Sharpe Ratio Calculator

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 was developed by William F. Sharpe and is used to help investors understand the return of an investment compared to its risk.

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.

The Sharpe ratio is a good way to compare investments with different levels of risk because it adjusts for the extra risk that is taken on when investing in a higher risk investment. For example, if two investments have the same return but one has twice the volatility, the one with less volatility will have a higher Sharpe ratio.

The Sharpe ratio can be used for any type of investment, including stocks, bonds, mutual funds, and ETFs. It is especially useful for comparing different types of investments or different strategies within the same asset class.

Sharpe Ratio formula

The Sharpe Ratio formula is:

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

When interpreting the Sharpe ratio, it is important to keep in mind that a higher Sharpe ratio does not necessarily mean that an investment is better. A higher Sharpe ratio simply means that the returns are higher relative to the risks taken.

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.

Investors should also be aware that there are some limitations to using the Sharpe ratio. First, it assumes that all investments are held for a year and does not account for taxes or transaction costs. Second, it assumes that investors are rational and have access to all information about an investment before making a decision. Finally, it assumes that markets are efficient and prices reflect all available information about an asset