Treynor Ratio

The Wrenfield Growth Fund returned 12.6% over the past year while Treasury bills returned 3.0%. The fund beta measured against its benchmark is 1.2. The fund Treynor ratio for the year is:

1. A.8.0Correct. (12.6 - 3.0) / 1.2 = 9.6 / 1.2 = 8.0.
2. B.10.5Incorrect. 12.6 / 1.2 = 10.5 skips the subtraction of the risk-free rate.
3. C.11.52Incorrect. 9.6 x 1.2 multiplies by beta instead of dividing by it.
4. D.3.2Incorrect. 9.6 / 3.0 divides the excess return by the risk-free rate rather than by beta.

Why: The Treynor ratio measures excess return earned per unit of SYSTEMATIC risk. Subtract the risk-free rate from the portfolio return to get excess return, 12.6% - 3.0% = 9.6%, then divide by beta: 9.6 / 1.2 = 8.0. A higher Treynor ratio means more reward per unit of market risk taken. Treynor is the appropriate measure when the fund is one holding inside an already diversified portfolio, because in that setting only systematic risk matters.

Consultant Marisol Etxeberria compares two funds that each returned 9% a year with the same 12% standard deviation. Fund Harlow bad years were few but brutal; Fund Ivorne dispersion came mostly from unusually LARGE POSITIVE years. She wants a statistic that penalizes only unfavourable variability. The SORTINO ratio serves this purpose because it:

1. A.Divides excess return over the risk-free rate by beta, so that only systematic risk is countedThat is the Treynor ratio, which measures reward per unit of market risk, not per unit of downside risk.
2. B.Subtracts the return CAPM would have required, given beta, from the return actually earnedThat is Jensen alpha. It is a measure of excess return, not a downside-risk-adjusted ratio.
3. C.Divides excess return over the risk-free rate by total standard deviation, weighting upside and downside variability equallyThat is the Sharpe ratio, the very measure Etxeberria is trying to improve on.
4. D.Divides excess return over a minimum acceptable return by DOWNSIDE deviation, the dispersion computed from only those returns falling below the targetCorrect. Excluding upside variability from the denominator is exactly what distinguishes Sortino from Sharpe.

Why: The Sortino ratio replaces total standard deviation with DOWNSIDE deviation, computed using only the returns that fell below a stated minimum acceptable return (often the risk-free rate or zero). Excess return over that target is divided by downside deviation. Because upside surprises are excluded from the denominator, a fund like Ivorne whose dispersion comes from big gains is not penalized, while Fund Harlow deep losses are.