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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.

apple

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.

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  • $\begingroup$ This may be too obvious (and therefore posted as a comment) but have you tried publishing some of it as working papers? I know a few examples of wp's that are often cited but not officially published. $\endgroup$ – Maarten Punt Oct 13 '19 at 15:14
  • $\begingroup$ @MaartenPunt I have tried that and had no impact in seven years. The first video is at youtu.be/R3fcVUBgIZw $\endgroup$ – Dave Harris Oct 13 '19 at 23:38
  • $\begingroup$ The "truncated Cauchy distribution"- on both sides? If yes, then it has all its moments. $\endgroup$ – Alecos Papadopoulos Nov 7 '19 at 23:07
  • $\begingroup$ @AlecosPapadopoulos no, just on one side. Although there is a planetary budget constraint, it is stochastic. There are a couple of ways to model it, such as treating it as a truncated Cauchy GIVEN liquidity. It can also be modeled through prices. There is a bit of skew in the distribution caused by liquidity effects. The budget constraint is wide, however. The probability that someone will accept 100 shares of IBM at 0 per share is 100% and at an infinite amount per share it is zero. $\endgroup$ – Dave Harris Nov 8 '19 at 0:38
  • $\begingroup$ @AlecosPapadopoulos In the US market you have examples of very side price swings. For example, my favorite is a firm that went from 5 cents per share, on a split adjusted basis to $35,000 per share, 365 days later, to 4 cents per share 365 days after that. It was undervalued at 4 cents per share. $\endgroup$ – Dave Harris Nov 8 '19 at 0:40
  • $\begingroup$ @AlecosPapadopoulos likewise because shares are purchased in nominal money, you could have Brazillian or Zimbabwean shares with extraordinary nominal returns. $\endgroup$ – Dave Harris Nov 8 '19 at 0:40
  • $\begingroup$ @AlecosPapadopoulos the mixture distribution has no point sufficient statistic, has no first moment, and in log form has no covariance matrix. $\endgroup$ – Dave Harris Nov 8 '19 at 0:41
  • $\begingroup$ @AlecosPapadopoulos and based on a population study of the CRSP universe, fits the data well. $\endgroup$ – Dave Harris Nov 8 '19 at 0:42
  • $\begingroup$ I have the impression that much depends on whether the Cauchy distribution you use has moments or not. If it is a matter of truncating the other tail also, then chose an incomprehensibly large number, I mean truly incomprehensible like Graham's number and truncate there. The distribution will then have moments, and the degree that it fits the data will not change. $\endgroup$ – Alecos Papadopoulos Nov 8 '19 at 6:23
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    $\begingroup$ I am afraid that this will further frustrate you, but to me it seems this is not at all a question for meta, which is supposed to be about discussing the Economics Stack Exchange.? $\endgroup$ – Jan Höffler Nov 22 '19 at 15:51
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1) I am not in a position to judge the interest of your work.

2) I am nevertheless sympathetic to your endeavor.

3) I believe it's pretty clear that, for better or for worse, even conditional on being "right" (i.e., having a better theory), it is very hard to overturn existing and established science (there is no lack of historical evidence thereof, including evidence of "failure to revolutionize" in which the new theory was actually "right", and I don't think anyone has a clear recipe for how to avoid these failures).

4) I believe everyone would also agree that it is even harder to overturn established science starting from an "outsider" position, which seems to be your case (sorry, I don't know the details of your story, so I might be off here).

5) This being said, I have scanned through your first video and based on this, I would strongly recommend that you do not pursue your video-producing efforts any further, or at least not with the kind of video-producing efforts you've started to undertake.

I might be wrong but I don't think that youtube videos are a good medium to present rich, new, and mathematically involved theories in detail. Even if there are benefits to producing these videos, these benefits are very unlikely to be worth the huge production cost you're about to invest in them.

If you're going to use youtube videos at all to spread interest in your theory, use youtube videos to present short, easily accessible, and intuitive examples of 1) what is wrong with existing theories and 2) how your alternative theory can help. That is, use videos to generate interest in your theory, not to lay it out in detail.

(Look at the drop out rates for many video playlists on economics that are much more accessible --- and, dare I say, entertaining --- than what you seem to be headed for --- say Marginal Revolution or Game Theory Online. Youtube viewers don't stick around very long.)

6) If I have a tiny piece of constructive advice for you it is to focus your efforts on addressing 4).

As terribly frustrating as it may be in your position, if you're 100% dedicated to advancing your theory, the best way might be to first "fall back in line". (Again, I don't know the details of your personal story, so you might have already tried this and the following might be irrelevant):

  • Try to convince established people in the field that you are not full of baloney.
  • This is not an easy thing to do, so start small!
  • In particular, do not start by trying to advance your own theory. Instead, start by trying to improve theirs.
  • To effectively "convince established people in the field that you are not full of baloney", you most likely will have to strategically/instrumentally move away from your beloved theory and show that you can make contributions to other issues and questions that others are interested in (even if you are not).
  • These contributions are likely to be more marginal (compared to your end-goal of "revolutionizing" the field) but they will, as a consequence, be easier to recognize as valid and useful by insiders.

    (This is the classical movie scene where an established figure starts paying attention to a newcomer because the newcomer found a "blatant and easily verifiable" error in one of the established person's paper or reasoning.

