Problems sometimes arise when standard deviation is used to measure risk. If an investment project is relatively expensive and has large expected cash flows, it will have a large standard deviation of returns without being truly riskier than a smaller project. Suppose a project has an expected return of $1 million and a standard deviation of only $1,000. Some might reasonably argue that it is less risky than an alternative investment project with expected returns of $1,000 and a standard deviation of $900. The absolute risk of the first project is greater; the risk of the second project is much larger relative to the expected payoff. Relative risk is the variation in possible returns compared with the expected payoff amount.
A popular method for determining relative risk is to calculate the coefficient of variation. Using probability concepts, the coefficient of variation is
Coefficient of Variation = v =
In general, when comparing decision alternatives with costs and benefits that are not of approximately equal size, the coefficient of variation measures relative risk better than does the standard deviation.
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