Sharpe Ratio

The Sharpe ratio is a mathematical formula that helps investors understand the risk and return of an investment. It's calculated by dividing the difference between an investment's return and the risk-free rate of return by the standard deviation of the investment's returns.
EXPLORE FUNDS
What Is Sharpe Ratio in Mutual Fund
EXPLORE FUNDS
3 min
16-July-2024

The Sharpe ratio of a mutual fund derives its name from Willian Sharpe, the American economist who worked on the concept in 1996. The Sharpe ratio in mutual fund is applied for analysing the performances of assorted securities. Understanding the Sharpe ratio is important for evaluating mutual funds’ performance. In this guide, we will explore the Sharpe ratio and the formula used to calculate it, provide step-by-step instructions on how to compute it and highlight key considerations to remember when using this metric. By the end, you will understand how the Sharpe ratio can help you make informed investment decisions.

What is the Sharpe ratio in mutual funds?

The Sharpe Ratio is a financial metric used to evaluate the risk-adjusted performance of an investment or portfolio. It measures the excess return per unit of risk, helping investors understand how well the return compensates for the risk taken. A higher Sharpe Ratio indicates better risk-adjusted performance.

Variable

Meaning

Return (R)

Expected return of the investment

Risk-Free Rate (Rf)

Return on a risk-free investment (e.g., Treasury bonds)

Standard Deviation (σ)

Measure of the investment’s volatility or risk

Sharpe Ratio (S)

(R - Rf) / σ, indicating risk-adjusted return


The Sharpe Ratio measures how much return a mutual fund generates compared to its risk. Here's what the numbers mean:

  • Above 1.0: This is considered acceptable to good by investors.
  • Above 2.0: This is considered very good.
  • Above 3.0: This is considered excellent.

A higher Sharpe Ratio means the mutual fund provides a better return for the amount of risk taken. So, a Sharpe Ratio between 1.00 and 1.99 indicates good risk-adjusted performance. This means the fund's returns are well-balanced with the risks involved.

In other words, the Sharpe ratio helps to work out any additional returns on a security above its benchmark return in proportion to the risks taken. The benchmark, basically, acts as a comparing standard that compares a security’s performance with that of its peers. For instance, an investment in a pharmaceutical stock has yielded a 12% annual return, whereas a Nifty Pharma has yielded 15%. This implies that the investment yielding 12% has failed to beat the benchmark.

Sharpe ratio formula

The Sharpe ratio of an investment can be calculated using the following formula:

Sharpe ratio formula = (R(p) - R(f))/SD

  • R(p) is the return on the investment for which you are calculating the Sharpe ratio. Please note that returns can be calculated for any period; however, it is always advisable to use a long-term period.
  • R(f) is the return of a risk-free investment (like a government bond or a fixed deposit in a bank).
  • SD is the standard deviation of the investment's returns. It measures how much the returns fluctuate over time. As a thumb rule, the higher the fluctuations, the higher the risk.
  • “R(p)—R(f)” is the part of the formula that shows how much extra return the investment gives compared to a risk-free investment. It is also called the "excess return".

How to calculate Sharpe ratio?

The basic calculation for the Sharpe ratio is done by subtracting the gain that is risk-free from the return on the investment, followed by the calculation of the extra gain. Subsequently, that extra return needs to be divided by the standard deviation.

The formula is as follows:

Sharpe ratio = (investment return – risk-free return rate)/standard deviation


The return on the investment may be monthly, weekly, or daily, and the return rate that is risk-free is gained from investments that are less risky like bonds. The higher the Sharpe ratio, the better it is.

Importance of Sharpe ratio

The Sharpe ratio is an effective way to measure the risk-adjusted performance of an investment (like a mutual fund or stock). Let’s see why it is a popular metric and used widely by investors and analysts:

Risk assessment

The Sharpe ratio helps you understand the risk involved in an investment. A higher Sharpe ratio means the investment has a better return compared to its risk. Essentially, it shows you how much extra return you get for the risk you are taking.

Funds comparison

It allows you to compare different mutual funds within the same category. By comparing the Sharpe Ratios, you can see which fund gives you better returns for the risk you are taking. This helps you choose the best fund based on your risk tolerance and financial goals.

Comparison with benchmark

You can compare a fund's Sharpe ratio with its benchmark's Sharpe ratio. For example, say you are analysing an ABC Small Cap Fund. Now, you can compare it to the XYZ SmallCap Index. This comparison helps you see if the fund has underperformed or overperformed the benchmark.

Portfolio diversification

The Sharpe ratio helps you see how risky your overall portfolio is. If you have invested in a fund with a high Sharpe ratio, it is always advisable to add another investment which is less risky and has a lower Sharpe ratio. This addition not only balances your portfolio but also reduces the overall risk and makes your overall returns more stable.

