Square each drawdown before averaging
At observation t, define peak Pₜ as the largest equity value observed from the start through t. The percentage drawdown is Dₜ = 100 × (Eₜ/Pₜ − 1). The Ulcer Index is sqrt(Σ Dₜ²/N). Drawdowns are zero whenever equity reaches or exceeds the running high. Squaring gives deeper declines a larger influence, while repeated underwater observations keep contributing until the path recovers to its previous peak.
A complete four-point calculation
For equity values 100, 90, 95, and 100, the running peak remains 100 throughout. Drawdowns are 0%, −10%, −5%, and 0%. Their squares total 125, so the mean square is 31.25 and the Ulcer Index is approximately 5.59. Repeating the 90 observation before recovery increases the time spent at a deep drawdown and changes the result even though the maximum loss remains 10%.
Keep the equity sampling consistent
Daily observations and monthly observations can reveal different portions of the same decline. Compare curves with matching frequency, date coverage, and valuation practices. Deposits or withdrawals should be removed through an appropriate return index before interpreting a raw account balance as strategy performance. The statistic does not identify the cause of losses, estimate future recovery time, or incorporate a peak preceding the first observation. A low sample value can reflect a quiet window rather than durable downside protection.