Ulcer Index and the Pain Ratio

Standard deviation treats an up move and a down move of the same size as equally "risky," but investors don't experience them that way — a fund that spends six months underwater below its previous peak feels far worse to hold than one with the same volatility that recovers within days. The Ulcer Index captures this by measuring drawdowns directly: at every point in time it computes the percentage decline from the running peak, squares it, and averages that over the whole period, so it grows large both when drawdowns are deep and when they last a long time, unlike maximum drawdown alone which only records the single worst instance.

Dividing average excess return by the Ulcer Index gives the Pain Ratio, a risk-adjusted performance measure analogous to the Sharpe ratio but built around drawdown pain instead of return variance — useful for comparing two strategies with similar Sharpe ratios where one happens to spend far more time in a deep hole than the other.

Because the squaring inside the Ulcer Index penalizes both depth and duration together, a strategy with one brief 20% drawdown can score better than one with a shallower but much longer 10% drawdown that drags on for a year, which is exactly the kind of "slow bleed" risk that standard deviation and even maximum drawdown alone tend to understate.