Example of how to use Sharpe ratio

The Sharpe ratio helps you understand which fund gives you the best return for the level of risk you are taking. It must be noted that higher Sharpe ratios indicate better risk-adjusted returns. Let's study a hypothetical example to understand the practical usage of the Sharpe ratio.

Below are four mutual funds with different historical returns and standard deviations:

  • Fund A: Historical return 18%, Standard deviation 9%
  • Fund B: Historical return 18%, Standard deviation 11%
  • Fund C: Historical return 28%, Standard deviation 14%
  • Fund D: Historical return 13%, Standard deviation 8%

The prevailing risk-free rate of investments is 5%. Now, let’s calculate the Sharpe ratio of all these funds using the formula:

Sharpe ratio formula = (R(p) - R(f))/SD

Fund A:

Sharpe ratio = (18% - 5%)/(9%) = 1.44

Fund B:

Sharpe ratio = (18% - 5%)/(11%) = 1.18

Fund C:

Sharpe ratio formula = (28% - 5%)/(14%) = 1.64

Fund D:

Sharpe ratio formula = (13% - 5%)/(8%) = 1.00

For more clarity, let’s summarise all the information in a table:

Parameter

Fund A

Fund B

Fund C

Returns (%)

18

18

28

SD (%)

9

11

14

Risk-free rate

5

5

5

Sharpe ratio

1.44

1.18

1.64


From the above example, we can observe that:

  • Fund A vs. Fund B:
    • Both Fund A and Fund B have the same return of 18%.
    • However, Fund B has a higher standard deviation (11%) compared to Fund A (9%).
    • This higher risk (or volatility) leads to a lower Sharpe ratio for Fund B (1.18) compared to Fund A (1.44).
  • Fund A vs. Fund C:
    • Fund C has a higher return (28%) than Fund A (18%).
    • But Fund C also has a higher standard deviation (14%) compared to Fund A (9%).
    • Despite the higher return, the increased risk results in a Sharpe ratio of 1.64 for Fund C, which is not too high than Fund A's 1.44.
  • It is worth noticing that Fund D has the lowest return (13%) and a standard deviation of 8%. Its Sharpe ratio is 1.00, which indicates that its return relative to its risk is the lowest compared to the other funds.

What is a good Sharpe Ratio?

A good Sharpe Ratio typically ranges from 1 to 3. A ratio of 1 indicates that the investment is offering a reasonable return relative to its risk. Ratios above 1.5 are considered good, suggesting that the investment provides high returns for the risk taken. A Sharpe Ratio greater than 2 is viewed as excellent, reflecting a strong risk-adjusted performance. Conversely, a ratio below 1 may imply that the investment does not adequately compensate for its risk, prompting investors to reconsider their options. Ultimately, the context and specific investment goals should guide the interpretation of the Sharpe Ratio.

How to read Sharpe Ratio?

Reading the Sharpe Ratio involves understanding its value in relation to risk and return. A ratio above 1 indicates acceptable performance, while above 1.5 suggests good risk-adjusted returns. A ratio above 2 is considered excellent. Conversely, a negative Sharpe Ratio signifies underperformance compared to a risk-free asset, indicating that the investment may not be worthwhile. Always consider the context of the investment when interpreting the ratio.

Impact of standard deviation on Sharpe ratio

One must acknowledge that even if two funds have the same returns, the one with the lower standard deviation (less risk) will have a higher Sharpe ratio, which is indicative of a better risk-adjusted performance. Higher returns with significantly higher risks do not always result in a better Sharpe Ratio.

Let’s study a hypothetical example and understand how the standard deviation impacts the Sharpe Ratio.

  • Fund A: Historical return 25%, Standard deviation 10%
  • Fund B: Historical return 25%, Standard deviation 14%
  • Fund C: Historical return 35%, Standard deviation 16%
  • Fund D: Historical return 18%, Standard deviation 10%
  • Assume the current risk-free rate to be 5%.

Fund

Returns (%)

Standard deviation (%)

Risk-free rate (%)

Sharpe ratio

Fund A

25

10

5

2

Fund B

25

14

5

1.43

Fund C

35

16

5

1.88

Fund D

18

10

5

1.30


From the above example, we can observe that:

  • Fund A vs. Fund B
    • Both Fund A and Fund B have the same return of 25%.
    • However, Fund B has a higher standard deviation (14%) compared to Fund A (10%).
    • This means Fund B is riskier.
    • As a result, the Sharpe ratio of Fund B (1.43) is lower than Fund A's (2.00).
    • This shows that, despite the same return, Fund A offers better returns relative to its risks.
  • Fund A vs. Fund C
    • Fund C has a higher return (35%) than Fund A (25%).
    • However, Fund C also has a higher standard deviation (16%) compared to Fund A (10%).
    • Despite the higher return, the increased risk results in a Sharpe ratio of 1.88 for Fund C, which is slightly lower than Fund A's 2.00.
    • This indicates that Fund A provides a better risk-adjusted return compared to Fund C.
  • Fund D
    • Fund D has the lowest return (18%) and the same standard deviation as Fund A (10%).
    • Its Sharpe ratio is 1.30, which shows that its return relative to its risk is lower than that of Fund A.

