Asset Pricing and Sports Betting

You’re watching “Economics Amplified,” the latest thinking on the biggest issues from U Chicago’s Becker Friedman Institute. STEVEN D. LEVITT: I’ve known Toby for a long time, and maybe the most worrisome conversation I ever had with Toby must have been about three or four years ago. So if you know Toby’s academic work, he does asset pricing and serious scholar. And he came to me and he said, hey, you know, I know you wrote this book Freakonomics.

And I’ve decided I’m going to write a popular book about sports. I said, OK. Great.

That sounds good.

And I was terrified.

He said, and I’m going to do all new research. I’m going to start from scratch and I’m going to do all–and I thought, OK, that sounds like a really bad idea.

But I wasn’t going to say anything, because everyone’s got their dream.

And then I said, well, what do you hope to get out of it?

And he said, all I want is to be able to go to the Super Bowl. And I thought, well, that doesn’t seem like a very high aspiration.

And I want to just be at the Super Bowl.

And I didn’t want to tell Toby, there are other ways to get to the Super Bowl besides writing a bestselling book about the economic of sports.

And then I said, well, it’s hard to write well. And he said, well, I got this other guy who’s going to write it.

And he’s written three or four bestselling books, and he writes for Sports Illustrated.

He’s my old doubles partner from tennis. Then I got a little more optimistic.

And still, you always dread it when people try to write popular books when they’re academics.

And then Toby sent me his book, Scorecasting.

And it was so good. Of all the books I’d read by economists trying to do popular things, it was by far the best.

Beautifully written. Great research.

And it’s fantastic.

So today, we invited Toby. He said, well, what should I talk about?

Should I talk about my work in asset pricing, or should I talk about my work on sports?

And I said, well, I think for this audience, people would be equally interested. So Toby decided once again to try to confound us.

And he says he’s going to talk about both today, about sports and asset pricing. And he’s going to show us how this going to be, in his own words, either the best or the worst thing he’s ever done his entire life.

We’ll find out soon. TOBIAS J. MOSKOWITZ: Thanks.

[APPLAUSE] TOBIAS J. MOSKOWITZ: Well, thanks, Steve, for that introduction.

Last time Steve spoke about me, it was in front of my alma mater at Purdue University where he was talking about his research on prostitutes and using me as an example, which didn’t go all that well over with my wife and my family.

But in any case. So Steve’s right. I’m putting together these two things, asset pricing and sports betting.

Really, this is an asset pricing paper more than it is a sports paper.

And it’s certainly the riskiest thing I’ve done.

So we’ll see. It’s either going to be really cool or really stupid, and we’ll find out shortly.

Oh, right, right.

So far, it’s not advancing.

So we may not find out what’s– that’s not– CREW: You can close that out.

That’s the previous. TOBIAS J. MOSKOWITZ: That’s the previous thing?

Way over there.

OK. There we go.

So let me start with– like I said, it’s an asset pricing paper. So let me start by– you can hear me with the microphone’s on here?


I like to walk around. So two of the most studied asset pricing phenomena out there are value and momentum. And those of you that have taken some asset pricing courses, you’ve heard these.

But let me just define what they are. These are two things that seem to predict returns in a very profound way.

So the value effect is really simple.

Assets that have a high fundamental value, whatever that is– we can define that.

You can think of it as a high book value, if we’re thinking of a stock, like high earnings, relative to a market-based measure of value like the price per share of the stock– tend to predict returns going forward.

So if you buy low earnings to price stocks and you sell high earnings to price stocks, you tend to do very well on average over time. DFS has made, what is it? They’ve got $320 billion under management using that strategy.

Pretty much, that’s their main strategy. Then there’s the momentum effect, which is assets that have done relatively well in the past continue to outperform on a relative basis.

So very simply, you can rank stocks, for instance, over the last year on their past performance and go along the ones that have done relatively well, short the ones or underweight the ones that have been relatively poorly, and that does very well over time. And just to show you how ubiquitous these effects are, this is related to a paper I wrote a few years ago called, very simply, “Value and Momentum Everywhere. ”

That pretty much describes all we did in this paper.

If you apply that very simple concept, buy value assets and buy momentum assets, and under-weigh or short sell non-value and non-momentum type assets, you can see in US stocks that momentum effect here is in red, value’s in blue.

Cumulatively, the returns are quite positive. Much better for momentum than value over this period. And that’s true.

In the UK, you’ve got the same sort of picture.

In Europe and in Japan, you’ve got pretty similar pictures.

But there’s some variation. You’ll notice, for instance, that in Japan, value– which is the blue line– has done incredibly well historically. Momentum, not so much.

In Europe, it’s kind of the opposite.

Momentum has been terrific, value’s been OK. And same in the US.

But I want you focus on the green line as well.

Because as you know when you build portfolios, you don’t think of these things as individuals.

You think of them as in combination in a broader portfolio. When you combine value and momentum, you get this tremendously profitable green line here that’s also very smooth.

So it’s not just the height of the line that matters here. Notice the number of wiggles.

That expresses volatility or risk.

You can see, for instance, here’s a great example. Go back to the height of the tech episode.

I won’t use the word “bubble” here.

But whatever you want to call it. The tech bubble, tech episode.

You can see that that was a time when value strategies did very poorly.

And why was that? Well, again, value says you buy assets that have lower earnings to price.

Well, during this time, assets with very high earnings to price kept getting better and better.

So it was a terrible time to be a value investor, but it was a great time to be a momentum investor.

And if you combine the two, you barely notice that episode even existed.

Now, that seems to be true in every market here. Here we’ve got the US, in the UK, in Europe, and even in Japan. In Japan, the green line, even though value’s great and momentum is basically nonexistent, the green line is still way better than the blue line.

Now, you don’t have to stick to stocks here. This is just stocks internationally.

If you do the same thing for equity futures contracts, for currencies, for bonds, government bonds, and even for commodities, you get a very similar picture.

And one of the things that we show in this study is that when you see these wiggles here, those wiggles tend to occur at the same time in very different markets and very different asset classes.

More formally, what that means is there’s correlation structure among these things. That there’s a value affect in markets, there’s a momentum affect in markets, and they pervade all sorts of markets. And they tend to do the same things in those different markets at the same time.

Now, we have a big debate as to what these things mean.

First of all, when you look at this evidence, you say, gee, what a great trading strategy.

