Compute and interpret maximum drawdown, drawdown duration, upside and downside capture ratios, the appraisal ratio and the Sortino ratio
The idea
The Sortino ratio = (Rp − MAR) ÷ downside deviation, where downside deviation counts only returns below the minimum acceptable return; a portfolio earning 9% with a 3% MAR and 8% downside deviation scores 0.75. The appraisal ratio = alpha ÷ standard deviation of residual returns, rewarding alpha per unit of non-systematic risk. Upside capture is the manager's return in periods when the benchmark rose ÷ the benchmark's return in those periods, and downside capture the same for falling periods; 110% up and 90% down gives a capture ratio of 1.22, a favourable asymmetry. Maximum drawdown is the largest peak-to-trough fall in cumulative value; drawdown duration is the time from the peak through the trough until the prior peak is regained.
Formulas
Sortino ratio
Sortino ratio = (Rp − MAR) ÷ downside deviation
- Rp
- the portfolio's return
- MAR
- the minimum acceptable return
- downside deviation
- volatility measured only from returns below MAR
Better than the Sharpe ratio for skewed returns, because upside variability is not penalised. It depends on the MAR chosen and needs enough returns below it to estimate.
Appraisal ratio
appraisal ratio = alpha ÷ standard deviation of residual returns
- alpha
- Jensen's alpha from a market or factor model
- standard deviation of residual returns
- non-systematic risk: the volatility the model leaves unexplained
Alpha per unit of the risk taken to earn it. It is only as good as the model: a wrong market proxy or a missing factor turns exposure into apparent alpha.
Capture ratio
capture ratio = upside capture ÷ downside capture
- upside capture
- the manager's return ÷ the benchmark's, over periods when the benchmark rose
- downside capture
- the same, over periods when the benchmark fell
Above one is a favourable asymmetry: 110% upside and 90% downside capture give 1.22. The answer depends on how up and down periods are defined and on the benchmark.
In the app: 4 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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