# Go big or go home? October 29, 2008 5:34 PM   Subscribe

The Dow Jones average on November 5th: Is it going up or down, help me decide.

The problem: You can wager between 1 and 100 points on whether the Dow Jones average is going to go up or down on November 5th, the day after the general election. The amount by which the market goes up or down is the multiplier by which the amount wagered is multiplied.

Lets say that I predict the Dow goes up, and wager 10 points. If the Dow gains 250 points that day, I wind up with a positive score of 2,500 points for the problem. If the Dow drops by 250 points and I chose that it would go up, I lose 2,500 points.

The Dow Jones following recent contested Presidential elections:

November 3rd, the day following Bush/Kerry 2004: Dow Jones gains/loses 0 points.
November 8th, the day following Bush/Gore 2000: Dow Jones loses 47 points.
November 6th, the day following Dole/Clinton 1996: Dow Jones gains 97 points.
November 4th, the day following Bush/Clinton 1992: Dow Jones loses 29 points.

There are many variables to this question, especially framed within the context of the day after the election. How would you approach this problem to achieve the best possible outcome against numerous other participants?

I am not putting money on this event, this is an exercise posed to an economics of gaming class.
posted by clearly to Grab Bag (33 answers total) 3 users marked this as a favorite

The answer depends heavily on starting conditions. Does everyone start with the same number of points? I'm going to assume yes because it becomes more complicated otherwise.

Whether the Dow goes up or down on nov 5th is more or less a coin flip. The more interesting question is how much to wager. If there are a lot of people in the game, you only have a chance to win by betting 100 points on either up or down. And you'll likely only tie at best. Actually, my intuition is that if everyone starts with the same number of points on nov 4th you should bet the maximum no matter how many people are in the game, but that's harder for me to defend and immaterial since there are numerous other participants in this case.

Look at it this way; if there are 30 people in the game, the odds are excellent (I would say practically guaranteed) that at least one person will bet 100 points on the Dow going up and at least one person will be 100 points on the Dow going down. So the only way you have a chance of even tying is by also betting 100 points on either up or day.

The equation changes if the game takes place over the course of many days, of course. The fewer days there are involved the more important it is to wager the maximum every day. And to guess the direction correctly, of course. The longer the game is, the more complicated the strategy becomes. In that case you would probably bet heavily the first day and then base your subsequent bets on the standings after each day. If scoring is secret, that again becomes much more complicated.

But as to how to decide if you should bet the Dow will go up or down on Nov 5th; you can't. And if you find you actually can, you are wasting your time in a gaming class and should be on Wall Street making billions.
posted by Justinian at 5:55 PM on October 29, 2008 [1 favorite]

Oh, it also matters if you're playing for real money and what the size of the stakes are. If it's just a game (no real money), somebody will bet the maximum every day no matter what. The bigger the stakes are relative to the wealth of the parties involved, the more likely they are to chicken out and not risk it.
posted by Justinian at 5:56 PM on October 29, 2008

forgive my typos. I was so excited by the awesome question that I didn't preview.
posted by Justinian at 5:58 PM on October 29, 2008

How are the Dow values distributed the day after election? You have some observed data -- do you have more? Is there are a correlation between elected party and Dow result, such that, given a certain election result you get a certain effect?

If you can see a connection between party and effect, and you feel confident that the polls are predicting the election correctly, perhaps you might bet that informed expectation plus or minus some multiple of standard deviation. A higher multiple likely lowers the likelihood of seeing that effect, and it might be a measure of how much risk you want to take on.

There might be other information that informs what you'd expect to happen. Like unemployment rate during the election, gas prices, cost of living, etc. Economic factors that color people's voting patterns, that sort of thing.
posted by Blazecock Pileon at 6:11 PM on October 29, 2008

One other thought: If you're looking at historical data to build a picture of how the Dow moves the day after an election, you might look instead at percentage shift, or some other normalized measure. Given where the market is, 40-point shifts in 2000, 2004 and 2008 are probably much less meaningful than a 40-point shift in 1932, relatively speaking. As far as betting goes, you'd then translate the normalized value back to a point shift.
posted by Blazecock Pileon at 6:19 PM on October 29, 2008

Response by poster: Does everyone start with the same number of points?

