Sortino ratio: define the target and downside denominator

The Sortino ratio compares mean return above a target with downside deviation below that target. It requires an explicit target and observation frequency.

Here it is a descriptive calculation from observed returns. It is not a complete model of future losses, and conventions can materially affect comparisons.

Define downside deviation as sqrt(sum(min(r−T,0)^2)/N), with returns and target T in the same period units. N includes every accepted observation; above-target terms contribute zero.

Mean-centered semivariance is sum(min(r−mean(r),0)^2)/N. Its square root differs from target downside deviation unless the target equals the mean. Neither is the standard deviation of only negative returns.

Four monthly returns are +2%, −1%, +3%, 0%, with a monthly target of zero. Mean return is 1%. Downside deviation is sqrt(0.01^2/4)=0.5%; the monthly Sortino ratio is 2.

Dividing by the single shortfall observation would give 1% and a ratio of 1, contrary to this definition. Mean-centered semideviation is sqrt((0.02^2+0.01^2)/4), about 1.118%.

Converting a 12% compound annual target to a monthly equivalent gives (1.12)^(1/12)−1, about 0.949%. Simple division by 12 gives a different convention.

No observed shortfalls produce a zero denominator and no ordinary finite ratio. Report observation and shortfall counts. Mechanical annualization need not match calculations on annual observations.

Check the return basis against KabuForge’s public portfolio records. This article does not establish a built-in GUI Sortino display or convention.

Read Sharpe ratio, maximum drawdown and out-of-sample evaluation.

Concept references: CFA Institute explanation of targets and downside deviation. Additional reference: official minimum-operation documentation, distinct from the financial ratio definition. Software workflow and limitations: KabuForge public GUI research course. Reviewed October 6, 2026. The fictional examples are teaching calculations, not course execution results.

The public course is research-only and does not certify historical information availability. A concept explanation does not establish that every method is implemented in the software. This article recommends no securities, trades or settings. Read the disclaimer.

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