# Sharpe Ratio: Meaning, Formula, Importance and Calculation

If we were to tell you that a mutual fund scheme gave 12% annualised returns (hypothetically), you might be tempted to invest in it for want of high growth of your invested money. This factor, the return garnered from the scheme, though a valid one, must not be the only factor behind deciding your investment. You must consider the risk too. Every investment has a degree of risk associated with it. In fact, it is often a higher risk that has the potential to produce a high return. But is the risk in your investment worth the returns? Or, in other words, how much return are you getting for every unit of risk that you undertake? One of the ways to assess this factor i.e. the return per unit of risk undertaken is called the Sharpe Ratio.

## What is Sharpe Ratio?

Sharpe ratio is a widely recognised and essential metric developed by Nobel laureate William F. Sharpe in 1966, hence the name. It helps assess the risk-adjusted performance of an investment and evaluates whether the returns generated by an investment are commensurate with the level of risk taken.

Here’s how you can interpret the Sharpe ratio meaning to make informed investment decisions:

• A higher Sharpe ratio indicates that an investment or portfolio has generated more returns for each unit of risk taken. In other words, a higher Sharpe ratio suggests better risk-adjusted performance. • A positive Sharpe ratio means the investment has generated returns above the risk-free rate. On the other hand, a negative ratio suggests returns below the risk-free rate and may also indicate that an investment isn't compensating investors for the level of risk they are exposed to. • The ratio is also valuable for comparative analysis of different investments or portfolios. It allows investors to assess which option may provide the best risk-adjusted return.

## Understanding Sharpe Ratio

Now, this extra risk is calculated with respect to the risk associated with that mutual fund scheme. For the calculation of Sharpe Ratio, this risk is determined and represented by the standard deviation. standard deviation (SD) attempts to calculate the extent to which a scheme’s returns may fluctuate and compares that with the historical return of the scheme. For example, if a scheme has an SD of 7% and a historical return of 12% (hypothetically speaking), then the scheme’s return could possibly range from 5% to 21%.

With this information, let us now derive at the calculation of Sharpe Ratio-

Sharpe Ratio= (Average return from the scheme-Risk-free return)/Standard Deviation of the scheme

As an example, let us calculate the Sharpe Ratio of a scheme with an average return of 12%. Assuming the risk-free return to be 5% and the SD to be 5%, the Sharpe Ratio becomes (12%-5%)/5%= 1.4. Thus, for every unit of risk undertaken, this scheme produces an extra 1.4% return every year. Obviously, a higher SR may be in your favour as it represents higher returns per unit of risk taken. But what if the SR is higher because the scheme has a lower SD and not because the returns are actually better? Hence, SR should always be looked at, in conjunction with SD. For example, a scheme with a higher SD may have to maintain higher returns to maintain a high SR, and similarly, the one with a lower SD can do so with moderate returns as well.

Now, the standalone figure of 1.4 may not mean anything to you when trying to gauge performance. For it to make sense, you will always need to compare the Sharpe Ratios of similar mutual fund schemes and understand which one is giving you a possibility of better returns with an optimal risk.

In Summary-

Measure | Importance |

Sharpe Ratio | Lower SD, Higher SR: Relatively lower risk Higher SD, Lower SR: Relatively higher risk |

## Sharpe Ratio Formula

Sharpe ratio has a relatively simple formula that packs a powerful punch to help you assess the risk-adjusted performance of mutual fund investments. To calculate this ratio, you need three key components:

### • Average return of the investment - R(p)

This is the average rate of return generated by the investment over a specific period.

### • Risk-free rate of return - R(f)

The risk-free rate represents the return you could earn with no risk, typically approximated using the 365-days treasury bill return having a similar time horizon to your investment.

### • Standard deviation of returns (SD)

This measures the volatility or risk of the investment. It tells you how much the returns of the investment deviate from their average.

The formula for the Sharpe Ratio is as follows:

Sharpe Ratio (SR) = {R(p)- R(f)} / SD

## Calculation of Sharpe Ratio

Now, let's break down each component with an example to illustrate how to calculate the Sharpe ratio.