Maybe I’ll go out there and make tons of money. And certainly, some firms have done that.

But there’s a debate as to what this all means. And by the way, if you do this globally in all asset classes, all the pictures become a lot smoother.

But you can see right here just how smooth that green line is.

So there’s a big debate as to what drives this.

One view is that this is all driven by risk. That all we’re really picking up here are different risk premia in the economy.

That risk isn’t just about equity risk or market beta, it’s about exposure to value.

It’s about exposure to momentum. You can think of Gene Fama.

That’s his camp. And there’s lots of flavors of these risk-based stories.

But somehow, value and momentum are compensating investors because they’re exposing them to more risk. Then you’ve got the other side of that coin, the behavioral models, which say these things aren’t risks at all.

They’re driven by mispricing. That they really are profit opportunities without that additional risk.

And that’s where Bob Schiller comes in.

And hopefully, you know– you certainly ought to know Fama’s name. And I hope you know Schiller’s name as well.

These two won the Nobel Prize this year, 2013, for these kinds of predictable patterns and returns, even though they fundamentally disagree on what drives those patterns.

So we all agree with the data.

We just disagree with the explanation. Now the risk models have lots and lots of different stories often involving some exposure to aggregate macroeconomic risk that’s related to these value and momentum characteristics.

Behavioral models typically also have a lot of varieties, but typically of one of two kinds. One is it’s a misreaction to information, typically either overreaction or under-reaction.

And just as frustrating as the risk-based stories are, we have models that say overreaction drives it, models that say under-reaction drives it.

You might wonder how could both of those be true?

Well, that is a bit of a problem. But can generate models that can explain these patterns.

Now, the real question is how can we distinguish between these two camps? Or can we even distinguish between them?

It’s almost impossible using financial market data because of what we call the joint hypothesis problem, which is really one of the most famous things that Fama contributed to in the literature, is any model of market, any explanation for market efficiency, implicitly relies on a model for prices or returns.

So in other words, I can’t tell whether markets are inefficient because of these value and momentum effects, or whether I’ve got the wrong model. And that’s why there’s a host of risk-based models that try to fill that gap. But same with the behavioral models.

We have to take a stand on what the model is.

We don’t just get to conclude or claim the residual, that since we don’t have a model that explains all these facts, it must therefore be behavioral.

We need some models to do both.

So how can we test these models? OK This gets me to sports betting.

So what’s the basic idea here? So I’m going to tell a quick outline.

I’m going to talk about the basic idea and why I want to look at sports betting markets to try to help resolve this conundrum.

As you can see, it’s an asset pricing paper, not really a sports paper.

So 3/4 of you may want to get up and leave, but I hope you won’t. Then I want to link this back to financial markets. What can we learn about financial markets from the sports betting market that maybe can shed light on breaking this logjam between behavioral and risk-based explanations?

And then I’ll talk about the tests that I’ve run so far and what we see in the data.

And by the way, I should mention I ran a lot of these things as of late this weekend.

So this is certainly ongoing and preliminary research.

But that’s why we’re at Chicago. So here’s the basic idea. I want to look at a market or a set of gambles where some explanations can’t possibly matter.

In particular, I’m going to focus on sports betting markets.

And the reason I chose those markets– well, one of them is data reasons, but I’ll get to that in a second– but the first reason is that aggregate risk or macroeconomic type stories related to Fama’s view of the world can’t possibly matter here. These are purely idiosyncratic gambles.

There’s no notion of macroeconomic risk affecting one game versus another.

And I want to be clear here.

Macroeconomics can affect the betting industry as a whole, but they cannot have anything to say about whether one particular game over this weekend is priced differently than another particular game. That just can’t possibly matter.

So the key here is I’m looking at the cross-section of games.

Now, the behavioral explanations, they should apply equally as well to these gambles as they do to financial markets. The behavioral explanations are really about how do investors as human beings react to information, to uncertainty, and how do they use probabilities to estimate expectations, and all that stuff.

All the evidence from psychology points to experiments in the lab that aren’t really related to financial markets.

There’s simple risky gambles.

So there’s no reason that those explanations shouldn’t matter here as well. So the question is, can we find the same patterns in this market where aggregate risk can’t possibly matter, and would that lend credence to some of these behavioral stories that suggest the same things are going on in financial markets?

There’s two key features of this market that are important for what I want to do. One is what I just mentioned. The bets are purely idiosyncratic.

So we can take the risk-based stories off the table.

The second thing, which is kind of nice, is that the betting markets have a finite and often very short terminal date where all uncertainty is resolved. So what you’ll see in the financial markets literature, when behavioral explanations are tested, often researchers will assume that there’s some finite period where prices get corrected. For instance, you might look at an earnings announcement and say, well, six months down the road, we figure all that information’s embedded in the price.

So we look at price patterns until then.

We like to pretend that we have a real terminal value then, when in fact we don’t because the stock could be going on forever.

Could be a perpetuity.

Here, it’s really nice.

You have a game that ends.

The payouts are determined on the betting contracts. And that’s it. The other nice feature is whatever investors are doing in betting markets has absolutely no implications for the outcome of the game. I mean, unless you really believe in conspiracy theories and game fixing.

But in the sports that I’m going to be looking at, that’s probably not going on.

So it’s really exogenous to the things that I want to look at, to the betting behavior that I’m going to look at. Now, I’m going to run these tests in a second.

But I also want to think about how I can link this back to financial markets.

Can I really learn something from looking at sports betting markets that can tell me what I want to know about financial markets, and in particular value and momentum.

I’ll look at size as well and other of these cross-sectional asset pricing effects. Well, first of all, you could argue that sports markets are just fundamentally different than financial markets.

In fact, Steve has a paper on this. There are some similarities and some differences.

But for my purposes, the differences are going to be important in highlighting the theories that I want to test, and the similarities are going to be important, I think, for generalizing, perhaps, to financial markets.

For instance, if you look at investors in sports betting markets, there’s a lot of uncertainty. And most investors there, yes, some of them bet for fun. But even when they bet for fun, they still want to win.

They still want to make money.

It’s not like the incentives are that different in that market.

What’s different, of course, is what I mentioned. They’re idiosyncratic and there’s a short terminal date.