Sharpe ratio and standard deviation of different mutual fund categories

The table below displays the Sharpe ratios for various mutual fund categories. Also, it highlights the funds with the highest Sharpe ratios in each category.

Mid-cap funds

SD (%23.83)

PGIM India Midcap Opportunities Fund

24.96

Quant Mid-cap Fund

23.83

SBI Magnum Midcap Fund

25.49

Axis Midcap Fund

19.54

Motilal Oswal Midcap 30 Fund

24.66

UTI Mid Cap Fund

23.30

Large-cap funds

SD (%)

Quant Focused Fund

21.84

Canara Robeco Bluechip Equity Fund

19.10

IDBI India Top 100 Equity Fund

19.80

JM Large Cap Fund

12.33

Baroda BNP Paribas Large Cap Fund

18.41

Kotak Bluechip Fund

20.94

Small-cap funds

SD (%)

Bank of India Small Cap Fund

25.17

Canara Robeco Small Cap Fund

26.11

Quant Small cap Fund

32.72

Kotak Small-cap Fund

27.74

Union Small-cap Fund

25.33


In the above table, you can see that small-cap funds have a higher Sharpe ratio. This means they have good risk-adjusted returns. However, these funds also have a higher standard deviation, which shows that they are more volatile and the returns generated by them experience rapid fluctuations.

Furthermore, you must consider the Sharpe ratio and the standard deviation together while making investment decisions. This combined usage will help you better understand the volatility with which the fund has generated returns for its investors.

Limitations of Sharpe ratio

One major limitation of the Sharpe ratio is that it relies on the standard deviation to measure risk. Numerous studies have shown that a higher SD usually brings down the Sharpe ratio. However, it must be acknowledged that standard deviation considers all types of returns generated by the fund, i.e., both negative and positive deviations from the average return.

This means that even if a fund has higher positive returns, these can still increase the standard deviation. As a result, the Sharpe Ratio might decrease, making the fund appear riskier than it actually is. This limitation causes the Sharpe ratio to sometimes misrepresent the true risk by not distinguishing between favourable and unfavourable fluctuations in returns.

Things to keep in mind while using the Sharpe Ratio

  • A Sharpe ratio, however, can also be inaccurate sometimes because the investment returns are distributed unequally. However, it works better for long-term portfolio evaluation.
  • Using the Sharpe ratio can lead to wrong results over the short term if there are any immediate price movements.
  • The ratio may not be useful if used to evaluate an isolated sector since it makes sense to compare it with its benchmark.
  • Investors may use the ratio along with other basic ratios for evaluating a security’s past returns. As technical or fundamental analysis is based on past performances, it may guarantee future returns also.
  • Fund managers may manipulate the ratio by falsely altering the time frame.

If you are an investor and want to start your investment journey, you may visit the Bajaj Finserv Mutual Fund platform to learn more about mutual funds and SIPs. Feel free to make use of their Lumpsum calculator and SIP calculator to calculate your financial goals better.

Key takeaways

  • To calculate Sharpe ratio, one needs historical data. However, it cannot guarantee returns in future.
  • The Sharpe ratio is applied to measure risk-adjusted returns.
  • The ratio indicates the volume of extra returns one gets by exposure to extra risk.
  • Fund comparison: The Sharpe ratio is usable for evaluating and comparing mutual funds. It also helps in gauging the level of risk and a mutual fund’s return rate. Hence the Sharpe ratio of a mutual fund helps in analysing its performance both in terms of returns and growth.
  • Understanding risk levels: Using a Sharpe ratio in mutual fund helps understand the risks that come with it. A low ratio indicates that the investment needs to be transferred.
  • Evaluation of risk and return rate: A high Sharpe ratio of a mutual fund is always better than a low one as investors will most likely earn higher returns.

Conclusion

The Sharpe ratio has several limitations. Besides being dependent on the standard deviation for measuring risk, it can also be manipulated by the portfolio managers. Usually, they extend the time period used to measure it. This manipulation makes the risk-adjusted returns of an investment look better. Therefore, relying solely on the Sharpe ratio to evaluate a mutual fund isn't a good strategy because it provides limited information.