Another analogy is: I took you seriously and decided to answer your question not because I understand your theory and believe it might be valid --- again I am not in a position to do that --- but, in part, because you're on the higher end of the reputation distribution for this site, which you must have predominantly earned by answering questions that are not related to your own new theory.)

  • If you are really motivated by eventually spreading your theory, "starting small" may require you to go "as low as" (and I would really need many more quotation marks around "as low as") getting back to school and obtaining a PhD in the most relevant discipline.
  • Once (if ever) you've done all this and established people begin to pay attention to you for reasons other than your own new theory, try to start pushing your theory as gently and slowly as you can (if possible at all, focus first on the minimal modifications of existing theories that somehow "go in the direction of your new theory" and make existing theories better).

PS: I don't think it matters much --- and it's certainly debatable --- but I think this could very well be on-topic on the main site as well (at least if you put more effort into striping-off your question from its self-promotional content).

PPS: The proof is also in the pudding. If, as you claim, existing theories imply that billions of dollars of assets are mispriced and your theory can price them better, am I wrong to assume that an investor using your theory would be able to take advantage of arbitrage opportunities and make a lot of money? If that's correct, then the best way to convince people your theory is "the one" would be to make a couple millions out of it (I am really not joking here).

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  • $\begingroup$ Thanks for your detailed reply. I will think about it. There is a problem with starting "small." The math implies most of financial economics and ALL of macroeconomics cannot use the method of least squares in regression, either in logs or in raw data. $\endgroup$ – Dave Harris Nov 7 '19 at 1:48
  • $\begingroup$ To help someone with their theory requires their theory to be defensible. I haven't found a mathematician or statistician that thinks I am wrong. But no one will publish the work. $\endgroup$ – Dave Harris Nov 7 '19 at 1:49
  • $\begingroup$ As to making money, I used to be a Franciscan. I am indifferent to being rich. I have managed money. Using the CAPM framework, my alpha is 15.75 and my beta is .75. Leaving that framework, my scale parameter is about two thirds of the market return and my return is over twenty percent above the S&P. $\endgroup$ – Dave Harris Nov 7 '19 at 1:51
  • $\begingroup$ As for getting another degree, I am near retirement age. I have no interest in another degree unless someone wants to pay me to get it, and I do not mean a stipend. $\endgroup$ – Dave Harris Nov 7 '19 at 1:52
  • $\begingroup$ I do agree with you about YouTube, but YouTube has one advantage, it cannot be censored easily. It also could force the discussion if the right person reads it and understands it. It really only takes one math major to read it to realize the consequences. It is clear as mud to an econ major. $\endgroup$ – Dave Harris Nov 7 '19 at 1:53
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I'd just like to reinforce Martin Van der Linden's point again. I would also like to first emphasize that I am not in a position to judge your work either.

The way I see it, your fundamental problem is how to get attention for your work. Especially from the right people.

In a comment about YouTube you say "It also could force the discussion if the right person reads it and understands it." Those are two very big ifs even if people were willing to quickly throw out everything they thought they knew about finance, which they probably are not. The most scarce resource on the planet is attention, especially that of big scholars who you need to convince.

Just putting out working papers hasn't helped get the attention. YouTube videos probably won't help much either.

The only way I can think of is to publish a couple papers first in good peer-reviewed journals by advancing someone else's research agenda. This will a) increase visibility of your other work and b) increase people's priors that your theory might be correct. Especially since understanding your technical work will require some effort on most people's part, it is unlikely someone will even start to read your papers if you don't have the aforementioned point b).

Good luck.

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  • $\begingroup$ I have tried all of the top journals. I was desk rejected except in two cases. In the first case, the editor rejected it as obviously wrong. I sent back a letter asking for peer review, so she sent it to a statistician and his response was "no, he is right the CAPM is derived wrong and violates the laws of mathematics." She was stuck publishing it. For the second, I am proposing a new branch of stochastic calculus. It first-order stochastically dominates Ito methods. It was accepted, but the editor sent me a copy of one of Einstein's annus mirabilis papers to copy off of for examples. $\endgroup$ – Dave Harris Nov 14 '19 at 4:23
  • $\begingroup$ The problem is that the answers do not come out the same at all. Not even close to the same. It was rejected with sincere regret but it was a bridge too far, even if it was correct, which the editor believed it was. $\endgroup$ – Dave Harris Nov 14 '19 at 4:24
  • $\begingroup$ I also submitted a population study of the CRSP universe using the uniformly most powerful test and the Bayesian test as well, closing the discussion in Bayesian and Fisherian likelihood-based methods. It excluded mean-variance based models with six and a half million zeros in front of the chance that mean-variance was correct compared to the proposed models. $\endgroup$ – Dave Harris Nov 14 '19 at 4:26
  • $\begingroup$ I would love to advance someone else's agenda, but most people's agendas get gutted by the math. $\endgroup$ – Dave Harris Nov 14 '19 at 4:27
  • $\begingroup$ Here is something I recently wrote in a blog. It will give you an idea of how far apart I am from most economists. It is the story of a mathematically guaranteed fair coin and an arbitrager who can correctly choose the coin 90% of the time. If you are experienced and clever enough, you can do this same thing in the financial markets but only because economists are doing it wrong. datasciencecentral.com/profiles/blogs/… $\endgroup$ – Dave Harris Nov 14 '19 at 4:33
  • $\begingroup$ Thank you for your input, however. $\endgroup$ – Dave Harris Nov 14 '19 at 4:41

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