One more extension to my asset allocation optimization journey

I thought I'd try another amateur hack at optimizing an asset allocation, this time using the Kelly Formula for bet sizing.  I'm pretty sure I don't have the math chops to get this completely right, hence the "amateur hack" comment.  I'm giving this a shot because I just finished "A man for all Markets" by Ed Thorp  and I'm in the middle of "Fortune's Formula" by William Poundstone that, among other things, profiles the Kelly math for optimizing bet-sizing for a given size of capital if you know odds and payouts.  What I'll do is a little bit of a bastardization of the math because I don't really understand what I've read on this in the book and other papers very well even though I have used rules of thumb in systematic trading that are vaguely similar.   So let's do this[1].  We'll make some really simple assumptions using some discrete numbers and analysis, some of which might be mis-matched to each other (or innumerate), like:

- 10 year rolling returns on S&P beats the 10-year Treas. real return 85% of the time [4]

- we'll use real returns on S&P and the 10-year yield for the betting math [2]

- mean returns for S&P/10year-total-ret since 1900 = 11.4/5.18% [3]

- so a spread of ~4.5% on average (?) [3]

- assume, perhaps wrongly, that a downside for stock total return over x years is 0%

- assume simplified Kelly math is "EV/odds-offered"

- let's say the winning bet is 11.4 - 5.2 = 6.2%

- let's say the losing bet is 0% return on stocks so a -5.2% opportunity cost

- that means EV = .85 x 6.2 +.15 x -5.2 = 4.5%

- that means odds-offered = winning bet = 6.2% (did I get that right?)

- let's also say we are a conservative investor that would use a "1/2 Kelly"

That means that if you buy those assumptions, and I really recommend that you don't, the result is:

[ ( (.85 x .062) + (.15 x -.052) ) / .062 ] / 2 =  36.2% allocated to the risk asset.

Ok, so this is, after all, just a dumb hack and probably stretching it a bit but what I find interesting is that after trying to do: 1) asset allocation optimization using a simulator, 2) AA optimization using backward induction and dynamic programming, and 3) using a weak attempt at Kelly criterion math with some stroked data to come up with an AA, I keep ending up with a rough (very rough!) estimate of around 40% to a risk asset when risk averse and 70% when risk taking.  That persistent kind of convergence is getting interesting especially since it doesn't match everything else I've read on asset allocation very well.   

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[1] anyone that knows this stuff: let me know and we'll profile a response as a guest post…

[2] maybe better to use earnings yield rather than return/total-return…??? I picked this because I had the data handy.  I use Aswath Damodaran's market data. This is likely similar to Shiller data.

[3] high expectations for 2017 going forward!…but let's keep playing… maybe we should use a different look-back…  It seems like this spread might look reasonable for any year in history except our current one. 

[4] this is a little bogus but I had to come up with something.  For 30 year rolling periods, stocks always won using the data I have (Stern) making the Kelly allocation 100% or 50% if halved.  But planning on a perfect record of stock returns always beating bond total return seems adventurous too given today's weird markets. I used a 10 year look-back to get a realistic probability less than 1 so I am, in fact, kinda stroking the data here…  On the other hand I don't think it is all that unrealistic either.