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QuantMage Library

Performance Metrics

Ever wondered how to gauge the effectiveness of your investment strategies? Beyond the well-known Sharpe ratio, there’s a whole world of metrics out there. Let’s unpack some of these, including the cool ones QuantMage offers, so you can better compare and evaluate your strategies.

Keller Ratios (K50 / K25)

These are return-adjusted-for-drawdowns indicators from the brilliant mind of Dr. Wouter J. Keller.

Calculation

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

Using the Dmax as the allowed maximum portfolio drawdown, these let you pick a strategy that matches how much risk you’re comfy with. They can be more intuitively compared and understood as adjusted returns in contrast to other ratios below.

Sharpe

It’s the go-to for measuring risk-adjusted returns.

Calculation

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

It tells you how much extra oomph you’re getting for each unit of risk measured in volatility.

Sortino

It’s like Sharpe’s cousin but only frets about the bad volatility.

Calculation

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

Interpretation

If you lose sleep over potential losses more than overall ups and downs, this is your go-to metric. Fun fact: To compare it with a Sharpe ratio, just divide the Sortino by the square root of 2.

MAR

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

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

Interpretation

A higher ratio indicates better performance, especially in managing drawdowns. The max drawdown can be more intuitive for many as a risk measure than the volatility Sharpe uses. The downside is the fact that the max drawdown in the past is not a good predictor of a future one while the past volatility is.

UPI

Short for Ulcer Performance Index. It’s like Sharpe, but uses the Ulcer Index for risk instead of the standard deviation.

Calculation

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

Higher UPI = more bang for your buck with less of the gut-wrenching drops. It offers a more comprehensive look by taking the entire drawdown record into account.

GPR

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

Calculation

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

Interpretation

Basically, it’s the measure of the treasure you’ve made versus the pain you’ve endured.

Win Rate

Simply, it’s how often you end up in the green.

Calculation

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

Interpretation

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

P-value

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

Calculation

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

A lower value (commonly less than 1%) suggests your results are statistically significant, meaning the performance is less likely to be the result of pure chance. However, beware of overfitting, as small sample sizes or cherry-picked data can give misleading results.

Bootstrap Loss

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

Calculation

  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

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

Each metric offers a different perspective on investment performance, focusing on aspects like risk-adjusted returns, downside protection, or the efficiency of capital utilization. Smart investors often mix and match these to get the full picture of how their strategies are doing.

Further Resources