# Sortino Ratio Definition Formula Calculation and Example

## Sortino Ratio: Definition, Formula, Calculation, and Example

The Sortino Ratio is a financial metric used to evaluate the risk-adjusted return of an investment or portfolio. It is an improvement over the widely used Sharpe Ratio, as it focuses on downside risk rather than total volatility.

### Formula

The formula for calculating the Sortino Ratio is as follows:

Where:

### Calculation

To calculate the Sortino Ratio, you need historical return data for the investment or portfolio, the risk-free rate, and the downside deviation. The average return is calculated by taking the average of the historical returns. The downside deviation is calculated by taking the standard deviation of the negative returns only.

### Example

Let’s say you have an investment with an average return of 8% and a risk-free rate of 2%. The downside deviation is calculated to be 5%. Using the formula, the Sortino Ratio would be:

A Sortino Ratio of 1.2 indicates that the investment has generated 1.2 units of excess return per unit of downside risk.

## What is Sortino Ratio?

The Sortino Ratio is a financial metric used to evaluate the risk-adjusted return of an investment or portfolio. It is an extension of the Sharpe Ratio, but unlike the Sharpe Ratio, which considers both the upside and downside volatility, the Sortino Ratio only takes into account the downside volatility.

The Sortino Ratio is often preferred by investors who are more concerned with the potential for losses rather than the overall volatility of an investment. It provides a more accurate measure of risk by focusing on the downside deviation, which is the standard deviation of negative returns.

To calculate the Sortino Ratio, the average return of the investment or portfolio is divided by the downside deviation. The higher the Sortino Ratio, the better the risk-adjusted return. A higher Sortino Ratio indicates that the investment or portfolio has generated higher returns relative to the downside risk.

The Sortino Ratio can be useful for comparing different investments or portfolios and determining which one offers a better risk-adjusted return. However, it is important to note that the Sortino Ratio is just one tool among many that investors can use to evaluate investments, and it should not be the sole factor in making investment decisions.

## Sortino Ratio Formula

The Sortino Ratio is a risk-adjusted performance measure that evaluates the return of an investment relative to its downside risk. It is a modification of the Sharpe Ratio, which takes into account only the standard deviation of returns, by considering only the downside deviation.

The formula for calculating the Sortino Ratio is as follows:

Where:

• R is the average return of the investment
• T is the target return, usually set to zero
• D is the downside deviation of the investment

The Sortino Ratio measures the excess return per unit of downside risk. A higher Sortino Ratio indicates a better risk-adjusted performance, as it means that the investment is generating higher returns while experiencing less downside volatility.

To calculate the Sortino Ratio, you need to first calculate the downside deviation. The downside deviation is the standard deviation of returns below the target return. It is calculated by taking the square root of the average of the squared differences between the returns and the target return, only considering the negative returns.

Once you have calculated the downside deviation, you can plug the values into the Sortino Ratio formula to obtain the ratio.

For example, let’s say you have an investment with an average return of 10%, a target return of 0%, and a downside deviation of 5%. The Sortino Ratio would be calculated as follows:

This means that the investment has generated a return that is 2 times its downside risk.

## How to Calculate Sortino Ratio?

The Sortino Ratio is a financial metric that measures the risk-adjusted return of an investment or portfolio. It is a variation of the more commonly used Sharpe Ratio, but with a focus on downside risk.

To calculate the Sortino Ratio, you need to follow these steps:

1. First, determine the average return of the investment or portfolio. This can be done by taking the average of the periodic returns over a specific time period.
2. Next, calculate the target rate of return, which is the minimum acceptable return for the investor. This can be based on the investor’s risk tolerance or the benchmark return.
3. Then, calculate the downside deviation, which measures the volatility of the returns below the target rate of return. This can be done by taking the square root of the average of the squared differences between the actual returns and the target rate of return.
4. Finally, divide the average return by the downside deviation to get the Sortino Ratio. The higher the ratio, the better the risk-adjusted return.

Here is the formula for calculating the Sortino Ratio:

 Sortino Ratio =

For example, let’s say you have an investment with an average return of 10%, a target rate of return of 5%, and a downside deviation of 3%. Using the formula, the Sortino Ratio would be:

 Sortino Ratio = = 1.67

The Sortino Ratio is a useful tool for investors and portfolio managers to evaluate the risk and return characteristics of an investment or portfolio. By focusing on downside risk, it provides a more accurate measure of the investment’s performance in unfavorable market conditions.

## Sortino Ratio Example

Let’s illustrate the concept of the Sortino Ratio with an example. Suppose you are considering two different investment options: Option A and Option B. Option A has an average annual return of 10% with a standard deviation of 15%, while Option B has an average annual return of 8% with a standard deviation of 10%.

Based on the Sortino Ratio, we can conclude that Option A has a higher risk-adjusted return compared to Option B. This is because Option A has a higher Sortino Ratio, indicating a higher return per unit of downside risk.

## QUANTITATIVE ANALYSIS: Catname

In quantitative analysis, the term “Catname” refers to a specific category or classification used to analyze and evaluate investment portfolios. This category can be based on various factors such as asset class, industry sector, geographic region, or investment strategy.

Quantitative analysts use Catname to group similar investments together and compare their performance against relevant benchmarks or other portfolios within the same category. This analysis helps investors and portfolio managers to gain insights into the risk and return characteristics of different investment options.

By analyzing the performance of investments within the Catname category, investors can identify trends, patterns, and potential opportunities or risks. This information can be used to make informed investment decisions and optimize portfolio allocations.