Evans Political Bull-Bear Indicator: August 2007

The people who bet money on their ability to predict political events are bullish on Mitt Romney. Every week or so I check the political futures market to see what the people who believe they know more than the average bettor who believes they know more than average bettor are thinking. (Got that?) Since February I’ve been tracking the relationship between the price of the candidates’ political futures with their average poll numbers. That relationship, which for fun I’m calling the Evans Political Bull-Bear Indicator, shows the bettors’ optimism about the candidate’s growth potential. When bettors put more money on a candidate than his poll numbers warrant, they’re communicating their confidence in the candidate’s future poll numbers, his upside. Scores above 1 indicate the market’s bullishness in the candidate’s future, scores below 1 indicate a bearish outlook. At some point, most likely next February, the futures for one candidate from each party will trade in the high 90s, the rest will hover near zero. The leading candidates’ Evans Political Bull-Bear Indicators will be around 2 (political futures will trade near 100, polling will be around 40-55%).

Among the candidates included in national polling surveys, Mitt Romney has consistently had the highest Evans Political Bull-Bear Indicator. On the Democratic side, bettors have been and currently are most bullish about Hillary.

This last week was also the first time I’ve seen Mitt place second among bettors. Giuliani’s been the leading candidate since last December. McCain was number two for the first months, then Thompson replaced him there when McCain’s campaign fell apart. Confidence in Thompson has faded over the past few weeks from a stable price in the mid-30s during June and July to his current price below 20. During that same stretch Romney’s price has gone from the high teens to the high 20s.

2007-08-20 Evans Bull-Bear Indicator Polling Average Political Futures Price
Romney 2.13 12.7 27.0
Giuliani 1.29 28.2 36.4
McCain 0.63 12.7 8.0
Gingrich 0.39 8.5 3.3
Thompson 1.06 17.0 18.0
Clinton 1.67 39.9 66.5
Obama 0.87 21.1 18.3
Edwards 0.58 12.0 6.9
Gore 0.55 13.5 7.4
Richardson 0.35 3.7 1.3

2007-02-28 Evans Bull-Bear Indicator Polling Average Political Futures Price
Romney 2.05 8.2 16.8
Giuliani 0.94 33.7 31.8
McCain 1.36 20.8 28.3
Gingrich 0.86 10.5 9.0
Thompson na na na
Clinton 1.26 38.9 49.0
Obama 1.05 20.6 21.6
Edwards 1.09 11.6 12.7
Gore 1.22 9.8 12.0
Richardson 1.21 3.4 4.1

Sources: Polling Averages from RealClearPolitics.com, Political Futures Prices from InTrade.com.

74 comments for “Evans Political Bull-Bear Indicator: August 2007

  1. This is fun, Matt. And your tables are beautiful.

    I imagine that some economist somewhere has tracked the accuracy of these futures markets–anyone know what they found?

  2. It would appear that EBBI = PFP/PA . Am I correct?

    If so, I would see the following conditions as posing red flags, where the cognoscenti and electorate are very far apart:

    EBBI greater than 2.5 and PFP greater than 40.
    EBBI less than 1 and PA greater than 30.

  3. Translating that into English, you’re saying that one should take a hard look when the political futures market are predicting that a candidate has near a 50% chance to get elected/nominated but less than one quarter of the voters indicate they support the candidate? That sounds reasonable.

    And you’re also saying that one should take a hard look when at least roughly one-third of the voters support a candidate and the political futures markets think the candidate has an ever-so slightly less than roughly one-third chance of making it? That does not sound so reasonable. What if a candidate’s polling average were 33% and the futures market had him priced at 32?

  4. The leading candidates’ Evans Political Bull-Bear Indicators will be around 2 (political futures will trade near 100, polling will be around 40-55%).

    Is this right? Once a candidate becomes inevitable in the primary process, do their poll numbers in their remaining primaries not rise above the 40-55% range? Higher than that, I would have thought.

