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Genetic Algorithms Cannot Commit Incest.

Writer's picture: Tian Khean NgTian Khean Ng

#Excuse the misspellings in the image below DALL_E does not seem to understand my instructions.

In my previous post (see https://www.asiapacstocksquant.com/post/trump-proofing-with-a-low-risk-portfolio-of-asiapac-market-index-etfs ) I wanted to use Genetic Algorithms (GAs) to construct a resilient portfolio of 6-country market index ETFs. GAs are really the best tool if you equate gene pool resilience with diversity just like in Nature as generations evolve through crossover and mutation of genes. GAs are created by representing them as Chromosomes with each segment representing an input variable like the illustration above shows.

Thus, the objective is to maximize variance through breeding over hundreds of generations with crossover and mutation of genes. Fitness Function is defined against this objective and the fitter candidates have a higher probability of mating to be parents of the next generation.

However, the program could not converge (again just like in Nature) because the input variables had too much common DNA, amounting to committing digital Incest if they mate, which means that the program cannot terminate  and you cannot achieve your objective for a more resilient and diverse population no matter how many generations of crossover and mutation of genes are carried out.  


In the above Table we show you how much common DNA there is between Hang Seng (HSI), Sensex, STI, JKSE, KLSE and SETI. We use a metric known as Mutual Information (MI) which, unlike Correlation, can handle non-linear inter-relationships. MI is defined as that which reduces the amount of Uncertainty between variables. The Table above shows that except for JKSE and SETI, all other markets have very high MI >1 measured against the DJIA. Which means that its easier to use the DJIA to construct prediction models of STI and HSO markets. But which also means that you cannot create the necessary diversity in your portfolio for resilience.

The GA program could not converge (again just like in Nature) because the input variables had too much common DNA, amounting to committing digital Incest if the chromosomes mate.


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