Tom Brady and Efficient Capital Markets

Two university professors use a football playbook to teach net-present value, IPO pricing, risk-shifting, and more to undergrads and MBA candidates.
Marie LeoneJanuary 25, 2008

When New England Patriots quarterback Tom Brady was spotted by paparazzi wearing a walking cast on his foot, a shock wave rumbled through Patriots nation. The frightful images also sent bookmakers scurrying to rework betting lines. A potential injury to the seemingly unstoppable New England quarterback had odds makers reworking the Super Bowl point spread, knocking 2 points off of the original calculation and making the Patriots a 12-point favorite over the New York Giants.

The Brady boot incident is an example of the efficient-markets hypothesis, says James Mahar, an assistant professor of finance at St. Bonaventure University, near Buffalo, New York. An efficient market adjusts rapidly to the arrival of new information, which means that current prices (or the line on the Super Bowl, in this case) will reflect all available information. From a theoretical standpoint, the revelation that Brady’s ankle may be weak when he takes the field on Super Bowl Sunday is an example of the so-called semi-strong form laid out in the theory. That is, a semi-strong form asserts that current prices reflect all new information. Meanwhile, a weak form factors into the price past market-based information, and a strong form includes insider information.

Mahar and Rodney Paul, an associate professor of finance at St. Bonaventure who teaches a graduate course called “Economics and Finance in Sports,” have come up with a handbook to teach undergraduate and MBA finance courses using football analogies. “Using Football to Teach Finance,” which was released in 2003, makes a connection between football, the leading spectator sport in the United States, and basic finance theories and practices. “Even though baseball is talked about as being America’s pastime, this generation of students has a greater interest in football, on both the professional and college levels,” Paul tells

The professors use the teaching technique to draw students into the often-abstract world of finance by using concrete sports examples. While the handbook won’t have faculty members ditching textbooks, it is a useful tool to help students make real-world connections to finance, adds Paul.

For example, one of the toughest concepts to explain to new finance majors is the time value of money, notes Mahar. And failure to grasp this “crucial topic” has caused many students to do poorly in the class, or drop out of the major entirely. To pique a student’s interest in present-value calculations, discount rates, and expected cash flows, the duo turns to player contracts.

Present-value calculations are based on the premise that money today can be invested to earn more in the future; or, a dollar today is worth more than a dollar tomorrow. Also, to estimate the present value of future cash flows, a discount rate must be applied, which is an interest rate that reflects a risk premium that the cash flow may not materialize in the future. Now add a pigskin to the equation.

In their handbook, the professors looked at three players for whom they obtained salary data when they all played for the Tampa Bay Buccaneers: Ronde Barber, Martin Gramatica (now with the New Orleans Saints), and Mike Alsott (who retired this year). They used the defined cash flow spelled out in the contracts and applied a marketwide interest rate out into the future to see what the gridiron gang would make over time.

Barber’s salary contract, for example, was reported to be $18.3 million for six years (see Table 1 at the end of this article), but many sportswriters just added up the annual totals without applying a discount rate. By running the contract through a present-value calculation, students are able to see that the adjusted worth of the contract is much lower than what the media reported (Table 2).

For instance, using a 5 percent discount rate over six years, Barber’s salary total drops to $15.3 million, while applying a 10 percent discount rate estimates he would bring home $13 million. (The estimates don’t include Barber’s $2.6 million signing bonus or $500,000 checks for being named to the Pro-Bowl team.)

Player contracts also can be used to explain expected present values and how they fluctuate with changes in interest rates (Table 3). This is especially useful when illustrating the importance of using correct probabilities in calculated expected values and to show how longer-term contracts are more sensitive to changes in interest rates. To be sure, Gramatica’s reported contract value was $12 million; however, after applying a discount rate of 5 percent and factoring in the probability of being cut loose from the team, the expected value of his salary contract sinks to $5 million.

The handbook also compares the role of stock-exchange specialist to a bookie or bookmaker. A bookie’s job is to set a point spread on a game that will balance the betting action between the favorite and underdog: the idea is to handicap the underdog so the same amount of money is bet on both teams. In the case of the Super Bowl spread, the Patriots have to beat the Giants by more than 12 points for bettors with money on New England to win.

