Sharpe Ratio Formula

Formula of Sharpe Ratio (Table of Contents)

• What is Sharpe Ratio Formula?
• Examples of Sharpe Ratio Formula
• Sharpe Ratio Formula Calculator

What is Sharpe Ratio Formula?

Sharpe ratio is used to help the investor understand the return on investment compared to risk on it. The ratio is the average return earned in excess of the risk-free rate per unit volatility or total risk

The mathematical representation of the Sharpe Ratio Equation is as follows-

Where,

• R_p = Return of portfolio
• R_f  = Risk-free rate
• σp = Standard deviation of the portfolio’s excess return.

Explanation of Sharpe Ratio Formula

• The Sharpe ratio formula is calculated by dividing the difference of return of the portfolio and risk-free rate by Standard deviation of the portfolio’s excess return. Through this, we can evaluate the investment performance based on the risk-free return.
• Higher Sharpe metric is always better than a lower one because higher ratio indicates that the portfolio is making a better investment decision.
• The Sharpe ratio equation also helps to explain whether portfolio excess returns are due to a good investment decision or a result of too much risk. As higher the risk higher return, lower the risk lowers the return.
• If one of a portfolio has a higher return than that of its competitors then it’s a good investment as a return is high and risk is the same. It’s about maximizing returns and reducing volatility. If any investment has a rate of return 15% and volatility is zero. Then Sharpe ratio will be infinite. As volatility increases, the risk significantly goes up as a result rate of return also increases.

Let us see the grading threshold of the Sharpe ratio.

1. <1 – Not good
2. 1-1.99 – Ok
3. 2-2.99 – Really good
4. >3 – Exceptional

Portfolio with zero risks like only Treasury bill, as an investment is risk-free there is no volatility and no earnings in excess of the risk-free rate. Thus, the Sharpe ratio has zero portfolios.

• A metric 1, 2, 3 have a high rate of risk. If the metric is above or equal to 3 it is considered as great Sharpe measurement and a good investment.
• Whereas is metric of between greater or equal to 1 and 2 less than 2, it is considered to just ok and if a metric is between greater than or equal to 2 and less than 3 than it is considered that it is really good.
• If a metric is less than 1 then it is not considered as good.

Examples of Sharpe Ratio Formula

Let us see some examples to understand the Sharpe Ratio Equation.

Sharpe Ratio Equation – Example #1

Suppose, there are two mutual funds to compare with different portfolio having different risk level. Now let us see Sharpe ratio to see which one is better performing.

Investment of Mid Cap Fund and details are as follows:-

• Portfolio return = 35%
• Risk free rate = 15%
• Standard Deviation = 15

So the calculation of Sharpe Ratio will be as follows-

• Sharpe Ratio Equation = (35-10) / 15
• Sharpe Ratio = 1.33

Investment of Bluechip Fund and details are as follows:-

• Portfolio return = 30%
• Risk free rate = 10%
• Standard Deviation = 5

So the calculation of Sharpe Ratio will be as follows-

• Sharpe Ratio Formula = (30-10) / 5
• Sharpe Ratio Formula = 4

Therefore the Sharpe ratios of an above mutual fund are as below-

• Bluechip Fund = 4
• Mid Cap fund = 1.33

The bluechip mutual fund outperformed Mid cap mutual fund but it does not mean that Mid cap mutual fund performed well relative to its risk level. The Sharpe tell us below things:-

• Bluechip mutual fund performed better than Mid cap mutual fund relative to the risk involved in the investment.
• If Mid cap mutual fund performed as well as the Bluechip mutual fund relative to risk, it would earn a higher return.
• The bluechip mutual fund has earner higher return this year but as risk is high. Hence, it will have high volatility in the future.

Sharpe Ratio Formula – Example #2

Here, one investor is holding $5,00,000 invested portfolio with an expected rate of return of 12%, and volatility of 10%. The efficient portfolio expects a return above 17% and volatility of 12%. The risk-free interest is 4%. The calculation of the Sharpe ratio can be done as below:-

• Sharpe ratio formula= (0.12 – 0.04) / 0.10
• Sharpe ratio formula = 0.80

Sharpe Ratio Formula Calculator

You can use the following Sharpe Ratio Formula Calculator

 

Advantages of the Sharpe Ratio Formula

Advantages of the Sharpe ratio are as follows:-

• Sharpe ratio helps in comparisons of investment.
• Sharpe ratio helps in risk-return comparisons.

There are some issues while using Sharpe ratio formula that it is calculated in an assumption that investment returns are normally distributed and that is resulting in relevant interpretations of Sharpe ratio to be misguiding.

Sharpe Ratio Formula in Excel (with excel template)

Now let us take the case mentioned in Sharpe Ratio Formula Example #1 to illustrate the same in excel template below.

In below-given template is the data for the Mid Cap Mutual Funds and Bluechip Mutual Funds for the calculation of Sharpe ratio formula.

In the below given excel template, we have used the calculation of Sharpe ratio equation to find the Sharpe ratio.

So the calculation of Sharpe Ratio will be-

Recommended Articles:

This has been a guide to Sharpe Ratio Formula. Here we discuss Sharpe Ratio Equation, its uses, advantages along with practical examples and Calculator. You can learn more about Portfolio Management from the following articles –

• Explanation of Risk-Free Rate Formula
• Explanation of the Portfolio Return Formula
• Calculation of Volatility Formula
• Treynor Ratio Calculation
• Variance vs Standard Deviation Differences
• Stock vs Mutual Funds Differences
• How to make a career in Portfolio Management?