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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ET Note: The Alchemy of Narrative

I revisited some of George Soros’s writing on reflexivity over the weekend (thanks Ben Hunt!). In doing so, I realized my initial reading, years ago, had been extremely superficial. Back then, I focused on feedback loops as amplifying the usual cognitive and emotional biases we point to in investment writing. Things like confirmation bias and loss aversion and overconfidence. This reading of Soros wasn’t necessarily wrong. But it was narrow and incomplete.

When Soros writes about reflexivity, he isn’t just arguing cognitive errors made by market participants cause prices to diverge from the objective reality of the fundamentals in self-reinforcing feedback loops. He’s arguing the fundamentals are often, if not always, themselves subjective realities.

Click through to Epsilon Theory to read the whole thing.

But since you got here through the blog, you also get some bonus content. Note that if you continue reading, things will get conceptual, abstract, philosophical, and maybe a little weird. Consider yourself warned. If you’re not interested in that kind of thing you can safely skip the rest of this post.

My ET note is about subjective reality in the context of financial markets. At the very end, it alludes to the fact that reflexivity and subjective realities influence all social systems. Politics. Geopolitics. Economics. It’s all reflexive. The Big Idea is this: reflexivity is what drives the cyclicality we observe throughout history. Reflexivity is why we appear to learn from history and yet are doomed to repeat it.

Back in 2013, Venkatesh Rao of Ribbonfarm wrote what turns out to be a pretty compelling explanation of how Missionaries come to an intuitive understanding of both reflexivity and subjective reality, in the context of the TV show, The Office. Rao uses “Sociopath” in place of “Missionary” in his piece, but for our purposes here the terms are interchangeable.

It’s important to understand that when Rao writes about Sociopaths, he’s not writing narrowly about serial killer wannabes. He’s writing about people who want to know The Truth. Specifically, Sociopaths want unmediated access to the Truth, because they (rightly) suspect other people have a vested interested in obscuring or distorting it for their own ends. The Beginner Sociopath is vaguely aware of Narrative. In pursuit of Truth she begins unmasking reality–ripping away Narrative abstractions.

Over to Rao:

As the journey proceeds, Sociopaths progressively rip away layer after layer of social reality. The Sociopath’s journey can be understood as progressive unmasking of a sequence of increasingly ancient and fearsome gods, each reigning over a harsher social order, governing fewer humans. If morality falls by the wayside when the first layer is ripped away, other reassuring certainties, such as the idea of a benevolent universe, and predictable relationships between efforts and rewards, fall away in deeper layers.

With each new layer decoded, Sociopaths find transient meaning, but not enduring satisfaction.

Much to their surprise, however, they find that in the unsatisfying meanings they uncover, lie the keys to power over others. In seeking to penetrate mediated experiences of reality, they unexpectedly find themselves mediating those very realities for others. They acquire agency in the broadest sense of the word. Losers and the Clueless delegate to them not mere specialist matters like heart surgery or car repair, but control over the meanings of their very lives.

So in seeking to unmask the gods, they find themselves turning into the gods.

When they speak, they find that their words become imbued with divine authority. When they are spoken to, they hear prayerful tones of awe. The Clueless want to be them, Losers want to defer to them.

[…]

Once the Sociopath overcomes reality shock and frames his life condition as one defined by an absence of ultimate parental authority, and the fictitious nature of all social realities, he experiences a great sense of unlimited possibilities and power.

Daddy and Mommy are not here. Anything is possible, and I can get away with anything. I can make up any sort of bullshit and my younger siblings will buy it.

The sense of freedom is one I like to describe as free as in speech, and as in lunch.

Free as in speech describes the Sociopath’s complete creative freedom in scripting social realities for others. Cherished human values are merely his crayon box.

Free as in lunch describes the Sociopath’s complete freedom from accountability, in his exercise of the agency ceded to him by the Losers and Clueless, via their belief in the reality of social orders.

Non-Sociopaths dimly recognize the nature of the free Sociopath world through their own categories: “moral hazard” and “principal-agent problem.” They vaguely sense that the realities being presented to them are bullshit: things said by people who are not lying so much as indifferent to whether or not they are telling the truth. Sociopath freedom of speech is the freedom to bullshit: they are bullshit artists in the truest sense of the phrase.

What non-Sociopaths don’t recognize is that these aren’t just strange and unusual environmental conditions that can be found in small pockets at the tops of pyramids of power, such as Lance Armstrong’s racing team, within a social order that otherwise makes some sort of sense.

It is the default condition of the universe. The universe is a morally hazardous place. The small pockets of unusual environmental conditions are in fact the fictional realities non-Sociopaths inhabit. This figure-ground inversion of non-Sociopath world-views gives us the default perspective of the Sociopath.