Assuming the operation is not corrupt and that the line is set correctly, the bookie doesn’t get involved in the wager, but rather collects a “vig” or commission on each bet. If betting tips too far one way or another, the bookie will place bets to restore balance. Similarly, when a stock-exchange specialist sets the price correctly, trades occur without the specialist being involved, and a commission is collected on each trade. When there is an imbalance, the specialist steps in and trades on his own account to restore balance.

What’s more, both bookies and specialists will temporarily stop trading when material information is about to be released. That likely was the case when the photos of Brady were released, the same way it would happen on Wall Street if a major merger was announced.

The professors also draw comparisons between ticket scalping and the “float,” as it relates to an initial public offering. The float is the total number of shares a company makes available to the public for trading. In one section, the handbook uses the football analogy to talk about underpricing IPOs and then driving up the price by timing the release of shares and manipulating the float. Since the number of shares is relatively fixed during the lock-up period, companies can choose to shrink the public float, which could cause demand to outstrip supply and drive up the IPO share price. Likewise, a scalper who knows there is a fixed number of seats in a stadium waits for demand to outstrip supply before releasing tickets — at a price far above face value.

As for understanding the natural risk-preference conflicts between bondholders and shareholders, the authors turn to the Hail Mary pass, football’s version of shareholders of a distressed company pushing for high-risk projects. When a company is teetering on the brink of bankruptcy, shareholders have more of an incentive than bondholders to accept management proposals for projects without any net present value. The reason: shareholders lose if conditions don’t change and the stock continues to plummet.

Bondholders, on the other hand, are paid before shareholders in the bankruptcy pecking order and stand to recoup some of their investment if a Chapter 11 reorganization is attempted or the assets are liquidated. This tug-of-war between risk-averse bondholders and all-or-nothing shareholders is one reason shareholders are more likely to heave up a Hail Mary pass than stick to a running game.

For their part, Mahar and Paul don’t have any finance formulas for predicting the Super Bowl winner. Mahar, a Buffalo Bills fan during the regular season, is rooting for a Giants upset, since the Bills finished second to the undefeated Patriots in the AFC East. Paul, who saw his Dallas Cowboys knocked out of the playoffs by the Giants, is hanging his hopes on seeing a good matchup. “New England is one of the best teams I’ve ever seen, but the Giants would go down in history if they won,” he says.

Table 1: A Gain of Six
A trio of pro-football player contracts used to teach college students the time value of money. (thousands of dollars) Player Signing bonus Salary Year 1 Salary Year 2 Salary Year 3 Salary Year 4 Salary Year 5 Salary Year 6 Ronde Barber 2,550 450 525 3,250 3,750 3,750 4,000 Martin Gramatica 1,700 450 1,700 700 1,150 1,650 2,150 Mike Alsott 2,500 600 1,400 1,500 2,000 Source: “Using Football to Teach Finance,” 2003, James Mahar, Jr., Rodney Paul, St. Bonaventure University.
Table 2: Dropping Back
The reported value of three NFL player contracts is reworked using a present-value calculation. (thousands of dollars) Player Reported value Present value Present value Present value Present value Present value r=5% r=8% r=10% r=15% r=20% Ronde Barber 18,275 15,270 13,826 12,982 11,213 9,825 Martin Gramatica 12,100 10,058 9,091 8,398 7,200 6,324 Mike Alsott 8,000 7,282 6,917 6,695 6,210 5,805 r = risk adjusted discount rate
Source: “Using Football to Teach Finance,” 2003, James Mahar, Jr., Rodney Paul, St. Bonaventure University.
Table 3: Out for the Season?
Unique and systematic risks play a part in the expected value of player contracts over time. Player Expected value p=0.8 Expected value p=0.8 Expected value p=0.8 Expected value p=0.8 Expected value p=0.8 Expected value p=0.8 r=5% r=8% r=10% r=15% r=20% Ronde Barber 18,275 7,644 7,118 6,809 6,154 5,632 Martin Gramatica 12,100 5,080 4,750 4,750 4,147 3,824 Mike Alsott 8,000 5,107 5,107 4,924 4,568 4,362 p = probability of remaining under contract for the entire year
Source: “Using Football to Teach Finance,” 2003, James Mahar, Jr., Rodney Paul, St. Bonaventure University.