# Sortino Ratio

We know that Sharpe ratio is a popular measure for measuring the reward (or excess return) of an asset per unit of risk.

One problem with Sharpe ratio is that it is dimensionless, that is, as it uses the standard deviation of returns as a measure of risk. It penalizes both upward and downward volatility equally.

Sortino ratio is a modification of the Sharpe ratio. Instead of considering both upward and downward movement in volatility, Sortino ratio focuses only on the downward volatility.

The ratio can be calculated using the following formula:

$S = \frac{R - R_{T}}{\sigma_{d} }$

Where RT is the target minimum required rate for the investment and σd is the downside deviation.

The calculation of downside deviation is a bit tricky.

The first step is to calculate the excess returns for all periods (R – Rt). Now, some of these returns will be positive while some will be negative.

The question is “Should you just replace all positive numbers with zeros and go about calculating Sortino ratio, or should you complete omit all the positive results?” If you are simply replacing positive results with zeros, you may underestimate the volatility. Instead the better way is to complete omit the positive results while calculating the standard deviation.

The Sortino ratio provides more realistic risk-adjusted returns on a security as it does not penalize the upward price change.

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