http://quant.stackexchange.com/questions/181/why-is-there-no-meta-model
hy is there no “meta-model”?
|
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. |
||||
|
feedback
|
|
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. |
|||
|
feedback
|
|
I would conjecture that the reason a proof does not seem to exist, is that in a purely theoretical framework, such a model could exist for 'corner cases'. Under the assumption that the existence of a meta-model would modify the usage of the model / effect the market, something like Russell's paradox would seem to occur. Except in the case where a stable market/meta-market relationship could be achived. I.e. we could construct some theoretical markets (i.e., not a model, but some purely theoretical complete description of the market) in which the existence of a meta-model would not effect the market or which in a finite number of steps would converge to final market / meta-model pair in which the existence of a final meta-model does not cause changes to the market. |
|||
|
feedback
|
|
Evolutionary economics provides a framework for reasoning about meta-models about markets. The primary one being ecological. Thus, predicting a model's half life would involve discussing market ecologies, niche specialization of a model, comparative fitness of models, and the like. |
|||
|
feedback
|
|
Imagine you had a formula that predicted what the S&P 500 would do every microsecond for the next 5 years. A parsimonious representation of this formula would stitch together simpler formulae that operate on disjoint, exhaustive sub-intervals of the next 5 years. So in a sense even a "perfect formula" would be made up of models that expire. I believe there are ways of meta-modelling just as there are ways of modelling — but there is no formula for the stock market because some determinants of the price are exogenous. Meta-models are imperfect for the same reason models are imperfect. |
|||
|
feedback
|
|
Without a stable covariance structure, I imagine the error terms driven by distributional assumptions and time elements of the underlying would kill any definitive statement one could make. |
|||
|
feedback
|
|
I see the meta model as the process you employ to develop a model. The important problem is that the real world changes from continuously in order to maintain your meta model you would need to constantly enhance your middling process to account for those changes. Good meta model is theoretical construct |
