Sharpe Ratio Formula

Formula to Calculate Sharpe Ratio

Sharpe ratio formula is used by the investors in order to calculate the excess return over the risk-free return, per unit of the volatility of the portfolio and according to the formula risk-free rate of the return is subtracted from the expected portfolio return and the resultant is divided by the standard deviation of the portfolio.

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For eg:
Source: Sharpe Ratio Formula (wallstreetmojo.com)

Where,

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

How to Calculate Sharpe Ratio?

• The Sharpe ratio is calculated by dividing the difference of return of the portfolio and risk-free rateRisk-free RateA risk-free rate is the minimum rate of return expected on investment with zero risks by the investor. It is the government bonds of well-developed countries, either US treasury bonds or German government bonds. Although, it does not exist because every investment has a certain amount of risk.read more by the Standard deviation of the portfolio’s excess return. Through this, we can evaluate the investment performance based on the risk-free return.
• A Higher Sharpe metric is always better than a lower one because a higher ratio indicates that the portfolio is making a better investment decision.
• The Sharpe ratio 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 the 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 are zero. Then the 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 the Treasury billTreasury BillTreasury Bills or a T-Bill controls temporary liquidity fluctuations. The Central Bank is responsible for issuing the same on behalf of the government. It is given at its redemption price and a discounted rate and is repaid when it reaches maturity.read more, 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 a great Sharpe measurement and a good investment.
• Whereas it is a 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 three, than it is considered that it is really good.
• If a metric is less than one, then it is not considered as good.

Examples

Example #1

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

Investment of Mid Cap stockMid Cap StockMid-Cap stocks are the stocks of the companies having medium market capitalization. Their capital lies between that of large and small cap companies and valuation of the entire share holdings of these companies range between $2 billion to $8 billion.read more Fund and details are as follows:-

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

So the calculation of the 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 the Sharpe Ratio will be as follows-

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

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

• Bluechip Fund = 4
• Mid Cap fund = 1.33

The blue-chip 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:-

• The blue-chip 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 Blue-chip mutual fund relative to risk, it would earn a higher return.
• The blue-chip mutual fund has earner higher return this year, but as risk is high. Hence, it will have high volatility in the future.

Example #2

Here, one investor is holding a $5,00,000 invested portfolioInvested PortfolioPortfolio investments are investments made in a group of assets (equity, debt, mutual funds, derivatives or even bitcoins) instead of a single asset with the objective of earning returns that are proportional to the investor's risk profile.read more with an expected rate of return of 12% and a volatility of 10%. The efficient portfolio expects a return above 17% and a volatility of 12%. The risk-free interest is 4%. The calculation of the Sharpe ratio can be done as below:-

• Sharpe ratioSharpe RatioSharpe Ratio, also known as Sharpe Measure, is a financial metric used to describe the investors’ excess return for the additional volatility experienced to hold a risky asset. You can calculate it by, Sharpe Ratio = {(Average Investment Rate of Return – Risk-Free Rate)/Standard Deviation of Investment Return} read more = (0.12 – 0.04) / 0.10
• Sharpe ratio = 0.80

Sharpe Ratio Calculator

You can use the following Sharpe Ratio Calculator.

Advantages

Advantages of the Sharpe ratio are as follows:-

• The ratio is the average return earned in excess of the risk-free rate per unit volatility or total risk
• Sharpe ratio helps in comparisons of investment.
• Sharpe ratio helps in risk-return comparisons.

There are some issues while using the Sharpe ratio that it is calculated in an assumption that investment returns are normally distributedNormally DistributedNormal Distribution is a bell-shaped frequency distribution curve which helps describe all the possible values a random variable can take within a given range with most of the distribution area is in the middle and few are in the tails, at the extremes. This distribution has two key parameters: the mean (µ) and the standard deviation (σ) which plays a key role in assets return calculation and in risk management strategy.read more, and that is resulting in relevant interpretations of Sharpe ratio to be misguiding.

Sharpe Ratio Calculation in Excel

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

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

So the calculation of the Sharpe Ratio will be-

Recommended Articles:

This has been a guide to Sharpe Ratio Formula. Here we discuss how the investors use this formula to understand the return on investment compared to risk on it along with practical examples and Calculator. You can learn more about Portfolio Management from the following articles –

• Calculate Risk-Free Rate
• Calculate Treynor Ratio
• Stock vs Mutual Funds Differences
• How to make a career in Portfolio Management?