Two of the most-well-known factors that help explain stock returns are the value effect (where equities with lower prices relative to metrics—such as book value, earnings, cash flow, sales and dividends—tend to outperform the equities with higher prices relative to those metrics), and the momentum effect (where assets that have outperformed in the recent past tend to continue to outperform in the near future).
Academic research has uncovered the fact that combining these two strategies (value and momentum) results in more efficient portfolios (because their correlation is highly negative).
Importantly, this holds true across the globe and across asset classes (meaning that it holds true not only for equities, but also for bonds, commodities and currencies). For those interested in the evidence, I recommend the study “Value and Momentum Everywhere,” which appeared in the June 2013 issue of The Journal of Finance.
While the existence and explanatory power of the value and momentum factors aren’t debated, there are two competing theories that attempt to explain the sources of their premiums: risk-based explanations (what we might refer to as the Eugene–Fama camp), and behavioral-based explanations (the Robert Shiller camp). Interestingly enough, Fama and Shiller shared the 2013 Nobel Prize in economics.
Behavioral research has found prices can deviate from their fundamental values due to cognitive biases (leading some investors to underreact and overreact to news) or erroneous beliefs. And because arbitrageurs cannot keep the market efficient by their actions—thanks to costs and limits to arbitrage—mispricings can persist.
University of Chicago professor Tobias Moskowitz sought to shed some light on the risk versus behavioral explanations for these premiums by testing the momentum and value effects in the world of sports betting. The theory is that if behavioral pricing models work, they should explain returns across all markets. Alternatively, if they don’t work, it becomes clear we need different models for different markets and/or asset types.
Why Sports Betting?
Sports betting provides a great laboratory, primarily because there are no macroeconomic risk explanations (only purely idiosyncratic ones) to account for the existence of a factor. In short, the only explanation possible is behavior-related.
If the value and momentum factors that appear in investing are indeed based on behavioral mistakes, then the same behavioral errors that materialize in investing should show up in sports betting. What’s more, sports betting (where terminal values are found very quickly) provides an excellent out-of-sample testing ground for behavioral theory, since any pricing errors are discovered quickly when bets pay off.
So the question becomes: Do we find the same patterns in sports betting and investing?
To supply an answer, Moskowitz looked at different sports betting markets to see if similar relationships and patterns appeared. He examined four sports—baseball (MLB), football (NFL), basketball (NBA) and hockey (NHL)—and three different contracts. That makes a total of 12 tests, greatly reducing the odds that any finding showing a consistent relationship was just lucky a coincidence. The three contracts were:
- Point spreads: For example, a team is favored by 3½ points. If you bet on the favorite and it loses or wins by less than 3½ points, you lose the bet.
- The over/under: This contract pertains to the total amount of points scored. For example, in an NBA basketball game, the over/under is 200 points. If you bet over and the total points scored add up to less than 200, you lose the bet.
- Money line: If you put money on the favorite, for example, you might have to bet $180 to win $100. And if you put money on the underdog, you may only have to bet $100 to win $170.
- In A and B, it’s typical to have to bet $110 in order to win $100. That’s the bookie’s cut, otherwise known as the vigorish (or vig).
The data that Moskowitz examined, which covered the period from 1999 through 2013 and about 120,000 different contracts, came from the largest Las Vegas and online sports gambling books. Moskowitz analyzed the returns to the three types of bets across time: from the opening price, which is set by the bookies; afterward, during which time individual betters are setting prices by their actions, until the game begins and betting ends; and the terminal value.
The theory he was testing was: Do the behavioral models explain returns? Or are the markets efficient? In other words, if markets were efficient, “sentiment” (what might be called “animal spirits” or “irrational exuberance”) shouldn’t predict outcomes; only new information (such as if an injury to a key player is disclosed) should.
On the other hand, if any new information is incorporated only slowly (the market underreacts) or there’s an overreaction (prices move up or down by too great an amount), we have a behavioral explanation that would be consistent with what we can observe in financial markets.