But there’s also a third thing that’s a little bit unknown here that may make it difficult to generalize the results, or at least make me cautious in generalizing the results, is that institutional frictions, or for another way of saying this is arbitrage activity, may be quite different in these markets.

So for instance, in the financial markets, if there’s a mispricing opportunity out there, we often view this as Fama’s view of the world, that there is smart money ready to take action and correct prices very, very quickly. In the sports betting market, that’s true as well.

There are professional gamblers.

There are institutions.

There are even hedge funds that do this as well. But there’s a deeper question as to how well does that work in sports betting markets versus how well does it work in financial markets?

That’s a question that I don’t really know the answer to.

So is that going to make it difficult to generalize the results? Perhaps. For instance, suppose I found nothing in sports betting markets related to value or momentum or any of those things.

Would that necessarily imply that the behavioral models can’t possibly explain anything in financial markets?


Surely not. It could just be the case that in sports betting markets, those things are arbitraged away much faster than in financial markets.

I would probably think the opposite, but it’s certainly possible.

On the other hand, if I find something positive in sports betting markets, does that necessarily mean that’s what’s going on in financial markets?

Not necessarily, but it would be an awful coincidence. For instance, the key thing that I’m going to look at here is I want to be careful and look at the exact same characteristics from financial markets. In other words, if I just said, I just want to see how sports betting markets react to any general piece of information and say something about financial markets, that’s much harder. Like for instance, suppose I just took some random characteristic in sports betting markets that really didn’t have anything analogous to financial markets.

I don’t really learn much from doing that.

What I want to do specifically here is to find the exact same– or as close as I can– the exact same things that we see in financial markets like momentum and value– I have to define those for you in a second– and see if those same predictors that we know work in financial markets also work in sports betting markets. That’s the key.

Because if I don’t have that analogous characteristic, then I have to worry about the generalizability of this stuff.

Whereas here if I show you that the exact same patterns, the exact same measures used in financial markets work just as well in sports betting markets, either you conclude that maybe there is something useful in these behavioral theories to explain the patterns that we see or it’s just a really lucky coincidence.

And when I say really lucky, I’m going to be looking at four different sports markets, different times, and three different contracts for each sports market. It’s a total of 12, essentially, out of sample tests.

It would be a very lucky coincidence if that showed up in those 12 independent tests and had no real content. So summing up, and then I’ll get to the test and the results, if I find a positive result, I think it can tell us something about what’s going on in financial markets.

If I find a negative result, I think that’s a little bit less useful.

In other words, if I find that the characteristics that we look at in financial markets don’t apply at all in sports betting markets, those may just be the wrong– it doesn’t necessarily mean that the risk-based stories are right and the behavioral models can’t matter at all. Maybe it moves your prior a little bit. But for me at least, I think my prior moves more if I find a positive result because these are the exact same characteristics that we already know work in financial markets.

That’s a little bit subtle, and I’m not sure I’ve got the logic right, by the way, but that’s my current thinking on it. But that’s the way I’m approaching this.

So I think the positive results are more generalizable, negative results less so.

But I still think it might move people’s priors into one camp or the other.

But here’s the problem.

The better this test is depends critically on how analogous I can define these characteristics. Momentum’s kind of easy.

It’s just past performance, right?

Seems like I ought to be able to define that pretty easily in the sports betting context, and I think that’s right.

Value, which is a measure of fundamental value to market value, that’s going to be a little harder. I’m going to have to do more work there.

And I’m not sure I’m going to convince people in this room that I’ve got it. But I’m working on it. That’s the idea.

Something like size, which is the third characteristic people often mention that I glossed over, that’s a little easier as well.

But I’ll get to that.

So let me start with the data.

First of all, the data I have comes from two sources, SportsDirect and SportsInsight.

I can tell you all the details about these. They’re basically online betting resources for betters, and they contain historical spreads.

SportsDirect has spread contracts only, which I’ll tell you what those are in a second. SportsInsight has the spread, money line, and over under contracts.

And for those of you that don’t know anything about the betting markets, I’ll come to this in just a second. Just to give you a sense, though, there’s a 99.99 correlation when the data overlaps.

So the spreads, the prices that are given from these different book makers– by the way, the bet lines come from Vegas.

And the three top online book makers, there’s very little variation across them.

I think there can be during the week for certain bets, but I’m going to focus on only three prices here.

The opening line, the closing line. So the opening line is when betting starts. Let’s say it’s an NFL game.

Monday morning, betting starts.

And that betting continues until right up until kick-off. That would be the closing line.

And then you have the outcome.

So if I’m just looking at these prices, there’s really not much variation across these different book makers. So just to give you a sense of the three contracts I’m going to look at, it’s little betting 101 here.

The spread contract is probably the one most people have heard of.

You bet for a given team to win by a certain amount of points. For instance, if I’m betting on the home team and they’re a 3 and 1/2 point favorite, it means they’ve got to win by more than 3 points. They’ve got to win by 4 points or more for me to cover the bet.

And what does the bet entail? It entails me putting $110 down.

If they win, I win $100.

That’s called covering. If they lose, I lose my bet, $110.

And if I push– in other words, if they win exactly by 3 and 1/2 points– which is impossible if it’s a half point spread– then I break even.

So that only works for full point spreads.

Then there’s the money line bet which is again a bet on who wins or who loses, but instead of adjusting by the points by which a team might win or lose, it’s a levered and a un-levered on either side of the contract on how much you win. So for instance, the money line would be quoted, let’s say, negative 180. That means you’re betting on the favorite team $180 to only win $100. And if you want to take the other side of that bet, the quote might be plus $170, meaning you would bet $100 to win $170.

So does everyone see here?

Up here, essentially what happens is the book makers are adjusting the number of points by which the team would win in order to make the betting odds roughly 50-50 on who wins or who loses.

Not quite, as some of Steve’s research has shown.

The money line basically says forget about adjusting the points.

I’m just going to adjust the payoffs. In other words, I understand that this team is more likely to win, so you’re going to win less money if they do.

Whereas this team is an underdog, you have a chance to win a lot more percentage-wise if you bet on that team. So there are two bets.

They’re going to be correlated. The payoffs on these are about 0.69 correlated, which makes some sense.

And then finally, we’ve got the over under, which is not betting on a particular team, just betting on the total score.

So for instance, say for an NBA game, if the over under is 175, if I bet the over, that means I win if both teams score more than 175 points combined. I lose if they score less than that.

