Sharpe ratio: formula, examples and what is a good one

Written by the Tactfolio research teamPublished 6 min read

The Sharpe ratio measures how much return an investment earned for each unit of risk it took. You take the return, subtract what cash would have paid, and divide by how much the returns swung up and down. A higher Sharpe ratio means a smoother ride for the same reward. A past Sharpe ratio does not predict the next one.

Key points#

  • Sharpe ratio = (return − T-bill rate) ÷ volatility.
  • Volatility is how much returns swing around their average, usually measured over a year.
  • The T-bill rate is what you could earn with almost no risk, from short-term US Treasury bills. Textbooks call it the risk free rate.
  • Economist William Sharpe created it in 1966. He first called it the “reward-to-variability ratio.”
  • There is no official “good” number. A high Sharpe ratio in a backtest is often partly luck.

How do you calculate the Sharpe ratio?#

You calculate the Sharpe ratio in three steps:

  1. Find the yearly return of the investment.
  2. Subtract the T-bill rate for the same period. What is left is the excess return, the extra you earned for taking risk.
  3. Divide the excess return by the yearly volatility.

Sharpe ratio formula:

Sharpe ratio = (portfolio return − T-bill rate) ÷ standard deviation of returns

Standard deviation is the math behind volatility. It measures how far returns usually land from their average.

A worked example#

Say you compare two portfolios over the same years. Treasury bills paid 4% a year.

Portfolio APortfolio B
Yearly return10%7%
Minus T-bills4%4%
Excess return6%3%
Volatility15%5%
Sharpe ratio6 ÷ 15 = 0.403 ÷ 5 = 0.60

Portfolio A earned more. Portfolio B earned more for each bump along the way. If you only care about the final number, A looks better. If you care about how hard the ride was, B looks better.

Neither answer is “right.” The Sharpe ratio helps you see the trade-off. It does not make the choice for you.

What is a good Sharpe ratio?#

There is no official cutoff for a good Sharpe ratio. It depends on the time period, the kind of investment and whether the number is real or from a backtest.

A few honest guidelines:

  • Compare like with like. Compare two strategies over the same dates, with the same T-bill rate.
  • Long periods matter more. A high Sharpe ratio over 2 years can be luck. One over 20 years, through several bad markets, means more.
  • Be wary of backtests. In a 2014 paper, Bailey and co-authors showed how fast luck creeps in. With 2 years of data, trying only 7 versions of a strategy can produce one with a Sharpe ratio of 1 on paper. Its true expected Sharpe ratio would be zero (Notices of the AMS).

Harvey and Liu made a related point in 2015. Some people cut a backtest’s Sharpe ratio in half to allow for data mining. They showed the cut should depend on how many ideas were tested. Middling results deserve bigger cuts than very strong ones (Journal of Portfolio Management).

Our guide to backtesting explains how to test a strategy without fooling yourself.

Where did the Sharpe ratio come from?#

William Sharpe introduced the measure in a 1966 paper, “Mutual Fund Performance,” in the Journal of Business (JSTOR). He used it to compare mutual funds. Today it is one of the first numbers people check in algorithmic trading and fund research. Sharpe later shared the 1990 Nobel Prize in economics for his work on how assets are priced (Nobel Prize).

In 1994 he wrote “The Sharpe Ratio” for the Journal of Portfolio Management (Stanford). In it he noted that his name for it, “reward-to-variability ratio,” never caught on. He also explained the difference between a Sharpe ratio measured on past results and one built on forecasts. Most numbers you see online are the first kind.

What are the limits of the Sharpe ratio?#

The Sharpe ratio is useful, but people often misread it. It has five main blind spots.

  • It treats gains and losses the same. A sudden jump up counts as “risk,” the same as a sudden drop.
  • It hides big crashes. A strategy can show a smooth record for years and then lose a lot at once. Check the max drawdown, the biggest fall from a high point, next to it. The Calmar ratio divides yearly return by that drop instead of by volatility.
  • It assumes swings are fairly normal. Strategies that sell insurance-like bets can look smooth until one bad event.
  • It depends on the period. The same fund can show very different Sharpe ratios over different years.
  • Leverage does not change it much. Borrowing to double a position roughly doubles both the excess return and the volatility, so the ratio barely moves. A high Sharpe ratio does not mean a strategy is safe to borrow against.

Risk parity funds lean on this idea. They aim for a high ratio first and then use leverage to reach the return they want.

Sharpe ratio on Tactfolio#

Every Tactfolio backtest shows two Sharpe figures. The main one divides the average yearly return by volatility, measured from zero, so it does not subtract the T-bill rate. The one labeled over T-bills subtracts the 13-week Treasury bill return first, as the standard Sharpe ratio does. When you compare with other websites, use the over T-bills figure. Our guide on how to read a backtest shows where it fits among the other numbers.

Try it on Tactfolio#

Open any of the 75 classic strategies to see its Sharpe ratio next to its return and worst drawdown, compared with the S&P 500. Each figure comes from a hypothetical backtest on daily prices with dividends reinvested and a 0.05% cost per trade. You can then copy a strategy into the builder, change one rule, and see whether the Sharpe ratio holds up.

Common questions#

What does the Sharpe ratio tell you?#

It tells you how much extra return an investment earned for each unit of volatility it took. A higher number means more reward per bump. It does not tell you how big the worst loss was.

What is a good Sharpe ratio?#

There is no official cutoff. Over long periods, compare a strategy with a simple benchmark, like the S&P 500 or a 60/40 mix, over the same dates. Treat very high Sharpe ratios in short backtests with suspicion, because they are often luck.

Can a Sharpe ratio be negative?#

Yes. If an investment earned less than the T-bill rate, its excess return is negative, so its Sharpe ratio is too. That means you would have done better holding Treasury bills.

What is the difference between the Sharpe ratio and the Sortino ratio?#

The Sortino ratio divides by downside volatility only, so upward jumps do not count as risk. The Sharpe ratio counts all swings. Sortino can make strategies with big gains look better than Sharpe does.

How do you annualize a Sharpe ratio?#

If you work from daily returns, multiply the daily Sharpe ratio by the square root of 252. That is about the number of trading days in a year. For monthly returns, multiply by the square root of 12. This assumes returns from one day to the next are not linked.

The details#

Written out, the ex post Sharpe ratio is S = (R̄ₚ − R̄f) ÷ σ, where R̄ₚ is the average portfolio return, R̄f is the average T-bill return, and σ is the standard deviation of the excess returns. Sharpe’s 1994 article defines it on the series of differences between the two returns.

Annualizing with √252 assumes returns are independent from day to day. When returns are linked from one period to the next, the simple scaling can overstate or understate the yearly figure.

Sources

Put it into practice