Formula to Calculate Sharpe Ratio

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Where,

  • Rp = Return of portfolioRf  = Risk-free rateσp = Standard deviation of the portfolioStandard Deviation Of The PortfolioPortfolio standard deviation refers to the portfolio volatility calculated based on three essential factors: the standard deviation of each of the assets present in the total portfolio, the respective weight of that individual asset, and the correlation between each pair of assets of the portfolio.read more’s excess return.

How to Calculate Sharpe Ratio?

  • The Sharpe ratio is calculated by dividing the difference in 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. 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 the higher the risk higher the return, and the lower the risk lowers the return.If one portfolio has a higher return than its competitors, it’s a good investment as the return is high, and the risk is the same. It’s about maximizing returns and reducing volatility. Any investment has a return rate of 15% and zero volatility. Then the Sharpe ratio will be infinite. As volatility increases, the risk increases significantly; as a result, the rate of return also increases.

Let us see the grading threshold of the Sharpe ratio.

  • <1 – Not good1-1.99 – Ok2-2.99 – Really good>3 – Exceptional

A portfolio with zero risks, like only the Treasury billTreasury BillTreasury Bills (T-Bills) are investment vehicles that allow investors to lend money to the government.read more, as an investment is risk-free; there is no volatility and no earnings over the risk-free rate. Thus, the Sharpe ratio has zero portfolios.

  • Metrics 1, 2, and 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 just ok, and if a metric is between greater than or equal to 2 and less than three, then it is considered that it is really good.If a metric is less than one, it is not considered 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 performs better.

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) / 15Sharpe Ratio = 1.33

Investment of Bluechip Fund and details are as follows:-

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

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

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

  • Bluechip Fund = 4Mid Cap fund = 1.33

The blue-chip mutual fund outperformed Mid cap mutual fund, but it does not mean it performed well relative to its risk level. Sharpe tells us below things:-

  • The blue-chip mutual fund performed better than Mid cap mutual fund relative to the risk involved in the investment.If the 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 earned a higher return this year, but as risk is high. Hence, it will have high volatility in the future.

Example #2

Here, one investor holds 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) / 0.10Sharpe ratio = 0.80

Sharpe Ratio Calculator

You can use the following Sharpe Ratio Calculator.

Advantages

The advantages of the Sharpe ratio are as follows:-

  • The ratio is the average return earned more than the risk-free rate per unit volatility or total riskSharpe 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, which results in relevant interpretations of the Sharpe ratio being misleading.

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-

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 its risk, along with practical examples and a Calculator. You can learn more about Portfolio Management from the following articles –

  • Calculate Risk-Free RateCalculate Risk-Free RateA risk-free rate of return formula calculates the interest rate that investors expect to earn on investment with zero risks, especially default and reinvestment risks. It is usually closer to the base rate of a central bank and may differ for different investors.read moreCalculate Treynor RatioCalculate Treynor RatioThe Treynor ratio is similar to the Sharpe ratio and it calculates excess return over risk-free return per unit of portfolio volatility using beta rather than standard deviation as a risk measure. As a result, it gives the excess return over the risk-free rate of return per unit of the beta of the investor’s overall portfolio.read moreStock vs Mutual Funds DifferencesHow to make a career in Portfolio Management?How To Make A Career In Portfolio Management?A career in portfolio management is full of challenging opportunities, from creating clients’ investment portfolios to managing their investments, wealth, and funds. To become a portfolio manager, you should complete graduation in finance, economics, or business, have a CFA or FRM certificate, and hold a FINRA license.read more