Suppose you are evaluating the performance of a mutual fund scheme as per the following information:

• Average return of the mutual fund -
**R(p)**: 15%

• Risk-free rate -
**R(f)**: 6%

• Standard deviation -
**SD**: 9%

By plugging these values into the Sharpe Ratio formula, you will get:

**Sharpe ratio = 1.00**

Here’s what it means:

• A Sharpe ratio in mutual funds greater than 0 indicates that the investment has generated positive returns above the risk-free rate. In this case, the mutual fund has provided a return of 1.00% above what could have been earned from a risk-free investment.

• This suggests that the mutual fund's return adequately compensates investors for its risk level. Hence, it can be considered a balanced risk-return profile.

• A Sharpe ratio falling within the range of 1.00 to 1.99 is generally considered a sign of good risk-adjusted performance. It indicates that the investment has done well in managing risk while delivering returns.

While the Sharpe ratio in mutual funds helps assess the risk-adjusted performance of mutual funds, it should not be viewed in isolation. To gain a more comprehensive view of a mutual fund's performance, you can consider supplementing the Sharpe ratio with other performance metrics such as the Sortino ratio (which focuses on downside risk), alpha (which measures a fund's excess return relative to a benchmark), and beta (which indicates a fund's sensitivity to market movements).

Additional Read: What is Sortino Ratio?

## Importance of Sharpe Ratio

Sharpe ratio offers several significant advantages making it an essential tool for professional investors and individual traders.

### 1. Risk-adjusted performance assessment

The primary purpose of the Sharpe ratio calculation is to evaluate an investment's performance in relation to the risk taken. It may provide a clear, concise measure of how well an investment has rewarded investors for the level of risk they assumed. This can be particularly crucial for Indian investors who face challenges related to varying asset classes and market conditions.

### 2. Comparative analysis

This ratio is invaluable for comparing the risk-adjusted performance of different investments or portfolios. By considering this ratio, you can make informed choices about where to allocate your capital.

### 3. Objective decision-making

Sharpe ratio meaning also provides an objective, quantifiable basis for mutual fund investment decisions. It can help remove emotional bias from the evaluation process and enables investors to focus on data-driven assessments. This can eventually help them avoid potentially impulsive or ill-informed choices.

### 4. Benchmark comparison

One of the key aspects of using Sharpe ratio effectively in evaluating mutual funds is its comparison with a relevant benchmark. A benchmark represents a standard against which one can measure the performance of a mutual fund. It typically reflects the broader market or a specific asset class.

Comparing the Sharpe ratio of a mutual fund scheme to that of its benchmark provides insight into whether the fund is outperforming or underperforming the market or asset class it aims to track. It aims to answer the fundamental question -
**‘Is the fund worth the investment?’**

## Limitations of Sharpe Ratio

Sharpe ratio is not without its limitations, one of which is its reliance on standard deviation (SD) as a measure of risk. Standard deviation measures the volatility or dispersion of returns around the average or mean. While this is a valuable indicator of risk, it has some inherent drawbacks.

Standard deviation takes into account all types of returns of the fund, including both negative and positive deviations from the mean. This means that even if the positive deviations (gains) are substantially higher than the negative deviations (losses), a high standard deviation may still be recorded. Hence, the ratio may portray the fund as riskier than it actually is. Investors could be misled into believing that the fund carries a higher level of risk when, in reality, it may have a strong track record of generating positive returns.

## Things to keep in mind

Always use SR as a comparison tool and use it to compare mutual fund schemes of the same category and similar investment objectives.

You will find different values of SR for the same mutual fund scheme from different sources. When comparing, choose one reliable source and get your data from that source only.

Look at the SR in tandem with the SD, and not alone.

You can check the SR against the benchmark performance, to see whether it is underperforming or overperforming against the benchmark.

It does not give you an idea about the kind of portfolio that works.

When choosing mutual fund schemes, SR can help you make a better choice. You can get in touch with your Mutual Fund Distributor if you do not understand any aspect of the comparisons of SRs for different schemes.

## Conclusion

Sharpe ratio does serve as a valuable compass in navigating the complex aspects of risk and return. While it provides crucial insights, it needs to be used judiciously in conjunction with other metrics, considering the full context of a scheme’s performance and objectives.

Additional Read: What is PEG Ratio?