Greengage, Inc., a successful nursery, is considering several expansion projects
ID: 2659605 • Letter: G
Question
Greengage, Inc., a successful nursery, is considering several expansion projects. All of the alternatives promise to produce an acceptable return. Data on four possible projects follow:
Project Expected Return Range Standard deviation
A 12.0% 4.0% 2.9%
B 12.5 5.0 3.2
C 13.0 6.0 3.5
D 12.8 4.5 3.0
A. Which project is least risky, judging on the basis of range?
B. Which project has the lowest standard deviation? Explain why standard deviation may not be an entirely appropriate measure of risk for pusrposes of this comparison.
C. Calculate the coefficient of variation for each project. Which project do you think Greengage's owners should choose? Explain why?
*Please provide explanation* Thank you
Explanation / Answer
A
Project A has the least range of 4%. Thus, it would be least risky in this measure.
B
Project A has the least standard deviation of 2.9%
Using standard deviation as a measure of risk can have its drawbacks. It's possible to own a fund with a low standard deviation and still lose money. In reality, that's rare. Funds with modest standard deviations tend to lose less money over short time frames than those with high standard deviations. For example, the one-year average standard deviation among ultrashort-term bond funds, which are among the lowest-risk funds around (other than money market funds), is a mere 0.64%.
The bigger flaw with standard deviation is that it isn't intuitive. Sure, a standard deviation of seven is obviously higher than a standard deviation of five, but are those high or low figures? Because a fund's standard deviation is not a relative measure which means it's not compared with other funds or with a benchmark it is not very useful to you without some context.
C
Coefficient of Variation = Std Dev / Mean
A = 2.9/12 = 24.1%
B = 3.2/12.5 = 25.6%
C = 3.5/13 = 26.9%
D = 3/12.8 = 23.4%
When comparing two assets, it's sometimes helpful to use the coefficient of variation (CV), which is the standard deviation divided by the mean, thus normalizing the standard deviation and facilitating the comparison of assets on a risk-to-return basis. This works well period-by-period but, because actual returns include the risk-free rate, which varies over time; it is not appropriate for period-to-period comparisons.
Thus, they should select D.
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