# Sharpe Ratio

The Sharpe ratio measures an investment’s risk-adjusted returns within a certain period, and it was originally developed by the American economist, William F. Sharpe.

In it, the number is useful to investors who want to gain valuable insight into their investments’ risk-adjusted returns. Or, simply the return on their investments compared to the risk they accompany.

Investors commonly use this ratio for comparison purposes. It looks at risk-adjusted returns of mutual funds, exchange-traded funds (ETF), stocks and other investments.

In calculating the Sharpe ratio, analysts typically use the rate for T-bills or cash. The 90-day T-Bill rate is a particular favorite in representing the risk-free rate. Investors may rely on the ratio to determine how much they are likely to earn against the investment’s risk.

Investors must be compensated for the risks they face, outside holding risk-free assets. The investment’s average rate of return is equal to the average rate for the stocks, ETFs and other types of individual security, or the portfolio assessed. This should be within the specific time frame.

When calculating a fund’s Sharpe Ratio, the risk-free asset’s return must first be taken from the fund’s returns within the period under study. You can then divide the difference by the standard deviation of the investment. When looking at an investment’s risk-adjusted return, the Sharpe Ratio makes use of that investment’s standard deviation. This is the investment return’s variability in relation to its mean return for a specific time frame. A high standard deviation indicates that the investment’s returns are widely variable in reference to  average return.

## Sharpe Ratio Formula

$$Sharpe\: Ratio = \dfrac{R_{p} - R_{f}}{σ_{p}}$$

• Rp = the portfolio return
• Rf = risk-free rate
• σp = standard deviation of the portfolio’s return

The formula might look a bit too complex for those who don’t know much about financial calculations. But the idea is quite basic. You can remove the risk-free rate of return from the mean return in order to separate the return for the risk level.

Investors can then assess performance based on the risk-free return. Essentially, the Sharpe Ratio equation adjusts portfolios based on risk while leveling the playing field so that fair and valid comparisons can be made.

Bad ratios are those below 1; acceptable ratios range from 1 to 1.99; ratios 2 to 2.99 are considered really good. Those 3 and higher are considered outstanding. Some portfolios may come with higher risk yet have a ratio of 1, 2, or 3. With all conditions staying the same, Sharpe Ratios 3 and up are considered exceptional. Ratios from 1 to 3 indicate how much excess return is earned from a risky investment versus an investment with zero risk. Somehow, it reveals the level of compensation received for the excess risk carried by the investment.

Another problem with the Sharpe Ratio is that it depends on standard deviation, which is based on the normal distribution curve. This distribution doesn’t cover certain strategies, despite being seen in many investments. For example, this is the case with large, but long-delayed, payoffs with practically zero returns. Skewed distributions with unusual events can lead to higher Sharpe ratios that fail to capture the entire picture of the investment’s volatility. An example of this would be selling deep out-of-the-money options. In these scenarios, the result would be an inaccurate and misleading Sharpe Ratio.

## Sharpe Ratio Example

Eli invested in a stock portfolio which he expects would return 18% within a year’s time. The risk-free returns are 7%, and his portfolio has a 0.09 standard deviation. Knowing this, what is the Sharpe Ratio for Eli’s portfolio?

Let’s break it down to identify the meaning and value of the different variables in this problem.

• Portfolio return: 18%
• Risk-free rate: 7%
• Portfolio standard deviation: 9%

We can apply the values to our variables and calculate the Sharpe Ratio:

$$Sharpe\: Ratio = \dfrac{0.18 - 0.07}{0.09} = 1.22$$

In this case, Eli’s stock portfolio would have a Sharpe Ratio of 1.22.

It means Eli’s portfolio carries 1.22 “units” of risk with each point of return it makes. His portfolio has a return of 18%. And there is another portfolio with the same return but a Sharp Ratio of 1.3. So, Eli’s portfolio is better since it is able to earn the same return with less risk.

## Sharpe Ratio Analysis

Generally speaking, the higher the Sharpe ratio, the better. This is because it shows that sounder investment decisions are being made despite the associated risk. For instance, Treasury bills are considered risk-free investments, both volatility and earnings outside the risk-free rate are zero. This gives the portfolio a Sharpe Ratio of zero.

Just like other financial metrics, the Sharpe Ratio has its own share of limitations. For example, some complain that the calculation is too vulnerable. It can be easily misinterpreted, causing data to become misleading. Two options to the Sharpe model are the Sortino ratio and the Treynor ratio.

The Sortino Ratio is an enhanced version of the Sharpe Ratio. Specifically, only returns that fail to reach the target or required rate of return, or “downside volatility,” are punished. Conversely, the Sharpe method equally penalizes upside and downside volatility. Also, the Treynor Ratio measures returns outside of what an investment with zero risk could have made for each risk unit taken.

Interestingly, the Sharpe Ratio has varied uses. For one, investors usually trust the equation when assessing their level of comfort with a specific investment. For instance, they may think the return isn’t high enough for a specific volatility level. This makes the investment a bad one, and the investor can begin exploring other options with a higher Sharpe Ratio.

## Sharpe Ratio Conclusion

• The Sharpe Ratio measures an investment asset’s risk-adjusted return.
• This formula requires three variables: portfolio return, Risk-free return, and the standard deviation of the portfolio.
• You can express the ratio as a plain numerical value.
• This tool adjusts a portfolio’s past or predicted performance for the additional risk faced by the investor.
• A portfolio with a lower ratio is better than a similar portfolio with the same return but a higher ratio.
• The Sharpe Ratio assumes a normal distribution of investment returns.

## ​Sharpe Ratio Calculator

You can use the Sharpe Ratio calculator below to quickly measure your investment’s risk-adjusted returns over a specific period by entering the required numbers.