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

![Sortino Ratio: A risk-adjusted measure of portfolio performance that only considers the standard deviation of the downside risk.](https://www.investopedia.com/thmb/aic8nEjievNP1IK4gZouZE7zF_0=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Sortinoratio_final-fde284faf27d43c2bb5269cb96cc8575.png)

*— Investopedia / Michela Buttignol*

> **Definition**
>
> The Sortino ratio can help investors and analysts evaluate an investment's return for a degree of bad risk.

## What Is the Sortino Ratio?

The Sortino ratio is a variation of the [Sharpe ratio](https://www.investopedia.com/terms/s/sharperatio.asp). It differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative portfolio returns or [downside deviation](https://www.investopedia.com/terms/d/downside-deviation.asp) instead of the total standard deviation of portfolio returns.

The Sortino ratio takes an asset's or portfolio's return and subtracts the risk-free rate. It then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.

### Key Takeaways

*   The Sortino ratio differs from the Sharpe ratio in that it only considers the standard deviation of the downside risk rather than that of the entire risk.
*   The Sortino ratio focuses only on the negative deviation of a portfolio's returns from the mean.
*   It's thought to give a better view of a portfolio's risk-adjusted performance because positive volatility is a benefit.
*   A higher Sortino ratio means that the investment is earning more return per unit of the bad risk it takes on.

## Formula and Calculation of the Sortino Ratio

﻿ $\begin{aligned} &\text{Sortino Ratio} = \frac{ R_p - r_f }{ \sigma_d } \\ &\textbf{where:} \\ &R_p = \text{Actual or expected portfolio return} \\ &r_f = \text{Risk-free rate} \\ &\sigma_d = \text{Standard deviation of the downside} \\ \end{aligned}$﻿

## What the Sortino Ratio Can Tell You

The Sortino ratio is a useful way for investors, analysts, and [portfolio managers](https://www.investopedia.com/terms/p/portfoliomanager.asp) to evaluate an investment's return for a given level of bad risk. This ratio uses only the downside deviation as its risk measure so it addresses the problem of using total risk or standard deviation. This is important because upside volatility is beneficial to investors and isn't a factor that most investors worry about.

## Example of How to Use the Sortino Ratio

A higher Sortino ratio result is better, just like the Sharpe ratio. When looking at two similar investments, a rational investor would prefer the one with the higher Sortino ratio because it means that the investment is earning more return per unit of the bad risk that it takes on.

Assume Mutual Fund X has an annualized return of 12% and a downside deviation of 10%. Mutual Fund Z has an annualized return of 10% and a downside deviation of 7%. The risk-free rate is 2.5%. The Sortino ratios for both funds would be calculated like this:

$\begin{aligned} &\text{Mutual Fund X Sortino} = \frac{ 12\% - 2.5\% }{ 10\% } = 0.95 \\ \end{aligned}$

$\begin{aligned} &\text{Mutual Fund Z Sortino} = \frac{ 10\% - 2.5\% }{ 7\% } = 1.07 \\ \end{aligned}$

Mutual Fund X is returning 2% more on an annualized basis but it isn't earning that return as efficiently as Mutual Fund Z given their downside deviations. Mutual Fund Z is the better investment choice based on this metric.

> **Important**
>
> An investor should be consistent in terms of the type of return to keep the formulas accurate.

Using the risk-free rate of return is common but investors can also use [expected return](https://www.investopedia.com/terms/e/expectedreturn.asp) in calculations.

## What Is Downside Risk?

[Downside risk](https://www.investopedia.com/terms/d/downsiderisk.asp) reflects the loss that an investor would most likely suffer when an asset's price plunges due to a volatile market. A security with significant downside risk should ideally hold the promise of greater returns to balance the roll of the dice.

## What Is the Risk-Free Rate?

The risk-free rate isn't technically a data point. It's hypothetical although it's generally accepted to be the equivalent of or close to what an investor would receive on an ultra-safe government-issued Treasury note, The risk-free rate is the return an investor should be able to expect assuming that an investment carries no or negligible risk.

## What Is Expected Return?

Expected return is just what it sounds like: It's the rate of return that an investor can expect to realize on an asset. It can be used to balance their risk tolerance and adjust their goals. It's typically based on historical data.

## The Bottom Line

The Sortino ratio improves upon the Sharpe ratio by dividing excess return by the downside deviation instead of the total standard deviation of a portfolio or asset, isolating downside or negative volatility from total volatility.

The Sharpe ratio effectively punishes the investment for good risk that provides positive returns for investors. Determining which ratio to use depends on whether the investor wants to focus on total or [standard deviation](https://www.investopedia.com/terms/s/standarddeviation.asp), or just downside deviation.

The choice comes down to your goals. Always seek professional advice if you're unsure.

_The comments, opinions, and analyses expressed on Investopedia are for informational purposes only. Read our [warranty and liability disclaimer](https://www.investopedia.com/legal-4768893#toc-warranty-and-liability-disclaimer) for more info._  

> **Article Sources**
>
> 1.  CME Group. "[Sortino: A ‘Sharper’ Ratio](https://www.cmegroup.com/education/files/rr-sortino-a-sharper-ratio.pdf)." Pages 2-3.
>     
> 2.  CFI Education. "[Downside Risk](https://corporatefinanceinstitute.com/resources/career-map/sell-side/capital-markets/downside-risk/)."
>     
> 3.  CFI Education. "[Risk-Free Rate](https://corporatefinanceinstitute.com/resources/valuation/risk-free-rate/#:~:text=The%20risk%2Dfree%20rate%20of%20return%20is%20the,the%20safest%20investment%20an%20investor%20can%20make.)."
>     
> 4.  Indeed. "[What Is Expected Return? (Plus How to Calculate It)](https://www.indeed.com/career-advice/career-development/expected-return#:~:text=Expected%20return%20is%20the%20anticipated,Guide%20to%20Rate%20of%20Return)."