Combining Trading Metrics with Standardization or Rank Averaging
Summary
The document considers how to combine several performance measures, including profit and loss, win-to-loss ratio, and gain-to-drawdown ratios, into one score. It describes two approaches: standardize each measure against a null model before combining them, or rank assets separately on each measure and average their ranks. Standardization can make differently scaled measures more comparable; estimating the null distribution for measures involving maximum drawdown may require Monte Carlo simulation. The answer cautions that squaring standardized values discards the sign and suggests averaging signed standardized measures instead.
The rank approach is nonparametric and allows explicit weights to reflect the relative importance of each measure, such as assigning greater influence to profit and loss. The examples illustrate how asset rankings can be averaged and then weighted. The document does not compare the methods empirically or establish that either score predicts future performance. The choice depends on the desired treatment of signs, scale, and metric importance.
Key ideas
- Standardizing metrics against a null model can make measures with different scales more comparable.
- Measures involving maximum drawdown may need Monte Carlo simulation to estimate their null variability.
- Summing squared standardized measures discards sign, so averaging signed values may be more appropriate for some goals.
- Averaging asset ranks offers a nonparametric way to combine measures.
- Weights on rank averages can emphasize metrics such as profit and loss.
Tags
Full text
# How to combine various equity measures into a single measure (vector magnitude) # How to combine various equity measures into a single measure (vector magnitude) I have several measures: ``` 1. Profit and loss (PNL). 2. Win to loss ratio (W2L). 3. Avg gain to drawdown ratio (AG2AD). 4. Max gain to maximum drawdown ratio (MG2MD). 5. Number of consecutive gains to consecutive losses ratio (NCG2NCL). ``` If there were only 3 measures (A, B, C), then I could represent the "total" measure as a magnitude of a 3D vector: R = SQRT(A^2 + B^2 + C^2) If I want to combine those 5 measures into a single value, would it make sense to represent them as the magnitude of a 5D vector? Is there a better way to combine them? Is there a way to put more "weight" on certain measures, such as the PNL? ## Answer by shabbychef (score 4, accepted) https://quant.stackexchange.com/a/205 One approach would be to rescale these metrics so that they are approximately normally distributed with unit variance under the null hypothesis that the stock's price is an unbiased geometric random walk (equivalently that the log returns are zero mean). This rescaling is effectively going to 'downweight' the statistics with a large amount of variance. Once they have been rescaled to approximate normality, one *could *combine them as you have done, in which case the sum of their squares would be a Chi square with 5 degrees of freedom under the null. It would probably be more appropriate, however, to simply take their mean, because sign should not be discarded, I think. The first two metrics should be easy to rescale. The metrics involving maximum drawdown, however, are a bit tricky. You probably want to estimate the variance of these statistics under the null via a Monte Carlo simulation. ## Answer by chrisaycock (score 4) https://quant.stackexchange.com/a/198 A multi-alpha trading model ranks each asset according to the individual signals. For example, if I have two metrics and three stocks, I could just create this reverse-sorted table: ``` Rank| PNL W2L ----| --------- 3 | AAPL AAPL 2 | MSFT YHOO 1 | YHOO MSFT ``` Because this ranking/sorting method is non-parametric, I can just average each metric's rank by stock: ``` stock| score -----| ----- AAPL | 3.0 MSFT | 1.5 YHOO | 1.5 ``` And now it's easy to make a weighted average of the ranks; if I want PNL to be 2/3 of the value and W2L to be 1/3, I have: ``` stock| score -----| ----- AAPL | 3.000 MSFT | 1.667 YHOO | 1.333 ```
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.