Limits of Current US Prediction Markets (PredictIt Case Study)

(Dis­claimers: I work in the fi­nan­cial in­dus­try, though not in a way re­lated to pre­dic­tion mar­kets. Any­thing I write here is my opinion and not that of my em­ployer.
This is a US-cen­tric piece based on a case study of Pre­dic­tIt: as some peo­ple have pointed out in the com­ments be­low, if you are out­side the US you may have sub­stan­tially bet­ter op­tions.)


SECTION I: INTRODUCTION

So there’s an ar­gu­ment that I’ve seen a lot over the past few years, par­tic­u­larly in LW-ad­ja­cent cir­cles, that goes some­thing like this:

You say you be­lieve X is likely to hap­pen. But pre­dic­tion mar­kets say X is likely not to hap­pen. Since mar­kets are effi­cient, you must be wrong. Or if you do know bet­ter than the mar­ket, why aren’t you rich? Since you haven’t bet on that mar­ket to make free money, you must be ly­ing. Or stupid. Or both!

This post is ded­i­cated to dis­agree­ing with that ar­gu­ment, not from an anti-Effi­cient-Mar­ket Hy­poth­e­sis po­si­tion, but from a pro-Effi­cient-Mar­ket Hy­poth­e­sis po­si­tion. My po­si­tion is:

The ar­gu­ment above is pretty much sound if we are dis­cussing main­stream fi­nan­cial mar­kets. If some­one claims to have bet­ter in­for­ma­tion than a main­stream fi­nan­cial mar­ket on the value of Google stock, or of cop­per, they ought to ei­ther use this knowl­edge to make a huge amount of money or stop talk­ing about it. How­ever, it is not true if we are dis­cussing pre­dic­tion mar­kets. Cur­rent pre­dic­tion mar­kets are so bad in so many differ­ent ways that it sim­ply is not sur­pris­ing for peo­ple to know bet­ter than them, and it of­ten is not pos­si­ble for peo­ple to make money from know­ing bet­ter.

I’ve been mean­ing to write this for a while, but got tipped over the edge by the re­cent post here, which talks about the limi­ta­tion of pre­dic­tion mar­kets be­ing the cor­re­la­tion of the events they pre­dict to other as­sets, and their con­se­quent value as hedg­ing in­stru­ments. That is...well...it’s not wrong ex­actly, but there are so many other prob­lems that are so much big­ger that I felt it was worth lay­ing (some of) them out.

Math fol­lows. I will be fo­cus­ing on Pre­dic­tIt for this anal­y­sis. Other pre­dic­tion mar­kets may work a bit differ­ently, but similar anal­y­sis is ap­pli­ca­ble to any of them. If you think the math is wrong I am happy to dis­cuss/​make changes, but I very much doubt any changes will ma­te­ri­ally al­ter the fi­nal mes­sage.

As of this writ­ing Pre­dic­tIt has Don­ald Trump at 40% to win the elec­tion (or, to put it an­other way, you can pay 40 cents for a share that pays out $1 if Trump wins). Sup­pose you think he is more/​less likely to win. How likely/​un­likely does it need to be for Trump to win for you to make money (in ex­pec­ta­tion)? Or, to put it an­other way, what range of prob­a­bil­ities for Trump to win are con­sis­tent with the pre­dic­tion mar­ket val­ues?


SECTION II: REASONABLY SIMPLE PROBLEMS

1: Spread.

This is only a small prob­lem, but it is non-zero. Pre­dic­tIt will sell me ‘Don­ald Trump wins’ shares for 40 cents, but will sell me ‘Don­ald Trump loses’ shares for 61 cents (which, from a fi­nance per­spec­tive, works out very similarly to let­ting me sell ‘Don­ald Trump wins’ shares for 39 cents). So if I think there is a 39.5% chance of Trump win­ning, there is no way for me to make money off of it: I can buy ‘Trump wins’ shares for 40 cents, or sell them for 39 cents, and if the true value is 39.5 cents both of these will lose me money.

The range of pos­si­ble prob­a­bil­ities for which you can­not make money starts at 39-40%.

2: Trans­ac­tion Fees.

Pre­dic­tIt charges a 10% fee on prof­its (see https://​​www.pre­dic­tit.org/​​sup­port/​​how-to-trade-on-pre­dic­tit). As far as I can tell, it does not net prof­its against losses be­fore calcu­lat­ing these fees. That is to say, if I make two $100 bets at even odds, win one, and lose the other, Pre­dic­tIt will charge me a $10 fee on my win­nings on the bet I won, even though over­all I have made no money.