Yes, but there are other wagering opportunities that will ultimately factor into the final score. This question provides the greatest amount of risk, and the greatest opportunity for reward. Other opportunities that factor in to the ultimate result are questions that begin with a starting value for an exact prediction and subtracting points from the starting value by the degree of deviation from the exact answer. The starting values for those questions are much lower than the potential score for the problem I have listed here.

Oh, it also matters if you're playing for real money and what the size of the stakes are.

There are grades involved, but this question is 1 of 3 in a portion of the exam that makes up about 25 percent of the total exam grades. I found the question really interesting and wanted to share it, and also make sure that I reviewed all possible options before making my decision.
The question has the potential to absolutely dominate this portion of the test, if the Dow goes up or down by 30 or more points. Considering its recent volatility, I would say that is highly likely.

With the election, does the winner even matter? FDR said "After all there is an element in the readjustment of our financial system more important than currency, more important than gold, and that is the confidence of the people." But in a majority system, doesn't the president simply winning mean that he has the confidence of the people? Is this only true when the Presidential winner has the confidence of the people regarding their handling of the economy? Does it even matter as the winner will not be inaugurated until January?
posted by clearly at 6:21 PM on October 29, 2008

Response by poster: "How are the Dow values distributed the day after election? You have some observed data -- do you have more? Is there are a correlation between elected party and Dow result, such that, given a certain election result you get a certain effect?"

Looking at past results of Dow movement the day following the election was my first instinct. Deciding whether Nov. 5th should be treated as any other day on the trading floor, or as the deciding day of monumental highly contested election that will have a great deal on the future of the market is a problem in itself.

Thanks for the responses so far!
posted by clearly at 6:30 PM on October 29, 2008

November 3rd, the day following Bush/Kerry 2004: Dow Jones gains/loses 0 points.
November 8th, the day following Bush/Gore 2000: Dow Jones loses 47 points.
November 6th, the day following Dole/Clinton 1996: Dow Jones gains 97 points.
November 4th, the day following Bush/Clinton 1992: Dow Jones loses 29 points.

Incumbent re-elected = Business as usual = Confidence = Gains
New president = Uncertainty = Lack of confidence = Losses

Obama is slated to win, which means new president of a different political party than the incumbent one, therefore uncertainty and therefore losses.

Disclaimer: I have no idea what I'm talking about.
posted by limon at 6:48 PM on October 29, 2008 [2 favorites]

Sorry, this question is part of an exam? Is it ethical for you to be discussing it on here? Are you allowed to work with other people on this exam?
posted by emyd at 6:50 PM on October 29, 2008

Your grade depends on whether you can accurately predict a Dow Jones intraday market movement? I would report your professor to his Dean; this is inappropriate.

Asking for help with a test on MeFi is also inappropriate.
posted by ikkyu2 at 6:55 PM on October 29, 2008

There's no reliable way to predict whether the stock market will go up or down on any given day. It's a coin toss.
posted by mr_roboto at 6:55 PM on October 29, 2008

There's no way to tell what will happen. You are trying to read the minds of the thousands of people also betting on the stock market that day. And the Dow is only a composite of 30 stocks, so not even indicative of the market as a whole.

Especially in the market these days, with all the volitility. It could be up 1000 or down 1000. Who knows? There are just as many traders who will be fearful of a new Demmycrat administration as who will be cheerful of it.

(Also useful when comparing the Dow to other historical Dow numbers is the percentage. I mean the Down "only" lost 30 points on Oct 29, 1929.)
posted by gjc at 6:57 PM on October 29, 2008

Asking for help with a test on MeFi is also inappropriate.