Non-Sociopaths, as Jack Nicholson correctly argued, really cannot handle the truth. The truth of an absent god. The truth of social realities as canvases for fiction for those who choose to create them. The truth of values as crayons in the pockets of unsupervised Sociopaths. The truth of the non-centrality of humans in the larger scheme of things.

When these truths are recognized, internalized and turned into default ways of seeing the world, creative-destruction becomes merely the act of living free, not a divinely ordained imperative or a primal urge. Creative destruction is not a script, but the absence of scripts. The freedom of Sociopaths is the same as the freedom of non-human animals. Those who view it as base merely provide yet another opportunity for Sociopaths to create non-base fictions for them to inhabit.

Regardless of how I qualify it in advance, the word Sociopath carries with it decidedly negative connotations. But again, Sociopaths as described here are not inherently evil. Rao only tangentially touches on the difference between Good Sociopaths and Evil Sociopaths. Here it is: Good Sociopaths choose to adhere to some kind of moral code. Evil Sociopaths choose to live in a state of amorality.*

I’ll expand on this slightly.

The Evil Sociopath embraces nihilism as a license to treat others as playthings. Most often Evil Sociopaths do this through legal means, for example under the cover of business and financial dealings. Others do it through criminal activity, or by playing manipulative games within their personal relationships. And yes, a very small minority of Evil Sociopaths go the serial killer route.

The Good Sociopath, on the other hand, rejects nihilism as a license to treat others as playthings. Critically, this is not because there is some fundamental, verifiable Truth out there affirming an underlying moral order. Instead it’s because, for whatever reason, Good Sociopaths find the thought of embracing nihilism repulsive. The Good Sociopath chooses to believe other people are worthy of some level of dignity.

I have been annoyingly consistent in highlighting the word choose here just to emphasize that we’re dealing with subjective reality. Social systems are reflexive. Facts and small-t truth do exist, but to Sociopaths they’re negotiable.

In the immortal words of Don Draper: “if you don’t like what’s being said, change the conversation.”

And the Sociopath/Missionary is free to do so.

Free as in speech.

Free as in lunch.

* For another pop culture reference that may make this more concrete, the first season of HBO’s True Detective is pretty explicitly about Rust Cohle’s Sociopath journey, and how he and various and sundry other Sociopaths cope with “reality shock.”

Beware Helpers Bearing Advice

Warren Buffett has this fantastically understated put-down he uses when he wants to needle investment professionals. He calls them “Helpers” (consultants are “Hyper-Helpers”). It’s a fantastic put-down because it’s simultaneously denigrating and dismissive, without being overtly crass or undignified. The way Buffett writes about Helpers he conjures up images of investment professionals as childlike buffoons. When the GOAT paints a picture of you as a childlike buffoon, there’s really nothing you can do about it.

Trust me, it drives us nuts.

Some day I will write a long post about Warren Buffett, Master of Narrative. There might even be a book in this. We think of Buffett as the greatest investor of all time but he might also the greatest salesperson of all time. He has, after all, sold thousands upon thousands of self-professed contrarians on making an annual religious pilgrimage to Omaha, Nebraska. I think Buffett knows exactly what he’s doing here. And I think he derives great pleasure from it. But that’s a topic for another day.

Here I want to borrow Buffett’s put-down to talk about another kind of Helper: the transactional financial salesperson.

Early in my career, I worked as a loan rep. Specifically, I sold consumer loans. Home equity loans, auto loans, unsecured personal loans and the like. You may not believe it, but this was actually fantastic experience. It was a very safe sandbox in which to learn how deals are structured, how risks are managed (or not managed), and most importantly, how deals are sold.

I was pretty good at selling loans.

If I’d stayed in the position long enough to build up a wider personal network, I think I would have gotten really good at selling loans.

Partly because I didn’t present myself as a person selling loans. I presented myself as a problem solver. There were many cases where I really did help people solve problems, or finance projects that were important to them. But in many cases I was just restructuring their problems. The best example would be the use of a home equity term loan to consolidate credit card debt. By the numbers, it always made sense to do this. It would save people thousands upon thousands of dollars in interest expense, plus term out the debt. Mathematically, you could prove the transaction made sense.

Behaviorally, things were a bit murkier. Because the math only held if the customer stopped racking up credit card debt. Of course, I would explain that to people. I wasn’t a charlatan.

If someone had racked up credit card debt because he used it to finance some kind of one-off project or business venture that went south, then this type of refinancing transaction was a no-brainer. (This setup was rare)

If someone racked up credit card debt because he was outspending his income, it was can-kicking by another name. If his pattern of reckless spending and debt consolidation were to continue, it could eventually end in bankruptcy and the loss of the home. (This setup was more common)

I have no idea how many of these debt consolidation deals worked out for people over time. As a loan rep, my job wasn’t to distinguish between the underlying causes of different individuals’ debt problems. My job was to sell financing solutions to people in need of financing solutions.