So if I think there is a 50% chance of Trump win­ning, and spend $100 buy­ing Trump Wins shares, in­stead of my ex­pected fi­nal money be­ing 50% * $250 = $125 for a $25 profit, my ex­pected fi­nal money is 50% * ( $250 - $15 ) = $117.5 for a $17.50 profit.

After ac­count­ing for this, the range of pos­si­ble prob­a­bil­ities for which you can­not make money is:

3: With­drawal Fees.

When I ac­tu­ally at­tempt to with­draw my money from Pre­dic­tIt, Pre­dic­tIt charges an ad­di­tional 5% fee on the with­drawal, giv­ing me only 95% of my money back. How im­por­tant this fee is to any given bet varies de­pend­ing on how many bets I make on Pre­dic­tIt (if I am mak­ing mul­ti­ple bets with­out with­draw­ing money the effec­tive im­pact of the fee on any given bet is smaller), but for now let’s as­sume that (like most peo­ple) I do not have a Pre­dic­tIt ac­count and would need to cre­ate one to make this bet, and then with­draw my win­nings im­me­di­ately af­ter­wards. If so, my effec­tive win­nings shrink again as 5% of my money (not just my win­nings, all the money I de­posited) dis­ap­pears to Pre­dic­tIt.

After ac­count­ing for this, the range of pos­si­ble prob­a­bil­ities for which you can­not make money is



4: In­vest­ment In­ter­est Rate/​Time Value of Money.

The pres­i­den­tial elec­tion will not hap­pen un­til Novem­ber. Let us be gen­er­ous and as­sume that Pre­dic­tIt set­tles bets im­me­di­ately there­after (though their page for the bet states ‘Pre­dic­tIt may de­ter­mine how and when to set­tle the mar­ket based on all in­for­ma­tion available to Pre­dic­tIt at the rele­vant time’ and ‘Pre­dic­tIt’s de­ci­sions and de­ter­mi­na­tions un­der this rule shall be at Pre­dic­tIt’s sole dis­cre­tion and shall be fi­nal’). It is cur­rently July. That means it will be ~4 months un­til the bet re­solves, dur­ing which time your money will be tied up in Pre­dic­tIt.

What else could you be do­ing with that money? Well, de­pend­ing on who you are, you could be get­ting rea­son­ably risk-free re­turns via e.g. Trea­suries or bank ac­counts, but those in­ter­est rates are low. On the other hand, your bet is de facto a loan to Pre­dic­tIt as well as what­ever bet you think you made. If Pre­dic­tIt sud­denly goes bankrupt in a mas­sive down­turn, or if who­ever runs it takes the money and flees to Dubai, you may not get paid back. So, what effec­tive in­ter­est rate would you charge to loan Pre­dic­tIt money in the cur­rent fi­nan­cial en­vi­ron­ment? How risky an in­vest­ment is it? If you would charge it 5% per year (which I don’t think is all that high by the stan­dards of bonds in risky com­pa­nies), then over those 4 months you could have made about 2% re­turn with­out the pre­dic­tion mar­ket in­volved.

(Side note: this effect is larger or smaller de­pend­ing on what event you are con­sid­er­ing and how far in the fu­ture it lies. There’s some rea­son to ex­pect that this will make pre­dic­tion mar­kets a lit­tle more effi­cient as the event they per­tain to draws closer, but there are still quite a few other prob­lems).

After ac­count­ing for this, the range of pos­si­ble prob­a­bil­ities for which you can­not make money is:


So at this point, the 40% prob­a­bil­ity we see for Trump to win on Pre­dic­tIt is com­pletely com­pat­i­ble with any prob­a­bil­ity from 31.8%-45.7%. This is already...rather a wide range. And this is be­fore we en­counter two rather larger is­sues:


SECTION III: HORRIBLE MESSY PROBLEMS

5: Taxes

Note: I am not a lawyer! I am par­tic­u­larly not a tax lawyer! This sec­tion is spec­u­la­tive, even more US-cen­tric than the rest of this piece, may well be wrong, and even if it is right your tax situ­a­tion may be differ­ent!

