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?
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.