Going into the Democratic convention this week, most polls of registered voters were showing the presidential race to be a statistical dead heat between Obama and McCain (although today’s Gallup Poll Daily tracking poll is beginning to reflect the typical convention “bounce” that Gallup has observed in most party conventions in recent decades). However, a more reliable indicator of what’s really going on is provided by intrade.com, which trades “all or nothing” futures contracts on a number of different contingent events, including who is likely to be elected the President of the United States. These contracts pay 100 points (where 1 point = $.10) if a specific contingent event occurs and 0 points otherwise otherwise; consequently the prices for these contracts represent discounted, risk neutral probabilities.

According to intrade.com, Obama currently has a nearly 3:2 edge over McCain (which is actually down considerably from the 2:1 advantage which Obama had a few months ago after he became the presumptive Democratic presidential nominee). An important problem with national polls such as Gallup is that these polls are designed to provide an overall snapshot at a given point in time of the nation’s political mood. However, the nation’s political mood doesn’t elect presidents; the electoral college does. While the race may appear to be close nationally, once you do the math state-by-state, you get a very different picture. This information is provided by the intrade political futures contracts, since they represent unbiased bets on the electoral college outcome. While information on overall popularity amongst registered voters is not without interest, the election obviously will come down to who actually turns up to vote, how the undecided segment is swayed, and how all this is distributed on a state-by-state basis. These important subtleties are implicitly captured by prediction markets prices but are completely lacking in the national polling data.

For more information concerning the topic of “prediction markets”, I recommend a Wall Street Journal essay entitled “Best Bet for Next President: Prediction Markets” by Wharton professor Justin Wolfers. Wolfers and Zitzewitz also published the following article in 2004 in the Journal of Economic Perspectives:

Wolfers, Justin and Eric Zitzewitz, 2004, “Prediction Markets”, Journal of Economic Perspectives, Vol. 18, No. 2 (Spring), pp. 107-126.

The idea of relying upon futures markets prices to forecast future events has an interesting history. Nearly 25 years ago, UCLA finance professor Richard Roll published a paper in the American Economic Review entitled “Orange Juice and Weather” which showed, among other things, that the futures market in orange juice concentrate is a better predictor of Florida weather than the National Weather Service. Since the only way one can earn excess profits in a speculative market is to gain an informational advantage over the competition, traders are strongly motivated to try to do just that. If markets are informationally efficient, it follows that market prices represent unbiased forecasts concerning future events. Technically, this means that on average, the market’s estimate of the average value of the event in question is likely to be quite accurate.

Since President Bush recently nominated Judge Samuel A. Alito to replace (retiring) Sandra Day O’Connor on the Supreme Court, this must mean that tradesports.com has a new senate confirmation contract trading, aka SC.CONFIRM.ALITO.  On its first day of trading, the price for this contract ranged from $75 to $84.90.  Lately the trading range has narrowed somewhat at a marginally higher price level (now $88.50), implying nearly a 90% likelihood of Senate confirmation.  Here’s the graph over the lifetime of the contract:

The idea of relying upon futures markets prices to forecast future events has an interesting history. Nearly 20 years ago, UCLA finance professor Richard Roll published a paper in the American Economic Review entitled “Orange Juice and Weather” which showed, among other things, that the futures market in orange juice concentrate is a better predictor of Florida weather than the National Weather Service. Since the only way one can earn excess profits in a speculative market is to gain an informational advantage over the competition, traders are strongly motivated to try to do just that. If markets are informationally efficient, it follows that market prices represent unbiased forecasts concerning future events. Technically, this means that on average, the market’s estimate of the average value of the event in question is likely to be quite accurate.

Consequently, I believe that political “futures” markets provide reliable indications of the odds that a political party or candidate will win an election.  Although the 2008 presidential election is still more than 3 years away, tradesports.com maintains an actively traded market for futures contracts which pay off $100 in the event that a specific political event occurs and $0 otherwise.  Essentially, prices represent “risk neutral” event probabilities. With this in mind, it is interesting to observe what the political futures markets are telling us at this time about the 2008 election.  Currently, three contracts are traded that involve bets on which party is likely to win the presidency in 2008; specifically, Democrats, Republicans, or none of the above:

