What you will learn
- Compute the Sharpe ratio of an investment
- Compare investments fairly on a risk-adjusted basis
- Connect the Sharpe ratio to the tangency portfolio
- Understand what the Sharpe ratio misses
You met the Sharpe ratio in Unit 5 as the basic measure of risk-adjusted return. Here it becomes a working tool of portfolio management. It is the number professionals reach for when they ask the fair question about any investment: how much return did you earn for the risk you took? A big return earned by reckless risk is not impressive, and the Sharpe ratio is how you tell the difference.
The Sharpe ratio explained (Ryan O'Connell)
Walks through the formula and what a good value looks like. Focus on why we subtract the risk-free rate and divide by volatility.
The formula in symbols
- r = the investment's return
- rf = the risk-free rate
- r − rf = the excess return
- σ = standard deviation of returns
So the Sharpe ratio is reward divided by risk: the excess return earned per unit of volatility. Higher is better, and as a rough guide, above 1 is good, above 2 is very good, and below 1 is modest.
Key terms
- Excess return
- The investment's return minus the risk-free rate, the reward for taking risk.
- Sharpe ratio
- Excess return divided by volatility, the return earned per unit of risk.
- Risk-adjusted return
- Return judged relative to the risk taken, so investments with different risk can be compared fairly.
Computing a Sharpe ratio
A portfolio returned 12 percent. The risk-free rate is 2 percent, and the portfolio's volatility is 15 percent. What is its Sharpe ratio?
- Find the excess return. 12 percent minus 2 percent is 10 percent.
- Divide by the volatility. 10 divided by 15.
- Read the result. That is about 0.67.
Why it matters: The portfolio earned about two-thirds of a unit of excess return for each unit of risk. On its own the number means little, and its power is comparison, as the next example shows.
Calculate a Sharpe ratio
A fund returned 9 percent with a volatility of 12 percent, while the risk-free rate is 3 percent. What is its Sharpe ratio?
Comparing investments fairly
The Sharpe ratio shines when two investments have different risk levels. Suppose Fund A returned 20 percent with a volatility of 40 percent, and Fund B returned 12 percent with a volatility of 10 percent, with a risk-free rate of 2 percent. Fund A looks better on raw return. But Fund A's Sharpe ratio is (20 minus 2) over 40, about 0.45, while Fund B's is (12 minus 2) over 10, which is 1.0. Fund B delivered more than twice the return per unit of risk, so on a risk-adjusted basis it is the better investment despite the lower headline number. Raw returns flatter whoever took the most risk, and the Sharpe ratio strips that flattery away.
A headline return tells you what someone earned. The Sharpe ratio tells you what they risked to earn it, which is the number that separates skill from recklessness.
Sharpe ratio (Corporate Finance Institute)
A concise recap of the formula and how to read the result, plus a note on its limits. Good reinforcement.
The connection to portfolio theory
The Sharpe ratio is not just a scorecard. It is built into the theory of this unit. Remember the tangency portfolio from the capital-market-line lesson, the single best portfolio of risky assets? It is precisely the portfolio with the highest possible Sharpe ratio. The slope of the capital market line is that maximum Sharpe ratio. So the entire search for the optimal risky portfolio can be restated in one line: find the portfolio with the highest Sharpe ratio. That is why this one number sits at the center of portfolio construction.
What the Sharpe ratio misses
The Sharpe ratio is useful but imperfect, and its flaws set up the next lesson. It uses standard deviation, which treats upside and downside swings identically, even though investors welcome big gains and fear only losses. It leans on the assumption of roughly normal returns, so for fat-tailed, crash-prone strategies it can badly understate the real danger, the exact warning from Unit 5. And it is backward-looking, so a high past Sharpe ratio is no promise about the future. Worst of all, a strategy that wins small and often while hiding the risk of a rare catastrophe can show a great Sharpe ratio right up until the disaster strikes. Use it, but never as the only lens.
Which fund is better risk-adjusted?
Fund X returned 30 percent with a volatility of 60 percent. Fund Y returned 10 percent with a volatility of 8 percent. The risk-free rate is 2 percent. Which has the better Sharpe ratio?
Fund Y wins. Its Sharpe ratio of about 1.0 far exceeds Fund X's 0.47, because Fund X's higher return came with disproportionately more risk. Raw return alone would have misled you.Why risk-adjust?
In your own words, explain why comparing two investments by their raw returns can be misleading, and how the Sharpe ratio corrects it.
Write an answer before comparing it with the model response.
Model answer
Raw returns ignore how much risk was taken to earn them. A fund with a higher return might have been far more volatile, meaning it could just as easily have suffered a large loss, while a lower-returning fund might have earned its return steadily and safely. Judging on return alone rewards whoever gambled hardest and got lucky. The Sharpe ratio corrects this by subtracting the risk-free rate to find the excess return and dividing by the volatility, giving the return earned per unit of risk. That lets me compare investments on an even footing, so a steadier fund with a lower headline return can rightly come out ahead of a wilder one.
The Sharpe ratio's biggest weakness is that it punishes upside volatility just like downside. The next lesson introduces the Sortino ratio and a family of other measures that each define risk differently.