Serenity Ratio Calculator

The published formula

KeyQuant's An Alternative Portfolio Theory, Part I defines penalized risk as Ulcer Index times the Pitfall Indicator. The paper uses returns net of the risk-free rate. This form expresses the final calculation as:

Serenity = (portfolio return − risk-free return) / (Ulcer Index × Pitfall)

Ulcer Index is the square root of the mean squared drawdowns over the chosen history. Pitfall divides the magnitude of conditional drawdown at risk (CDaR) by annualized return volatility. CDaR summarizes tail drawdowns at a chosen confidence level. These inputs cannot be reconstructed from an arithmetic average drawdown alone.

Worked arithmetic example

For hypothetical inputs of 12% portfolio return, 4% risk-free return, 8% Ulcer Index, and Pitfall 2, excess return is 8 percentage points and penalized risk is 16%. Serenity is 8/16 = 0.5. Dividing by 8% average drawdown instead would calculate a different metric.

Prepare comparable inputs

1. Choose a return history, currency, sampling frequency, and fee treatment. Use the same window for all statistics.
2. Document how risk-free returns were removed. The original research evaluates excess-return paths; raw-portfolio drawdowns and excess-return drawdowns can differ. This form cannot reconcile them.
3. Calculate Ulcer Index and CDaR from that drawdown series. Record the confidence level and empirical tail convention used for CDaR.
4. Divide the positive CDaR magnitude by annualized volatility to obtain Pitfall. Enter percentage values for returns and Ulcer Index, and a unitless multiple for Pitfall.

Interpretation and limits

The ratio describes the supplied historical inputs. It does not infer future tail losses, liquidity, leverage limits, or the probability of ruin. The authors' follow-up paper cautions that the historical Serenity statistic does not predict future deeper drawdowns. No result here is a portfolio recommendation.

For the same positive excess return, reducing the denominator increases the ratio. With negative excess return, reducing the denominator makes the ratio more negative. Ranking negative-return strategies by this number alone can therefore be misleading. Zero Ulcer Index or Pitfall produces an undefined ratio, not proof of risk-free performance.

Serenity, Martin, and Calmar

The Martin or Ulcer Performance Index uses excess return divided by Ulcer Index. Serenity adds the Pitfall multiplier. Calmar uses maximum drawdown under its specified return and evaluation-window convention. Keep those denominators distinct and use matching definitions when comparing reported statistics.

Sources: KeyQuant, An Alternative Portfolio Theory, Part I, sections II–V; Part II, introduction; and TradingView's Ulcer Index reference. The publisher's legacy white-paper URLs may redirect; the cited definitions refer to those historical papers.

Frequently Asked Questions