# What Is the Sharpe Ratio and How to Use It?

Investing in a financial portfolio will require a well-planned and accurate strategy for an ideal outcome. To calculate a portfolio’s expected returns, investors will need to calculate the expected return of each of the holdings, including the overall weight of each holding. Traditionally, the formula to calculate the basic expected return would include multiplying each asset’s weight in the portfolio by its expected return, the sum of which would provide the required result. However, since the expected returns would be based on historical data, actual results could not be guaranteed. This was where the Sharpe Ratio came into play.

Named after American economist William F. Sharpe, the Sharpe Index is used to measure an investment’s performance by comparing it against its risk.

### What Exactly Is the Sharpe Ratio?

Sharpe ratio is the measure of the risk-adjusted return of a stock or investment portfolio. The variables used in the Sharpe Ratio include the portfolio return, risk-free rate of return, and the standard deviation of the portfolio.

### What Does it Mean?

In general terms, a risk-adjusted return can happen when the returns earned are over and above the returns that are generated by a risk-free asset. Risk-free assets can include fixed deposits, treasury bills, or government bonds. Excessive returns are calculated in terms of the extra risks an investor will normally take upon investing in a risky asset, such as those of an equity fund.

In such a case, the risk inherent in an investment is ascertained using the standard deviation. The higher the ratio, the greater the investment return will be relative to the risk taken. This will result in a better investment. This ratio can be used to evaluate a single stock, several investments, or an entire portfolio.

### What Is the Sharpe Ratio Formula and How Do You Calculate it?

The Sharpe Ratio is calculated by subtracting the risk-free return from the portfolio return, known as the excess return. The excess return is divided by the standard deviation of the portfolio returns. It is used to measure the excess return on every additional unit of risk that is taken.

In other words, the formula will look like the following:

{R (p) – R (f)} / s (p)

Where:

R (p): Return generated by the portfolio
R (f): Risk-free rate of return
s (p): Standard deviation of the portfolio

### What Does It Really Mean?

The ideology behind any investment strategy is to calculate the right investment strategy to maximize your returns while reducing the volatility included. It may be impossible to have zero volatility, even when government bonds are included, especially since their pricing fluctuates up and down. However, if the volatility increases, the expected return also increases significantly to compensate for the additional risk.

The Sharpe Ratio has become the de-facto formula to calculate the risk-adjusted return. This formula reveals the average investment returns while excluding the risk-free return rate, divided by the standard deviation of investment returns. This ratio formula is used to evaluate a portfolio’s past performance, where the actual returns are taken into consideration in the formula.

When you calculate your results, you can compare them to the following thresholds:

2 to 2.99: Very good
Greater than 3: Excellent

The greater the ratio, the better the risk-adjusted performance of a stock or portfolio is. If the resulting analysis showcases a negative Sharpe Ratio, it either means that the portfolio’s return is expected to be negative, or the risk-free rate is greater than its return. In either case, negative Sharpe Ratios do not convey positive returns. Additionally, the Sharpe Ratio can also help in explaining the portfolio’s excess returns. This could be the result of smart investment decisions or a result of too much risk. While a portfolio can enjoy higher returns than its peers, it is only a good investment if the consecutive higher returns do not come with additional excess risk.

### Example of How to Use Sharpe Ratio

An investment portfolio can consist of a mix of options, such as shares, bonds, ETFs, deposits, precious metals, or other securities. Each option holds its own underlying risk-return level that influences the ratio. When a new stock, investment, or asset class is added to the portfolio, the Sharpe Ratio will compare the changes in the overall risk-return characteristics.

The portfolio adjustment can increase the overall risk level by pushing the ratio up, thus representing a more favorable risk or reward situation. Alternatively, if the ratio goes down with the addition of the security while offering attractive returns, it would represent an unacceptable risk level. The portfolio change may not be made.

Here is an example of how to evaluate different investments using the Sharp Ratio:

Two fund managers, A and B, have respective portfolio investments in the market. While A has a return of 20%, B has a return of 30%. In the case of B, the S&P 500 performance is 10%. While it does indicate that B’s portfolio performs ideally better in terms of return, the results indicate differences in terms of the Sharpe Ratio. After analysis, A shows a ratio of 2, while B’s ratio only indicated a 0.5.
In other words, B’s portfolio has a substantially higher risk than A, which explains the higher returns. However, B also has a higher chance of eventually sustaining losses.

### Limitations of the Sharpe Ratio

Using the standard deviation of returns in the denominator, the Sharpe Ratio assumes that the returns are distributed normally. A normal distribution of data is like calculating the outcome with a pair of dice. If you roll the dice enough times, you will notice that the dice’s most common result will be seven, with the least common results being two and twelve.

However, returns in the financial markets are distorted away from the average. This is due to a large number of surprising drops or spikes in asset value. Additionally, the standard deviation assumes that value movements in either direction are equally risky.

Additionally, the Sharpe Ratio can be manipulated to boost apparent risk-adjusted returns. Simply increasing the measurement interval would result in a lower estimate of volatility. Similarly, instead of choosing a neutral look-back window, a manipulator could also choose a convenient time period for analysis where the Sharpe Ratio is the highest.

#### Variants of the Sharpe Ratio

Sortino Ratio: The Sortino Ratio is a variation of the Sharpe ratio. This ratio removes the effects of upward value movements based on standard deviation to focus on the distribution of returns that are below the required return. The Sortino Ratio also replaces the risk-free rate with the required return in the numerator of the formula. This makes the portfolio return less the required return, divided by the distribution of returns below the required return.

Treynor Ratio: Another variation of the Sharpe ratio is the Treynor Ratio. It uses a portfolio’s beta or correlation between the portfolio and the rest of the market. (As you might recall, Beta is a measure of an investment’s volatility and risk compared to the overall market). This ratio aims to determine whether an investor is being compensated for taking on additional risk above the inherent risk of the market.

### Conclusion

Risk and reward must be considered together when considering investments. The Sharpe Ratio can help you ascertain investment choices that will deliver the highest returns while considering risk. Adjusting for standard deviation normalizes your returns for the risk you assumed. Always address the risk along with the reward when choosing investments.

Vikram Raghavan is a value investor, technologist, and Finexy co-founder. In addition to stock market investing, Vik also invests and advises startups on growth marketing and product management. Vik's work is focused on themes of marketplaces, micro-entrepreneurship, marketing automation, and user growth. Previously, Vikram led product and growth teams at Overstock.com, focusing on efforts across acquisition, new user experience, churn, and notifications/email. He holds an MBA in Finance from Temple University and a B.S. in Computer Information Systems and Finance from Bemidji State University.