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CMA Intermediate · Financial Management and Business Data Analytics · Risk and Return

Security X has an expected return of 15% and a standard deviation of 6%. Security Y has an expected return of 20% and a standard deviation of 10%. Which statement about relative risk per unit of return is correct?

X has a coefficient of variation of 0.40 against 0.50 for Y, found by dividing standard deviation by expected return. Since X bears less risk per unit of expected return, it is relatively less risky even though Y offers a higher return.

  1. AX has a coefficient of variation of 0.40, lower than Y's 0.50, so X is less risky per unit of returnCorrect
  2. BX has a coefficient of variation of 2.5, higher than Y's 2.0, so X is riskier per unit of return
  3. CY has a lower coefficient of variation because its standard deviation is higher
  4. DBoth have the same coefficient of variation because return rises with risk

Explanation

CV = SD / expected return. X: 6/15 = 0.40; Y: 10/20 = 0.50. Lower CV means less risk per unit of return, so X is relatively less risky. Option 2 inverts the ratio.

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