This is really just a long-winded way of describing agency problems and information asymmetry. In finance, these issues come up all the time. There’s this meme out there that anyone who does transactional business in finance is necessarily some kind of snake-oil salesman or charlatan. This simply isn’t true. Not all Helpers are looking to rip your face off. But not all Helpers have a fiduciary responsibility to act in your “best interest”, either. I put “best interest” in quotes because, as my home equity refinance example illustrates, it’s not always as straightforward to identify what’s in someone’s best interest as certain people would have you believe.

Transactional business isn’t inherently evil. I do transactional business with people all the time, both personally and professionally. Transactional business can work out quite well for everyone involved.

Where you run into trouble is when you mistake a TRANSACTIONAL relationship for a FIDUCIARY relationship. (See also: It’s Just Business)

If you are the finance director of a small municipality, or the CEO of a small company, and your banker comes to you with an interest rate swap that will “protect you” from interest rate risk, and you are not well-versed in the mechanics of a swaps, then you need to think long and hard about doing that deal. Because ultimately, your banker isn’t compensated to advise you. Your banker is compensated to transact business with you.

I address the finance directors of small municipalities and the CEOs of small companies specifically here because you are often seen as the suckers at the institutional poker table. There is potentially a lot of money to be made Helping you.

With apologies to The Godfather, Part II: you can respect Helpers, you can do business with a Helpers, but you should never trust a Helper.

ET Note: They Live!

They-Live-3

My latest Epsilon Theory note is live. A quick teaser:

If ever you find yourself struggling to keep the difference between Narrative and narrative straight, think of John Carpenter’s 1988 sci-fi action flick, They Live. No doubt it’s a goofy movie. The basic premise will be familiar to anyone who’s seen movies like Dark City or The Matrix. Reality, as we perceive it, is an illusion. But, if you obtain the gift of special sight, you may see the world as it is. In the case of They Live, you put on a pair of special sunglasses only to discover the world is, in fact, controlled by hideous aliens, which use mass media to shape our behavior with subliminal messaging. […]

It’s a wonderful visualization of how symbolic abstraction operates in our world. And who knows, maybe Jerome Powell and Janet Yellen really ARE hideous aliens.

But this isn’t a note about your Friendly Neighborhood Central Bankers, or even how symbolic abstraction can be weaponized to sell you a new refrigerator. This is a note about how symbolic abstraction is used to shape your investment behavior. Both your behavior and your clients’ behavior.

Click through to Epilson Theory to read the whole thing.

I’m quite pleased with the way this note turned out. Even more so because this is an instance where a little editorial input went a long way toward improving the final product. Some ideas more or less show up on the page fully formed. Others require a bit of workshopping. Still others end up being workshopped, killed and then harvested for their vital organs. I’m glad this one not only survived, but flourished!

Gluttons For Punishment

If you’re a longtime reader, you may recall my little hypothesis about active mutual fund manager and hedge fund performance. The aggregate performance of active mutual fund managers and hedge funds will not, and cannot, improve while Market factor performance dominates everything else. You’ll certainly have individual managers perform well here and there. But in the aggregate, performance versus long-only benchmark indexes will remain unimpressive.

If you’re wondering exactly what the hell it is I’m talking about here, compare the pre-financial crisis and post-financial crisis periods on the below chart.

4Q18_3YR_Trailing_FACTORS — Data Source: Ken French’s Data Library

And just for fun, here’s another chart, focused on the last five years or so:

4Q18_Trailing_Factor_Returns — Data Source: Ken French’s Data Library

If there’s one thing you should take from this post, it’s this: the market is conditioning you to be fully invested and in particular to be long US equity market beta. We can certainly debate the “whys” and “hows” of this (for instance, how it’s the stated policy goal of our Friendly Neighborhood Central Bankers to keep us allocated to equities for the long run). But as a practical matter, if you’re overweight US stocks, particularly large cap US stocks, you’re receiving positive reinforcement. If you’re underweight US stocks, particularly large cap US stocks, you’re receiving negative reinforcement. And god help you if you’ve been significantly overweight small cap value stocks or ex-US stocks over the last couple of years. If so, you’re being subjected to corrective shock therapy.

I don’t say this to make value judgments.

I say this to explain what’s driving investment decisions all over the United States, and indeed the world. I say this to contextualize why the most common conversation I have with investors of all types lately seems to be: “why do we own foreign stocks, anyway?”

If you’re the kind of person who likes to extrapolate historical return data to make asset allocation decisions, all the data is screaming for you to be fully invested in US large cap stocks. You’d be a complete idiot to do otherwise. Perhaps you’ve told your financial advisor this. Perhaps you’ve fired your financial advisor over this.

