What Is the Sharpe Ratio?

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What Is the Sharpe Ratio?

You need to know that the Sharpe ratio shows whether a portfolio's excess returns are from smart investment decisions or just luck and risk. I developed it—well, economist William F. Sharpe did—in 1966. It compares an investment's return with its risk. The numerator is the difference between realized or expected returns and a benchmark, like the risk-free rate or a category's performance over time. The denominator is the standard deviation of those returns, which measures volatility and risk.

Key Takeaways

William F. Sharpe proposed this ratio in 1966 after his capital asset pricing model work. It compares a fund's historical or projected returns to a benchmark, against the variability of those returns. Excess returns mean those above an industry benchmark or risk-free rate.

Formula and Calculation of the Sharpe Ratio

Sharpe called it the reward-to-variability ratio, and he won the Nobel Prize in 1990 for his CAPM work. The formula is Sharpe Ratio = (Rp - Rf) / σp, where Rp is the portfolio return, Rf is the risk-free rate, and σp is the standard deviation of the portfolio’s excess return. You derive standard deviation from the variability of returns over time intervals that add up to the total sample.

Calculate the numerator as the average of return differentials over incremental periods. For a 10-year ratio, that might be the average of 120 monthly differentials versus a benchmark. For the denominator, take the variance from the average return in each period, square it, sum them, divide by the number of periods, and take the square root.

What the Sharpe Ratio Can Tell You

This is one of the most used methods for measuring risk-adjusted relative returns. It compares returns to a benchmark against their variability. The risk-free rate in the formula represents the premium over a safe asset like a Treasury bill.

When you benchmark against a sector or strategy, it measures performance not due to those factors. It shows how much excess returns came with excess volatility. The ratio assumes historical records predict future performance. Generally, a higher ratio means more attractive risk-adjusted returns.

You can use it to evaluate a portfolio’s past performance or estimate a projected one ex-ante. It explains if excess returns are from smart decisions or luck and risk. For instance, speculative stocks can outperform blue chips temporarily, like during the Dot-Com Bubble, but the Sharpe ratio adjusts for volatility to provide a reality check.

A greater ratio means better risk-adjusted performance. A negative one means the benchmark exceeds the portfolio’s return, or the return is expected to be negative.

Sharpe Ratio Pitfalls

Portfolio managers can manipulate it by lengthening measurement intervals to lower volatility estimates. Annual returns are less volatile than monthly or daily ones, so analysts usually use monthly returns.

Cherry-picking the best performance stretch distorts the data. The standard deviation assumes a normal distribution, which is fine for symmetrical curves but understates tail risk in markets prone to extremes or herding.

Market returns show serial correlation, which can lower volatility and inflate ratios for strategies relying on it. Think of picking up nickels in front of a steamroller—it gives high ratios most of the time, but rare disasters make it misleading.

Sharpe Alternatives: The Sortino and the Treynor

The Sharpe ratio treats upside and downside volatility the same, but most see low returns as riskier than high ones. The Sortino ratio focuses on downside deviation, measuring variance of negative returns below a benchmark relative to their average.

The Treynor ratio divides excess return by beta, which measures correlation with market volatility. It checks if you're compensated for extra risk beyond the market.

Example of How to Use the Sharpe Ratio

Say you're considering adding a hedge fund to a portfolio that returned 18% last year, with a 3% risk-free rate and 12% standard deviation, giving a Sharpe of 1.25: (18% - 3%) / 12%. Adding the fund drops expected return to 15% but volatility to 8%, for a projected Sharpe of 1.5: (15% - 3%) / 8%.

Even with lower absolute return, the risk-adjusted performance improves. If it lowered the ratio, it'd hurt based on forecasts, assuming historical and projected ratios are comparable.

What Is a Good Sharpe Ratio?

Ratios above one are generally good, offering excess returns relative to volatility. But compare it to peers or sectors—a 1 might be lacking if rivals have 1.2 or more.

How Is the Sharpe Ratio Calculated?

Subtract the risk-free rate from the portfolio’s return, then divide by the standard deviation of excess returns. Use Treasury yields as the risk-free proxy.