Sorry, this question is part of an exam? Is it ethical for you to be discussing it on here? Are you allowed to work with other people on this exam?

It said exercise. Lighten up, people.
posted by gjc at 7:00 PM on October 29, 2008

gjc: "

It said exercise. Lighten up, people.
"

He says, "this question is 1 of 3 in a portion of the exam"
posted by emyd at 7:02 PM on October 29, 2008

Intrade right now figures the odds at about 85-15 for Obama. Assuming traders on the NY exchange see it about the same way, an Obama victory is already discounted into the market right now. If he wins, and there no other major development impacting the market the day after the election, there's no change. This is what happened when Bush beat Kerry in 04 as predicted. If McCain wins, the market will have to adjust to whatever its expectations are under McCain (along with a strongly Democratic Congress). Does Wall Street like McCain better than Obama? If so, the market would rise as a result of his unexpected victory. If the opposite, it would fall, but again, other factors, like, say, GM declaring bankruptcy might negate the effect that day. In other words, what mr_roboto said.
posted by beagle at 7:09 PM on October 29, 2008 [1 favorite]

Response by poster: Your grade depends on whether you can accurately predict a Dow Jones intraday market movement? I would report your professor to his Dean; this is inappropriate.

He says, "this question is 1 of 3 in a portion of the exam"

This is a Economics of Gaming course. The exam consists of 3 portions, one is based upon research and course material and makes up the vast majority of the grade.

The portion that this question is on is part of a gaming/wagering exercise. This part is take-home and any and all resources are available to be used to determine what and how much to wager on the problems. In answering Justinians query whether or not all participants begin with the same score, I had to frame it in the exam context. People may be likely to gamble on this part if they are not going to do well on the aforementioned meat of the exam covering course material.

I found the problem very interesting, and I would like help with the approach on the possible factors to consider before making my decision. I am not asking for the "right" answer, only the possible ways to approach the problem.

I hope this clears up any concerns.
posted by clearly at 7:12 PM on October 29, 2008

Wait, there are actual grades involved?

In that case, my strategy would be to study for the real portions of the exam and bet nothing whatsoever. And to put some choice comments about intentionally giving grades a strong stochastic component on my course evaluation.

If you're going to bet, then just flip a coin. Heads you bet up, tails you bet down. Bet whatever you're comfortable losing.
posted by ROU_Xenophobe at 7:22 PM on October 29, 2008 [2 favorites]

Clearly: Well, the fact that there is a grade involved changes the situation significantly. In that case your goal isn't to "win" like it would be in a blackjack tournament or whatever, but instead to give yourself the best chance at a good grade. The answer depends on whether you are a good student or not.

If you are a poor student, you would wager a lot and hope pure luck would help you get a lot of points to help make up for poor answers to more knowledge-based questions. If you are a good student, you would wager nothing at all in the assumption that you will do well on the questions that aren't based on pure luck and that ending up with the same number of points on this question as you start with should neither help you nor hurt you.

So, in this case, you would expect poor students to wager in an effort to get luck points and good students to wager nothing or very little as they have no need for luck points.

If you actually get a poorer grade if you don't accurately predict whether the Dow will go up or down (as opposed to give a good answer as to why you bet the way you do from a game theory standpoint), the question is inherently bullshit and the professor should be reported to the Dean. And is an asshole to boot.
posted by Justinian at 7:41 PM on October 29, 2008

How exactly is this section graded? The more I think about it, the more I believe betting 0 is the correct answer if you are a good student; good students don't rely on luck even in an economics of gaming class. But how the question is graded affects that. If ending up with the same number of points as you started with gets you a bad grade, you have no choice but to bet.
posted by Justinian at 7:47 PM on October 29, 2008

ROU_Xenophobe: stochastic

Oh no you didn't, ROU_Xenophobe!

