# Sharpe Ratio: Definition, Formula, Advantages

by Angel One
Can you evaluate the best investment unless you understand how much your risk exposure increases for an additional unit of return? Sharpe ratio does that job for you.

Investing is all about maximizing returns while reducing risks. Usually, returns from an investment increase with additional risks. But how do you calculate that? You probably have heard finance experts talk about risk-adjusted returns. It is a measure to compare the returns of an investment against its risk. The ratio that measures the risk-adjusted return is the Sharpe ratio, named after American economist Willan F. Sharpe. In this article, we will discuss how to calculate sharpe ratio and use it to make sound investment decisions.

Here is a quick recapitulation of ‘what is the Sharpe ratio?’

## What is the Sharpe ratio?

Introduced by Willan F. Sharpe in 1966, the Sharpe ratio suggests earning extra returns, one must take additional risks. The excess return on investment is often a result of more volatility and risks than investment skills. Sharpe called it the reward-to-variability ratio.

## Sharpe Ratio Formula

The calculation of the Sharpe Ratio follows the formula below.

Sharpe Ratio = E [Rp-Rf] / σp

E = Expected value of

Rp = return on a portfolio

Rf = risk-free rate

σp = standard deviation of the portfolio’s excess return

The standard deviation of the portfolio equates to the series of the variability of returns adding up to the total performance sample in consideration.

The Sharpe ratio is used to measure the performance of mutual funds. A higher Sharpe ratio indicates better return-yielding capacity of the fund for every unit of additional risk taken. You may wonder ‘what is a good sharpe ratio?’. We have discussed it below.

## How does the Sharpe ratio work?

Investors and market experts have two conflicting goals. The first is to optimize returns from an investment. And second, they try to minimize the risks or their chances of losing money. You can evaluate an investment option based on its projected returns. But having an understanding of the risk factors helps with judgment. Sharpe ratio gauges the extra risk that you must take for higher returns. It is a way to measure the performance of an investment by taking risk into account. You can apply the Sharpe ratio to evaluate your portfolio or individual stocks. It gives a score, calculated against a risk-free return of government bonds, that describes if the higher return on the investment is adequately compensating for the additional risk.

Sharpe ratio comes in handy in measuring the risk-adjusted returns on mutual funds. The higher the score, the better is the investment in terms of risk-adjusted returns. You can use a Sharpe ratio to compare funds.

## What is a good Sharpe ratio?

After understanding the importance of the Sharpe score, we must find out its acceptable value. A Sharpe value above 1 is considered acceptable by good investors.

•  2 – 2.99: Very good
•  More than 3: Excellent

The Sharpe ratio calculates the average returns, minus the risk-free return divided by the standard deviation of the returns from the investment.

Let’s understand with an example.

Portfolio A is expected to earn a return of 13% in the next twelve months, while portfolio B is likely to generate 11% during the same period. Now without considering the risk, portfolio A is a superior option.

Let’s assume portfolio A has a standard deviation of 8% and portfolio B has 4%. The risk-free return on government bonds is 3%.  Let’s calculate the Sharpe ratio of each portfolio using the sharpe ratio formula expressed above.

Sharpe ratio of portfolio A = 13-3 / 8 = 1.25

Sharpe ratio of portfolio B = 11-3 / 4 = 2

Clearly. Portfolio 2 has a better Sharpe ratio or risk-adjusted return. Sharpe ratio provides a more holistic analysis of your investment.

Sharpe ratio measures an investor’s desire to earn higher returns than risk-free returns given by government bonds. The calculation is based on standard deviation which depicts the total risk inherent in an investment. Hence, the ratio measures the returns generated by the investment after considering all risk factors. In other words, the Sharpe ratio is the most holistic measure of an investment’s risk-adjusted return and as an investor, you must know the Sharpe ratio meaning.

## Limitation of Sharpe Ratio

Portfolio managers can alter the Sharpe ratio to improve their history of apparent risk-adjusted performance. This can be accomplished by increasing the return measurement intervals, which lowers the volatility estimate. In addition, another technique for selecting the data that will skew the risk-adjusted returns is to calculate the Sharpe ratio for the performance period that has been the most profitable rather than an objectively selected look-back period.

