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Sharpe ratio explained : Definition, formula, and examples

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Published Date: 29 Oct 2024Updated Date: 29 Oct 20246 mins readBy MOFSL

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Introduction

When you analyse investments, the most attractive aspect is mostly higher returns. If a financial instrument offers favourable gains, you will likely add it to your portfolio. While considering returns is crucial, it's one of the many factors and not the only one. Often, high returns are backed by a higher risk. You want to consider if the risk you take is worth the returns. This is where the Sharpe ratio comes into the picture. It evaluates an investment's performance based on the risk-adjusted return. Read along to learn more about what it entails.

What is the Sharpe ratio?

The Sharpe ratio is a measure that helps you understand whether an investment's returns compensate for the risk you take on. Named after and developed by Nobel laureate William F. Sharpe in 1966, this ratio is widely used to compare the risk-adjusted return of various assets or portfolios.

With a Sharpe ratio, you can quantify how much excess return you earn for the extra risk you are taking by investing in volatile assets compared to risk-free assets like government bonds. A higher Sharpe ratio indicates better risk-adjusted performance. On the other hand, a low or negative ratio could signal that the risks are not justified by the returns.

Sharpe ratio formula

The formula for calculating the Sharpe ratio is as follows:

SR = (R(p) – R(f))/SD

Here, SR stands for the Sharpe ratio

· R (p) indicates the fund's historic return. The return you calculate can be for any period. However, it is advisable to consider a long period.

· R (f) represents the risk-free return. You can take a risk-free investment for this like a government bond or a fixed deposit in a bank.

· SD refers to the standard deviation of the investment's returns. It measures how much the returns tend to deviate over time. Higher fluctuations mean higher risk.

· R(p) – R(f) in the shape formula shows how much extra return you can get on an investment as compared to a risk-free investment. This is termed as "excess return".

Example of using the Sharpe ratio

With a Sharpe ratio, you understand which fund gives you the best return for the level of risk you undertake. Higher Sharpe ratios are assigned to better risk-adjusted returns and vice versa. Here's an example of using it to understand and compare risk-adjusted returns on two funds.

· Fund no. 1: Historical return 18% and a standard deviation of 9%

· Fund no. 2: Historical return 18% and a standard deviation of 11%

Let's say the prevailing risk-free rate of safe investments is 5%. Now, the calculation of the Sharpe ratio would go as follows:

· Fund no. 1: Sharpe ratio = (18% - 5%)/ 9% = 1.44

· Fund no. 2: Sharpe ratio = (18% - 5%) / 11% = 1.18

Based on this example, you will notice both Fund No. 1 and Fund No. 2 have similar returns = 18%. However, Fund no. 2 has a higher standard deviation of 11% than Fund no. 1 with 9%. This increases risk or volatility and lowers the Sharpe ratio for Fund no. 2 (1.18) compared to Fund no. (1.44).

Effect of standard deviation on Sharpe ratio

As noticed in the above example, the standard deviation is a critical component in calculating the Sharpe ratio. The standard deviation is used as a proxy for risk in the formula. A higher standard deviation makes the asset riskier and consequently leads to a lower Sharpe ratio and vice versa. Hence, two portfolios with identical returns but different levels of volatility or standard deviation will have vastly different Sharpe ratios.

Advantages of using the Sharpe ratio

Some of the core benefits of the Sharpe ratio are:

· Easy way to compare investments.

· Makes it simpler to analyse multiple investments by condensing the risk and return into a single number.

· Helps you assess if your portfolio is providing adequate returns for the risk level.

· Acts as a standard to assess Mutual Fund performance.

· Applicable across various asset classes, ranging from stocks to mutual funds and ETFs.

Limitations of Sharpe ratio

Some of the drawbacks of the Sharpe ratio are:

· Reliance on standard deviation causes overlooking of other risks like liquidity or extreme downturns.

· Assumes a normal distribution of returns, which may not be true for all investments.

· Assets with irregular pricing or low liquidity may show inflated Sharpe ratios.

Conclusion

The Sharpe ratio is a powerful tool that helps you evaluate the risk-adjusted return of an investment. When you take both returns and risk into account, you get a clear picture of whether an investment justifies the risk you take. The Sharpe ratio is generally a widely accepted metric. However, you should use your conjunction with other tools and measures as well for complex assets and non-traditional risk profiles. Keeping this in mind, incorporating the Sharpe ratio into your investment strategy can help you make smarter decisions.