  5. Thanks, Julie. I’d be interested in seeing a research paper, too. From my own experience they’ve been very good. I’d followed the California special gubernatorial election closely, and the weekend before voting there were some new sexual allegations made against Schwarzenegger, who had been leading in the polls by a hair to that time. On election morning I scoured the news websites in vain looking for a prediction about the outcome. Everyone was saying it was too close to call. I went to InTrade (which was actually TradeSports back then) and Schwarzenegger’s futures were trading at 95%. Given that I’d just spent an hour looking for information to help me know who would win, and couldn’t find anything helpful, I’m curious to know what made the bettors so confident.

    queuno, You’re right. I should have been more explicit in my post. The relationship I’m tracking is the Political Futures Price divided by the Polling Average.

    Because your red flags are based on the Political Futures Price, they merely indicate when you think the market futures price would be too high or too low. Which of course means only that you think you can predict the political future better than can the average person who thinks they can predict the political future better than the average person who thinks they can better predict the political future. : )

  6. Once a candidate becomes inevitable in the primary process, do their poll numbers in their remaining primaries not rise above the 40-55% range?

    Those figures are my best guesses, and I admit I’m not Michael Barone.

  7. Dear America,
    I don’t care what you do, just don’t give the world President Rudi Giuliani.
    Love, The World.

    P.S. Nice work, Matt. So, why do you think there’s this level of confidence in Mitt?

  8. Ronan, the main reason the elite have more confidence in Mitt than his poll numbers warrant has been his success at getting key supporters. I think they also believe the more people get to know him, the more they’ll like him, which isn’t true of all candidates, and I think Giuliani’s one of them. I think (and hope) the GOP nomination will come down to Romney and Thompson. Romney would be a great president, Thompson would probably be fine, and I think both of them would be formidable in the general election.

  9. Matt, where is Mike Huckabee in all this? I’m beginning to see him as a formidable candidate after reading that article on NRO yesterday. It portrayed him as having all the things that voters like about Mitt, but with a better sense of humor and a more down home approach, and without the Mormon downside and the vascillation on issues social conservatives care about.

  10. He is formidable, Mark IV. I don’t like his tax-and-spend views but I don’t think they’ll hurt him much.

  11. Interesting, Matt. To someone who still is a social studies teacher at heart, the Republican race will be the most fascinating primary in years.

  12. Thanks Matt.

    Journal of Economic Perspectives had a piece within the last year or two on prediction markets. Justin Wolfers at Penn has done some interesting work on it. By and large, prediction markets seem to work reasonably well at, well, predicting. But I think we’ve been getting a lot more data in the last few years so I would expect more and better research is to come. Of course, sports gambling markets have been around for a long time, so we know quite a bit about the sports prediction markets.

    I would guess that one thing going in Mitt’s favor is his strong standing in early primary states. That is the sort of thing that does not always show up in national polls, but President Howard Dean can tell you how crucial it is.

  13. Mark Intravenous, Huckabee’s futures are currently trading at 3% on InTrade.com. Both Ron Paul and Newt Gingrich are trading higher. The bettors think there’s a 42% chance Huckabee will drop out by year end.

    Adam, were you as surprised as I was to see how cynical the press was about Mitt’s language? I know lots of educated Mormons who talk that way, and as I’ve watched the Home & Garden channel too much lately, I’ve noticed most Americans talk that way, too. When someone sees their newly remodeled room or back patio, a surprisingly high number say “Holy cow” or “Oh my gosh,” even young urbanites updating their city-center loft condos.

  14. Frank, I can’t tell if my Bear-Bull Indicator adds anything, or if all of the relevant and interesting information is captured by the futures price. What do you think?

  15. Adam, were you as surprised as I was to see how cynical the press was about Mitt’s language?

    I was, Matt E. I can see why national press figures would make fun of his clean talk, though to me its endearing. But gee, what possible basis do they have for accusing him of doing it just as a cynical marketing ploy? Personally I don’t see any. If you read the Boston Globe article, after accusing him of talking that way cynically, they grudgingly report that his friends and family say that talking like that is the real Mitt. But even then the Globe reports it as “friends and family insist he really talks that way” and “insist” can be a word the press uses when they want you to disbelieve someone.

