Downside Deviation

Downside deviation is volatility, but only for the bad days -- returns below a target (usually the risk-free rate).

That's why it powers the Sortino ratio.

The formula

We calculate downside deviation as:

$$\sqrt{\frac{1}{T} \sum \min(0, r_t - MAR)^2} \times \sqrt{N}$$

Where:

• $MAR$ is the daily target return (we use the daily risk-free rate).
• $T$ is the total number of daily observations in the window.
• $N$ is 365 for crypto or ~252 for trading-day assets.

A practical note

If an asset has no downside days in the window, downside deviation is effectively 0 -- and Sortino becomes undefined. We show that as N/A instead of pretending it's infinite.