Nov 1, 2017

Kelly allocation bet with regime suppression?

I think I tried something like this before but I am still not sure if I have this right or if this is a corrupt way of applying the principle but since I am neither academic nor practitioner I can proudly wear my amateur hack hat (I should make some real RiversHedge amateur hack hats for give-aways) just to play around and see what happens.  Now that I have a few more readers, maybe someone can step up and guest-post some better math for us if they think I am too far off track.

Here is the basic setup for the baseline (if I am taking us in the right direction).  I have some annual S&P data from Stern which I mainly use because its in an excel sheet on my PC where I can remember to find it, which is why it is still only current to 2015.  This is convenience data not rigor-data.  I split it into two: winner returns and loser returns.  That allows me to get a win rate and lose rate 73%:27% and an average win .208 and loss -.137.  Now I normalize the odds to 1.52:1 and calculate the edge as 1.52*w% - l% or .834. Edge/over odds is 54.8% so, if I am doing it right, I'd allocate ~55% of my wad to equities in a series of bets (here's where that sequential-independent thing might give me pause...)

Now I want to go darker or at least more conservative.  To do that I: 1) clip the 5 top returns from the win pile to take out some of the odd ducks from the early 20th century as a conservatising assumption , 2) I subtract an arbitrary .02 from both piles because all those genius pundits tell me I should expect lower returns for a long while, 3) I move any wins that are now losers to the lose pile, and 4) I recalculate.  w/l = .67/.33, avg win is .175, avg loss is -.1405, normalized odds are calculated as 1.25 rounded, edge as 1.25*w% - l% = .516.  So edge over odds in this darker regime suppression scenario would be .413 or a ~41% allocation "bet" on the risk asset. 

Even if that is not legit, it is not totally out of the bounds of reasonable experience I think.  That's also roughly about the shift I made in mid 2007 which saved me a bundle going into March 2009 even though I had no idea what a Kelly criterion was back then.   Maybe I should think about trying that shift again. 


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