To reduce the risks of data mining, Moskowitz examined different momentum and value metrics, and different horizons, and averaged the results. He even tested for outcomes using only even and odd years as different metrics.
Measuring Momentum And Value
In finance, there are conventional measures of momentum and value—not so in the world of sports betting. With momentum, it is relatively easy to come up with some appropriate and useable metrics.
For example, Moskowitz examined lagged measures of performance based on metrics such as wins, point differential and dollar returns on the same team and contract type over the past one, two and even eight games (eight games, for instance, is roughly 10 percent of the NBA season).
In terms of value, it’s more difficult. Moskowitz chose to use long-term reversals as one measure. With equities, stocks that have done poorly over the past five years are considered value stocks. Thus, as a measure of value, he used past performance during the previous one, two and three seasons.
As other measures of value, Moskowitz took various book values of the team franchise—including book value of the team, ticket revenue, total revenue (gate sales plus souvenir sales, TV rights and concessions) and player payroll—and then divided each by the current spread on the spread betting contract.
Moskowitz also used the sabermetric (statistical analysis of sports) score known as the Pythagorean-win-expectation formula. The formula provides an expected win percentage for teams based on past wins, point differential and strength of schedule, much like a power ranking.
Moskowitz used this score as a relative strength measure by taking the difference between the measures for each team he analyzed and then dividing that difference by the current betting line or contract price (similar to the earnings-to-price, or E/P, ratio).
Fama And Thaler On Momentum And Value Measures In Sports Betting
Of particular interest is that, before running the data, Moskowitz asked his University of Chicago colleagues Eugene Fama (the leading “cheerleader” of the efficient markets and risk-based explanations for premiums) and Richard Thaler (the leading “cheerleader” of the inefficient markets and behavioral explanations for premiums) if they agreed with his choice of metrics.
Fama and Thaler had to base their evaluation ex-ante, not ex-post (after seeing the results). And they both generally agreed that the choice of value and momentum metrics were good and consistent with the way those terms are defined in financial markets. The following is a summary of Moskowitz’s findings:
- Aggregate returns in sports betting are flat and slightly negative (because of the vig), indicating that systematically betting on the home team, the favored team or the over is not profitable. Markets are efficient with respect to these attributes.
- As you would expect, Moskowitz discovered no correlation between the outcomes of sports bets and returns to the stock market. This demonstrates that sports bets are, in fact, independent.
- When betting lines move between the open of “trading” and the close of “trading,” the return from open-to-close is slightly positively correlated with the open-to-end return, and is negatively correlated with the close-to-end return.
- Sports betting markets do exhibit a tendency toward overreaction in prices. The overreaction is revealed (reversed) at the terminal value (when the game ends).
- There’s a strong pattern revealing that momentum exists and it predicts returns. Just as in financial markets, bettors push up prices. And again, just as in financial markets, there’s predictive value (there is reversal at terminal value, meaning there’s a delayed overreaction). In other words, the opening price (set by the bookies) was more correct than the price that existed when betting was closed at the start of the game. This was true across the different sports and the different, and uncorrelated, betting contracts. And with the exception of hockey, the t-stats were significant.
- There is also a strong, though opposite, pattern with value. Cheap bets tend to get cheaper as time passes, and then a reversal occurs as the true value is revealed at the terminal value when the results become known. This negative relationship between momentum and value is the same as we see in financial markets. However, while a strong pattern for value bets did exist, the results didn’t come with the same strong statistical significance as they did with momentum. And while it’s easy to come up with the momentum definitions, with value, it’s not so clear-cut.
- Moskowitz also examined the size effect. To measure size, he used annual franchise value, ticket revenue, total revenue and player payroll. These measures are highly correlated with the size of the local market in which the team resides. He found no explanatory or predictive value in the data.
