The question
One fund earned more. The other was calmer. How do I put return and risk on one scale?
The idea
- A risk-adjusted return divides a reward by a risk. It answers: how much did I earn for each unit of risk I took? The reward is usually the return above Treasury bills, the very short government loans from Beginner lesson 1. You could earn the bill rate with almost no risk, so only the extra counts as pay for risk.
- The three common ratios differ only in which risk they divide by:
| Ratio | Reward | Divided by |
|---|---|---|
| Sharpe | Return above bills | Volatility: all the swings, up and down |
| Sortino | Return above bills | Downside deviation: like volatility, but counting only the weeks that did worse than bills |
| Calmar | Return a year (by convention, bills not taken off) | The worst fall |
- Higher is better for all three.
Worked example
JEPI is a JPMorgan fund that holds US stocks and sells options on them for income. SPY tracks the S&P 500. ETFIQ's scorecard covers both over the same 336 weeks, May 29, 2020 to Nov 6, 2026. Over those dates Treasury bills paid an average of 3.1% a year. (JEPI is an example, not a pick.)
| JEPI | SPY | |
|---|---|---|
| Return a year | 10.5% | 16.2% |
| Return above bills | 7.5 points | 13.3 points |
| Volatility | 10.5% | 16.0% |
| Downside deviation | 7.1% | 10.5% |
| Worst fall | −13.1% | −23.9% |
(The return above bills is roughly the return a year minus 3.1%; the scorecard works it out week by week. The steps below use its numbers to two decimals.)
Sharpe: reward ÷ volatility.
- JEPI: 7.47 ÷ 10.50 = 0.71
- SPY: 13.26 ÷ 16.04 = 0.83
Sortino: reward ÷ downside deviation.
- JEPI: 7.47 ÷ 7.11 = 1.05
- SPY: 13.26 ÷ 10.49 = 1.26
Calmar: return a year ÷ worst fall.
- JEPI: 10.52 ÷ 13.12 = 0.80
- SPY: 16.23 ÷ 23.93 = 0.68
2 ratios favour SPY, 1 favour JEPI, and all three readings are correct. JEPI's volatility was about two thirds of SPY's (10.50 ÷ 16.04 = 0.65), but its reward was barely over half (7.47 ÷ 13.26 = 0.56). Its options gave away much of the upside. Reward fell more than risk, so JEPI loses on Sharpe and Sortino.
But its single worst stretch in 2022 was about half as deep as SPY's, and Calmar looks only at that stretch.
Each ratio answers a different question. Sharpe: did the whole ride pay? Sortino: did the downside pay? Calmar: did the worst crash pay?
The common mistake
"The higher ratio made more money." No. JEPI won on Calmar, but $10,000 grew to $19,083 in JEPI against $26,426 in SPY over these dates. A ratio measures pay per unit of risk, not total pay.
A second mistake: comparing ratios across different windows. A ratio over six years that held one crash cannot be set beside one over sixteen years that held three. ETFIQ's scorecard always puts both funds on the same dates.
Check your understanding
Pick an answer to see why. Two of three right passes the lesson.
1. A fund returned 4 points a year above Treasury bills, with volatility of 8%. What is its Sharpe ratio?Answer: B. 0.5. 4 ÷ 8 = 0.5. Not C: 2.0 is volatility divided by reward, upside down.2. A reader says the swings don't bother them, but one deep crash would make them sell. Which ratio speaks most directly to that worry?Answer: A. Calmar. Calmar divides by the worst fall, the one stretch this reader fears. Not C: Sortino counts every down week, not the single deepest fall.3. Fund A shows a Sharpe of 0.9 over 2021 to 2026. Fund B shows 0.7 over 2010 to 2026. What can you conclude?Answer: D. Nothing yet: the windows differ. Different dates hold different markets, so the ratios aren't comparable. Put both on the same window first. Not A: 0.9 beats 0.7 only when the dates match.
Takeaways
- Every ratio is a reward divided by a risk; name the risk before you read the number.
- When Sharpe and Calmar disagree, the fund's worst fall differs from its usual swings: read both.
- Compare ratios only on the same dates, and check total return beside them.