more unsystematic risk

State of Economy Probability of State Stock A Return Stock B Return

Recession 0.15 0.14 -0.18Normal 0.60 0.24 0.10

Boom 0.25 0.28 0.40