Some of you will have seen my posts. I am looking for advice. I am not posting it on the main site as this is about the process of economics as a science rather than the contents.
For about a decade now, I have been trying to get a set of articles published, with great vigor recently. I have, in the last year, developed a new stochastic calculus that first-order stochastically dominates both Ito calculus and Stratonovich calculus.
As important, it makes it obvious why mean-variance finance models could never work empirically. I have also replaced the options pricing model with something that works. I also am about to replace optimal portfolio construction.
No one wants to be near it, with maybe one regretful exception. One editor that did read it, did want to try to fit it into his journal's mandate but couldn't figure out how to. I am trying to reground the entire mathematics of finance and much of macroeconomics. No one wants that even if it works.
The problem is that the work would imply that over half a quadrillion dollars in face values of derivatives contracts are mispriced (BIS data). Of course, if you look at the mountain of papers on how and why certain things do not work, that should be no surprise.
I am starting a series of YouTube videos since I have been desk rejected out the ears. I am up for any better idea. There is no point in submitting papers to editors if three or six months later I get a desk rejection letter and no review.
My argument is mathematically simple. If you drop the assumption that returns are known, and of course they are not or the field of econometrics wouldn't need to exist, then returns are $$R_t=R_G\times{G}+R_M\times{M}+0\times{B}+\sum{}R_{\delta_i}{D_i}-R_L-1,$$ which could be that total return is the return due to being a going concern multiplied by the probability of survival over the interval plus the return due to a merger times the probability of a merger plus the return due to bankruptcy plus the returns on dividends and the loss of return due to liquidity costs.
Simplifying a bit to make the post shorter, $$R_G=\frac{p_{t+1}q_{t+1}}{p_tq_t}.$$ As the distribution of this one component lacks a first moment and lacks a covariance matrix in logs, it is sufficient to undo mean-variance methods in both raw form and in logs. If we assume no stock splits or stock dividends and given Bayes rule, $q_t=q_{t+1}$, where $q$ is a quantity purchased and $p$ is a price. So, $$R_G=\frac{p_{t+1}}{p_t}.$$
If we posit that the equilibrium price at any time is $p_t^*,\forall{t}$, then equilibrium reward can be defined as $$R_G^*=\frac{p_{t+1}^*}{p_t^*}.$$ The density for $R_G$ could be understood as $$R_G=R_G^*+\xi_t.$$ Since $p_t$ could be decomposed to $p_t=p_t^*+\epsilon_t$, the distribution could be solved as $$\xi_t=\frac{p_{t+1}^*+\epsilon_{t+1}}{p_t^*+\epsilon_t}-\frac{p_{t+1}^*}{p_t^*}.$$
A direct attack on the problem yields no useful answer because it creates more parameters to solve for than there are observations. An attack in polar coordinates, however, makes it possible to focus on the distribution of the slope of the vector $$\begin{bmatrix}\epsilon_t\\ \epsilon_{t+1}\end{bmatrix}.$$
Dropping the rest of the math for brevity as the above mechanism works in some varied form for any asset including antiques, the return for equity securities, ignoring dividends, liquidity costs, merger risks and bankruptcy and after several transformations, the distribution of $R_G$ becomes the truncated Cauchy distribution.
It lacks a mean. In 1851 Augustin Cauchy proved that such a problem would cause least squares models to always produce spurious results, hence the name. Interestingly, it fits the data very well. Also, not unimportantly, the normal and log-normal do not fit well.
As an example, this is the fit for Apple. It could be improved by accounting for the uncertainty in the estimate, accounting for dividend effects and liquidity effects. I did not. Still, it is quite good.
Once it is part of YouTube, it lands in the hands of grad students, which is good, but also the press. Whereas a journal article is boring, YouTube videos are accessible.
I am planning three dozen videos of around fifteen minutes each, one of thirty minutes. At the end, an entirely new model that doesn't depend on knowing any of the parameters, does not have expectations, uses all the information in the data, and can have fair gambles placed on it is created. It is going to take me months.
Nothing of the CAPM is left. No WACC, no frontier, no systematic versus idiosyncratic risk, no least-squares regression, and even diversification no longer automatically holds as a protective measure due to the absence of a covariance concept. Indeed, many people in 2008 found themselves in well-diversified holes.
I am writing this late at night and might not have posted this in the day but I would prefer to stay inside the lines and not color outside of them.
If not, have your grad students start watching YouTube about a month from now. The first video is actually out but I am revising it and have completed the scripting for the second. I am working to revise it now so I can create it.
I am looking for any idea that is better than YouTube. The only plus is that YouTube allows for a substantial expansion of the math so it is both primer and proof. The downside is a lack of criticism until after it is out there.