Market movements are not stochastic; they are determined. Only the models are stochastic.
posted by ikkyu2 at 8:18 PM on October 29, 2008

Response by poster: This section is graded along with another section of different prediction which can be more reliably predicted. An example of a question on the other section is predicting the winners of the presidential electoral votes by state. The class is ranked in each of the two sections, and then re-ranked with the cumulative score for both sections to get the grade for the wagering portion of the exam.

So if I rank well in the other section, and poorly in this section, I'll fall somewhere in the middle of the class. The top 10% get A's the next 10% A-'s etc.
posted by clearly at 8:24 PM on October 29, 2008

Market movements are not stochastic; they are determined. Only the models are stochastic.

ikkyu2,
posted by lukemeister at 8:30 PM on October 29, 2008

There are a few different things you need to consider here.
(1) First you need to assign values to the different outcomes, and by outcomes I mean your final grade. This isn't a simple linear relationship between score on the test and the value of the outcome. Let's say you just want to pass the test and can do that by scoring 60% or above. In this case, getting 90-100 isn't that much better to you than 60-70%. What if, however, you have a scholarship riding on you getting an A in this class, which in turn is riding on you getting in the 90-100% on this test? In this case scoring 20%, 50%, or 80% are all pretty worthless to you. You can imagine other situations where the value of each outcome is different. So think hard about your situation and honestly assess the various outcomes. To visualize this, draw out a graph with the x-axis as the score and the y-axis as its value to you.

(2) Ok, now you need to figure out the payoff system for this question. If you're being graded on an absolute scale, it's straightforward and you just get whatever the wager is along with the multiplier. The size of your bet and how much the Dow moves will be important. If, however, you're being graded on a curve (so you're competing against the other students), you need to first try to guess how they will wager because only the relative sizes of everyone's bets matter. This is the hard part, but try to draw out a distribution that you think might be realistic (from -100 to 100 for up or down). There will probably be a decent amount of people who wager one or close to it, and there will probably be people betting 100 or -100. Do you think they'll be more likely to choose that it goes up? Equally distributed? It's hard to say, but if you're allowed to gather information from other students that obviously would help. Now the way the payoff is determined (just in the case of a curved grade) is where your wager falls on this second graph compared to everyone else's. Let's say you choose to bet 60 that it'll go up, and you think that means 75% of the class are betting less (down to -100). If it goes up, regardless of how much, you score 75% and if it goes down you score 25%.

(3) Now the really tricky part is combining the two graphs you drew to find what strategy gives the highest expected value. If grading is on a curve, you can test various wagers along the payoff graph, plugging the payoff into the value graph. This is kind of hard to explain. Going back to the scholarship example where you need to get 90%, you'd have to choose an extreme wagering strategy that will either win big or lose big, but there'd be no use in wagering very little cause you'd end up around 50%. For more complicated non-linear payoff and expected value graphs, you'd ideally run a Monte Carlo simulation of some sort to find the best strategy.
posted by Durin's Bane at 8:50 PM on October 29, 2008

I didn't really explain how to calculate expected value in the last part. You multiply the probability of each possible result with the payoff of that result and add them all up. In the case of the curved grading, the only results that matter is the Dow goes up or the Dow goes down, safe to say it's 50% either way. So you'd choose a strategy, then calculate the value of that strategy if the Dow goes up (and multiply by 0.5) added to the value if the Dow goes down (multiplied by 0.5). It's more complicated if grading is absolute because then the size of the Dow change is relevant and you need to make a model (a third graph) incorporating the distribution of Dow changes. Calculating the expected value is much harder by hand in this case because of the many, many more possible payoffs. Again, this is easier if you run a computer simultion.
posted by Durin's Bane at 9:07 PM on October 29, 2008

There are a few different things you need to consider here.

