5-18 Interpreting beta. A firm wishes to assess the impact of changes in the market return on an asset that has a beta of 1.20.
a. If the market return increased by 15%, what impact would this change he expected to have on the asset’s return?
b. If the market return decreased by 8%, what impact would this change be expected to have on the asset’s return?
c. If the market return did not change, what impact, if any, would be expected on the asset’s return?
d. Would this asset be considered more or less risky than the market? Explain.
Manipulating CAPM Use the basic equation for the capital asset pricing model (CAPM) to work each of the following problems.
a. Find the required return for an asset with a beta of 0.90 when the risk-free rate and market return are 8% and 12%, respectively.
b. Find the risk-free rate for a firm with a required return of 15% and a beta of 1.25 when the market return is 14%.
c. Find the market return for an asset with a required return of 16% and a beta of 1.10 when the risk -free rate is 9%.
d. Find the beta for an asset with a required return of 15%. when the risk free rate and market return are 10% and 12.5% respectively.
5-1 Rate of return Douglas Keel, a financial analyst for Orange Industries, wishes to estimate the rate of return for two similarrisk investments, X and Y. Keel’s research indicates that the immediate past returns will serve as reasonable estimates of future returns. A year earlier, investment X had a market value of $20,000, investment Y of $55,000. During the year, investment X generated cash flow of $1,500 and investment Y generated cash flow of $6,800. The current market values of investments X and Y are $21,000 and $55,000, respectively.
a. Calculate the expected rate of return on investments X and Y using the most
recent year’s data.
b. Assuming that the two investments are equally risky, which one should Keel
5-12 Portfolio return and standard deviation Jamie Wong is considering building a
portfolio containing two assets, L and M. Asset L will represent 40% of the
dollar value of the portfolio, and asset M will account for the other 60%. The
expected returns over the next 6 years, 2004-2009, for each of these assets, are
shown in the following table.
Year Asset L Asset M
2004 14% 20%
2005 14 18
2006 16 16
2007 17 14
2008 17 12
2009 19 10
a. Calculate the expected portfolio return, kp for each of the 6 years.
b. Calculate the expected value of portfolio returns, kp, over the 6-year period.
c. Calculate the standard deviation of expected portfolio returns, over the 6-year period.
d. How would you characterize the correlation of returns of the two assets L and M?
e. Discuss any benefits of diversification achieved through creation of the
5-8 Standard deviation versus coefficient of variation as measures of risk Greengage, Inc., successful nursery, is considering several expansion projects. All of the alternatives promise to produce an acceptable return. The owners are extremely risk-averse; therefore, they will choose the least risky of the alternatives. Data on four possible projects follow.
Project Expected return Range Standard deviation
A 12.0% .040 .029
B 12.5 .050 .032
C 13.0 .060 .035
D 12.8 .045 .030
a. Which project is least risky, judging on the basis of range?
b. Which project has the lowest standard deviation? Explain why standard deviation is not an appropriate measure of risk for purposes of this comparison.
c. Calculate the coefficient of variation for each project. Which project will Greengage’s owners choose? Explain why this may be the best measure of risk for comparing this set of opportunities.
5-14 Correlation, risk, and return Mart Peters wishes to evaluate the risk and return behaviors associated with various combinations of assets V and W under three assumed degrees of correlation perfect positive, uncorrelated, and perfect negative. The expected return and risk values calculated for each of the assets are shown in the following table.
Asset Expected return Risk
V 8% 5%
W 13 10
a. If the returns of assets V and W are perfectly positively correlated (correlation coefficient = +1), describe the range of (1) expected return and (2) risk associated with all possible portfolio combinations.
b. If the returns of assets V and W are uncorrelated (correlation coefficient = 0), describe the approximate range of (1) expected return and (2) risk associated with all possible portfolio combinations.
c. If the returns of assets V and W are perfectly negatively correlated (correlation coefficient = -1), describe the range of (1) expected return and (2) risk associated with all possible portfolio combinations.