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QuantMage Library

Performance Metrics

This page summarizes the performance metrics available in QuantMage and how to interpret them when comparing investment strategies.

Keller Ratios (K50 / K25)

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These are return-adjusted-for-drawdown indicators introduced by Dr. Wouter J. Keller.

Calculation

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K(Dmax) = R * (1 - f * D / (1 - f * D)) where f = 0.5 / Dmax,
if R >= 0% and D <= Dmax, and K = 0% otherwise.

K50 sets Dmax to 50% and K25 to 25%.

Interpretation

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Using Dmax as the allowed maximum portfolio drawdown, these metrics help you choose a strategy that matches your risk tolerance. Compared with some of the ratios below, they can be easier to interpret as adjusted returns.

Sharpe

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This is one of the standard measures of risk-adjusted return.

Calculation

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It’s calculated as the difference between the portfolio’s return and the risk-free rate (assumed to be 0 in QuantMage), divided by the standard deviation of its returns (a.k.a. volatility).

Interpretation

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It tells you how much excess return you are receiving for each unit of risk, where risk is measured by volatility.

Sortino

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This is similar to Sharpe, but it only penalizes downside volatility.

Calculation

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It’s your return over the risk-free rate, divided by the downside volatility.

Interpretation

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If you care more about downside risk than total volatility, this metric is often more useful than Sharpe. To compare it roughly with a Sharpe ratio, divide the Sortino by the square root of 2.

MAR

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Short for Managed Account Reports. Named such since it was introduced in the namesake newsletter. It compares the compound annual growth rate (CAGR) to the maximum drawdown.

Calculation

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Divide the CAGR of a portfolio by its maximum drawdown over the period.

Interpretation

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A higher ratio indicates better performance, especially in managing drawdowns. Maximum drawdown can be a more intuitive risk measure than the volatility used by Sharpe. One limitation is that past maximum drawdown is not a strong predictor of future maximum drawdown, while past volatility is often somewhat more stable.

UPI

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Short for Ulcer Performance Index. It is similar to Sharpe, but it uses the Ulcer Index instead of standard deviation as the risk term.

Calculation

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Divide your CAGR by the Ulcer Index, which looks at both the depth and the time you’re in the red by averaging the squares of percentage drawdowns over the period and square-rooting it.

Interpretation

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A higher UPI indicates more return per unit of drawdown-related risk. It takes the full drawdown record into account rather than focusing only on volatility.

GPR

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Short for Gain to Pain Ratio. Measures the return per unit of risk.

Calculation

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It’s the sum of all daily returns divided by the absolute sum of negative daily returns.

Interpretation

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This measures how much gain was produced relative to the losses endured along the way.

Win Rate

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This measures how often returns are positive.

Calculation

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Count your winning days and divide by the total (winning + losing) days.

Interpretation

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A higher rate means more good days than bad, but doesn’t weigh how big your wins or losses are.

P-value

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A statistical measure that evaluates whether your trading strategy’s returns are due to skill or luck.

Calculation

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Use hypothesis testing to determine the likelihood of observing your strategy’s performance under the assumption that it has no actual edge. For example, compare your strategy’s returns against a randomly generated null model.

Interpretation

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A lower value, commonly less than 1%, suggests that the observed performance is less likely to be explained by pure chance. However, overfitting, small sample sizes, or cherry-picked data can still produce misleading results.

Bootstrap Loss

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A risk-focused metric that quantifies potential underperformance by simulating alternate historical scenarios through resampling.

Calculation

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  1. Perform bootstrapping on your portfolio’s historical returns, randomly sampling with replacement to create many alternative one-year return paths.
  2. Measure the percentage of bootstrap iterations where the cumulative return falls below zero.

Interpretation

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The bootstrap loss percentage highlights the likelihood of encountering significant underperformance across varied resampled scenarios. A lower percentage indicates greater robustness, while a higher value suggests greater vulnerability under adverse conditions.

Each metric highlights a different aspect of performance, such as risk-adjusted return, downside protection, or capital efficiency. In practice, it is often useful to review several metrics together rather than relying on only one.

Further Resources

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