Sortino ratio

The Sortino ratio is a risk-adjusted performance metric that evaluates the return of an investment relative to its downside risk. Unlike the Sharpe ratio, which considers total volatility, the Sortino ratio focuses only on harmful volatility by using the downside deviation instead of the total standard deviation. This distinction leads to different applications and interpretations of the two ratios. Its formula is:

Here, $R_p$ represents the portfolio return, $R_f$ is the risk-free rate, and ${\sigma }_d$ is the standard deviation of the negative asset returns, also known as “downside risk”. This ratio differs from the Sharpe Ratio by only considering the negative deviations of returns from a target or required rate of return, often the risk-free rate.

The downside risk ${\sigma }_d$ is calculated using a continuous formula:

where $T$ is the target or minimum acceptable return (MAR), $r$ is the random variable representing the return, and $f(r)$ is the probability distribution of returns, e.g., the log-normal distribution. This continuous approach allows for the use of annual returns directly, aligning more naturally with how investors typically set their investment goals. In contrast, the discrete method requires conversion of annual targets into monthly targets to accumulate enough data points for meaningful analysis, potentially misrepresenting the actual risk involved.

Applications:

Both ratios are widely used in finance for portfolio management and performance evaluation. The Sharpe ratio is beneficial for general risk assessment, providing a quick snapshot of how much excess return you are receiving for the extra volatility endured by holding a riskier asset. In contrast, the Sortino ratio is particularly advantageous when an investor wants to focus on downside risk, which can be more relevant during periods of market volatility or for loss-averse investors.