Contract
PRESIDENT.DEM2008 (Democratic Party Candidate to Win 2008 Presidential Election) – 48.30% chance
PRESIDENT.REP2008 (Republican Party Candidate to Win 2008 Presidential Election) – 50.50% chance
PRESIDENT.FIELD2008 (The Field (Any Other candidate) to Win 2008 Presidential Election) – 1.20% chance

tradesports.com also makes a market in futures contracts on specific candidates winning either the Democratic or Republican nomination for president.  Currently, Senator Hillary Clinton (D., NY) leads the Democrats (43.7% chance), whereas Senator George Allen (R., Virginia) leads the Republicans (20%).  At this time, it would appear that the Republican race for the nomination is more competitive than the Democratic race; Governor Mark Warner (D., Virginia) comes in second after Hillary with a 10.9% chance, whereas Senator John McCain (R., Arizona) is close behind Senator Allen at 17.2%.  The product of the nomination probability times the party probability listed above represents the market’s best guess at who the next president will likely be.  Currently, the top 5 candidates are as follows:

Hillary Clinton – 21.11% chance
George Allen – 10.10% chance
John McCain – 8.69% chance
Rudy Giuliani – 6.57% chance
Mark Warner – 5.26% chance

Interestingly, the market believes that Governor Arnold Schwarzenegger (R., California) has a better shot of becoming president than the following set of potential candidates: Governor Brian Schweitzer (D., Montana), Retired General Colin Powell (R.), Senator Pat Leahy (D., Vermont), Senator Chris Dodd (D., Connecticut), Representative Harold Ford (D., Tennessee), Senator Joseph Lieberman (D., Connecticut), Senator Elizabeth Dole (R., North Carolina), and Retired General Tommy Franks (R.).  This would quite a feat, since in order for the Arnold to become president, it would require an amendment to the U.S. Constitution (since Arnold was born in Austria).  In other words – not going to happen – not for Arnold, and not for the rest of these “candidates”.

Today’s Wall Street Journal article entitled “For Math Whizzes, The Election Means A Quadrillion Options” provides an overview of the various quantitative techniques being employed by geeks all over the country who typically are tenured college professors who probably have too much time on their hands.  Notwithstanding the barrage of criticism which has been leveled at the prediction markets (e.g., one commentator has described the Iowa Electronic Exchange Market as “college students playing with their lunch money”, and others have offered even more unflattering comments which will not be repeated here), I remain a fan and am looking forward to how the realized election results line up with these markets’ predictions.

Speaking of the prediction markets, the prices on the state-specific “Bush win” contracts offered on tradesports.com suggest that Bush currently (as of 10 a.m. on October 26) has a 19 electoral college vote advantage over Kerry; specifically, 253 to 234.  The basis for this assessment involved allocating electoral college votes to Bush in states with “Bush win” contract prices exceeding $60, and to Kerry in states with “Bush win” contract prices less than $40.  In my opinion, the states which are really in play are those with “Bush win” contract prices between $40 and $60.  There are five states which fit this criterion: Wisconsin, Ohio, New Mexico, New Hampshire, and Minnesota.  The following table lists the current prices for Bush contracts in these states, along with the number of electoral college votes which each state owns:

If Bush holds onto the states with contract prices exceeding $60, a win in Ohio would put him over the top.  If Bush does not win Ohio, he can still be reelected by taking Wisconsin, New Mexico, and New Hampshire.  Kerry on the other hand, will not likely win the election without taking Ohio.  Of course, various other permutations are possible.  The prediction markets data suggest the possibility of a 269-269 tie in the electoral college, which would happen if Kerry wins Ohio, New Hampshire and Minnesota, while losing Wisconsin and New Mexico to Bush.

Certainly the quantitative models are interesting, and as indicated by the Wall Street Journal article referenced above, suggest that the election may very well be somewhat of a toss-up.  However, there is probably no predictive indicator which has been as consistently accurate as the Weekly Reader poll.  Since 1956, Weekly Reader students in grades 1-12 have correctly picked the president.  As noted on the Weekly Reader website, “President Bush was a strong winner in the student poll; the only state Senator Kerry won was Maryland. Senator Kerry was also in a statistical dead heat with President Bush in New York, Massachusetts, Washington, D.C. and Vermont. President Bush won most grades, although Senator Kerry did win among tenth-graders.”  Also, results by grade are shown on the Weekly Reader website, in case if you are interested.

