"My portfolio made 12% last year." Good or bad?
You can't tell. A 12% return with gentle swings and a 12% return that went through a 40% drawdown are very different things. Risk-adjusted measures put the return next to the risk it took. This tutorial covers the three used throughout our Wealth Principles series, and what people get wrong about each.
Quick check. Portfolio A earned 8% with 10% volatility. Portfolio B earned 12% with 20% volatility. Cash pays 2%. Which one was the better deal?
Hold your answer: the three ratios don't all agree.
1. Sharpe ratio: return per unit of total swing
William Sharpe proposed it in 1966:
Sharpe = (return − risk-free rate) ÷ volatility
- A: (8 − 2) ÷ 10 = 0.60
- B: (12 − 2) ÷ 20 = 0.50
By Sharpe, A wins: it earned more excess return per unit of volatility.
Common mistake: "higher volatility always means a lower Sharpe". It doesn't. The ratio depends on the numerator too. A volatile strategy with a big enough excess return can have a higher Sharpe than a calm one.
2. Sortino ratio: only the bad swings count
Sharpe punishes upside swings as much as downside ones. Frank Sortino and Lee Price argued that investors don't mind surprises on the upside, so the Sortino ratio uses only the downside deviation, the swings below a minimum acceptable return (MAR):
Sortino = (return − MAR) ÷ downside deviation
Say A's downside deviation is 5% and B's is 8% (B's volatility came mostly from big up-moves). With a MAR of 2%:
- A: 6 ÷ 5 = 1.20
- B: 10 ÷ 8 = 1.25
Now B wins. Same two portfolios, opposite ranking.
Common mistake: computing a plain standard deviation of the negative returns only. Downside deviation is measured against the MAR and over all periods, so state which convention you use.
3. Omega ratio: the whole distribution
Con Keating and William Shadwick (2002) proposed a measure that uses the entire distribution of returns rather than just two moments:
Omega = expected gains above a threshold ÷ expected losses below it
An Omega of 1.5 at a 0% threshold means that, on average, the gains above zero are 1.5 times the losses below zero. It captures skew and fat tails that Sharpe ignores.
Common mistake: treating Omega as the perfect measure. It depends heavily on the threshold you choose and on the quality of your sample. A single extreme month in a short history can swing it a lot.
The trap: a ratio is an estimate, not a fact
Andrew Lo showed in 2002 that Sharpe ratios estimated from data carry large statistical error. In the simple case of independent returns, the standard error is roughly:
SE ≈ √((1 + SR² ÷ 2) ÷ T)
With 10 years of annual returns and a measured Sharpe of 0.5, the standard error is about 0.34. The 95% range runs from roughly −0.2 to +1.2. Ten years of data cannot tell a Sharpe of 0.5 from zero. Lo also showed that annualising monthly ratios with the usual √12 shortcut can misstate them badly when returns are serially correlated.
The principle
No single number proves a strategy is good. Use several ratios, state your threshold and conventions, compare over the same period, and remember that a ratio from a short history is mostly noise.
Your checklist
- Compute your portfolio's Sharpe ratio for the last 3–5 years (volatility from monthly returns × √12).
- Compute Sortino with a MAR you actually care about, such as inflation.
- Compare against a simple index over exactly the same period.
- Before trusting a ratio, check how many years of data it rests on.
Sources
- Sharpe, W. F. (1966). Mutual Fund Performance. Journal of Business, 39(1), 119–138.
- Sharpe, W. F. (1994). The Sharpe Ratio. Journal of Portfolio Management, 21(1), 49–58. Link
- Sortino, F. A. & Price, L. N. (1994). Performance Measurement in a Downside Risk Framework. Journal of Investing, 3(3), 59–64. Link
- Keating, C. & Shadwick, W. F. (2002). A Universal Performance Measure. Journal of Performance Measurement, 6(3), 59–84. Link
- Lo, A. W. (2002). The Statistics of Sharpe Ratios. Financial Analysts Journal, 58(4), 36–52. Link
- Kidd, D. (2012). The Sortino Ratio: Is Downside Risk the Only Risk that Matters? CFA Institute. Link
Educational content, not financial advice. Portfolios A and B are illustrations. Investing carries the risk of loss.