And the payoffs are very similar to the spread contract. I bet $110 to win $100.

Now, that extra $10 or 10% is known as the vig or vigorish, which is a trading cost. In the money line, you can see it expressed more in the difference.

You notice these prices are typically not symmetric when you look at the money line contracts.

That’s a way for the book maker to make their spread, their commission.

So let me talk about the data I have.

I’ve got basically 14 years of data in the NBA, roughly 19,000 games or about 39,000 betting contracts.

Because especially post-2005, there are three contracts per game.

The spread, the money line, and the over under. For the NFL, I’ve got betting contracts back to 1985 through 2013.

It’s about 7,000 games and about a little under 11,000 betting contracts.

And again, it’s not exactly three times because prior to 2005, I only have the spread contract, just to make that clear. For baseball, it’s 2005 to 2013, about 24,000 games, and about 48,000 betting contracts. Just to be clear here, notice I’ve got the summary statistics on each of the three contracts– spread, money line, and over under. You’ll notice in baseball, the spread is always negative 1 and 1/2.

It’s called a run line.

It’s just not useful.

Basically, who wins and who loses. So the spread contracts aren’t used in baseball.

The scores are simply too low.

There’s just a money line bet and an over under.

Same in hockey. There’s no real spread contract. It’s called the puck line.

And it’s just a bet on who wins or who loses, so it’s really the money line and the over under that matter here.

And again, for hockey, about 10,000 games, about 20,000 betting contracts.

So overall, there’s 120,000 gambles here, if you add up all the contracts and all the sports.

What’s nice is they’re independent. They’re purely idiosyncratic, not only to the market or anything we care about in the macro-economy, but also really to each other.

It’s certainly across sports.

Even within a sport, it’s very rare that one game would influence another game. Maybe a very rare situation where someone plays in the morning, has playoff implications for the team in the afternoon, and then they rest their starters. But even so, that’s extremely rare.

Now, there’s a whole bunch of things I need to do to convert these payoffs into what we would consider financial returns or price returns.

So I’m not going to go through the math on this.

I have a paper that I’ll put online that people can look at.

But basically, all I’m trying to do is back out what the probabilities are of the different payoffs, what that means for prices based on the way these contracts pay off, and I’ve got to estimate those probabilities somehow. So just to give you a quick flavor of what I do here, here’s an example. This is just for the spread contract, the closing spread.

This is just for the NBA.

The black marks here are the actual probability of winning the bet at various spreads. And the thickness of them determines how many contracts are at that spread.

So you can see for spreads that are way negative or way positive, there’s very few contracts. But in the middle here, you have a lot. And then I’ve got a model of what these probabilities are which is the red line is a theoretical model.

That just says, suppose all bets are fair.


50% are going to win, 50% are going to lose.

As Steven Levitt’s research shows, it’s not quite true. But that’s pretty close to the truth because the blue line here is basically a non-parametric estimator of all this data to take into account what book makers are actually doing when they set spreads. And it’s pretty damn close to 50-50.

Why do I have to do that? Well, you can see here there’s so few contracts at the extremes.

For instance, look way up here.

You can barely see it.

There’s a contract here that at negative 14 and 1/2 point spread, those contracts all paid off.

But at positive 15– here it is– none of them paid off. Well, that would be a little crazy to assume that those were real probabilities. So you have to use some model.

You can get more sophisticated and use logit and probit models and other things.

But basically, it’s what we try to do.

We have to build a mixture of model and data to estimate what these things really look like. Now, it turns out– I’m going to go back a second– the correlations across all the different methods– there are four different ones. A theoretical approach, a non-parametric approach, a logit, and a probit type model.

The correlations are high 99% across these different methods.

So it’s capturing the bulk of the data no matter what I do.

Let me move on. Real quick, once I calculate all those returns for all those betting contracts, suppose I was just going to compare, let’s say, what $1 bet would look like, bet in the stock market, versus $1 bet in sports betting markets. It’s not quite a fair comparison because in sports betting markets, there’s a winner and loser here, whereas if I hold the market, that’s $1 long investment.

But you can see here that here’s the stock market in blue over time.

Here’s if I just bet on the home team, bet on the favorite, or just bet on the over, I typically have close to a 0 or even slightly negative return. But more importantly, the wiggles in these lines are completely unrelated. These are idiosyncratic.

Another way of saying this is they are devoid of any macroeconomic or market conditions. The correlation between the stock market and any of these bets is essentially 0.

So let me get to the actual test.

And I’ve got about 20 minutes, I think, to get through this.

But let’s see how far we get. Once I explain the tests, the tests themselves are pretty straightforward.

I’m going to be looking at three horizons of returns.

Here’s just a simple timeline of what I’m going to do. Book makers set an opening price on all these contracts and all these sports.

Let’s say it’s the spread, for instance. But whatever.

I’ve converting these all to prices.

So they set a price for the bet. Then betting continues, or betting takes place.

And that betting takes place right up until the game starts, which is the closing price.

So I want to look at the return from the opening to the close.

And then once the betting stops here at the close, the game takes place and there’s an outcome. And that determines the final payoffs on the bet.

And so there’s a return here from the close to the end as well. And then I can also look at the return from the open all the way to the close. If I made a bet here on the open and then held it, that would be my total return, which is going to be the sum of these two over those two horizons.

Now, the behavioral models I’m going to test have implications for the patterns of these different returns.

Let’s just think about it intuitively for a second.

So the first question you ought to ask is why do prices move at all.

Well, if there’s new information, prices would move, for instance. Suppose a key player gets injured. So you thought that the spread out to be three points.

Suddenly, Peyton Manning’s not playing. The spread’s now going to drop. So if it’s information, what would that imply?

Well, that would imply you’d get movement from here to here.

But if markets are efficient in the way Fama coined, then there’s no predictability from this closing price to the final game outcome. If Peyton Manning’s hurt, prices will adjust.

And then there’s no predictability.

So what we would see in that case is some return, positive or negative, between P0 and P1, and then 0 on average from P1 and beyond.

Now, contrast that to a pure noise story.

Suppose prices move from here to here because people are stupid. That there’s no information content in it, but they get excited about a team.

They like the color of the jersey. Whatever it might be, it has no information content. Then when prices move from here to here, whether it’s up or down, what’s going to happen?