  16. Awesome charts. This is fun stuff. I remember these futures markets from 2004.

    Look at Hillary Clinton with $66.50. I think she’d crush Fred Thompson in a general election.

  17. Matt,

    One thing to watch is how many people are trading. If the market is too thin, it probably is not going to be as good a source.

    As for your index, I think if what you are interested in is predicting the outcome, you haven’t added anything. If you are interested in the difference between where we are now (in polls) and where we are likely to go, then you’ve got something interesting as I think you’re right that the index captures that flavor.

  18. Everyone, as I was looking at the numbers I was stunned that Newt Gingrich polls as high as he does. 1 in 12 Republicans want Gingrich to be the GOP nominee? Do any Republicans here want Gingrich over the others? Does anyone here know a Republican who wants Gingrich at the top of the GOP ticket?

    Thanks, Frank. It does capture whether the market price is bullish or bearish.

  19. Not a registered Republican, but I know hundreds and hundreds – and I have not heard a single one support Gingrich as their top choice. I have a feeling the result might be different in the South, but I still have a hard time believing it’s over 8%.

  20. “Look at Hillary Clinton with $66.50. I think she’d crush Fred Thompson in a general election.”

    Which state that didn’t choose Al Gore or John Kerry do you think would choose Hillary? I think national security is still paramount to most Americans, and even if they think Bush went too far, they’ll be reluctant to place their security in the hands of Hillary, Obama or Edwards.

  21. I’m not a registered Republican (might have to for the primaries though) but no, I don’t have interest in Gingrich as a candidate. I’d likely only vote for him as a vote against the Democratic candidate. Earlier in the year there seemed to be a fair amount of enthusiam present for Gingrich among the base as seen on various conservative message boards. This was back when it was Giuliani, Romney, and McCain as the real contenders. Gingrich was seen as an alternative for those that didn’t like the three main candidates, with the assumption being that he’d wait until the fall to drop in and save the party. Now that Fred Thompson is being talked up as a strong candidate I’ve seen a lot less people talking about Gingrich. I think Thompson killed any chances that he had. Which is fine by me. I prefer Romney but I’d be happy with Thompson.

  22. A Democrat could easily win those states (Florida, too), but I don’t think Hillary could win any of them. I just don’t know anyone who didn’t vote for John Kerry who would vote for Hillary. An educated woman who voted for Bush or Nader, perhaps, but I think any gain there would be more than offset by those who voted for Kerry but couldn’t stomach Hillary, especially if the alternative is someone like Romney or Thompson.

  23. Matt, It would appear that Hillary Clinton has a fine chance of being the next President– as compared to Mitt, anyway. Here’s the Intrade numbers.

    Hillary Clinton 41.10
    Rudy Giuliani 19.00
    Barack Obama 12.00
    Fred Thompson 8.50
    Mitt Romney 8.40

  24. Those values mirror the result of Likelihood Candidate Nominated by Party (which I’ve used above) multiplied by the Likelihood Party Wins Election. The current prices for the party of the winning president are 58% and 40% in favor of the Democrats. (By the way, I notice that Mitt Romney has moved from 8.4 to 10.4 today. There are arbitrage possibilities in here.)

    I agree that many people think Hillary can win, but I’ve read many Democrats who are scared to death she’s unelectable. I’m with them. The Democrats’ key strength in 2008 is Republican discouragement, and the RNC couldn’t invent a better get out the vote tool than the historic opportunity to vote against Hillary. Politics would be fun again.

  25. Hillary would probably be more energizing than Thompson. So I think people would find her more appealing.

  26. Here is another handy graph showing how prospects have changed over time, from IEM (which I think has limited bet sizes which might be argued to reflect less bias due to a few large bettors, but on the other hand might reflect more of a student bias or more noise because “there’s less at stake”….).

  27. …the public is starting to realize that it takes an uncommon executive just to get the bureacracy to stop resisting the President.