Today, the Tradesports website made high, low, and closing daily price data available for the PRESIDENT.GWBUSH2004 and PRESIDENT.KERRY2004 futures contracts.  Below, I provide the graph of daily closing prices for the period August 11, 2004 (which is the first day that the Kerry contract started trading) through October 20, 2004.

Yesterday (Monday, September 20, 2004), E. S. Browning (Staff Reporter of the Wall Street Journal) wrote a very interesting article entitled “As Bush Goes, So Goes Market”.  He basically makes many of the same points which I made on Saturday, September 11 in my entry entitled “Update on the relationship between stock market returns and presidential futures returns“; i.e., that the presidential futures contracts appear to be pointing to a Bush victory this coming November, and that the stock market appears to be responding favorably.  Or does the direction of causality move in the opposite direction?; i.e., as the stock market improves, this implies that investors are more confident about the economy’s future prospects which which in turn improves the electoral prospects of the incumbent president (as reflected in futures prices).  Professors Naveen Khanna and Jennifer Brooke Marietta-Westberg (both finance professors at Michigan State University) make the latter (rather compelling) argument in their paper entitled “Is it ‘Kerry up, Market Down’ or ‘Market Down, Kerry up?’ Correlation versus Causation“.

In an earlier post entitled “Kerry Up, Markets Down? A Regression Analysis“, I reported the results of the following regression equation:

(1) r_S&P500,t = a + br_Kerry,t + e_t,

where r_S&P500,t = daily return on the S&P 500, r_Kerry,t = daily return on the Kerry Futures contract, a = intercept, b = slope; and e_t= error term.  I was motivated to estimate this regression equation after reading a Wall Street Journal article entitled “Kerry Up, Markets Down” which claimed that “…when Kerry’s political fortunes rise, the stock market tanks.”  The evidence presented in this article for this conjecture did not seem all that robust; specifically, it was based upon graphically comparing 5 day moving averages of Kerry Futures Contract prices (available from the Iowa Electronic Markets website) with 5 day moving averages of the S&P 500 index.  A more convincing analysis is possible by running this very simple regression equation given in (1) above. I found that while there is statistically significant inverse relationship, the economic significance of the effect is rather negligible; specifically, a 1 percent change in the value of the Kerry Futures contract is associated with a -0.0389% change in the value of the S&P500 index.

It struck me that if Kerry was “bad” for the stock market, it would be interesting to find out whether Bush was “good” for the stock market, so I decided to reestimate regression equation (1) and also run a similar regression (given by equation (2) below) on the Bush Futures contract.

(2) r_S&P500,t = a + br_Bush,t + e_t,

where r_Bush,t represents the return on the Bush Futures contract.  For both contracts, I used realized daily returns from the period June 2, 2004 through September 9, 2004, resulting in 69 daily observations for the futures contract and stock market returns.

The “new” Kerry results are given in the following table:

Kerry Regression Statistics
R² = 0.0508
Observations: 69
a = 0.00001 (P-value = 0.9921)
b= -0.03789 (P-value = 0.0626)

Compared with the original regression results from August based upon 47 daily observations from the period June 2, 2004 through August 10, 2004, there has hardly been any change in the parameter values.  The correlation between daily returns on the Kerry Futures contract and daily returns on the S&P 500 index is -0.225, and although this inverse relationship is statistically significant (as indicated by the low “P-value” in the table above), it is not economically significant, since it implies that a 1 percent change in the value of the Kerry Futures contract is associated on average with a -0.03789% change in the value of the S&P500 index.

Next, let’s turn our attention to the parameter estimates for regression equation (2), which relates stock market returns to Bush Futures contract returns.  There, we find the following:

Bush Regression Statistics
R² = 0.1007
Observations: 69
a = -0.00005 (P-value = 0.9525)
b= 0.06997 (P-value = 0.0079)

The correlation between daily returns on the Bush Futures contract and daily returns on the S&P 500 index is .317, and although this positive relationship is statistically significant (as indicated by the negligible “P-value” in the table above), it also (like the Kerry contract) is not economically significant, since it implies that a 1 percent change in the value of the Bush Futures contract is associated on average with a 0.06997% change in the value of the S&P500 index.

