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Comparing Weekly Model P&L with Daily Backtest P&L

Article Quant Q&A · Author: Wheelin' and Dealin'
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Summary

The question concerns comparing quarterly P&L projected from weekly portfolio sensitivities with daily backtesting P&L. One suggested approach is to aggregate daily returns over matching periods or convert returns to a common interval using an appropriate annualization convention. The goal is to align the measurement horizon before comparing results.

The response also identifies a separate limitation: weekly sensitivity updates can miss portfolio changes that occur and reverse between observations. That does not make a comparison meaningless, but it means the model’s sampling schedule constrains what it can represent. The document does not provide a detailed method for reconciling changing portfolio composition or explain how to align P&L measures that are not returns; its advice is general and depends on what the two P&L series represent.

Key ideas

  • Aggregate or rescale returns so that the compared series use a common measurement interval.
  • Weekly sensitivity updates can miss portfolio changes that occur between observations.
  • A frequency-aligned comparison remains informative but reflects the model’s update schedule.
  • The correct comparison depends on the precise definitions of the model and backtest P&L.

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BacktestingStatistics
Full text
# Backtesting model results, but backtesting output sampled at different frequency than model output


# Backtesting model results, but backtesting output sampled at different frequency than model output












So, I'm trying to backtest a model that computes P&L. This model pulls sensitivities on a weekly basis and applies market shocks to these sensitivities to project quarterly P&L. I want to compare this to clean (backtesting) P&L. The issue is that the backtesting P&L is daily. One could aggregate the daily P&L over a given quarter to compare against the model... but since the model only pulls sensitivities weekly, if the portfolio were to change materially intra-weekly (e.g., pull the sensitivities on Monday of Week 1, but on that Wednesday the portfolio changes, and then the portfolio composition pulled on Monday of Week 2 is similar to that of Monday Week 1) it would not be captured. Is there any way to compare the two results?

## Answer by Chris (score 1)

https://quant.stackexchange.com/a/44805

It's not clear what you're asking or even trying to do.

Based on my read, you have a trading model you're using that takes inputs weekly to produce some kind of PnL. It's not clear what you mean by 'clean (backtesting) P&L' for the comparison.

As a general matter though, comparing one set (for simplicity's sake) of returns to another set aggregated over a different interval can be dealt with by bring return interval of each in line (eg, average daily return by some annualization figure (250/252) to compare to annual returns elsewhere).

As to your model potentially missing something by only taking inputs weekly...well, yeah, that's a limitation of updating only weekly. That doesn't mean a comparison is any less valid...just that your model only incorporates updates weekly, part of the framework you've chosen.

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.