And you know what? You might be right.

In my own humble opinion, the number one question confronting anyone allocating capital right now is whether or not this market is “for real.” If it is, and you decide to fight it, either as a private individual or as a professional investor, you’re toast. But if this market isn’t “for real”–if it’s all just an artifact of easy monetary policy, and you decide to “go with the flow”, and it all unwinds on you, then you’re also toast.

In thinking about my own portfolio, what I want is to develop a financial plan offering me a decent chance of hitting my goals while assuming as little risk as possible. Those of you well-versed in game theory, such as my friends over at Epsilon Theory, would call this a minimax regret strategy.

Notice I wrote “financial plan” and not “investment portfolio” above. From a pure portfolio perspective, you’re facing a no-win scenario. You have to handicap whether, when and how the whole QE-as-permanent-policy project comes undone. This is nigh on impossible. Investors have been trying and failing to do this for at least a decade now. When faced with a no-win scenario, your best strategy is to change the conditions of the game. In order to do that, you first have to understand the game you’re playing.

We investors and allocators like to believe we’re playing the investment performance game.

We’re not.

We’re playing the asset-liability matching game.

Investment performance only matters inasmuch as it helps us match assets and liabilities. You probably don’t need to “beat the S&P 500” to fund your future liabilities. You can probably afford to take less market risk. And investment performance is hardly the only lever we can pull here. We can increase our savings rates. We can decrease our spending. We can allocate some of our capital to the real economy, instead of remaining myopically focused on increasingly abstracted, increasingly cartoonish financial markets. We can start businesses that will throw off real cash flow, and own real assets.

We don’t have to remain fully invested at all times. We don’t have to be 100% net long and unhedged with the capital we do have invested.

We don’t have to be gluttons for punishment.

The Confidence Meter

If you are anywhere near as strange a person as me, you spend a lot of time thinking. And not only thinking, but thinking about thinking (whether any good ideas actually come out of this process is a discussion for another time). Over the years I’ve become more and more interested in epistemology. Is there a such thing as Truth with a capital T? If so, how would we know if we found it? How can we better manage the Bayesian updating of our priors?

Personally, as far as epistemology is concerned, I come down on the side of fallibism. Whether fallibism is, or should be, applicable to moral questions lies beyond the scope of what I write about here. But when it comes to our beliefs about economics, geopolitics, and investing, I think fallibism is an eminently sensible position.

Now, it’s important to distinguish between fallibism and nihilism.

Nihilism is extreme skepticism in the existence of Truth.

Fallibism is extreme skepticism in the provability of Truth and in the methods we use to arrive at Truth. (See also: The Problem of Induction; The Trouble With Truth)

For a fallibist, acquiring knowledge is a relentless, grinding process of formulating conjectures, challenging them, adjusting them, discarding them, and so on. It never ends. By definition, it can’t end. So if you’re bought-in on fallibism, you need to seek out people and ideas to challenge your priors.

This is not fun. In fact, we as humans pretty much evolved to do the opposite of this. For most of our history, if you were the oddball in the tribe you risked being exiled from the group to make your way in a harsh and unforgiving world, where you would likely die miserable and alone (albeit rather quickly), without the consolation of having passed along your genetic material.

The Confidence Meter is a little mental trick I use to mitigate my evolved distaste for challenging my priors, as well as my evolved distaste for being wrong. It’s something I think about when I want to judge how tightly to grip an idea (such as an investment idea). It also helps interrupt emotional thought patterns around certain ideas. For fans of Kahneman, I use it to interrupt System 1 and activate System 2.

The Confidence Meter (A Stylized Example)

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At 0% confidence, I shouldn’t even be making a conjecture. At 0% confidence, I should just be gathering information, and soaking it all in without an agenda. (Not always easy)

At a toss-up, I could make a conjecture and support it with evidence, but I wouldn’t put anything at risk.

At 75% confidence and greater, a willingness to bet money on the outcome implies a sound grasp of the theory underlying my idea, as well as the empirical evidence. It also implies I have a sound grasp of the arguments and empirical data challenging my position.

Using this framework, how many of your beliefs do you suppose merit a >=75% confidence level?

For me, it’s a very small number. To the extent I’m >=75% confident of anything I believe, it’s elementary, almost tautological stuff, like how you make money investing.

The empirical data around the impact of the minimum wage on unemployment? Meh.

The relationship between marginal tax rates and economic growth? Meh.

That doesn’t mean I don’t have beliefs about these things. I’m just leaving an allowance for additional dimensions of nuance and complexity. Particularly when we’re inclined to look at relationships in linear, univariate terms for political reasons. The world is a more complex place than that admittedly powerful little regression model, Y = a + B(x) + e, would lead us to believe.

The Confidence Meter helps me keep that in perspective.