August 24, 2015

(see **part 1**) The evolution of a portfolio is determined by its ongoing inventory composition. It can be written as a time function:

A(t) = A(0)*f(n, q, Δp, I, D, t).

The information set (I) can be independent of everything. It's just one's way of looking at things and reaching trading decisions or not (D).

Some basic trading styles can be explained using A(0)*f(n, q, Δp, I, D, t). For instance, the Buy & Holder, as a long-term player, will have fixed q looking for the large Δp that will develop over long holding intervals while keeping n relatively small. Mr. Buffett's trading style fits in this category. It is as if he went for large Δp, large q with n not so big. He solved his optimization allocation problem by growing n, q, and Δp over time which enabled him to exceed long-term market averages.

In his dealings, he gradually went for the larger q (elephants) coupled with large Δp. It has proven to be most effective. But it's not everyone that can go elephant hunting, even Mr. Buffett started with a smaller game. It is just that with time, that is where traders/investors need to end up. It is not how they can start, but it is what they should aspire to. You can't nickel and dime the market or flip your entire portfolio on a weekly or daily basis. Your trading strategy has to evolve and be conscious of the law of diminishing returns as the portfolio grows.

At the other end of the time spectrum, you have HFT. It relies on large n, small q, and small Δp. It's not that they would not like large Δp, it's just that they are not necessarily available under their short trade time horizon. So to compensate, they go for high frequency, really high frequency. A million $1,00 profit is still a million dollars, and HFT firms understand this quite well. There is no elephant hunting here, just grazing on their small change diet without bothering the elephants or even letting them know.

Traders are all shades of in between mostly limited by A(0), their initial capital. They can't do HFT, resources being too limiting. Nor can they afford elephants. So they jump with both feet on the Goldilocks Δp of their choice using whatever kind of "predictive" future they can find. Their hope is that based on their unique information set they can make favorable, meaning on average profitable trading decisions. However, some might not have fully grasped the word "coincidental".

Most short-term traders go for Ʃ(n) q(i)*Δp(i), and kind of forget that n and t also matters. They design trading strategies capable of generating a positive average Δp producing a positive outcome: Σ(**H**.*Δ**P**) > 0. And because of their size are forced to have relatively low q(i) which will let their portfolio grow but not at high speed. Δp's take time to develop. Since their strategies were not designed to generate a large *n* either, they were limiting their potential.

Their strategies often seem to break down with time or need optimization all the time to compensate debilitating deficiencies, when the designer could have easily remedied the problem in his/her code. If they don't initially address the problem in their code, how could it ever be solved?

This kind of changes the nature of the game. Instead of trying to find trading strategies by mimicking past observations, anomalies or price patterns and applying those to future price movements; one could look at ways to increase n, the number of trades, increase q(i), the quantity traded as profits increases and also try to increase Δp(i) even with its limited range in price movements due to its limited trade time. It becomes a bean counting proposition, akin to finding a mathematical solution to: how many trades with such and such characteristics will I be able to extract from future price movements over the long haul?

My research resumes this in matrix notation to Σ(**H**(1+g)^t.*Δ**P**). It says: increase the holding inventory at an exponential rate in order to compensate for return degradation and accelerate performance. This can be done by increasing n, q(i), and Δp(i) as the portfolio grows.

Created... August 24, 2015, © Guy R. Fleury. All rights reserved.