    What I hope the public has been realizing is that the root of most of our problems over the last six years has come from the “bureaucracy’s” (as well as the other branches of government’s) inability to sufficiently resist the President, and the President’s remarkable success in driving out career civil servants who were in his mind, insufficiently personally loyal to him, and replacing them with incompetent flunkies.

    What the public might do with this emerging awareness with respect to Romney’s political fortunes I can’t guess.

    However, many people may be buying the Romney futures, not necessarily because they think he will prevail in the end, but because they think he will be higher at some future point when they can sell and lock in the profits.

  28. Bill,
    I’m guessing that not very many of the GOP primary electorate shares your realization that the real problem is that the President has been too effective at controlling the bureacracy. i would expect that to have precisely zero effect on the GOP race.

  29. Adam,

    I guess when I read 28 I didn’t realize you were using the word “public” in such a narrow and restrictive sense.

  30. The numbers in #29, divided by the numbers in the original post, suggest (very roughly speaking) conditional probability that a candidate wins election given that he/she wins nomination (i.e., an indicator of electability).

    Hillary Clinton 41.1/66.5
    Rudy Giuliani 19/36.4
    Barack Obama 12.00/18.3
    Fred Thompson 8.5/18
    Mitt Romney 8.4/27

    In particular, these figures predict that Giuliani would fare significantly better than Romney in a general election (not surprising if you believe Giuliani is further left that Mitt), but that there is not a huge difference in electability between Clinton and Obama.

  31. Timer, I think it’s more likely that the discrepancies between Giuliani’s and Romney’s nomination and election numbers reflect an opportunity for arbitrage than they do the market’s belief that Giuliani would fare better in the general election. (As I pointed out to Frank, Romney’s election number rose to 10.4 today, a correction of nearly 25%. I think it’s more likely that some people noticed the discrepancy between his two values than that the market decided he was 25% more electable today than he was yesterday.)

  32. Romney’s chief asset is his ferocious desire to want to be president; his chief weakness is his ferocious superficiality. I know ward clerks I think would make a better president.

  33. The trouble is that Romney’s conditional probability has been consistently lower than that for Clinton, Giuliani, and Barack. (And I’ve checked this a few times in the past.) Of course, the market is fairly thin and imprecise (not tons of volume and often sizable spreads), but there seems to be a consistent belief that Romney is somewhat less electable than the others. Maybe this will change.

    I don’t know what arbitrage opportunity you have in mind. Can you be specific? The mere fact that you personally feel the market is incorrectly evaluating Romney’s conditional probability of winning general election (given that he wins the nomination) is _not_ an arbitrage opportunity.

  34. I agree with timer about what the market has consistently been saying about Mitt in the general election.

    I follow Slate’s agglomeration and there have been several times when the price for Mitt has shown large deviations across the futures markets. Large enough that there probably have been traditional arbitrage opportunities at several points. In fact, in the early days I recall the price of all candidates added up being somewhere around 125% probability– but whether or not you could have arbitraged it depends on the transaction costs for Intrade, which I don’t know. Thin markets will do that.

    RayB, I was a financial clerk. Do I make the cut?

  35. timer, I’ve seen significant variation between a candidate’s likelihood of nomination and their likelihood of winning the general election, and I think that relationship is close to a constant. No matter what special hurdles bettors think a candidate will face in the general election, their odds are better if they win their party’s nomination. It was predictable that Romney’s general election future would rise from 8.4 once his nomination future was trading at 26, since it was around 8.4 when when his nomination future traded at 20.

  36. Matt, imagine Mitt comes out with a platform deeply appealing to the Republicans but almost completely unelectable. Now, the Republicans might demur because the platform is not tenable in a general election, but suppose they endorse it. Thus, there are circumstances that can raise one’s odds of getting the nomination even as one’s general election chances fall.

    I’m not saying that is what happened, just that it ain’t impossible. One’s arbitrage would actually involve some risk.

  37. This is what bettors think the candidate’s chances are of winning the general election if they win their party’s nomination. (WinNomination / WinElection)

    Clinton: 60%
    Obama: 58%
    Gore: 55%
    Edwards: 56%

    Giuliani: 55%
    Thompson: 45%
    McCain: 43%
    Romney: 38%

    Romney’s general election numbers are definitely depressed, but I think Giuliani’s number is the hardest to explain. (The futures for winning party are trading at GOP: 38.9, Dems 58.2).

