What is Sharpe Ratio?
The Sharpe Ratio formula measures the risk-adjusted return of a portfolio by dividing the excess returns by the standard deviation of the portfolio returns.
How to Calculate Sharpe Ratio?
The Sharpe ratio evaluates the risk-adjusted performance of an investment portfolio by determining the excess return received for the extra risk/volatility associated with a riskier portfolio.
Economist William Sharpe came up with the Sharpe ratio as well as the CAPM model.
Investors can determine the risk-adjusted returns by assessing the excess returns earned over the risk-free rate.
A core principle of valuation theory is that investors should receive more compensation for the incremental risk of holding a risky asset, rather than a risk-free asset.
If not, the investor has made an irrational choice, as the same return could have been obtained without the added risk.
The steps to calculate the ratio are as follows:
- Step 1 → First, the formula starts by subtracting the risk-free rate from the portfolio return to isolate the excess return.
- Step 2 → Next, the excess return is divided by the portfolio’s standard deviation (i.e. the proxy for portfolio risk).
Sharpe Ratio Formula
If we put the steps from the prior section together, the formula for calculating the ratio is as follows:
Where:
- Rp = Expected Portfolio Return
- Rf = Risk-Free Rate
- σp = Standard Deviation of Portfolio (Risk)
What is a Good Sharpe Ratio?
Since the formula adjusts a portfolio’s historical or future performance for the excess risk taken on, a higher ratio is preferred when comparing across portfolios.
- Ratio < 1.0: Sub-Par Portfolio Return
- Ratio > 1.0: Acceptable Returns Given Risk
- Ratio > 2.0: Strong Portfolio Returns
- Ratio > 3.0+: Exceptional Risk-Adjusted Returns
Generally speaking, the Sharpe ratio is used to assess the risk/return of a portfolio, or an individual investment – however, most use it for a basket of investments (e.g. mutual funds).
More specifically, the Sharpe ratio helps when comparing performance among portfolios, especially when it comes to the selection of mutual funds.
Yet, in practice, the Sharpe ratio is most commonly referenced in academia and among everyday retail investors because of its relative simplicity and ease of calculation.
Learn More → Hedge Fund Quick Primer
What is the Difference Between Sharpe Ratio vs. Sortino Ratio?
The most frequent critique of the Sharpe ratio is how the standard deviation of the portfolio is used as the proxy for risk.
Certain academics and practitioners argue that this is an oversimplified assumption, since it implies portfolio returns fall on a normal distribution.
Hence, there are many variations that have emerged to account for portfolio risk in different ways, such as the Sortino ratio.
One example that emerged to address that risk component is referred to as the Sortino ratio, which uses downside deviation as the risk measure, as opposed to the standard deviation of the portfolio’s returns.
The Sortino ratio also uses the required rate of return instead of the risk-free rate, so the numerator consists of the portfolio return minus the required return.
Sharpe Ratio Calculator
We’ll now move to a modeling exercise, which you can access by filling out the form below.
Sharpe Ratio Calculation Example
Suppose a portfolio has an expected return of 10% and a standard deviation of 6%.
- Expected Portfolio Return (Rp) = 10%
- Risk-Free Rate (Rf) = 2.5%
- Standard Deviation of Portfolio (σp) = 6%
If the risk-free rate is currently at 2.5%, the Sharpe ratio equals 1.25x.
- Sharpe Ratio = (10% – 2.5%) / 6% = 1.25x
