# Greengage, Inc.: Standard Deviation vs. Coefficient of Variation for Measuring Risk

Greengage, Inc., a 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% 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 is not an appropriate measure of risk for purpose 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.

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#### Solution Preview

a) The actual range of each project is as follows:

A=4.0

B=5.0

C=6.0

D=4.5

Judging from this, the least risky of the projects is A, because it has the smallest range.

b) The actual standard deviations are as follows:

A=2.9

B=3.2

C=3.5

D=3.0

Project A has the lowest standard deviation. The standard deviation is a good comparison tool in this example only if the expected rate of return for each project is the same. Because the expected ...

#### Solution Summary

With expected return, range, and standard deviation, the risk of four possible investments is analyzed with calculations and discussion of 219 words.