There are some limitations to the Sharpe Ratio listed below:

• The Sharpe ratio cannot distinguish between intermittent and consecutive losses since the risk metric is unaffected by the sequencing of distinct data points.
• The Sharpe ratio concentrates on volatility but ignores its direction because it cannot discriminate between upswing and downswing. Even if equity retracements were slight, the ratio would punish a system that displayed intermittent substantial equity rises.
• The individuals can alter the ratio to show their best selves. In addition, the fund manager could calculate 5 years knowing that the portfolio had previously performed well if the portfolio’s 3-year Sharpe ratio does not offer an appealing proposition.

## Alternatives to Sharpe Ratio

The Sharpe ratio’s standard deviation presupposes price changes in either direction are equally dangerous. Most investors and analysts consider the danger of an abnormally low return very different from the potential for an abnormally high return. However, there are two alternatives to Sharpe ratios listed below:

### 1. Sortino Ratio

The Sortino ratio evaluates the risk-adjusted return of a portfolio, strategy, or investment asset. Despite being a variation of the Sharpe ratio, it solely penalises returns that fall below a user-specified target or needed rate of return.

The difference between the Sharpe and Sortino ratio is that it considers the standard deviation of the downside risk, not the total (upside plus downside) risk. Investors, analysts, and portfolio managers can assess an investment’s return for a specific degree of bad risk by using the Sortino ratio.

Formulae to Calculate Sortino Ratio

Sortino Ratio = R – Rf /SD

Where,

• R denotes the expected returns.
• Rf signifies the risk-free return rate.
• SD states the negative asset return’s standard deviation.

### 2. Treynor Ratio

The Treynor ratio is a performance indicator for calculating how much excess return was produced for each unit of risk taken on by a portfolio. It is also known as the reward-to-volatility ratio. The excess return is a return that was obtained over the return that would have been possible from a risk-free investment. Treasury Bills are frequently employed to represent the risk-free return in the Treynor ratio, despite the fact that there is no real risk-free investment. Generally, a portfolio is a more suited investment if the Treynor ratio is higher.

Formulae to Calculate Treynor Ratio

Treynor Ratio = (Returns Generated by Portfolio – Risk-free return rate) / Beta value

Investors should know how to calculate the Sharpe ratio because it has multiple advantages. You can use the Sharpe value to compare multiple investment options.

### A measure of risk-adjusted return

Sharpe ratio gives a comprehensive measure to determine the performance of an investment against the risk-free return. A higher value of the Sharpe ratio indicates better risk-adjusted performance.

### Comparing funds

Another use of the Sharpe ratio is a comparison between funds while investing. Experts use the ratio to compare the performance of mutual funds facing similar risks or generating the same level of returns.

### Comparison against benchmark

Sharpe ratio can tell investors whether their chosen fund offers competitive returns when checked against other funds from the same category. It offers a broader perspective by allowing comparison against market benchmarks to determine whether the fund is overperforming or underperforming.

## How Sharpe ratio helps in choosing mutual funds

### Analyzing the fund strategy

Sharpe ratio offers objective feedback on the fund’s performance. You can use it to compare the degree of risk the two funds face while earning returns over risk-free bonds.

While comparing a fund with a higher Sharpe ratio is desirable. A fund achieving a comparatively lower return with moderate volatility is more desirable than a fund with higher returns and higher volatility.

### Limitations of Sharpe ratio

Like any other financial ratio, the Sharpe ratio also has limitations. Fund managers can manipulate the value of the Sharpe ratio by extending the return measurement intervals to make their funds look more acceptable to investors. It results in lowering the estimate of volatility.

The standard deviation, which measures the portfolio’s proxy risk, isn’t a true measure of volatility. Financial market volatility is often a result of herding behaviour which can often move further from the standard deviation.

Secondly, market returns are also subject to serial correlation, meaning the returns from the intervals can be correlated or influenced by the same market trend.

## The bottom line

Despite limitations, the Shrape ratio is one of the most powerful financial ratios. Experts use it as a yardstick to determine the inherent risk of an investment option. Calculation of the Sharpe ratio offers a holistic understanding of risk-adjusted return. Many mutual fund companies publish the Sharpe ratio of their funds’ performance annually.