Use returns on a fixed time basis
For example, use daily account returns with consistent treatment of deposits and withdrawals. Dollar results from trades of different sizes are not a comparable daily return series. A day without trading may still belong in the chosen account-return series.
Distinguish the dispersion measures
The Sharpe ratio divides average excess return by its standard deviation. For the Sortino convention below, we use the square root of the mean squared negative deviations from the target; observations meeting the target contribute zero. The denominator includes all observations.
The example uses sample standard deviation with n − 1 for Sharpe. Sortino averages over n days. These choices matter because software may implement different conventions.
Four synthetic daily returns
Returns of +1%, −1%, +2% and 0% have an arithmetic mean of +0.5%. The risk-free comparison return and Sortino target are both assumed to be 0% each day. Sample standard deviation is about 1.291 percentage points, giving Sharpe ≈ 0.387.
Only the second day falls below zero. Downside deviation is therefore √(1 / 4) = 0.5 percentage points; Sortino = 1. Neither value is annualized. Four days are used only to make the arithmetic transparent.
Avoid rankings with inconsistent assumptions
Compare matching periods, costs, valuation methods and return frequencies. Annualizing by the square root of the number of periods requires additional assumptions about the time series. Zero dispersion or no downside deviations requires an explanation of the undefined quotient.
| Day | Return | Negative target deviation |
|---|---|---|
| 1 | +1 % | 0 |
| 2 | −1 % | −1 % |
| 3 | +2 % | 0 |
| 4 | 0 % | 0 |
Sources and methodology
Sources explain concepts or the respective provider’s product descriptions. Worked examples are original and synthetic. Verify current contract specifications before use.