While this represents an interesting statistical exercise, the low goodness of fit (R²) and the b values reported in these tables indicate that there are other (probably much more) important determinants of stock market returns other than the odds of who our next president will be. On the other hand, it is interesting to note that if you take the net difference in the two beta values for Kerry and Bush (0.10786) and assume an expected annual return of 7-10% on the S&P 500, Kerry “costs” investors roughly 75 to 100 basis points per year, the order of magnitude of which is comparable in many cases with the management fees that are typically charged by actively managed mutual funds.

In the August 11, 2004 issue of the Wall Street Journal, an article by Eric Engen (resident scholar at the American Enterprise Institute) entitled “Kerry Up, Markets Down” appeared which makes the following claim: “…Sen. Kerry has promised to repeal a significant portion of (the Bush) tax cuts if elected, including the tax rate reductions on dividend and capital gain income. With the growth rate of the economy high but slowing somewhat, there are signs that this promise is rattling financial markets. The evidence suggests that when Sen.Kerry’s political fortunes rise, the stock market tanks.” Steve Forbes, editor in chief of Forbes and former (Republican) presidential candidate, weighed in with a similar opinion piece (entitled “The Rubinian Candidate”) in today’s Wall Street Journal.

Mr. Engen’s analysis is based upon graphically comparing 5 day moving averages of the 2004 US Presidential “Winner Takes All” Kerry Futures Contract Prices with 5 day moving averages of the S&P 500 index. While it appears that the two time series move in opposite directions, a more convincing analysis requires determining whether what seems visually apparent is statistically significant. Experimental evidence shows that people tend to see order even when the charts they are looking at consist of randomly generated numbers. Therefore, I computed daily returns on the S&P 500 and the Kerry Futures contract and regressed stock returns on Kerry Futures contract returns for the period June 2, 2004 through August 9, 2004. I selected this period because the data source (the Iowa Electronic Markets database) has a continuous price history on the Kerry Futures contract which began on June 1, 2004.

The regression equation that I estimated is specified as follows:

r_S&P500,t = a + br_Kerry,t + e_t,

where r_S&P500,t = daily return on the S&P 500, r_Kerry,t = daily return on the Kerry Futures contract, a = intercept, b =slope; and e_t= error term. The following table summarizes the regression statistics:

This regression equation has (as one would expect) a relatively low coefficient of determination, or R² of only .068. In other words, there are other (probably much more) important determinants of stock market returns other than the odds of a Kerry presidency. Furthermore, since 1) the sign of the regression coefficient associated with returns on the Kerry Futures contract is negative, and 2) the correlation coefficient between the dependent and independent variable in a univariate regression equation equals the square root of the coefficient of determination, this implies that the correlation coefficient between returns on the Kerry Futures contract and the S&P500 index is -.26.

Two important questions remain: 1) is the effect statistically significant and 2) is the effect economically significant? The answers to these questions are 1) yes, and 2) no.

Let’s look first at the question of statistical significance. Whether a particular independent variable is statistically significant depends upon the P-value associated with its regression coefficient. A regression coefficient’s P-value indicates the probability of “Type 1” error. Type 1 error occurs whenever one concludes that a relationship exists when in fact it does not. Furthermore, one must differentiate between “1 tail” and “2 tail” tests. The P-values listed here are for 2 tail tests, meaning that the “null” hypotheses we are trying to reject are a = 0 and b = 0. In the case of Engen’s theory, since the null hypothesis we are trying to reject is that b is non-negative, a 1 tail test is more appropriate. Consequently, based upon these test statistics, we would conclude that a is not statistically different from 0, and that the negative relationship between returns on the Kerry Futures contract and the S&P500 index is statistically significant (at the 7.66%/2 = 3.83% level). Technically, the 1 tail P-value of 3.83% suggests that the probability of committing Type 1 error (i.e., concluding that a negative relationship exists when in fact it does not) is very small.

Next, consider the economic significance of the effect. Even though it is statistically significant, the actual magnitude of the effect is quite small. Specifically, on average, a 1 percent change in the value of the Kerry Futures contract is associated with a -0.0389% change in the value of the S&P500 index. Based upon this result, I would have to conclude that Mr. Eng
en’s basis thesis (that when Sen. Kerry’s political fortunes rise, the stock market “tanks”) does not represent a particularly fair characterization of this relationship. There is an inverse relationship, but the economic significance of the effect is rather negligible.