Well, if prices move for non-information reasons, they’ve got to get corrected by the time the game ends, because the game outcome is not affected at all by betting behavior.

And so for instance, if people get too excited about a team and they push this price too high, then that’s going to predict a negative return from here to here on average. Or if it pushes it too low, it’s got to be a positive return.

So to formalize this– oh, sorry.

I had a little graphic here.

True prices are revealed. So the mispricing is corrected if there is any.

To operationalize this, I’m going to run two really simple regressions. If I regress the total return over the life of the contract from the open to the end on any movement from the open to close, and then if I do the same thing from the close to end return on the movement from the open to close, an information story would predict the following.

That beta zero should be 1 and beta one should be 0.

In other words, all of the return information is coming from the movement to open to close if it’s just information that’s being released. And then there’s no predictability after that.

So that’ll be 1.

These two things will essentially be the same. And that’s got to be 0.

A pure noise story predicts the opposite. It says that nothing actually changed.

There was no information content in prices being moved.

People were just doing it for whatever. Schiller calls it animal spirits or irrational exuberance.

Whatever it is, prices are going to move but they have no information content, meaning that there’s going to be a 0 beta for beta zero here, that the open to close movement is not going to affect the open to end return because that stays constant.

But in order for that to be true, it has to be the case that whatever movement happens between the open to the close, it’s got to be fully corrected by the close to end. In other words, beta one has got to be negative 1. This is why I got excited about this.

It’s such a simple test, and it’s got such opposite implications. I can really see whether this is 1 and 0 versus 0 and negative 1.

Now, notice this has nothing to do with value or size or momentum yet.

I’ll get to that in just a second.

There’s actually a third, more complicated story, which is, I think, really what the behavioral models are about, which is the following. Information moves prices, but not fully rationally. There’s a misreaction to that information.

And here’s where it gets a little tricky, but I’ll try to make it pretty simple.

Suppose that there is real information coming out– Peyton Manning got hurt– but that the market misreads to that.

In other words, Peyton Manning getting hurt should cost the Broncos, let’s say, 4 points.

But the market says, eh, it’s only 2, because there’s a little bit of under-reaction or conservativism to it. And then that slowly trickles out.

Well, if that’s the case, you’ll get the following. First of all, the movement in prices from open to close will be informative, but it will continue to be informative.

Another way of thinking about under-reaction is that we’re getting closer and closer to the truth, but prices keep getting updated in the same direction.

So all the betas are moving in the same direction. It also means, though, that the open to end return will have a beta greater than 1 and this thing will be positive.

Because remember, this return is the sum of this and the sum of this.

Another possibility, though, is that people don’t under-react to the news of Peyton Manning getting injured. They overreact to it, meaning they thought it should be a 4 point change in the spread, but actually investors overreact.

It’s a 6 point spread.

In that case, you get the opposite, which is this beta is going to be between 0 and 1, and beta one’s going to be negative.

In other words, there’s some offsetting here.

Just to make it really simple, all that’s going on– if I go back to this graph– is under-reaction would say prices move up and then they continue to move up. They don’t move up far enough here.

Overreaction would say prices move up, but they move up too far, so they’ve got to come down a little bit. So it’s not as strong as 1 or negative 1, but it should be positive and continue to be positive, or positive and then negative.

Now, how does momentum, value, and size fit into all these?

Oh, so first of all, let me start with the first test. Forgetting about momentum, value, and size, suppose I just ran this regression for all sports contracts.

In other words, all I’m asking here is on average, when price is moved from the open to close, does it have any predictive content? And if so, is it positive or is it negative?

Is it consistent with under or overreaction?

Well, here are the beta zeroes and here are the beta ones for the NBA, NFL, baseball, and the NHL.

And you can see that the beta zeroes are just about all positive. Sometimes here in the NHL for the over under contract, it’s 0.

But basically, they’re all positive and significantly less than 1 except for right here, which I’m going to look into, actually. I just noticed that.

So the rest of these are all quite a bit less than 1. And you can reject that they are different from 1. And consistent with that, when they’re less than 1, the beta ones are negative, meaning that you’re getting this counter-reaction.

So that’s very consistent with the overreaction story.

Now, I’ve never had a paper where it works everywhere all the time perfectly.

But on average, that seems to be the case.

And that’s true for both the spread, the money line less so, and the over under contract. What’s interesting, by the way, about the money line contract is anecdotally, at least, what I’m told is that that’s a market where mostly professional betters play in, that your average retail local better who’s betting not for their career typically does the spread or the over under contract. So it’s interesting– you’re going to see this throughout– the results are always stronger for the spread and over under contract than they are for the money line.

I’m not sure if that’s the right reason, but that’s certainly consistent with that story. Panel B here just does the same thing, but conditional on a price move. I’m just throwing out all the times where the spread never moves.

Because there are lots of games where the opening and the closing price are identical.

But if I throw those out, I get actually sharper results.

So what does this tell you?

Well, this tells you on average, at least in these four sports, that when there’s price movement, a good deal of the time it gets reversed. That’s interesting.

Does it have to do with value and momentum?

Well not yet. So how do I do that?

Well, now in order to incorporate the financial market anomalies that I’m really interested in testing, I want to see if that reversal effect that we see on average for a lot of these contracts, is it at all related to value, momentum, or size, for that matter? And the way I want to do this is, the way to think about it, is there’s movement from the open to close that we know is generating some predictability.

Is that movement at all related to past performance of the team or any of these other value measures that I could come up with? So what I’m going to essentially do is run a regression of the open to close return on whatever characteristic I’m interested in, whether it’s momentum or value. You can think of this– those of you that know what an instrumental variable is– this is basically an instrumental variable, say momentum, for the price movement in the betting contract.

And then I want to see if the movement caused by that characteristic has the patterns either consistent or inconsistent with the under-reaction or overreaction type stories.

Now, it could very well be the case that sports betters don’t care at all about these characteristics.

Maybe prices don’t move at all for value, momentum, size.

If that’s the case, then that’s the end of the story. And that’s the end of the paper, that the financial market anomalies don’t really have any relation here to the sports betting market.

But if I can get this first stage to work strongly, then I’m interested in seeing what the patterns look like after that. And there’s all kinds of possibilities.

Could be that yes indeed, past performance impacts betting behavior which moves the open to close, but that has no predictive content for the close to end, meaning that maybe there really is information embedded in momentum.

