Risk equalization part three

Bloomberg:

Bloomberg

Previously and in the last post we looked at this sequence as a binomial with an unfair coin. We noted there is enough noise in the series to limit this to four coin flips to identify each of the values. There is only one term for no heads ut of four tries. We then folded in a compounding interest rate and that would be the cost or gain for total return adjusted by investment size when all terms were treated like options pricing.

Investors may have three or four of these sequences, each representing the complete peak to peak sequence of a sector in the portfolio. They all have various amounts of noise, the effect of which is to reduce the number of coin tosses in support. They will all be converted to fair coin flips, be independent, and thus the arrival rate, when drawing from the binomial, will be relatively prime and order, and adjusted by investment size to balance total return. The effective coin toss number is the effective trading rate for each of the members of the portfolio. Spit the model between trading space and Bayesian space. The Botzmann constant for doing so in in the interest rate adjustment needed, which takes you from the individual model to the distributions in the collective model. That constant is set different for 3,4,5 element portfolios, as is the fundamental limit on trading rate and the one fundamental rule, only rarely is any sector trade third place in the trading pit, when trading 3-tuples..

Sort of the basic theory, needs proof that it maximizes total return. I have not put this to the numbers. I would compress the values above, low pass the noise, in essence. But the noise is uncertainty in N, total trade space, a fuzzy constant. Coin tosses are those Markov sets at each node. And the rules apply about how often you must and must not coin toss twice around the total Bayesian sequence, to maintain integer mapping.

It boils down to removing gain when you are cheating and adding losses when being cheated. Cheated means, is the limited trade space congested too much.

In a 3 tuple economy, like our, this boils down to, we all minimize the probability of being stuck third in line. The fundamental truth in macroeconomics. Optimum congested means this math to balance the coin using compounded gains and losses. Overly congested means we get Antificants,  N out of balance and the current economy of scale is not maintained. Shit happens, everyone do the math and make a fair coin for a while.

In the portfolio the investor trades then updates hi board.  If the investor mistakenly gets stuck behind on a trade, then is board is not settled before another element in the portfolio issue an update request. Hence, all elements are traded to conserve trade space, finite. Most of the simple portfolios are simple triples.

Losses? The case where you mostly lose but when you win you win big. There is the other case. Both rebalanced by compounding gains or losses. None of this has been put to the test, it is just following the logic of sandbox.  The balancer is like a pit boss, removing skew. Relative under sampling balances variance, and amount invested balances mean.

But a portfolio can have groups of these. Use 4 and 5 tuples for estimating term structure with a clock. Or break out energy into its own dimension and run tests against it. Lot of games.