- The returns generated from momentum and value per unit of risk (volatility) are about one-fifth as large as those found in financial markets, suggesting that the majority of the return premia in financial markets could be originating from other (risk-based) sources. Or it could be that the measures being used in sports betting markets are noisy, and hence don’t supply predictive content quite as clearly.
Moskowitz went on to examine the data from a different perspective. He writes: “An additional implication of the overreaction is that the effects are greater when there is more uncertainty or ambiguity about valuations.”
Because the quality of any team is more uncertain near the beginning of a season, Moskowitz separately examined games early in each season and also instances where the volatility of betting prices was higher. He found results consistent with overreaction—momentum and subsequent reversals are stronger, while value effects are weaker.
He applied the same idea to the returns of financial securities by using the passage of time from the most recent earnings announcement. He found: “Immediately following an earnings announcement, firm valuation should be more certain, since earnings provide an important piece of relevant information.”
Splitting firms into companies who recently announced earnings versus companies whose last earnings announcement was several months prior (greater uncertainty), Moskowitz found stronger momentum profits and subsequent reversals for the firms with stale earnings and negligible profits for firms recently posting earnings.
The opposite held for value. Value profits are strongest among firms with recent earnings and nonexistent among firms with stale earnings. Moskowitz explains: “These results match those found in sports betting markets and are consistent with a delayed overreaction story, where sports betting provides a novel test and new set of results for momentum and value in financial markets.”
Moskowitz concluded: “The remarkably consistent patterns found across different sports and different contracts within a sport make the results very unlikely to be driven by chance. The evidence is consistent with momentum and value return premia being generated by investor overreaction, providing an out of sample test of behavioral theories. In addition, the returns are wiped out by trading costs in sports betting markets, preventing arbitrageurs from eliminating these patterns in prices and allowing them to persist.”
What, If Any, Conclusions Can Be Drawn?
Given the nature of Moskowitz’s findings, what conclusions can we draw? First, the momentum and value effects move betting prices from the open to the close of betting. These patterns are completely reversed by the game’s outcome, and in a manner that is consistent with how these premiums work in financial markets.
Second, the fact that both momentum and value have predictive value in sports betting markets, and that these factors have the same negative relationship (momentum pushes prices up and value pushes prices down) that they demonstrate in the financial markets, provides support for the idea that these factors do incorporate at least some behavioral components in financial markets.
In other words, the risk-based versus behavioral-based explanations aren’t really competing, but complementary. The answer isn’t black or white, but some combination of the two competing theories is likely the correct explanation. I think about it this way: The value and momentum premiums aren’t free lunches, but they might be a free stop at the dessert tray.
Third, given the independent nature of the tests (which were across four different sports and three different contracts for a total of 12 betting markets) as Moskowitz noted, it would be a remarkable coincidence, and difficult to believe, that the findings were just a random outcome.
Also of interest is that Moskowitz found, just as in the world of investing where frictions prevent the “smart money” (arbitrageurs) from correcting mispricings, there are frictions (the cost of betting in the form of the bookie’s spread) that prevent smart money from correcting the pricing errors of individual bettors.
In other words, frictions allow the mispricings to persist even when the “smart money” knows that there are mispricings. In addition, the finding provides evidence that, after the cost of implementing a strategy is considered, the sports betting markets—like the financial markets—can be considered highly efficient.
With that said, if you can make “friendly” bets (without a bookie in the middle taking the vig), the evidence suggests that you should be able to exploit mispricings that occur after the opening line is established by the bookies, especially if you combine the two strategies of value and momentum.
Finally, Moskowitz noted that competition from online betting sites, predictably, has led to spreads smaller than the traditional 10 percent set by bookies. However, even lower spreads (as low as about 7 percent) are not low enough to exploit mispricings.
I’ll leave you with one last item of interest. Moskowitz is also the author of an outstanding book on sports and statistics. In my opinion, “Scorecasting” is a must-read for sports fans.
Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.