Edge Over Odds

Kelly Criterion

This the Kelly Criterion. It is a formula well-known to both gamblers and investors. It solves for the optimal bet size, relative to your bankroll, as a function of the probability of winning a bet and the payoff for the win. The underlying intuition is often summarized as “edge over odds.” The greater your edge, the more you should bet. For example, any time you have a 100% probability of winning, Kelly says you should bet your entire bankroll, regardless of payoff.

In investing, we often throw the word “edge” around in imprecise ways.

“What’s your edge?”

We hear this question all the time. In many cases we answer with things like “no career risk,” “longer time horizon,” and “better behavior.” These may well be competitive advantages but they are not themselves edge. At least not in the Kelly sense. In Kelly terms, you have edge to the extent the probability of winning a bet exceeds the probability of losing it. When we talk about edge, we’re talking about positive expected value.

In that sense, there is “Kelly edge” to be found in many investment strategies. Buy and hold equity investing, value investing, momentum investing. These are just a few strategies where we have pretty robust evidence supporting positive expected values over time and thus at least some degree of Kelly edge. All these strategies are potentially worth a bet.

What is considerably more controversial are the sources of the Kelly edge associated with these strategies. Because when we think about investing, as opposed to gambling, there’s a distinction to be made between the Kelly edge associated with fair odds and the Kelly edge associated with mispriced odds.

A casino is a controlled environment with set payoffs that favor the house (“house edge”). Beating the dealer is an uphill battle. Simply being able to make bets with positive expected values, however small, is the holy grail for every casino gambler.

Taking the odds in craps is a “good bet” because it offers fair odds (there is no “house edge”). The payoff fairly compensates you for the risk of the bet. Whether you ultimately win or lose the bet is the outcome of a random process.

In blackjack, the basic strategy is a “good bet” because it gets you very close to fair odds, although technically the house still has a slight edge.

Card counting in blackjack, on the other hand, is a strategy for identifying and exploiting mispriced odds.

Now, it’s more complicated in investing because investing isn’t a casino game. Financial markets aren’t controlled environments where payoffs are static and specified in advance. Investing is a game where it’s possible to make all kinds of different bets with positive expected values. Moreover, the implied odds and payoffs change on a daily basis. Here the distinction between fair odds and mispriced odds is more subtle and nuanced.

I’ve deliberately avoided using the words “alpha” and “beta” up until now. But here’s how I’m thinking about these terms in this context.*

A beta process earns returns simply as compensation for bearing risk in a fair odds bet. Buying and holding a global market cap weighted equity portfolio is an obvious example of this. But plenty of active discretionary strategies make money this way, too.

An alpha process earns returns by explicitly identifying and exploiting mispriced odds. Alpha processes are about exploiting Information (in the formal sense). I provide a specific example of this further below.

A somewhat inscrutable definition of Information that I quite like is the one from Gregory Bateson: “a difference that makes a difference.”

Do value investors make money over time by making “good bets” with positive expected values, or by identifying mispriced odds? In more academic terms: is the value premium simply fair compensation for bearing a specific type of risk? I’m not going to pretend I have the definitive answer to that question. It’s a debate that’s raged for a long time. I’m certainly not going resolve it on this blog.

My personal view on the subject is that “it depends.” Event-driven value investments such as value + catalyst trades and special situations investments are more like alpha bets. The defining characteristic is the presence of a hard catalyst, usually a corporate action. Hard catalysts, after all, are the very definition of Information. In the absence of a hard catalyst, however, buying a “quality company on sale” (something I am fond of personally) is more of a fair odds bet. A value investor may well think in terms of mispriced odds. But in the absence of Information, it’s an implicit mispricing of odds.

Incidentally, this is also where investor behavior comes back into the picture. Investor behavior is quite plausibly responsible for the historical success of systematic Value and Momentum strategies, and their persistence over time.

At the risk of overreaching, I’m going to go out on a limb and suggest most of us investors earn a greater proportion of our returns from making good bets, as compensation for bearing risk, than by exploiting Information.

Does this mean we should give up on security selection and put all our money into SPY? No. Not in the least. It is plenty difficult to distinguish whether a bet is fair and worth taking, thank you very much. Furthermore, I do believe it’s possible to outperform SPY or any other capitalization weighted index by betting smart over time. Particularly if you’re able to play in less liquid market niches with less carrying capacity and thus less appeal to larger pools of capital managed by folks with a lot of money and resources to throw at Information gathering and processing.

How do you know if you’re exploiting Information versus simply placing good bets? Here is my simple test:

Ask: Do I know for sure? If so, how?

For example, I met a muni bond trader who bought a micro issue at 60 even though there was public record of it having been called at 100. This is perhaps the single best example of an alpha trade I have ever seen in my life. It is the kind of thing that should literally never happen in a reasonably efficient market. It’s the Platonic Ideal of an alpha trade. It’s a real-life version of the old joke about the academic economist who won’t pick up the $20 bill lying on the ground in front of him because he believes people are rational actors and someone should have picked it up already.

Did the trader know for sure? Yes.

How? The issue being called was a matter of public record.

It doesn’t get much cleaner than this. And of course, examples like this one are rare.

By contrast, I had a stock in my PA go up 3x over the last two years. I was of course happy about this. It is fun to make money. I modeled the business out based on publicly available information and felt the market price reflected neither the quality of the business nor its growth prospects.

Did I know for sure? No. Not even close. I simply felt I was being fairly compensated for bearing the risk associated with the bet. But I had no Information in the formal sense–no way of knowing the odds were mispriced.

Fortunately, the P&L doesn’t distinguish between money earned by exploiting Information and money earned as compensation for bearing risk. This discussion is academic. But I sure find it fun to think about. And I do believe it’s beneficial to try to reason clearly about how and why you’re making money over time.

Why?

So you can diagnose problems and potentially make adjustments if a strategy ever stops working.

 

* A somewhat similar formulation of the difference between beta and alpha bets:

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