Financial
Omega Ratio & Ulcer Index drawdown risk formulas for skewed portfolios
Evaluate non-normal return distributions via Keating-Shadwick Omega Ratio SUM(MAX(0, R - MAR)) / SUM(MAX(0, MAR - R)) and Martin's RMS drawdown Ulcer Index.
Two descriptive measures with different inputs
Omega here uses four equally weighted simple returns and a threshold of the same periodicity. Sum the positive deviations above the threshold and divide by the total shortfalls below it. With a positive denominator, a ratio above one means the sample arithmetic mean exceeds that threshold; it does not guarantee future performance or that every period beats it.
The Ulcer Index is the root mean square of percentage drawdowns from the running peak. An observation remains below its peak even during a partial recovery. New highs have zero drawdown. The four equally spaced NAV observations below are a separate illustrative series, not a compounded reconstruction of column A.
Use a cash-flow-adjusted total-return series and consistent sampling intervals for comparison. The first recorded NAV initializes the peak; any earlier peak is omitted. Four observations demonstrate arithmetic, not a reliable estimate of future risk. Neither statistic captures all portfolio risks.
| Observation (independent sample series) | Return vs MAR=1% (A:C) | NAV Curve (D) | Drawdown % Squared (E) |
|---|---|---|---|
| Month 1 | +6% -> Gain +0.05, Loss 0 | 100 (Peak 100) | 0% -> 0 |
| Month 2 | -2% -> Gain 0, Loss 0.03 | 96 (Peak 100) | -4% -> 16 |
| Month 3 | +4% -> Gain +0.03, Loss 0 | 98 (Still below 100!) | -2% -> 4 |
| Month 4 | -3% -> Gain 0, Loss 0.04 | 92 (Peak 100) | -8% -> 64 (UI = SQRT(21) = 4.5826) |
Discrete sample Omega Ratio at threshold MAR (F2)
B and C are guarded positive-deviation helpers. No Downside denotes a positive numerator with zero denominator (an unbounded sample ratio), not absence of investment risk. All returns exactly at the threshold produce zero divided by zero, reported separately as undefined. Missing or text returns invalidate this complete four-return example.
=IF(OR(COUNT(A2:A5)<>4,COUNT(F2)<>1),"Invalid inputs",IF(SUM(C2:C5)=0,IF(SUM(B2:B5)=0,"Undefined (all at threshold)","No Downside"),ROUND(SUM(B2:B5)/SUM(C2:C5),4)))Peter Martin's Ulcer Index = SQRT(AVERAGE(DrawdownPctSq))
E holds squared drawdowns in percentage-point units, so the result is 4.5826, not a fraction of 0.045826. The initial NAV must be positive and later NAVs nonnegative. Equal observation weights reflect time below the peak only when intervals are equal.
=IF(COUNT(E2:E5)<>4,"Invalid inputs",ROUND(SQRT(AVERAGE(E2:E5)),4))Try the example
Use the original values or change them to test your understanding.