Sharpe, Sortino and Treynor ratios
Put a return into context: how much excess return did each unit of risk buy? Sharpe and Sortino use total risk, Treynor and alpha use only the systematic part, and the panel shows why the four can disagree.
| Ratio | Value | Denominator | Reading |
|---|---|---|---|
| Sharpe | 0.512 | σ 16.8% | Acceptable |
| Sortino | 0.768 | σ_down 11.2% | Acceptable |
| Treynor | 0.0796 | β 1.08 | Good |
| Information | 0.829 | TE 4.1% | Excellent |
| Calmar | 0.696 | MaxDD 18.4% | Good |
| Jensen alpha | +2.98% | β 1.08 | Outperforming |
Sharpe and Sortino measure total risk; Treynor and alpha measure only the systematic part. Use the latter when the portfolio is one sleeve of a diversified whole.
(R_p − R_f) / σ_p · total volatility in the denominator
(R_p − R_f) / σ_down · only below-target deviations count
(R_p − R_f) / β · systematic risk only
R_p − [R_f + β(R_m − R_f)] · return above the CAPM prediction
A clear path from inputs to results.
A return number without a risk number is not a performance measure. These five ratios all divide some measure of excess return by some measure of risk — the differences are entirely in which risk they charge you for, which is why they can disagree about the same portfolio.
How to use
- Enter the portfolio’s annualised return.
- Set the risk-free rate over the same period.
- Enter annualised volatility for Sharpe, and downside deviation for Sortino.
- Add beta, the benchmark return and tracking error for Treynor, alpha and the information ratio.
- Add maximum drawdown for the Calmar ratio.
- Read the panel: total-risk ratios suit a whole portfolio, systematic-risk ratios suit one sleeve of a diversified whole.
The formula
Reference: Sharpe (1966, 1994); Sortino & Price (1994); Treynor (1965); Jensen (1968).
Worked example
12.8% return, 4.2% risk-free, 16.8% volatility (default inputs)
- Portfolio return 12.8%; risk-free rate 4.2%.
- Volatility 16.8%; downside deviation 11.2%.
- Beta 1.08; benchmark 9.4%; tracking error 4.1%; max drawdown 18.4%.
- 1
Excess return: 12.8% − 4.2% = 8.6%.
- 2
Sharpe: 8.6 / 16.8 = 0.512.
- 3
Sortino: 8.6 / 11.2 = 0.768 — better, because only downside deviations are penalised.
- 4
Treynor: 8.6 / 1.08 = 0.0796 per unit of beta.
- 5
Alpha: 12.8% − (4.2% + 1.08 × 5.2%) = 2.98%.
Sharpe 0.51 · Sortino 0.77 · Treynor 0.0796 · information ratio 0.83 · alpha +2.98%.
Interpreting the result
A Sharpe of 0.51 is unremarkable; the Sortino of 0.77 is better because this portfolio’s volatility is asymmetric — its upside is doing work that Sharpe does not credit. The positive alpha of 2.98% says the return exceeds what beta alone would predict, which is the only one of these numbers that claims genuine skill rather than favourable risk exposure.
Assumptions & limitations
- Returns are annualised and the risk-free rate matches that frequency.
- Volatility is the standard deviation of returns, which penalises upside and downside equally.
- Downside deviation is measured against the risk-free rate as the minimum acceptable return.
- Beta and the benchmark return are estimated over a period consistent with the return figures.
- Ratios are not adjusted for skewness or fat tails; they assume roughly normal returns.
Frequently asked questions
What is a good Sharpe ratio?
Above 1 is generally good for a diversified portfolio, above 2 is excellent, and below 0.5 means the risk taken was poorly compensated. Comparisons are only valid within the same asset class and time period.
When should I use Treynor instead of Sharpe?
When the portfolio is one component of a diversified whole. Treynor charges only systematic risk, on the argument that idiosyncratic risk has already been diversified away. For a standalone portfolio, Sharpe is the right measure.
Why can alpha be positive while Sharpe is mediocre?
They answer different questions. Alpha asks whether the return beats the CAPM prediction given the beta taken. Sharpe asks whether the return compensated for total risk. A portfolio can take a lot of diversifiable risk, beat its beta benchmark and still be a poor risk-adjusted proposition.
Why is Sortino higher than Sharpe here?
Because downside deviation is lower than total volatility, so the same excess return is divided by a smaller number. That happens when a portfolio’s volatility is driven by large upside moves, which Sharpe penalises but Sortino does not.
What does the information ratio measure?
Active return per unit of tracking error — how efficiently the manager deviates from the benchmark. Above 0.5 is good, above 0.75 is very good, and it is the standard measure for active managers.
Can these ratios be negative?
Yes, when the return is below the risk-free rate. A negative Sharpe means you would have been better off in Treasury bills. The magnitude still matters for ranking, but interpretation becomes awkward.
Methodology last reviewed 2026-10-18. Results are informational and not financial or engineering advice — see our disclaimer.