Furthermore, in India, there are many mutual funds operating at different scales. This makes it challenging to choose the right scheme, especially for beginners or those with little market knowledge. These individuals can use the Sharpe Ratio to help evaluate and compare mutual funds. The Sharpe ratios of various Indian mutual funds are readily available online.

However, while the Sharpe ratio is a useful evaluation tool, it shouldn't be the only factor considered. Other metrics and tools should also be used for a comprehensive analysis to fully understand a mutual fund's performance.

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Frequently asked questions

What is a good Sharpe ratio?

A good Sharpe ratio is that which is above 1, and indicates that the return on the investment is higher than the volatility of the risk-free rate per unit, which suggests a more favourable return that is risk-adjusted. However, a good Sharpe ratio may vary on factors like investment strategies, market conditions, and risk tolerance.

What does a Sharpe ratio of 0.5 mean?

A 0.5 Sharpe ratio indicates that the return on the investment, which is risk-adjusted, is half the size of the risk-free rate per unit of volatility. In simpler terms, for every single unit of risk or volatility taken, the investment will most likely return half of what could be earnable from an investment that is risk-free, like government bonds.

What if Sharpe ratio is high?

A higher ratio indicates that the investment has yielded superior returns that are risk-adjusted as compared to an investment that is risk-free.

Is 7 a good Sharpe ratio?

A 7 Sharpe ratio can be said to be exceptionally high and is considered outstanding by a majority of financial professionals and investors. The ratio proves that the investment’s returns have been significantly higher when compared to the risks taken, and which far exceeds most investment scenarios.

How to calculate Sharpe ratio?

The basic calculation for the Sharpe ratio is done by subtracting the gain that is risk free from the return on the investment, followed by calculation of the extra gain. Subsequently, that extra return needs to be divided by the standard deviation.

What if Sharpe ratio is 0?

A 0 Sharpe ratio suggests that the investment’s returns are equal to the risk-free rate of return per unit of volatility.

Is Sharpe ratio 8 good?

Yes, it is considered to be outstanding by all financial professionals and investors. The 8 Sharpe ratio shows that investment is generating risk-adjusted returns that are significantly higher when compared with the risk-free return rate per volatility unit.

Can a Sharpe ratio be negative?

Yes, it can be negative and indicates that the given investment has generated returns lower than the risk-free return rate per volatility unit.

What is the difference between Sharpe ratio and Treynor ratio?
The Sharpe ratio considers the standard deviation or total risk; the Treynor ratio takes into account only beta or systematic risk. Hence, the Treynor ratio is considered more suitable to evaluate portfolios more sensitive to movements in the market. The Sharpe ratio on the other hand, is more general and is applicable to a wider investment range.
Why is a higher Sharpe ratio better?

The Sharpe ratio is commonly used to evaluate how well a particular stock performs relative to its risk. It can also compare two funds with the same risk or returns. The information gained helps investors understand which offers better compensation for the risk taken. A higher Sharpe ratio indicates that an investment provides greater returns for the level of risk involved.

Is a negative Sharpe ratio bad?

Generally, a higher Sharpe ratio of your portfolio indicates better risk-adjusted performance. This means your portfolio provides more returns relative to the level of risk taken. Conversely, a negative Sharpe ratio indicates poor performance. It shows that the investment returns are lower than the risk-free rate, which is usually not considered favourable by investors.

What is a zero Sharpe ratio?

The Sharpe ratio measures the performance of an investment compared to a risk-free asset after adjusting for its risk. A zero Sharpe ratio means that the investment's returns are exactly equal to the returns of a risk-free asset, like government bonds or treasury bills. Such a situation indicates that the investment has not provided any extra return for the risk taken.

What is the 3-year Sharpe ratio?

The 3-Year Sharpe ratio evaluates the risk-adjusted performance of an investment over a period of 3 years. It is calculated by taking the investment's average monthly returns and subtracting the average monthly return of a risk-free asset (government bonds and treasury bills) to find the excess returns.

These excess returns are then divided by the standard deviation of the investment's monthly returns. It must be noted that a higher 3-year Sharpe ratio indicates better returns for the level of risk taken during this period.

What is the monthly Sharpe ratio?

The monthly Sharpe ratio measures an investment's risk-adjusted performance on a monthly basis. It's calculated by taking the average monthly excess return (returns above a risk-free asset) and dividing it by the monthly standard deviation of these excess returns. This shows how much return is earned per unit of risk each month.

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The information contained in this article is for general informational purposes only and does not constitute any financial advice. The content herein has been prepared by BFL on the basis of publicly available information, internal sources and other third-party sources believed to be reliable. However, BFL cannot guarantee the accuracy of such information, assure its completeness, or warrant such information will not be changed. 

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