Kelly bet sizing for me with parameter uncertainty

Kelly criterion math is fun to play with because it has some neat properties and shows up in the literature as the way, ex-utility function conversations, to maximize geometric mean returns over time.  Even Markowitz in his 2016 book, vol 2 has some interesting (consistent with mean-var, even) things to say about it.  Given a demonstrable strategy edge it's totally the way to fame and fortune, right? I want to think so because after about a billion years of trying to trade I finally have a strategy with a small edge and I want to cash in and be a big shot (not really, but that'll be the set up in this post; I know for sure at least that I have been undersizing risk, though, and I want to try and fix that).  But wait, not so fast.  Forget that the strategy can be hair raising -- because in the intermediate years between the now and the later that it takes the strategy to work one's capital can get pretty low which brings behavioral issues to the table; also it may take more years than a lifetime to recover -- and  focus on the fact that edges (and odds) are not immutable facts of nature, they are transient ephemeral things that are either illusions or if not illusions at least not very stable.  If one's parameters are unstable what is to be done?  And if one has simultaneous "bets" along with parameter uncertainty, it's even worse, right? I suspect there is a whole body of literature out there that does all sorts of super-math on this kind of thing but that's not the plan today (contra my usual style I have not bothered to look but I should; I think Aaron Brown has written some things on this).  Today I'm just going to do one of those amateur hack things to see what might work for me as a retail investor for what I am trying to do.


Let's start with the game I am playing and the wrapped box it comes in fresh from the store[1]. The game is selling options short to capture the volatility risk premium (VRP).  I will assert but not prove that the edge can sometimes be expected to be about an 80% win rate and the odds, if I manage to my own plan, are about 1:3 if the risk return controls are tight. If you run Kelly math on that (not described here) that means I should bet ~20% of my bankroll per trade. That seems pretty high given that, with my normal trader hat on, I usually don't wager more than 2.5% on a bankroll. But this is a different game with upside down risk return and relatively high probability.  But 20%? really?  That bet I'll call the "fresh from the store bet."

Ok, well let's look at the trading data now.  I have about 5 years of data so that's good but some of it is naive and experimental trading and some of it reflects the drag of trying to scale up rather than managing a stable strategy. But let's roll with this anyway.  Looking over that total time the average win rate or edge is around 82% and the average win$/average loss$ (odds) is ~.71 (I hope I got that right).  But that data is insanity because if I plug it into Kelly I get a 57% bet size.  There is NO chance I am going to do that. I do not have the courage or the confidence to bet that big.  The reason, I think, is that the average can be meaningless (lets reflect back on the Newfound post on the lie of averages while we contemplate this) and I know that the parameters are really unstable. I have no idea day-to-day what the edge or the odds really are or will be. Let's take a look now at that uncertainty.

Here is the strategy's realized edge in terms of a win/loss rate over time. This is with a 30 trade lookback which is short and arbitrary but makes the point. Ignore the dotted lines for now

Figure 1. Edge

Now here are the realized odds in terms of the average win / average loss over a 30-trade lookback. Again short, arbitrary, and unstable. Again, ignore the dotted lines.

Figure 2. Odds

These are generally gratifying results (though that downtrend in odds, now that I see it, is kinda bumming be out) and make me feel like I am not a total moron which, if I were to listen to some of the people around me, can sound like a take-away on certain days.  This also validates the "total" averages for edge and odds and the "fresh from the store" edge and odds but we can see that all of this is really a moving target.  If it is a moving target how can I possibly optimize my bet size to extract what I want from what little edge I have?  I have no idea and, I think in the end, it is more or less impossible in a world where strategies decay rather than stay vibrant forever.  So, let's look at it this way.  The dotted lines in the charts, the ones I said to ignore, are the ranges where I think I should really be playing my game rather than where the data of averages or even of recent history might be telling me to go.

Let's put a range of edge and odds in a table with this data and see what it looks like:

Yellow corresponds to the regions in the charts where I think I should be playing the game.  So rather than a 57% bet based on totals and averages we really have something quite a bit lower. That's great but I'm still a little freaked out about bet size recommendations of 1/4 or 1/3 from a more "conservative" approach.  That's because I realize that with a little tiny shift in the parameters, a little less edge, a little lower odds, I suddenly have a Kelly "no-bet" and if I do bet in that situation I will start to destroy net worth rather than create it.  I am right on the cusp of a failed strategy; I am hard up against the unfriendly side of risk. Regard those red negative numbers in the table.

But, I do have an edge I say! Right, don't count on it my shoulder angel tries to tell me. Well, I do for now anyway and I will try to exploit it  because it looks like it is really there and if I can do it it has accretive features for me, my efficient frontier, and my family.  But I will not max out on Kelly because it seems way too sketchy.  Here is what I will do for now:

• I will stay well under a 1/2 Kelly until I know better. For now I'll stick with my risk size of ~5% (or less) or, for the aggregate of 5-6 trades, 10% . 
• If the process stabilizes I will increase my risk sizing. If it destabilizes I will reduce.
• I will now watch the process closely and if either edge or odd drift I will freeze or shutter the strategy until I know what is going on
• For simultaneous trades I will limit myself to something like 5-6 trades that represent 10% of the bankroll. I've read that simultaneous bets can be sized each around or a little less than a full kelly but I am not going to do that. (I forgot to get into more detail on simultaneous bets. We'll do that later I guess). If I have multiple trades on I will be very self conscious about reining in risk across the board. 
• When I decide to scale the strategy, by which I mean when I consciously start to increase either the baseline capital in play or I get more aggressive about the full risking of individual trades, I will be super cautious and review all of the data and trends at that time.

[1] there are some good articles from AQR and Swedroe and others that give a good cover of the nature of the risk premium that I am working with here. If I get a chance I will link them in