And maybe book makers aren’t the ones being perfectly rational.

So there’s lots of possibilities here.

So now let’s talk about what measures I can use that can draw analogies to financial markets. Momentum, as it’s operationalized in financial markets, is really simple. It’s typically the past 12 month return, the one year return, on any asset.

This is what we use for currencies, commodities, stocks, futures contracts.

It’s just a past performance measure, the past return on any investment. That seems pretty easy to define.

And by the way, there’s different kinds of momentum.

That’s what I would call price momentum. There’s also something known as fundamental momentum, which is, say for a stock, it’s not just the past price performance but the past earnings performance relative to some consensus analyst forecast. We could define the same things in sports.

Momentum can just be short term past performance.

A year is probably too long.

But some measure of past performance over the last certain percentage of games or certain number of games.

That could be in terms of who wins and who loses.

It could be in terms of points scored and score differential. Or to make a direct analogy to the financial markets, I could actually look at the actual past returns on betting on this team in sports markets. That’s like betting on IBM’s share price. Here, I’m betting on the Cowboys covering the spread in their last eight games.

I can do that here as well. So what I’m going to do is play around with all different kinds of measures at various horizons, because theory doesn’t tell us what horizon to look at.

But very much similar to what’s been done in financial markets.

And then take an average of all those things.

I can compute a composite momentum index, because hopefully these things are correlated.

Hopefully they’re all picking up the same phenomenon. And then we’ll see what happens. Another thing I’ve done– you worry about data mining– is I chose these measures using alternate years of the different contracts, and then tried to test them on, say, on even years, then test it on odd years, and vice versa.

Because there’s always a danger that if I stood up here and said, well, the only one you really want to look at is the past four game measure, nothing else works, you’d be concerned I just cherry picked that.

So trying not to do that. I’m going to try to present as many things as possible.

And in the paper, I’ve got these massive tables that do that.

But that’s the idea here.

For value, it gets a lot harder. How do I measure fundamental value relative to market value?

Well, this is also a problem, by the way, when we go outside of the equity world, when we do this in financial markets.

For instance, like in commodities. What’s a natural fundamental measure of a commodity? There’s not really a good measure.

So what people often use is a long term past performance measure.

This is actually Dupont and Thaler created this in 1985.

The idea, say for a commodity, is look at what the average price was five years ago relative to the price today.

And that’s a measure of a long term fundamental measure relative to today’s circumstances. That tells you whether something looks cheap or expensive.

Cliff Asness at AQR, they use this a lot. He often refers to this as the poor man’s value.

When you’ve got nothing else to use, long term past return measures are pretty good. Just to give you a sense, if I use, say, a five year long term past return measure and form portfolios and equities, versus, say, like the book to market or earnings to price ratio, the correlation between those two portfolios is about 0.86 globally.

So it is picking up a lot of the same stuff.

So I can define past performance over longer periods.

I can also look for this idea of book value or fundamental value relative to market value by doing the following.

I’ll pick my favorite here. My favorite– not that it works that well– but my favorite one is take player payroll.

That is, a team that on paper looks better than another team. And why is payroll a good one?

Well, if you think that the labor market is pretty efficient here, then you’ve got to expect the ones that are paying their players more often have a better team. But look at that relative to what the market currently thinks in terms of the spread on the game they’re about to play.

That would encompass other information that maybe matters.

So here’s the idea. Two teams, let’s say.

One has a much bigger payroll than the other. But let’s say the spread is really narrow.

That would look like a cheap bet. You don’t have to pay much to actually bet on the better team, because they don’t have to win by that much.

That’s the idea.

And you can do the same thing not just with player payroll, but revenue, franchise value, all these other things.

And then size is pretty simple. Just the size of the market would work or the size of the franchise.

So let me get to the results.

By the way, before I use these, I have– for each of these, I tried to come up with dozens of different measures and take average of all these measures. But before anyone saw the results, I asked Fama and Thaler what they thought of these measures. Now, both of them– especially Dick was funny.

Dick said, I want to know what the results are first.

I said, no, no.

You don’t get to do that. So I said, look.

You’re welcome to say to me, I don’t think any of these measures are good.

They’re crap and I don’t think we’ll learn anything from this. That’s fine. But you’re not allowed to bitch ex post if you don’t like the results.

So I sent these to Fama.

His response was the following. “Most of these makes sense to me.

I like past team record, longer term for value, shorter term for momentum.

But the rest seemed OK.” And the reason he’s saying that is we use these same measures in financial markets and they do a decent job. Thaler was a bit funnier.

Momentum’s easier, he agreed.

And I would agree as well. For value, he conceded he has to like the long term past performance because it’s his measure with Dupont.

So he really can’t argue with that one.

So when I want all these regressions– and I’m going to wrap up here, leave some Q&A– this is an average of the t statistics of all the coefficients that I find on all the different momentum regressors. So I haven’t cherry picked the best ones.

Some work much better than others.

But I don’t have a good theoretical reason to believe why they should. It’s just really an average of all those different momentum measures. Oh, and I should be clear here.

When two teams are playing each other for the spread or money line, the momentum measure is the difference in momentum measures between the two teams.

That’s the idea.

For the over under, it’s the sum of those measures, because it’s the total points. So just to make sure we’re measuring this right.

But here’s what’s interesting.

It’s hard to read, I’m sorry.

The blue line is the spread contract. The money line is red.

And the green is over under. And these are the momentum beta patterns.

So this is just looking at momentum for open to end returns, open to close, and close to end.

And what’s really interesting is you find this pretty strong pattern that momentum predicts positive price movement from open to end to open to close.

In other words, when the betting line opens, people chase returns and they push up the price.

Very much like the behavioral theories suggest is occurring in financial markets. Perhaps more interestingly, it reverses by the time the game ends. In other words, there’s no information content in chasing returns.

The game outcome is unrelated to that.

So what that means is these contracts are overpriced right here and that the true return would’ve been just betting at the open.

Your return is essentially flat. That’s also true, by the way, for the over under contract. And again, I want to emphasize this.

The over under contract is completely uncorrelated to the spread contract on the same game.

One is a bet on who wins by how much. The other is a bet by the total points scored.

And I know sports enthusiasts think that offensive teams are more likely to win if there’s more points scored and defensive teams are more likely to win if there’s fewer points scored.

