If I design a trading model, I might want to know the model's half life. Unfortunately, it doesn't seem possible to predict alpha longevity without a meta-model of the market. Intuitively, such a meta-model does not exist, but has that ever been proven? This sounds like a Russell's paradox or Gödel's incompleteness theorems for the financial markets.
I'm adding a bounty to see if I can get some more responses.
Answer
There are plenty of market models -- capital asset pricing model (CAPM), conditional CAPM (CCAPM), intertemporal CAPM (ICAPM), and arbitrage pricing theory (APT). But any model, finance or otherwise, requires assumptions. Under these models the market may pay you to play your strategy, but in return you must accept risk. So with one of these models you could determine the half-life of your trading model, but it would require you to make some forecast about the relevant factors in your model. And even then you would have to accept some risk-return trade-off.
The required assumptions for these models -- typically things like common information set and expectations for all players, no arbitrage, and complete markets -- aren't perfect, but I think they are the only way to build a tractable model for the whole market. It is difficult to justify a model that has predictable risk-free profit opportunities. There are just too many smart, hardworking people in financial markets.
I am not saying that I think markets are completely efficient, just that it would be difficult to build such a model.
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