  38. “Thus, there are circumstances that can raise one’s odds of getting the nomination even as one’s general election chances fall.”

    I think those circumstances would seldom change during the primary on a week-to-week basis. Most of the challenges a candidate has in the general election that he doesn’t in the primary are probably very stable (Romney’s Mormonism, can’t win his own state; Hillary’s 49% unfavorability rating; Obama’s middle name Hussein). For that reason I’d expect the two futures to be nearly constant. It seems unlikely to me that the frequent variations between Romney’s nomination and general election futures are rational — occasions where candidates do something that obviously helps them win the primary but will cost them in the general election do not happen as often as the relationship between the two futures do.

  39. Matt said: I agree that many people think Hillary can win, but I’ve read many Democrats who are scared to death she’s unelectable.

    I’ve seen such articles, and I notice one interesting thing about them. Not one is by a professed Democrat. None refer to actual polls. They simply state, as you have repeated, that “many Democrats” fear that Senator Clinton can’t be elected.

    I think it’s more likely than not that these articles are Rove-style campaign strategies. Start a whisper campaign, claiming that “many” of Senator Clinton’s party don’t think she can win. Then maybe you’ll dupe enough Democrats into “sharing” what they’re fooled into thinking is a majority view within the party. Dupe them well enough, and they’ll vote in primaries for their second choice, and result in a weaker opponent for whichever candidate comes out of the Republican primaries.

  40. Matt, that’s all perfectly reasonable, but its the difference between a good bet and arbitrage (which is riskless).

  41. Might there be some opportunities for arbitrage in the glaring differences between the price for a GOP general election win and the average price for a win by the leading GOP candidates? I suppose not, because of the possibility that one of the non-leading GOP candidates could be the nominee, but it still looks like there are some possibilities there.

  42. I’m gonna go out on a limb here and suggest that perhaps ‘arbitrage’ was not really the most apt description of this ‘opportunity’ … Granted, I’d have more credibility if I’d made this observation before #40, but I’m not a high finance guy and I figured some properly credentialed someone would step up with an objection …

    All that aside, Romney deserves the GOP nomination. Look at the rest of the field. Are you kidding me? At the very least, I think Mitt, for all his blindspots and bluster, is a decent and competent human being.

  43. Adam observed in #3, regarding my analysis in #2: And you’re also saying that one should take a hard look when at least roughly one-third of the voters support a candidate and the political futures markets think the candidate has an ever-so slightly less than roughly one-third chance of making it? That does not sound so reasonable. What if a candidate’s polling average were 33% and the futures market had him priced at 32?

    Excellent point. 30% is probably not the right level, at least with more than 3 candidates in the field. I’m not sure what it should be, exactly, but I think there’s a legitimate question to be raised if the cognoscenti and the electorate are far apart (how exactly to delineate that is an open question).

    Ronan – The SINGLE best way for “The World” to ensure Rudy Giuliani does NOT get elected president is for “The World, especially Europe” to start championing Rudy Giuliani. Loudly. Vociferously. With advertisements in USA Today and “American Idol” and on the NFL saying how much Europe and Asia love Rudy. Then he’s sunk.

  44. What’s cool about Romney is that he’s really trying hard to get it. That makes it interesting.

  45. Chino,

    An arbitrage opportunity would be Mitt selling for 20 cents on one exchange and 27 on another. Such things have happened this year, though I don’t remember the exact spread so I might be exaggerating it.

  46. I got mugged in New York when Dinkins was in charge. Didn’t enjoy it.

    All I had to do was visit Tompkins Square Park after Giuliani got in, and I understood that the city had changed. Giuliani was a great mayor, with no apologies to my comrades on the left. Get over it. Maybe Bloomberg’s even better, I don’t know, I don’t live there now, you tell me.

    Anyway, nobody’s talking about a mayoral race here, and presidential material, Rudy ain’t.

