Tuesday, July 14, 2020

Port folio management and risk equalization, a continuing series

{\displaystyle {\binom {n}{k}}p^{k}q^{n-k}}

This is a term in the probability distribution in one of some M  investment groups.
Link to previous discussion of the topic.

It is an unfair coin.  And you have a complete sequence and know it is no more accurate than four coin tosses.You have access to a fir trade pit to bet the distribution.

When you bet, you will look at the board and estimate p^k * q^(N-k), N = 2k. You will adjust your current bet by that ratio and return to update your portfolio. You total bet will go as 2^N,  I think.

The number of coin tosses across your whole portfolio is conserved. If you get stuck in third place, your whole portfolio gets a bit out of whack.

The whole thing really gets adjusted on those major deju vu moments, when a complete sequence reveal itself, everyone know the loop.  In fair trade pit, common knowledge becomes a bettable distribution.

If you count integers in a self sampling system you have to manage round off error. The good portfolio counts down the sequence of optimally congested bets.

We are limited to a finite number of integers, we count deviations from optimum, a small number. If we take the total number of all possible bets then it must be of the form x^x,  all possible paths with replacement.   If you have 50 solid trade points that mean something, then in deviation count, you coin tosses are close to 2 * 4, or less.  The aggregate economy is very uncertain, a 3% price variation seems standard across the year. The number of variations from optimum about 30-40. That is what you are tracking, ultimately.

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