Coefficient Of Variation

An adviser compares two strategies for a client who has no other holdings. Strategy M has an expected return of 12% with a standard deviation of 20%. Strategy N has an expected return of 7% with a standard deviation of 10%. Using the coefficient of variation, which strategy delivers less risk per unit of return, and what is its value?

1. A.Strategy M, at 1.67The arithmetic is right for M but the direction is backwards. A higher coefficient of variation means MORE risk per unit of return, so 1.67 is the worse figure.
2. B.Strategy M, at 0.60This inverts the ratio to return divided by standard deviation. That inversion is a legitimate measure in its own right, but it is not the coefficient of variation.
3. C.Strategy N, at 0.70This also inverts the ratio, dividing 7 by 10. It happens to identify the same strategy for a different reason, but the stated value is not a coefficient of variation.
4. D.Strategy N, at 1.43Correct. 10 / 7 = 1.43, below Strategy M 1.67, and a lower coefficient of variation means less risk per unit of return.

Why: The coefficient of variation divides standard deviation by expected return, giving the amount of total risk taken per unit of return. Strategy M: 20 / 12 = 1.67. Strategy N: 10 / 7 = 1.43. The LOWER coefficient is better, so Strategy N is more efficient on this measure at 1.43, even though Strategy M offers the higher absolute return.

The Meridian Fund produced an average annual return of 9 percent with a standard deviation of 12. The Calder Fund produced an average annual return of 5 percent with a standard deviation of 5. Using the COEFFICIENT OF VARIATION, which fund took less risk per unit of return, and what are the two figures?

1. A.Calder, with a coefficient of variation of 0.75 versus Meridian's 0.42.Wrong. These figures invert the ratio and also misassign it; neither value follows from standard deviation divided by mean.
2. B.Calder, with a coefficient of variation of 1.00 versus Meridian's 1.33.Correct. 5/5 = 1.00 and 12/9 = 1.33; with risk in the numerator, the lower figure is the better risk-per-unit-of-return.
3. C.Meridian, with a coefficient of variation of 0.75 versus Calder's 1.00.Wrong. 0.75 is 9 divided by 12 - the ratio inverted. The coefficient of variation puts standard deviation on top.
4. D.Meridian, with a coefficient of variation of 1.33 versus Calder's 1.00.Wrong conclusion from correct arithmetic. Both figures are right, but a HIGHER coefficient of variation means MORE risk per unit of return.

Why: The coefficient of variation divides standard deviation by the mean return, answering "how many units of volatility did the investor absorb for each unit of return?" Meridian: 12 divided by 9 equals 1.33. Calder: 5 divided by 5 equals 1.00. A LOWER coefficient of variation is better, so Calder delivered less risk per unit of return even though its absolute return was smaller. This is the mirror image of the Sharpe ratio's logic - Sharpe puts excess return on top and rewards a higher figure, while the coefficient of variation puts risk on top and rewards a lower one.