  47. “What’s cool about Romney…”

    I’m miserable today, but that phrase made me laugh.

  48. #52, yeah, but I’ve gotta be able to make that trade pretty much simultaneously to put any easy money in my pocket, am I missing something? To h*ll with the country, what am I missing here?

  49. OK, I have no idea what that ‘to h*ll with the country’ was supposed to mean, other than I should probably be cuddling with the wife at this point in the evening/morning …

  50. The latest Rasumssen poll suggests that Romney has a problem. His negatives match Clinton’s–44/43. Worse yet for Romney, 25 percent of Republicans say they would definitely vote against him.

  51. That is bad. The good news is that his negative ratings seem to correlate with his unfamiliarity ratings. Polls that show lower degrees of unfamiliarity with him tend to show lower degrees of negativity towards him.

  52. In any event, I have been impressed with the organiztion of Romney’s campaign. They have a smart strategy.

  53. The arbitrage I was thinking of is something like: buy Giuliani win GOP nomination futures (currently 38.0), buy GOP win presidency futures (currently 38.9), sell Giuliani win election futures (currently 0.20).

    I think that successfully exploits the fact that 1 / (0.38 * 0.389) > 1 / 0.20

  54. I agree that the Rasmussen numbers do not look good for Romney. 25% of Repubs not willing to vote for him would be the kiss of death in a general election.

    I am becoming begrudgingly convinced that the US is not ready for a LDS President

  55. So let me ask this (bbell gives me an opening) –

    If Romney is Mormonism’s Alfred E Smith, who is the next potential Mormon candidate, to run in 2016 or 2020? Are there any potential candidates whose names we’d recognize now?

  56. will those same 25% continue to vote against romney if the choice is romney or hillary? i think not. these poll numbers have more to do with unfamiliarity with romney and dislike of the mormon church.

  57. Matt,

    Your arbitrage doesn’t work. There are four scenarios:

    1. Giuliani loses primary, GOP wins election.
    2. Giuliani loses primary, GOP loses election.
    3. Giuliani wins primary, GOP wins election.
    4. Giuliani wins primary, GOP loses election.

    Let A, B, C, and D be the probabilities (actually, technically, “discounted risk neutral probabilities” or something, but ignore that for now) of these four events. The contract prices you mention determine C+D, A+C, and C, and since we expect A+B+C+D = 1, this gives us enough information to work out A, B, C, and D. But your data do not lead to a contradiction in the risk neutral probability determination (which you would need for an arbitrage). They only show that Giuliani winning the nomination is not independent of GOP winning the election (which you seemed to be assuming before).

    To explain why you don’t get a risk-free profit from your proposed portfolio, I would have to know how much of each of the three items you were purchasing, and then I could find one of the four scenarios in which you lose money (or maybe you can work that out yourself).

  58. timer, thanks for helping me figure this out. I was imagining that I’d need to get equivalent end-values of Giuliani Wins Election sells, and Giuliani Wins Nomination and GOP Wins Election buys. So if we call them A, B and C, respectively, I’d buy end-values so that A=B+C. Because of the current prices, buying 1B and 1C would be a little cheaper than selling 2A. Using your scenarios:

    1. Win A, Lose B, Win C
    2. Win A, Lose B, Lose C
    3. Lose A, Win B, Win C
    4. Win A, Win B, Lose C

    I thought that I’d at least break-even in 2 and 3, come out ahead in 1 and 4. The only risk that I can see, and if arbitrage has to have zero risk then this will disqualify it, would be Giuliani’s losing the GOP nomination but winning the election (raising the possibility that scenarios 1 and 2 result in Lose, Lose, Lose).

  59. Timer and Matt Evans, interesting discussion. I think I’m going to write up a little bonus quiz or homework problem based on this example for the finance class I teach. Stay tuned and I’ll write up a little example here in the next few days (I think there’s a nice way to think of this simply using Baye’s Rule that doesn’t require thinking about risk-neutral probabilities, since I don’t get into that in my class, and that doesn’t require constructing a specific arbitrage portfolio…).