There’s no evidence of that in the data that I’m looking at here. That’s true in the NBA.

And then look at the NFL. Completely independent sample period and completely independent contracts, different sport, similar pattern.

By the way, notice the money line again, not much going on.

So it doesn’t work for the money line.

Even though the money line is pretty highly correlated with the spread contract, it’s different on this dimension.

For the NFL, pretty similar picture. The spread contract has this up and down movement which is very consistent with an overreaction story of chasing returns. Over under, a little less so, but still there.

The money line, not much.

And then for baseball and the NHL, notice the money line– there’s no spread contract here– you get a very similar pattern.

But just to be cautious here, the t statistics here are pretty strong for the NBA and NFL.

Much weaker for baseball and the NHL, though still significant for baseball. NHL’s weird. There’s not a lot going on, although the pattern looks very much the same.

And then we can flip this over to value.

Value has the opposite– not always opposite– but somewhat opposite pattern.

So assets that look cheap– that’s what you do for value.

You go long, cheap assets, you short expensive ones. They get cheaper between the open to close, but they get too cheap. And so there’s predictability when the game resumes.

That’s also true in the NFL, baseball, and NHL to a certain degree. Oh, that shouldn’t be spread.

The blue here shouldn’t be spread.

It should be the over under. The over under results are a bit more mixed.

And again, I ran this actually on Friday.

So I got to look at this a little bit more.

But there’s some consistent patterns here opposite of momentum, which is exactly what you’d expect because value and momentum are negatively correlated. And you see that a little bit here.

That’s very consistent with the behavioral stories that are being told in financial markets.

Now, just a caveat here.

The results for momentum are statistically much stronger than they are for value. For value here– this is where I’m going to fight with Fama and Thaler– it’s a question of whether you think the glass is half full or half empty.

The patterns look somewhat compelling, but the statistical significance is really slight. In fact, borderline not there.

So Fama may look at this and say, ah, there’s nothing there for value.

I can believe there’s something there for momentum.

Thaler may be happy with the momentum result, but maybe want to get greedy and say the value result’s there too.

But this is certainly a lot less compelling. It’s also the case, as we talked about, measuring value is a lot harder, too. So one of the reasons this might be less compelling is it’s just harder for me to come up with an analogous measure in financial markets.

So that’s just a summary of the patterns that I find. There’s continuation or sort of pushing up of returns in the momentum direction that gets reversed.

And for value, it goes in the opposite direction because it’s essentially pushing prices down further for those chief assets. Both are consistent with what people call the delayed overreaction story.

And we all agree, risk can’t explain this.

There’s no changing risk factor or anything like that.

That’s off the table here. Finally, the last thing I want to do is cut the– I haven’t done this yet– but I have some interesting data on high volume and low volume games where there’s a lot of betting activity versus a little.

I also have games that involve a parlay, which are known as sucker bets.

A lot of retail investors like to do these. So one interesting question would be whether the results are much stronger when I cut the data along these dimensions, and I haven’t done that yet. And then finally, can you make money off this?

Well, if there were no vig, the answer would be yes.

So that 10% transaction cost that sports betting book makers charge is pretty hefty to overcome. So if you run a trading strategy using momentum, value, or size– by the way, there’s nothing going on for size, that’s why I skipped over that.

But kind of makes sense.

It’s a very slow moving variable. You could make money trading momentum in sports betting markets until you have to pay that 10%.

and then you lose money pretty consistently.

In other words, you make a few percent betting on momentum or even betting on momentum with value, but it’s not enough to cover the vig, which in some sense is a nice story because if there were lots of money on the table here, you’d expect someone to jump in and take advantage of this.

Well, you can’t because that spread’s pretty wide.

What’s interesting is in sports betting markets, that spread’s come down. A 10% vig has come down now a lot on online book makers. It’s more like 7%. That’s still too high to make money, but at least you’re getting a little bit closer.

So let me stop there and let me open it up to some questions. It’s just a conclusion slide, but it just reiterates the points that I’m hoping to make.

So let me open it up.


TOBIAS J. MOSKOWITZ: Any questions?

AUDIENCE: I have one question for you.

TOBIAS J. MOSKOWITZ: Figured you might. AUDIENCE: So another way of getting at this would be in game trading.

It seems like that would actually have more parallels, if you thought about it, to financial markets, if you thought about it. Maybe explain those markets and then talk about it. TOBIAS J. MOSKOWITZ: Yeah.

So what Steve’s talking about is once the game starts, you can start betting on that same game within the game, as the score changes, as people move.

I don’t have that data.

I think that would be very cool data to look at this, and much more micro. So I think there’s things I could get at with that data that I couldn’t get at here.

The one thing I do like about this broader view, though, is it’s more analogous to financial markets in terms of selecting across contracts, the cross-section of returns.

So I think there’s two things that are interesting here. One is if you just wanted to test the behavioral theories in and of themselves, looking at the within game stuff, I think, would be a more powerful way to do that, as Steve’s suggesting. But if you want to link this to the cross-sectional asset pricing anomalies that I’m looking at, which is why do some stocks outperform others– and in this case, why is betting on some games better than betting on others– then I think you want to look at that broader view.

Both would be very cool to look at.

So here, I’m just exploiting the cross-section.

But looking within a game, I think, would be very neat if I had that data. I’m actually working on getting something like that. So I think that’s interesting.


AUDIENCE: Thank you for speaking with us today.

Warren Buffett is offering $1 billion to anyone who completes a perfect March Madness bracket.

TOBIAS J. MOSKOWITZ: Yeah. AUDIENCE: The odds are about one in 4.3 billion.

My question is, what do you think your odds are, and if you’re planning on entering, and if so, can I see your data and your bracket before we do?


Let me put it this way. So I think my odds are no better than the average person.

In fact, I do a NCAA auction with a bunch of other professors at Harvard and UCLA and across the country. And I had my buddy Nate Silver prepare a cheat sheet.

He and I put one together where we had all the numbers you could possibly want from all the sports betting markets, from all of his own analysis, because he was writing a column for The New York Times, now Grant Land.

Or now ESPN, I should say. And so we put it all together.

And I thought I made great bets And I was the biggest loser in the entire thing. So I lost it by far, like by a factor of two or three to the next person who lost money.

So it’s tough.

If you think these markets are pretty efficient, just looking at the point spreads is your best bet.