Naw. If you factor in the costs of that decision process, the only winning move is not to play.
posted by ROU_Xenophobe at 9:24 PM on October 29, 2008

So if I rank well in the other section, and poorly in this section

I think I didn't make myself understood very well; I don't mean how is this section weighted, I mean how is this particular section graded? I'm asking if the prof expects you to actually predict the market and is grading this question based solely on how many points you end up with, or are you being evaluated on how well you explain your decision on what to wager on the principles of economics and game theory?

What constitutes "ranking well" in this section?
posted by Justinian at 9:31 PM on October 29, 2008

Response by poster: What constitutes "ranking well" in this section?

Achieving the maximum number of points. The highest number of points on the section receives the highest rank.
posted by clearly at 11:51 PM on October 29, 2008

Best answer: Then I'm afraid this is an absurd assignment. I would suggest wagering nothing. And file a complaint that you are paying to receive grades based on a coin flip.
posted by Justinian at 12:30 AM on October 30, 2008 [1 favorite]

Your best strategy is to collude with everyone else taking the test and have them all make the same bet of 1 point on the market going up (or down--which direction doesn't much matter, **as long as you all do it the same**).

Even better would be for everyone to bet 0 points but the rules (as you outlined them above) don't seem to allow this.

Assuming everyone bets 1 point on the market going up:

As long as < 10% of your classmates defect from your plan, everyone who is colluding is guaranteed to be in the top 10% of scores, thus putting everyone in A range.

Even if up to (approx.) 20% of your classmates defect, assuming they are all random actors and not themselves colluding against your collusion, you'll still be OK as (roughly) half of them will choose the wrong direction, leaving less than 10% of the class ahead of the colluding group's score, and leaving everyone in the colluding group still in A range. Even if somewhat more than 10% of the defectors manage to choose the correct direction, you're still in A- range. So the collusion fails very gracefully.

And worst case (the collusion totally falls apart and everybody starts acting for their own individual interest only) you'll end up with a middling grade.

There is a strong incentive for people to stick with the collusion, because anyone who deviates will have a 50% chance of the best possible grade and 50% chance of a disastrous grade. Whereas if they stick with the collusion, they have a high probability of the best possible grade, if things go a little wrong the grade will still be pretty good, and absolute worst case scenario is a middling grade.

So it's pretty much the best of all possible worlds--a very good chance of getting the highest possible grade, worst case is a middling grade, and a strong incentive for people to stick together rather than going off on their own to try to take advantage.

Also, you've moved the problem space from something that is inherently completely unpredictable (behavior of the stock market) to something that can be predictable with some mutual understanding and coordination (behavior of your classmates).

And assuming that (as you indicate) **all** resources are available, I'd say the idea of colluding is perfectly legal as well. All resources include other people in the class and also include the possibility of gaming the system in some way if the classmates can mutually agree upon it and if the rules, as stated, allow it.

On the other hand, if the teacher has said you can't talk with others in the class about the test, that could be dicey . . .

[Now if your class were made up entirely of completely logical blue- or brown-eyed islanders, you would have no need to collude, as exactly X days later at 12 noon everyone would realize the answer I've outlined above is the only logical answer and you would all just proceed in lockstep to write it down and get the best possible grade. X being same as the number of students in your class, of course.]
posted by flug at 12:53 AM on October 30, 2008 [2 favorites]

BTW, everyone above seems interested in working out the problem so as to maximize gain.

The other way to think about it is: how do you minimize your potential loss?

Even if you could predict the stock market with fair accuracy (say, correct 75% of the time), you are still going to lose 25% of the time. If that loss is devastating, you can't afford to accept it even if it is somewhat less likely, or if the potential gain is very high.

Example: Say you're playing a game where you flip two coins and if both are tails you must immediately pay \$1 million. Any other combination and you win \$1 million instantly. Despite the favorable odds and theoretical high average payoff, most of us can't even play this game because we don't have anything like \$1 million in liquid assets. Now if you had a rich banker who would cover any transient losses while you played the game 20 or 50 times, the whole situation would change. But if you have no banker or (even worse) if you are playing the game only once, the maximum potential loss becomes the primary consideration.

