Sortino Ratio

The Sortino ratio differs from the Sharpe ratio principally in that the Sortino ratio:

1. A.Uses beta rather than standard deviation in the denominatorThat describes the Treynor ratio, not the Sortino ratio.
2. B.Divides excess return by downside deviation rather than by total standard deviationCorrect. Sortino penalizes only returns below the minimum acceptable return.
3. C.Measures return relative to a benchmark rather than to a risk-free rateThat describes the information ratio, which uses active return over tracking error.
4. D.Ignores the risk-free rate entirely and reports raw return per unit of riskSortino still measures return in excess of a threshold, commonly the risk-free rate.

Why: The Sortino ratio measures excess return above a minimum acceptable return per unit of downside deviation, whereas the Sharpe ratio divides excess return by total standard deviation. By penalizing only returns below the threshold, the Sortino ratio does not treat upside volatility as risk. It is therefore preferred when a return distribution is skewed or asymmetric, as with strategies that use options or that have infrequent large gains.

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.