DashCalculator

Sharpe Ratio Calculator

Calculate the Sharpe Ratio of a portfolio.
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Sharpe Ratio
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Using this calculator

Using beta to calculate the expected return of the portfolio

If you want to estimate the expected return on the portfolio based on the beta, use the CAPM Calculator. The CAPM calculator will tell you the expected return of the portfolio, which you can input above.

Risk-free rate

The risk-free rate is usually the rate of a government bond, such as a 30-year Treasury Bill.

Expected return of the market

You can compare the expected return of the portfolio against common market benchmarks like the S&P 500, Dow Jones, and Russell 2000.

BenchmarkHistorical returnTime period of return
S&P 5007.96%1957 to 2018
S&P 5005.90%1999 to 2019
Dow Jones Industrial Average5.42%1896 to 2018
Russell 20007.70%1999 to 2019
MSCI EAFE4.00%1999 to 2019

What is the Sharpe Ratio?

The Sharpe Ratio is an investing metric used to evaluate the performance of a portfolio, after adjusting for its riskiness. It is a reward-to-risk ratio.

It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment returns. It represents the additional amount of return that an investor receives per unit of increase in risk.

Sharpe Ratio formula

The Sharpe Ratio formula is:

Sharpe Ratio=Expected portfolio return - risk free rateStandard deviation of the portfolio\textrm{Sharpe Ratio} = \frac{\textrm{Expected portfolio return - risk free rate}}{\textrm{Standard deviation of the portfolio}}

Let's breakdown the formula. We will look at the numerator first.

  1. The higher the expected portfolio return, the higher the Sharpe Ratio.
  2. The lower the expected portfolio return, the lower the Sharpe Ratio.
  3. When the risk free rate is high, the Sharpe Ratio is lower.
  4. When the risk free rate is low, the Sharpe Ratio is higher.

The numerator represents the excess return of the portfolio. Excess means above the risk-free rate, which is usually the rate of a government bond, like the 30-year Treasury bill.

The Sharpe Ratio increases when the excess return of the portfolio increases.

Now, let's look at the denominator, which is the standard deviation of the portfolio. A higher standard deviation represents a more risky portfolio, and therefore, reduces the Sharpe Ratio. Conversely, a lower standard deviation represents a less risky portfolio, and thus, increases the Sharpe Ratio.

The Sharpe Ratio is highest when the expected portfolio is higher and the portfolio standard deviation is low.

Interpreting the Sharpe Ratio

Sharpe Ratio rangeInterpretation
< 1.0Subpar portfolio return
> 1.0Acceptable returns given risk
> 2.0Strong portfolio returns
> 3.0Exceptional risk-adjusted returns

Criticism of the Sharpe Ratio

The Sharpe Ratio measures risk by using the standard deviation of the portfolio, which assumes a normal distribution of risk. However, financial assets are often not normally distributed. For example, Ponzi schemes will have a highe Sharpe Ratio until they collapse. The Sharpe Ratio does not properly capture assets with a black swan risk. Black swans are unpredictable events with potentially catastrophic consequences.