Coefficient of variation (V) = standard deviation/mean returnRanking from lowest to highestA300/1,200 = .25C (.09)B600/800 = .75E (.22)C450/5,000 = .09A (.25)D430/1,000 = .43D (.43)E13,200/60,000 = .22B (.75)
8.Coefficient of variation (LO1) Five investment alternatives have the following returns and standard deviations of returns.AlternativeReturns:
Expected ValueStandard DeviationA$ 1,000$ 590B3,000600C3,000750D5,0002,300E10,000800
Using the coefficient of variation, rank the five alternatives from lowest risk to highest risk.13-8.Solution:
Coefficient of variation (V) = standard deviation/expected valueRanking from lowest to highestA$590/$1,000 = .59E (.08)B$600/$3,000 = .20B (.20)C$750/$3,000 = .25C (.25)D$2,300/$5,000 = .46D (.46)E$800/$10,000 = .08A (.59)
9.Coefficient of variation (LO1) In problem 8, if you were to choose between Alternatives B and C only, would you need to use the coefficient of variation? Why?13-9.Solution:
You would not need to use the coefficient of variation. Since B and C have the same expected value, they can be evaluated based solely on their standard deviations of return. C has a larger standard deviation and so is riskier than B for the same expected return.
10.Coefficient of variation and time (LO1) Sensor Technology wishes to determine its coefficient of variation as a company over time. The firm projects the following data (in millions of dollars):YearProfits:
Deviation1$ 90$ 313120 526150 839200 146
a.Compute the coefficient of variation (V) for each time period.
b.Does the risk (V) appear to be increasing over a period of time? If so, why might this be the case?13-10.Solution:
a.YearProfits: Expected ValueStandard DeviationCoefficient of Variation1 90 31.343120 52.436150 83.559200146.73
b.Yes, the risk appears to be increasing over time. This may be related to the inability to make forecasts far into the future. There is more uncertainty.
11.Risk-averse (LO2) Tim Trepid is highly risk-averse while Mike Macho actually enjoys taking a risk.
a.Which one of the four investments should Tim choose? Compute coefficients of variation to help you in your choice.InvestmentsReturns:
DeviationBuy stocks$ 8,800$ 5,600Buy bonds7,0002,060Buy commodity futures16,90022,100Buy options11,60012,400
b.Which one of the four investments should Mike choose?13-11.Solution:
Coefficient of variation (V) = standard deviation/expected value.
Buy stocks$5,600/8,800 = .636
Buy bonds$2,060/7,000 = .294
Buy commodity futures$22,100/16,900 = 1.308
Buy options$12,400/11,600 = 1.069
a.Tim should buy the bonds because bonds have the lowest coefficient of variation.
b.Mike should buy the commodity futures because they have the highest coefficient of variation.
12.Risk-averse (LO2) Wildcat Oil Company was set up to take large risks and is willing to take the greatest risk possible. Richmond Construction Company is more typical of the average corporation and is risk-averse.
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