Sunday 16 September 2018

The anti-FOMO movement

There are n strategies, each with returns $r_i$.  Ranked top to bottom, so $r_1$ is the strategy with the highest return (long term).  Why not just put your wealth all in strategy 1?  Putting only a fraction of it in 1 and fractions in 2,3,...n leaves one with a feeling of missing out.  I suspect if you live to be 640, then this would be the effective result of the ideal allocation strategy.  Indeed if you have a 60 year perspective, this might also be the case.  But history doesn't always repeat itself.  So you can never be sure the future will continue sufficiently to be like the past.  Hence you'll want to diversify.  For example if you are Russian, living at the turn of the twentieth century and happened to note in 1901 that the St Petersburg stock exchange was your $r_1$, and decided to put all your wealth in there, then you'd be in for a shock when the Russian revolution came and wiped your wealth to zero.  If you were an ultra risk-adverse German post WW1 and thought you'd keep your money in nice liquid deutsche-marks, then the hyper-inflation would have likewise wiped you to effectively zero.
The degree to which you trust the institutions which underpin the strategy returns you feel you have access to is the degree to which larger and larger fractions of your wealth will go into strategies 1, 2 etc. rather than into tail end strategies.  Conversely, the degree to which you are uncertain of the future of those enabling institutions (and this, to be sure, is an uncertain act of political tea-leaf-reading) determines how distributed your wealth will be.  Your degree of confidence in strategies 1, 2 also grow to the extent that your future wealth-investment time horizon is long.

Besides the above unknown unknown, is the idea of correlation.  If all strategies 1,...,n are fully correlated with each other, then each of n is as good, in this one respect, as all the others.  But the degree to which any two (or more) strategies are uncorrelated or lowly correlated, opens the possibility that there was a combination of these strategies which was ideal, in some wider, as yet to be defined sense.  

So a world with a lot of serious unknown unknowns presents a difficult environment for the ideal strategy allocation algorithm, as does a world with cross strategy high correlation.  Thankfully so far the world we live in is somewhat known, somewhat predictable .  And this is the space that the theory of the ideal strategy allocation algorithm can work within, where the past can tell us something about the future, and where strategies have less than perfect correlation.


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