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As far as I know there is no APM that is able to explain all stock market anomalies. However, my search for papers empirically test a set of widely accepted APMs was not very successful. I would like to know more about this though and would be glad about any direction you can lead me to.

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  • $\begingroup$ Do you want an "asset pricing model" or an "equity pricing model"? $\endgroup$
    – demully
    Nov 8, 2019 at 2:37

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No, but I am getting close to building one. You can take my article on the construction of the distribution of returns and apply the Kelly criterion to it. It will generate a subjectively optimal solution. Equivalently, you can assume log utility and include the presence of constraints. It maps to the same solution as the Kelly bet, but it has the advantage of being capable of fully accounting for the consequences of loans and so forth in the model construction.

Harris, D. E. (2017). The distribution of returns. The Journal of Mathematical Finance, 7(3):769–804.

Kelly, J. L. (1956). A New Interpretation of Information Rate. Bell System Technical Journal. 35 (4): 917–926.

It does not constitute a pricing model, I am close but there are larger issues out there. The challenge is that the multivariate truncated Cauchy and the multivariate hyperbolic secant distributions, the two primary distributions involved, lack a covariance matrix even in log form so anything resembling a least squares model is either strictly invalid in the case of raw data, or highly questionable as in the case of log data.

I am personally a bit pre-occupied at the moment or I would probably be done. I am looking for a new institution to do research at. Colleges are closing around the US and/or downsizing and I seem to have made an unfortunate choice of schools. I am also proposing a new stochastic calculus for finance. You can find it at: Harris, David E., A Generalization of Stochastic Calculus--A Conjecture (November 29, 2018). Available at SSRN: https://ssrn.com/abstract=3197451 or http://dx.doi.org/10.2139/ssrn.3197451

It is in peer review with example cases not in the original. It will be followed by a new options pricing model that lacks the craziness built into Black-Scholes and Ito models. If I can find a research home, I plan to finish replacing the mathematics of finance within the year and complete the high-level empirical solutions in another year.

I used to manage a portfolio. I have solved the math behind Graham and Dodd methods. There is a mathematically compelling case for them. If you are looking for a tool, pick up the Graham and Dodd's Security Analysis.

I would suggest both the fifth and the sixth edition.

Six is https://smile.amazon.com/Security-Analysis-Foreword-Buffett-Editions/dp/0071592539/ref=sr_1_1?crid=2D29Z8VDF8HFD&keywords=graham+and+dodd+security+analysis&qid=1560200633&s=gateway&sprefix=graham+and+dodd%2Caps%2C227&sr=8-1

I cannot find references to edition five. It is the better one for someone who would prefer to think algorithmically. The sixth is better for one who wants an intellectual grounding. Six, however, is really edition the 1940 edition reprinted with updates by leaders in finance and the field of accounting to bring the rules up to date with modern accounting and markets practices.

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  • $\begingroup$ Are investor expectations endogenous in your model? $\endgroup$
    – Jj Blevins
    Jun 11, 2019 at 9:39
  • $\begingroup$ @JjBlevins sorry, I didn't see your comment til now. I am sure I got the note and I told myself I was going to answer and probably did something like restart my machine. Read the working paper at SSRN. It introduces a broader estimator, called the anticipation operator and two special operators to deal with your question. $\endgroup$ Nov 9, 2019 at 0:06

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