# What is the Sortino Ratio?

## What is the Sortino ratio?

The Sortino ratio is a risk-adjusted performance measure that is similar to the Sharpe ratio. However, while the Sharpe ratio uses the standard deviation of returns to calculate the risk, the Sortino ratio only considers the downside risk, which is defined as the standard deviation of negative returns.

The Sortino ratio is calculated as the excess return (return above a risk-free rate) divided by the downside risk. The higher the Sortino ratio, the better the risk-adjusted performance.

The Sortino ratio is often used by investors and fund managers to evaluate the performance of an investment strategy or a portfolio, especially in cases where the downside risk is of particular concern.

## Sortino ratio formula

The formula for the Sortino ratio is:

**Sortino ratio = (Rp – T) / Dd**

Where:

- Rp = the average return of the investment or portfolio
- T = the target rate of return (usually the risk-free rate)
- Dd = the downside deviation of the investment or portfolio

The downside deviation (Dd) is calculated using the same formula as standard deviation, but only takes into account returns that are below the target rate of return (T). We don’t want to scare you, but mathematically, it can be expressed as:

**Dd = sqrt([sum of (Ri – T)^2 / N] * [N / (N-1)])**

Where:

- Ri = the return for each period
- T = the target rate of return
- N = the number of periods

Once the target return rate is determined, you can calculate the downside deviation as follows:

- Calculate the squared difference between the actual returns (R) and the target return rate (T) for each period of investment.
- Sum up the squared differences for all periods.
- Divide the sum by the number of periods.
- Take the square root of the result to obtain the downside deviation.

## Why is the Sortino ratio needed for small businesses?

Taking risks is a critical part for any business. However, small businesses often have limited resources and cannot afford to take significant losses. Therefore, it is important for them to assess the potential downside risk of their investments and make informed decisions. The Sortino ratio provides a useful tool for small businesses to measure their investment performance in a way that accounts for the downside risk they face.

In addition, the Sortino ratio can also help small businesses compare the performance of different investment strategies or portfolios. By looking at the Sortino ratio of each strategy or portfolio, small business owners can identify which ones are generating the highest returns for a given level of downside risk.

Overall, the Sortino ratio is a valuable metric for small businesses because it provides a way to evaluate investment performance that takes into account the potential downside risk, which is particularly important for businesses with limited resources.

## What the Sortino ratio can tell you

Unlike the Sharpe ratio, which takes into account both the upside and downside variability of an investment’s return, the Sortino ratio only considers the downside volatility.

The Sortino ratio is calculated by taking the portfolio’s excess return over the risk-free rate, and dividing it by the portfolio’s downside deviation. Downside deviation is the standard deviation of negative returns, or returns below a certain threshold.

The Sortino ratio is useful for investors who are particularly concerned about downside risk, and want to evaluate the performance of an investment with that in mind. A higher Sortino ratio indicates that the investment has generated higher returns for the amount of downside risk taken on.

However, it’s important to note that the Sortino ratio is just one tool for evaluating investment performance, and should be used in conjunction with other financial metrics and industry benchmarks. Additionally, the threshold used to define negative returns can have a significant impact on the calculated Sortino ratio, so it’s important to carefully consider the threshold used when comparing different investments.

## What is a good Sortino ratio?

There is no specific threshold for what constitutes a good Sortino ratio, as it can vary depending on the investor’s risk tolerance and investment objectives. Generally, a higher Sortino ratio is better, as it indicates that the investment is generating higher returns for the same level of downside risk or lower risk for the same level of return.

However, the interpretation of the Sortino ratio should be done in the context of the specific investment being evaluated and compared against similar investments in the same asset class or industry. Moreover, investors should not rely solely on one metric but rather consider a range of factors when making investment decisions.

## Example of the Sortino ratio

Here’s a simple example to calculate the Sortino ratio:

Assume you have two investment portfolios, A and B, with the following characteristics:

Portfolio A:

- Annual return: 10%
- Downside deviation (or downside risk): 5%

Portfolio B:

- Annual return: 10%
- Downside deviation: 7%

To calculate the Sortino ratio for each portfolio, we first need to determine the downside risk-adjusted return, which is the excess return of the portfolio over a minimum acceptable return (MAR) divided by downside deviation.

The MAR is typically defined as the risk-free rate of return, which is assumed to be 2% in this example.

For Portfolio A, the downside risk-adjusted return is calculated as follows:

**Downside risk-adjusted return = (10% – 2%) / 5% = 1.6**

For Portfolio B, the downside risk-adjusted return is calculated as follows:

**Downside risk-adjusted return = (10% – 2%) / 7% = 0.857**

The Sortino ratio is then calculated by dividing the downside risk-adjusted return by the downside deviation:

- Sortino ratio for portfolio A = 1.6 / 5% = 0.32
- Sortino ratio for portfolio B = 0.857 / 7% = 0.12

Therefore, Portfolio A has a higher Sortino ratio, indicating better risk-adjusted returns.

## Sortino ratio vs Sharpe ratio

Both the Sortino ratio and Sharpe ratio are commonly used to evaluate the risk-adjusted returns of investment portfolios. However, there are some key differences between the two:

### Definition

The Sharpe ratio measures the excess return of a portfolio relative to its total risk, while the Sortino ratio only considers the downside risk.

### Calculation

The Sharpe ratio is calculated by subtracting the risk-free rate of return from the portfolio’s expected return and then dividing by the portfolio’s standard deviation. The Sortino ratio is calculated by subtracting the risk-free rate of return from the portfolio’s expected return and then dividing by the portfolio’s downside deviation.

### Interpretation

A higher Sharpe ratio indicates better risk-adjusted performance, while a higher Sortino ratio indicates better downside protection.

### Bias

The Sharpe ratio may be biased if the returns of the portfolio are not normally distributed, while the Sortino ratio is less sensitive to non-normal returns.

In summary, both ratios have their strengths and weaknesses and can be used in different scenarios depending on the nature of the portfolio and the investor’s preferences. The Sharpe ratio is more widely used and more appropriate for portfolios with a symmetric return distribution, while the Sortino ratio may be more useful for portfolios with a skewed return distribution or investors who are more concerned with downside risk.

## Using financial modelling instead of Sortino ratio

While financial modelling can be a useful tool for analyzing investment opportunities, it is not a direct substitute for the Sortino ratio. The Sortino ratio specifically measures an investment’s performance relative to downside risk, which can be an important consideration for investors who are risk-averse or seeking to limit their losses.

That being said, financial modelling tool can provide a more comprehensive analysis of an investment’s potential performance, taking into account a range of factors such as market trends, economic conditions, and industry-specific risks. By using financial modelling tools like Brixx, investors can gain a more nuanced understanding of an investment’s potential risk and return profile.

In summary, while financial modelling can be a useful tool for investment analysis, it should be used in conjunction with other risk management techniques such as the Sortino ratio to ensure that investors are fully evaluating an investment’s potential risks and returns.

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