Here’s the problem. To get a perfect bracket, you got to bet on volatility. So you just really have to get lucky.

You’ve got to pick whichever 15 seed might win and go from there.

Yeah. Buffett should be putting up $4.3 billion, actually, if he’s really meaning to pay.

AUDIENCE: Well said.

TOBIAS J. MOSKOWITZ: So we’ll see. Yeah.

AUDIENCE: Thank you, Professor Moskowitz. Could factors that universally affect player health be considered a case of macroeconomic variables?

TOBIAS J. MOSKOWITZ: Well, they could.

But remember, it’s a zero sum game.

You got two teams playing each other. So suppose there was a break out of the flu, right, and the starters on all teams can’t play.

That’s true for both teams.

So in terms of the difference, I don’t think that that’s going to matter. And that’s the key about looking at the cross-section of returns.

Not only am I looking at the difference between two teams, looking at the difference between two games. And there’s nothing that I can think of in a macroeconomic sense that would tell me that the Giants-Eagles game is priced differently than the Cowboys-Redskins game at the same time.

So that that’s kind of the way we’re approaching it– I’m approaching it.

Any other questions?

You guys were hoping to hear about home field advantage or something, right. Go ahead.

AUDIENCE: You ever consider looking at sub-samples where [INAUDIBLE] might be occupied, like just post-season games?

TOBIAS J. MOSKOWITZ: Yeah. So that’s a good question.

So I’ve tried to cut it. There’s not that many post-season games, so you lose a ton of power.

But if I put in like a post-season dummy and tried to interact it, I don’t see anything incredibly different. One way– that’s why I was talking about it at the end– cutting it by trading volume, which actually post-season games are much more heavily betted than regular season, is one way to look at it.

So that’s something I’m planning to do.

At least for the initial bounce back effect, the reversal effect, I don’t see big differences between highly bet games versus not so highly bet games.

One thing I could do, but it’s a big pain in the ass, is I actually have all the college sports as well, which are very illiquid, many of them.

I could see if those are different. The problem is some of those are illiquid games are so illiquid, the prices are just a little crazy in general, which means you probably couldn’t transact that, then. That’s the problem.

They’re not real prices. So it’s something that I’m considering doing.

That’s one thing to look at it.

I thought of also looking at televised versus non-televised games, or nationally televised games, that is.

That kind of thing.

Or looking at big events, Super Bowl, whatever. The BCS championship, all that stuff. But again, you lose data really fast.


AUDIENCE: When looking at momentum, would you cut off [INAUDIBLE] the season [INAUDIBLE].


TOBIAS J. MOSKOWITZ: Yeah. The measures are a little tricky.

So momentum is pretty easy because I just looked at things like– and I went over this too quickly– but like in football, I’m looking at momentum, it’s like 4 game streaks, 5 game streaks, that kind of thing.

In basketball, I look as much as 8 to 10 games for momentum, because obviously it’s the same percentage of the season.

And baseball, similarly. When I start looking at the longer term performance measures like past performance over 40 games in the NBA, or even multiple seasons, yeah. You have to be careful about those season cut-offs.

So none of the momentum measures– for instance, if I’m using, say, the past 10 games, then the season would start with the 11th game.

I don’t want to spill over into the previous season. The team was different.

There’s been a huge lag between them.

So I try to do that.

It actually does make a difference, because I think the first time we ran it, we didn’t do that. And the results were a lot weaker, which is good.

They should have been, right?

There’s less information, you would think, when you do that for momentum. So these are all within season for the short term measures. Yeah.

AUDIENCE: How big is the momentum effect relative to whatever the baseline return is, compared to the financial market?

TOBIAS J. MOSKOWITZ: That’s a great question, and I don’t know how to answer it.

I really want to answer that question. You know, I can do it terms of like– so getting back to one way think about it. Where’s this?

Go back. Oh, I don’t have it on here.

That’s stupid.

Oh, yeah. I do.

The Sharpe ratios.

One way to think about is looking at the Sharpe ratios.

These Sharpe ratios are way smaller than what you get in financial markets. Maybe that just means that what you’re seeing in financial markets is a bit of behavioral stuff plus a lot of risk premia. I don’t know what the right story is.

But even Sharpe ratios aren’t necessarily the best measure.

Just to give you a sense, the return distribution here, because it’s so 0-1, the volatility of these sports betting contracts on average can be something like 100% per year on an annualized basis. It’s like five or six times market volatility.

Sharpe ratios should adjust for that.

But there’s no natural compensation for risk here because it’s idiosyncratic.

It’s really hard to compare. Another thing I tried to do was think about it in an r squared context.

Actually Steve and Jesse, if you have any ideas, this would be great.

But thinking about how much of the cross-sectional variation in returns is momentum explaining relative to how much cross-section variation there actually is, that’s even a really hard number to come by in financial markets. I would love to get that number, because that would be the exclamation point on this.

So if anybody here has any ideas, I’m still thinking about how to do that. I don’t know how to do that right.

That’s an excellent question. Yeah.

AUDIENCE: Have you looked into, I guess, the closing parts and the result at the end, those are widening out? But access to the opening lines likely to be really limited.

Have you looked at what percentage of that run-off takes place right away, whereas you may not have been able to have access to the opening lines? TOBIAS J. MOSKOWITZ: So I don’t have that data yet, but I’m working on it from the same vendor that gave me this.

He’s actually got time stamped price movements between the open to close as well as betting volume tied to that.

He won’t disaggregate it for me, but I don’t care. I just need to see the total number of contracts or the total number of dollars bet, would be even better.

That would be a really cool thing to do, and I haven’t done that yet. It’d also allow me, getting back to related to what Steve was saying about the within game, this would be before the game starts.

But I’d also be able to see the price patterns themselves.

So for momentum, it’d be interesting if you saw a steady increase in prices as people piled on, or whether this was just one big jump and maybe that has different pricing implications going forward. I’d love to. I don’t have that data yet.


Now for some of these contracts, like in the NBA and baseball and hockey, often there’s only a few hours between the open and the close.

So there’s not going to be huge movements, I would think there.

But for something like the NFL, that could be really interesting. We have a week of betting. So it’s a great idea.


Other questions?

All right.

Well, that’s what I’m doing currently.

We’ll see. I got a lot of work to do still, though. Thanks.