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The only volatility that matters: the kind that takes money away from you.
Downside deviation is the standard deviation of returns that fall below a target threshold (usually zero or the risk-free rate), ignoring upside volatility entirely. It is the denominator of the Sortino ratio and gives a more honest picture of "unpleasant risk" than standard deviation.
DD = sqrt((1/n) · Σ min(Rᵢ − T, 0)²)DD = sqrt((1/n) · Σ min(Ri − T, 0)2)For each return below target, square the shortfall. Sum, average, take the square root. Returns above target contribute nothing.
Downside deviation acknowledges that investors do not dislike upside volatility — they only dislike losing money. By measuring only negative deviations, it gives a more honest picture of the kind of dispersion that actually hurts.
Monthly returns: +3%, −2%, +1%, −4%, +5%, −1%. Target = 0%.
Returns below target: −2%, −4%, −1%. Squared shortfalls: 0.0004, 0.0016, 0.0001. Sum: 0.0021. Average over all 6 observations: 0.00035. sqrt = 1.87%.
Monthly downside deviation: 1.87%. Annualized: 1.87% · sqrt(12) = 6.5%.
Downside deviation is always less than or equal to standard deviation. For positively-skewed portfolios, the gap is large. For negatively-skewed portfolios, the two converge.
Zero is most common. Risk-free rate is more theoretically correct (you only count returns below what you could earn risk-free). Foliolytic uses zero by default.
Semi-deviation typically uses the mean as the threshold; downside deviation uses an arbitrary target (often zero). Otherwise identical.
As the denominator of Sortino ratio. It is the right risk measure for any strategy with non-symmetric returns.
Yes — used in the Sortino calculation, shown in the risk-adjusted section.
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