I took a look at some other sources (for example: transaction costs - Typical coefficients uses in square-root model for market impact - Quantitative Finance Stack Exchange, https://static.autobahn.db.com/microSite/docs/DBTradingCostModels-v1.1.pdf and God rule of thumb avgdaily volume vs position size? - #3 by yuvaltaylor) that also use similar formulas for transaction costs and I think it is actually fair to say that this seems more fitting than the way P123 calculates transaction costs as of now (based on price*volume for slippage and price for commisions from what I understand)
I thought about the implications of this when it comes to using P123. In doing so, I read some more of the older posts you wrote. I like the idea of linking stock ranks to expected returns as mentioned here : How to find cross-sectional Rank or RankPos - #5 by primus and after that subtracting transaction costs. As mentioned, this can then be used in formula weighting or buy/sell rules.
However, If I would use this ‘expected returns based on ranks’ type thinking and a formula for transaction costs based on volatility, transaction size and volume in for example a simulation with formula based weighting, then it probably will not backtest well.
This is because the assumption that P123 has about how to punish for transaction costs differs from the way I correct my rankings based on transaction costs.
Hence, I think the correct way to go about this is to first backtest using the definition for transaction costs that P123 itself uses. And then, when this approach gets validated and indeed improves returns (or other performance metrics) compared to not taking into account transaction costs, change the transaction costs formula to one based on volatility, transaction size and volume. Of course, this might not backtest well. But it should improve returns in practice (out-of-sample) anyhow.
For me, this raises the question whether it should be possible for users to adjust the variable slippage formula in their simulations.