Kelly betting: Bet your beliefs in the stock market

Research
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From Fortune’s Formula about betting on horses:

“Kelly’s gambler …places bets according to his best informed estimates of the probabilities. When you believe that War Admiral has a 24 percent chance of winning, you should put 24 percent of your capital on War Admiral. This approach has come to be called “betting your beliefs.” In the long run, “bet your beliefs” will earn you the maximum possible compound return—provided that your assessment of the odds is more accurate than the public’s.”

Usually, for stocks, this does not work because the payouts and odds are not like a racetrack. But can stocks be adapted?

I think they can. Suppose you took SPY, GLD and TLT and you measured the returns in EXCESS OF THE MEAN!!!

Then the payouts are similar to the racetrack (with no rake) where the wins and losses sum to zero. One difference is that you generally do not lose all of you money on the days that TLT underperforms SPY and GLD. But this COULD be addressed with appropriate leverage.

So one could “Bet their Beliefs” under this scenario and be doing something similar (in many ways) to Kelly betting. The differences are important and can be expanded upon. Most can be addressed, I think. For example, leverage could be used to bring this to fully Kelly Betting (which I would not recommend).

So how does one form their beliefs? I think I will look at this: Algorithm for Finding the Best Trading Strategy Quickly

This example of Thompson Sampling is actually a Bayesian method with a uniform prior that anyone skilled at Python could program. It can be expanded to include a prior belief about how SPY, GLD and TLT will perform as well as any recent data to form the posterior belief.

In other words: form a posterior belief with Bayesian statistics then Bet Your Beliefs using Kelly Betting.

This way, one could fuse Bayesian Analysis and Fractional Kelly Betting into an easy algorithm that can be done on a laptop.

So this actually gets to the best Fractional Kelly without leverage. Or the best compounding (Relative to the Mean of these ETFs) without leverage at a minimum drawdown risk. So it should get you the best compound returns (relative to the mean) with the least drawdowns.

So, without leverage, it is a way of controlling risk. It will NOT maximize your returns.

Just the start of an idea—probably with a more than a few flaws. Okay, I am sure it has some flaws. Comments appreciated.

edit One serious flaw, I think, is that none of this gives any basis whatsoever for picking TLT, SPY and GLD. And therefore the mean is arbitrary. To some extent you would select ETFs that gave you a favorable mean to build upon. Perhaps, you would want ETFs that had little correlation or were inversely correlated. The criteria for ETF selection would need to be expanded without a doubt.

But once you have decided on those ETFs, for whatever reason, I think it might be pretty solid method for balancing the returns and the drawdown risk. Again, it does not guarantee the maximal return (without leverage): that would probably come from putting everything into SPY long-term.

Jim

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All,

I find Thompson sampling (and related Bayesian ideas) very interesting and cannot stop wondering how this might be useful to a variety of applications. But the above is not well developed for portfolio construction—to say the least. To be clear, I do not know how to use this for portfolio construction (if it is useful at all).

For those interested, here is a better-developed discussion by Pimco of Kelly betting, Risk Parity and Modern Portfolio Theory (and how they are connected): An Asset Allocation Primer: Connecting Markowitz, Kelly and Risk Parity.

Jim

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So I just reread “The Black Swan” and I just finished “Against the Gods.”

I didn’t love “Against the Gods” but it is a broad discussion of risks. Yuval mentions it in one of his posts (although, like me he probably finds some parts more useful than others). For me, reading it right after the Black Swan makes me wonder about my ability to predict risks based on history.

And makes me think about the limits of Modern Portfolio Theory–which may use past correlations to try to predict risk. These historical risk may not hold up for Black Swans or even your run-of-the-mill correction/recession.

So getting to how this relates to the Pimco article. From Fortune’s Formula:

“Another method of taming the Kelly system is diversification. Blackjack players sometimes pool their bankrolls. Each takes a share of the group bankroll and plays it independently.”

This independence is important. Risk parity and Kelly Betting are very similar IF YOU CAN FIND ASSETS THAT ARE INDEPENDENT.

Risk parity assumes no correlation and each asset is levered up to to the same level of risk. Sometimes it is assumed that the assets also have the same expected returns. This last assumption makes each position (in risk parity) the same as what the Blackjack players are doing to diversify their risk above.

Assuming that you can find assets that are not correlated, risk parity is like the diversification described in Fortune’s Formula for the Blackjack players. In fact it is the same, I believe.

My only point is that it may not be a bad idea to look at historical correlations and use Modern Portfolio Theory for some of your assets. In a regular market these correlations can be useful.

But there is also something to be said for diversification that may not be correlated in the next Black Swan. This is admittedly hard to predict. But is is also true that—by definition—MPT’s historical calculations will not be so good either. If there is an historical prescient then it is not a Black Swan—except for the very forgetful.

Maybe, with some thought, we can improve on the diversification provided by simple MPT assumptions. Probably should think about it at least.

Along those lines some risk parity funds use stocks (including international stocks), commodities (including gold), levered TIPS and levered long bonds.

Better ideas for diversification into uncorrelated assets?

Jim

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Jim - I challenge you to find assets that are uncorrelated during a crisis :slight_smile: You might have to invest in old wine bottles.

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Steve, I do not disagree. -Jim