Downside Deviation is the standard deviation calculated only on returns that fall below a minimum acceptable return (MAR) — it quantifies the volatility of losses, not total volatility.
Standard deviation captures all variability — both positive and negative surprises. Downside Deviation filters to only below-MAR returns: (1) Identify your Minimum Acceptable Return (typically 0% or the risk-free rate). (2) For each period where the return is below MAR, square the difference. (3) Average the squared differences (including zero for periods above MAR). (4) Take the square root. The result quantifies how volatile the bad periods are. It is the denominator in the Sortino Ratio.
If your fund returned: +5%, +10%, -3%, -8%, +7%, +2% over six months — standard deviation treats all six months. Downside Deviation only uses the -3% and -8% months (the months you fell below your target). If your MAR is 0%: Downside Deviation captures only the magnitude and frequency of your negative returns. Smaller Downside Deviation = your bad months are less severe.
Set Minimum Acceptable Return (MAR): typically 0% or risk-free rate.
For each period: excess loss = max(0, MAR − return). Square it.
Average the squared losses across all periods (counting zeros for above-MAR periods).
Take square root → Downside Deviation.
Divide excess return by Downside Deviation → Sortino Ratio.
DD = √[ (1/n) × Σ min(0, Rt − MAR)² ]