xQuant

One would like to think that an investment in stocks can not result in a complete meltdown, except in some strange pathological cases. Yet it can be easily shown that by the mere structure of stocks, such a meltdown (or its bubble counterpart) is largely unpreventable in a systematic way.

If one can hope to have price stability, it could only be found in the form of a “fundamental value” around which market’s participants could stabilize the price. If prices becomes to low, an agent would then buy because he knows he can extract some money directly from the company, in the form of dividend. In the lack of such capacity, buying at a “good price” does not mean anything, as nothing prevents the price to go even lower, at some even ‘better’ level..

So at the heart of price stability lies in that fundamental value, which as every other investment can be obtained by adding up all the present value of future forecasted cash flows. Given a set of hypothesis on future profits, this gives the company a fundamental price, under which one can decide whether or not the stock is over or undervalued. But….. beyond that mere number, one can wonder how firmly grounded such a value can be.

Let’s consider a simplistic example company whose business yieds 1 dollar per year. Let’s assume that interest rates are on average at 5%. For each year i, the present value of a dividend would be 1 USD * 0,95^i , and the current value the sum of those would then be 20 USD. Out of those 20 USD, 8 comes from the next ten year’s dividends, and 12 comes from all the years beyond that.

For a hypothetical investor who has formidable insight about the next 10 years for the company (quite a genius really), and intending to bring back market value with the fundamental one, it means that despite his formidable insight his investment is still subject to 60% of sheer uncertainty after 10 years, and to the market’s evaluation of that uncertain period of 9 years and beyond before. The inability to evaluate the correct price of stock is fundamental and can not be overcome by the mere construction of what a stock financially is. Even this is a very rough case, it does show that the level of uncertainty contained in stock prices is pretty much irreducible, and for its main component, driven by the market itself. What Keynes called the beauty contest is not a secondary but a primary, essential effect.

In real life though, one can hope that other stabilizing forces come at play, and that through time and diversification, good judgment becomes recognized by the market. And technique can tentatively be put in place to try to isolate as much as possible the judgment and eliminate other effects (global market or sectoral movement etc…) . However, there are deep consequences of this fundamental uncertainty :

• A lot of a corporation’s energy is spent to control market’s feeling (avert fear, suscitate enthusiasm). Although necessary when a nothing can flip your stock, that diverted energy, in the end, does produces nothing.

• It boldens the case for investors who have a edge in really understanding a business. An obvious illustration of this is Mr Buffet. (real) private equity investments has been historically successful it seems as well.

• It tends to imply that stock market should not be a straight mass-investment vehicle for retirement or for the general public. If a successful investment implies a certain craftiness, the current plain vanilla stock investment by armies of zombies is poised to be profited from by unscrupulous financiers.

The market legitimacy in classical economy lies in its ability to have a match between investors willing to taker some risk, and companies in need of financing. The current “stock” does not seem to be able to fulfill that role, at least in the way it is used today. It can be seen as easy to say so now that the market crashed, but I guess I have some credential there, having blogged about it before the meltdown..

An interesting discussion by a Stanford professor

I have been looking a long time for a way to represent on the web a mathematical corpus. It would be tremendous if one could find on the web the different books written on a subject, in a form that enables verification of theorem and proof.

Let’s reflect on what a lesson is : Mostly a lesson is about learning one by one different entities, and the relations that those entities share. It is all about serializing a graph.

If we were to improve this process of learning, we should identify what represent the most effort and the least added value in the making of it, and I see 3 big bottleneck.

• This process has to occur at a level the audience can understand :

The same lesson can take a day or 5 minutes depending on the knowledge of the audience. One of the big problem that clutters reuse of lessons on a large scale basins is that every time one wants to adapt the level, a whole rewrite is necessary. Having a formal representation of books would allow for seamless rewrite of proof down to the basic axiom if necessary.

• Another variability is how does one reuse the theorem or presentation of another.

Dissemination now is informal, slow, and based on individual reading. Few ways exists to have clever solution to emerge. A repository of steps for proofs, which would allow reuse in other context, would enable indirect voting, and promote the best practices.

• Finally, another problem is the sheer size of the domain which can only be tackled with by many specialists.

Sometimes the difficulty lies not in the domain itself but in the many ways there are to show one same effect. There is no place for such collaboration to take place in a fruitful way, with people ranging from high school students to phd’s to contribute and enrich each other. Wikipedia exists, but is completely out of scope : what if I was to see the 10 differents ways to prove an assertion, and how the theorems used apply in the specific case i am looking at ? wikipedia can’t handle this kind of data explosion and no onewill contribute this to the details I might need (and some other person won’t)

So, facing those issues, one might think that the computer science people in universites found a way ? No, you want to know why ? They are research ways not tho share proof and have a formal system for proof and representation. no. they are *waaaaayy* behond that : they are looking to *automate* the creation of proof. This really is for me the completely wrong way to go, and we should first concentrate on having a formal description system to tackle those 3 points I exposed. *Then*, with such a useful formal description, will we get ammo for automated proof, if we ever can solve it.

That’ll do

Dir.glob(”#{RAILS_ROOT}/app/models/**/*rb”).each{|m| Dependencies.require_or_load m }

Object.subclasses_of ActiveRecord::Base

In a brilliant demonstration of technical expertise and non-conformist brio, that is, of utter elegance, “xQuant(xQuant)”:http://www.xquant.net is now equipped with a “Wiki section(Wiki)”:http://maths.xquant.net that will enable users to render their thoughts in plain English and Latex.

This “Wiki(Wiki)”:http://maths.xquant.net is particularly meant to be used to develop themes including inference, categories, and stochastic finance.