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In the world of mathematics and statistics, when one individual develops a theorem or formula, over time, it is usually revised and/or used to derive other formulae and theories in the industry. In the case of the Sortino Ratio, **it is an offshoot of what Professor William F. Sharpe came up with** when he introduced the world of investing to his Sharpe Ratio in 1966.

**Dr. Frank Sortino came up with the Sortino ratio in the early 1980s** after undertaking intensive research to come up with **an improved measure** of risk-adjusted returns. Dr. Sortino improved upon the Sharpe ratio by only using **the downward deviation** rather than the standard deviation, to measure risk.

## Sortino Ratio Defined

Therefore, the Sortino Ratio is similar to the Sharpe Ratio but with a major difference when it comes to the deviation it uses in the calculation. **Sortino ratio is a statistical tool that measures the return on an investment relative to the downward risk involved in holding the asset.**

By considering only the downside deviation or risk, the Sortino ratio is sometimes preferred by investors and fund/portfolio managers. The Sortino ratio provides a better picture of the potential of incurring losses than the Sharpe ratio which considers the positive deviation in its calculations. The Sortino ratio is preferred by investors and fund managers who prefer to ignore upward volatility which is in favor of their portfolios.

As with the Sharpe ratio, **an asset or portfolio with a higher Sortino ratio is consequently viewed as a better choice** when compared to other investments in the same category. A high Sortino ratio translates to high returns while taking minimal risks on the investment.

## Calculating a Sortino Ratio

The Sortino ratio is calculated using the following formula.

Sortino Ratio = ( R_{p} – r_{f} ) / StdDev^{d}

The terms used are further defined as follows.

p = The investment being analyzed

R_{p }= Expected return on the investment

r_{f }= Risk-free rate of return

StdDev^{d}_{ }= The standard deviation of R_{p} on the downside

Further elaborating on each term, the investment being analyzed can be a security, portfolio, currency, or a new asset class such as Bitcoin or other cryptocurrencies. **Thus the expected return on the investment** is what the investor or fund/portfolio manager expects to gain in a set time frame. This can be analyzed over various time periods such as daily, weekly, monthly or annually.

As with the Sharpe ratio, **the risk-free rate of return** is the theoretical rate of return of an investment with zero risks. With this regard, investors use the returns on the shortest-dated government T-Bill. This type of asset is considered the safest type of asset in the financial markets as it is backed by the Treasury department.

Lastly, **the standard deviation on the downside** is the amount of negative variation in the value of the asset over a set time period. This means that it is measured using only the negative returns witnessed over the set time period and leaves out all positive returns in its calculations.

## What Does the Sortino Ratio Tell Us?

Investors and fund/portfolio managers use the Sortino ratio **to evaluate the return of an investment per unit of bad risk**. It evaluates the performance of an investment in relation to the negative risk undertaken when owning the asset.

By using the standard deviation on the downside, **investors get a clearer picture of the returns expected** from the asset being considered. This, in turn, helps investors to define their goals and targeted rates of return.

Therefore, the Sortino ratio better analyzes the performance of a security, currency or portfolio, for **it ignores the positive variances** while calculating the risk. The positive variances are considered a plus when investing and many believe they should not be considered when calculating risks.

**A higher Sortino ratio corresponds to the investment being a better choice**. This means that the investment is earning more per unit of bad risk taken when holding the asset being analyzed. As with the Sharpe ratio, a Sortino ratio between 1 and 2 is considered a good investment. A Sortino ratio above 2 is considered an excellent choice.

One unique aspect of the Sortino ratio is that **it can have negative values**. Such values indicate that the investor or fund manager is not being rewarded for taking the high risk involved in holding the asset.

## Applications

The Sortino ratio is sometimes referred to as **the ‘Sharper’ ratio** for its use of only the downside volatility in its calculations and thus considered as a better measure of risk. Therefore, **it is often preferred **by investors and portfolio managers when gauging the return of a particular investment.

As earlier mentioned, a higher Sortino ratio is often preferred for it shows the investment is providing more returns per unit of risk. Therefore, the ratio can be used to evaluate a variety of asset classes such as mutual funds, stocks, indices or even when investing in cryptocurrencies.

In the latter case, **the Sortino ratio would be ideal due to the high risk involved** when trading this relatively new asset class. A fund or portfolio manager can use the ratio to explain the risks involved to an audience of investors who are more conversant with the traditional financial markets. The Sortino ratio will, therefore, provide a better understanding of the risk involved when holding a potentially volatile asset such as Bitcoin (BTC), Ethereum (ETH) or XRP.

### Examples

**For example**, let us assume we are analyzing two different portfolios that constitute different assets such as stocks, currencies or cryptocurrencies. After rigorous analysis, we determine that the first portfolio **can provide an annual return of 20%**. However, **the downward risk involved is also considerably high at 18%.**

For our second portfolio, we have **an annual return of 7% and a corresponding downward risk of 1.25%**. Using a hypothetical Treasury bill with a risk-free return of 3%, we get the following comparisons between the two portfolios.

1st Portfolio | 2nd Portfolio | |

Rate of Return | 20 | 7 |

Risk-free rate of return | 3 | 3 |

Downward volatility | 18 | 1.25 |

Sortino Ratio | (20 – 3)/18 = 0.94 | (7 – 3)/1.25 = 3.2 |

After completing our calculations to determine the Sortino ratios, it is clear that **the first portfolio incurs more risk** than the second portfolio. The first portfolio offers a high potential for gains as well as losses.

## Limitations

The Sortino ratio also has similar limitations to the Sharpe ratio in that **it is dependent on the time period being analyzed**. Ideally, the period being analyzed should be a complete business cycle or multiple years. However, fund and portfolio managers can arbitrarily pick a time period to suit their immediate needs thus skewing the results.

Additionally, **in the case of illiquid assets**, the Sortino ratio might provide results that indicate that there is minimal risk undertaken when investing. This includes assets such as stocks of new companies or recently launched cryptocurrencies yet to find a crypto exchange with adequate trade volume. In these instances, a Sortino ratio might provide a picture that indicates they are low-risk assets whereas this is not the case.

## Sharpe Ratio vs Sortino Ratio

Generally, **the volatility of the asset** is what determines which ratio to use between the Sharpe and Sortino ratios. Fund and portfolio managers often prefer to use the Sharpe ratio when measuring an asset with a low volatility. **The Sortino ratio is preferred when evaluating high-volatility assets **or portfolios for it gives a better picture of the risk involved since it only uses the downward volatility.

## Concluding Thoughts

In conclusion, and as earlier mentioned, the Sortino ratio is often considered to be the ‘Sharper ratio’. Its derivation by Dr. Frank Sortino was as a result of enhancing the findings of William F. Sharpe. The Sortino ratio provides a better representation since it only considers the downside deviation in its calculations.

By only considering the downward risk, the Sortino ratio is more suitable when analyzing high-risk assets such as currencies, high-yield bonds, real estate and cryptocurrencies.

**What is the Sortino ratio?**

The Sortino Ratio is a statistical tool that measures the return on an investment relative to the downward risk involved in holding the asset.

**What information does the Sortino Ratio provide?**

The Sortino ratio provides a measure of the return of an investment per unit of bad risk

**Which ratio should I use between the Sortino and Sharpe ratio?**

The Sortino ratio is best suited for high-risk investments whereas Sharpe ratio does a better job evaluating low risk investments.

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