  60. Hmmm, on second thought, as long as nomination probabilities (i.e. futures prices) add up to one (plus the “house edge”) and the election probabilities for each of the candidates in the party add up to the “marginal” probability of that party winning the election (plus a house edge), then there will be no arbitrage. That is, if these conditions hold, then conditional probabilities (i.e. a state price density function or pricing kernel) exist which rationalize these prices. In other words, Matt, I think your intuition about there being an arbitrage just by looking at the ratios of nomination prices and election prices was wrong (so I’m not going to bother writing up the homework problem I promised above…).

  61. Robert, isn’t there a way to exploit the difference in price between futures that are effectively equivalent? Shouldn’t “Giuliani Wins Election” equal “Giuliani Wins GOP Nomination * GOP Wins Election + Giuliani Wins Election OFF GOP Ticket”? Because “Giuliani Wins Election” was trading 30% higher than “Giuliani Wins GOP Nomination * GOP Wins Election,” I think that means the market was implicitly pricing the ghost bet “Giuliani Wins Election OFF GOP Ticket” at 30%. Aren’t there strategies and tools to exploit a future mispriced so badly?

    If I’m wrong about all this, do you know where my reasoning error is in 67? It seems that buying and selling futures in quantities to break even in scenarios 2 and 3 would cause gains in 1 and 4.

  62. Matt, thanks for pressing me on this, I think my comments above were wrong (or at least premature and sloppy!) I don’t really have good intuition on this yet, but it seems you’re right that there is an arbitrage (well, given a few assumptions, like ignoring transaction costs!). Here’s the revived homework problem I’ve come up with (according to my example, the strategy of buying 1 B contract, 1 C contract and selling 3.845 A contracts is an arbitrage—assuming I haven’t made any mistakes, which is perhaps an heroic assumption!):

    Assume no transaction costs (i.e. “no house edge”), a risk-free rate of 0 and a market risk premium of 0. Suppose the futures contract A is trading for $20 and pays off $100 if Giuliani wins the election. Suppose the futures contract B is trading at $38 and pays of $100 if Giuliani wins the Republican nomination. Suppose the futures contract C is trading at $38.90 and pays off $100 if a Republican wins the election. For simplicity, assume that there is 0 probability of Giuliani winning the election if he does not win the Republican nomination. Consider the strategy of buying 1 B contract, 1 C contract, and short-selling 3.845 A contracts. What is the cost of this strategy? What are the payoffs in each state? What is the expected payoff for this strategy?

    (Matt, I’ll email you my spreadsheet with the solution at your T&S account. If anyone else is interested in the solution, email me at: [email protected], without the ZZZ’s.)

  63. Hmmm, I’m not sure why this intuition wasn’t obvious to me before, but contracts B and C are sufficient to span the four possible outcomes. This means that contract A is redundant, which means that its price can be determined by a combination of contracts B and C. Since A is not trading at the price that the B and C prices imply it should be, there is an arbitrage opportunity.

    This is really a very basic and frequently used argument (e.g. the frequently used Black-Scholes formula is based on this same notion of redundancy), so I’m quite embarrassed I didn’t think about it this way from the beginning (in an effort to save face, I only started thinking about this with the selfish intention of getting a nice homework problem out of it, and I was hoping to approach this without really getting into arbitrage arguments since I was thinking about using this in the decision tree portion of my corporate finance class…).

  64. Ah ha, I think I’ve figured it out. The problem is that A is not the equivalent of BC. The ratio of A:BC necessary to cover the A downside is different from the ratio of A:BC necessary to cover the BC downside. It’s not possible to buy them so they cover each other up and down.

    Market 1, Matt 0.

  65. Matt, actually, short-selling 3.845 shares of contract A (using the numbers in my example) is in fact just enough to cover the downside in each state, so this is an arbitrage in the sense that you will come out even or better in every possible state. Also, this is a unique solution in the sense that if you sell epsilon more or epsilon less, you will face downside risk in one of the states. (By the way, your timesandseasons.org email bounced, so if you want to peek at the spreadsheet answer I came up with, email me per #71….)

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