Whether you can afford to play a game depends very much on whether you can afford to accept the maximum possible loss, and when you play a game only once the maximum possible loss is far more important than the "odds".

If you could play this game repeatedly, say every day for a year, then the law of large numbers comes to your rescue. You could afford to take the losses because you know there will be more gains in the long run and it will all average out.

However when you play a game once, there is no averaging.

Therefore--minimize your potential loss. You can't afford even a 20% chance of a D- . . .

The strategy for minimizing potential loss is very obvious--simply bet the minimum allowable amount.
posted by flug at 1:15 AM on October 30, 2008 [1 favorite]

Your grade depends on whether you can accurately predict a Dow Jones intraday market movement? I would report your professor to his Dean; this is inappropriate.

Then I'm afraid this is an absurd assignment. I would suggest wagering nothing. And file a complaint that you are paying to receive grades based on a coin flip.

I'm afraid (as someone who has taught quite a lot of college and other classes in my life) that I'm going to have to disagree with this sentiment fairly strongly.

Because something real is at stake, students are going to spend a lot more time and effort thinking about this question and really understanding the ramifications than if they were dealing with a similar scenario in a merely theoretical context.

And (if I understand how this question fits into the entire context of the test and the class grade, which is may not be entire clear from the comments the OP made in the thread), if you pick the right strategy the chance of it having a really large effect on your final class grade are practically nil, but if you pick the wrong strategy it could indeed have quite a negative effect (although still in terms of the grade for the entire class, probably not *that* large).

Since the whole point of the class is being able to understand a problem well enough to pick the best strategy, that seems entirely appropriate.

Furthermore I would just imagine that a course like "Economics of Gaming" probably has an element of trying to help someone understand how the element of risk is managed as part of a larger system.

In this case the element of risk is the grade for one question on one section of one test. The larger system(s) are the whole class and the overall grade you get from it, your entire degree and the GPA you'll earn overall, and then of course your entire career and life.

Especially if you take steps to minimize your risk of loss on that one question (if you take that step, and I understand the grading system correctly, the worst possible outcome is a low B grade on that section of one test out of the entire class), the realistic chance of it having a noticeable effect on the larger systems--class grade, overall GPA, career--are pretty much zero.

What's more, the chances of you actually remembering this one question out of all the hundreds and thousands you'll see on tests before you finish your degree, is pretty high. Seems a pretty fair trade-off to me--practically nil downside (affect on overall GPA) with significant upside (actually learned something real).
posted by flug at 7:36 AM on October 30, 2008 [1 favorite]

And maybe even more important than what I wrote above, people who study economic behavior have increasingly realized that people do not always or even often respond to economic decisions--such as how to deal with risk--in a rational way.

Emotions, personality and all sorts of other "crazy stuff" gets involved and in many real-life situations have a far stronger effect on economic behavior than the theoretical and rational best response. Of course the stock market is a prime example of a place where human psychology--emotion, personality, tradition, rumor, expectations, authority, herd behavior, etc.--has at least as prominent a place as purely rational behavior in determining the outcome.

I might suggest that as a result of wrestling with this question and its real-life ramifications for you, you're feeling some of those emotions and they are affecting your economic behavior right now.

That's something you'll never get by working out "story problems" . . .
posted by flug at 7:55 AM on October 30, 2008

if you pick the right strategy the chance of it having a really large effect on your final class grade are practically nil

Which is why I suggest wagering nothing (if that's possible). That's pretty clearly the right strategy so as to minimize the effects this question could have. There is no way to predict whether the Dow will go up or down on Nov 5th with any reliability, so betting a lot has roughly a 50% chance of helping and a 50% chance of hurting. The expected value of any bet is essentially 0.
posted by Justinian at 9:55 AM on October 30, 2008

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