As far as I can tell, Pre­dic­tIt win­nings are treated by the US gov­ern­ment as in­come. This means two things: first, that if you win money on Pre­dic­tIt the US gov­ern­ment will tax it; and sec­ond, that if you lose money on Pre­dic­tIt the US gov­ern­ment will not let you net it against any­thing. So, just like Pre­dic­tIt’s fees did, taxes re­quire you to have a much higher chance of win­ning in or­der to be net-pos­i­tive.

If you have a good ac­coun­tant and think you can net Pre­dic­tIt losses against an­other tax bill, or avoid pay­ing taxes on Pre­dic­tIt win­nings, this might not be ap­pli­ca­ble to you.

If we as­sume you pay a 15% tax rate (ac­cord­ing to Google this is pretty close to the na­tion­wide av­er­age), the range of pos­si­ble prob­a­bil­ities for which you can­not make money is:



And if we as­sume you are pay­ing 35% in­come tax (which re­quires a high salary, but I sus­pect a lot of the peo­ple who we’re hop­ing will come and cor­rect the pre­dic­tion mar­ket for us have high salaries...) then the range of pos­si­ble prob­a­bil­ities is:



So now we’re fully com­pat­i­ble with Trump be­ing any­where from be­low a one-in-four to above a one-in-two chance! And then we en­counter the re­ally big one.


6: Bet­ting Limits

Part of how mar­kets work is that peo­ple who know bet­ter will even­tu­ally be able to com­mand more of the money. If I am able to pre­dict the price of Ap­ple stock bet­ter than any­one else, I can mul­ti­ply my money faster, I can use my track record to get other peo­ple to in­vest with me, and I can di­rect large quan­tities of money, which both makes me a lot of money and al­lows me to move the mar­ket to a more ac­cu­rate val­u­a­tion.

Pre­dic­tIt places a limit of $800 on your po­si­tion in any one bet.

At the mar­ket level, this means that you can no longer rely on small num­bers of in­tel­li­gent peo­ple to fix mar­ket prices for you. Since a small num­ber of in­tel­li­gent peo­ple can only mo­bi­lize at most $800 each, you are re­li­ant on lots of differ­ent peo­ple in­tel­li­gently pick­ing the right price.

And at the in­di­vi­d­ual level, this makes it difficult to make any amount of money that mat­ters off a pre­dic­tion mar­ket.

In a real fi­nan­cial mar­ket, peo­ple will in­vest large amounts of money. If a hedge fund pays ten mil­lion dol­lars a year hiring dozens of smart peo­ple to dis­cover a way of mak­ing 1% ex­cess re­turn, so long as they are in­vest­ing at least a billion dol­lars that is worth it. There­fore, in a real fi­nan­cial mar­ket, there is rea­son to ex­pect that any anal­y­sis that can cor­rect mar­ket prices will be done, even if it is difficult and ex­pen­sive to do.

Pre­dic­tIt can just about man­age to let peo­ple who can cor­rect mar­ket prices make enough money to merit cre­at­ing an ac­count there.

Re­call that, even with zero taxes, the range of pos­si­ble prob­a­bil­ities for which you could not make money was:


But this is the range of prob­a­bil­ities for which you can­not make any money at all.

Sup­pose that you think Trump’s chance to win is 50%. If you in­vest the max­i­mum $800, you will end up with in ex­pec­ta­tion:

which gives an ex­pected profit of about $75, and that was with­out con­sid­er­ing taxes.

If you face a 35% tax rate, and think Trump’s chance to win is liter­ally zero, af­ter in­vest­ing $800 you end up with:

mak­ing a profit of about $250 in ex­change for know­ing with ab­solute cer­tainty that an event a pre­dic­tion mar­ket has at a 40% prob­a­bil­ity is guaran­teed not to hap­pen.

This is not suffi­cient to merit ded­i­cat­ing time and effort to re­search.


SECTION IV: CONCLUSION

If some­one claims that they are ab­solutely cer­tain Trump will/​will not win the elec­tion, they should be able to make money on a pre­dic­tion mar­ket from this pre­dic­tion. How­ever, they may not be able to make very much money at all, and even if they are quite con­fi­dent that the pre­dic­tion mar­ket is wrong it may not be worth their time. As­sum­ing that this per­son should be will­ing to bet on their views on a pre­dic­tion mar­ket may be mer­ited, but even from a purely fi­nan­cial view it is a much closer af­fair than you may think.

If some­one claims that Nate Silver and 538′s anal­y­sis team know bet­ter than a pre­dic­tion mar­ket what Trump’s odds of win­ning the elec­tion are, they are quite likely cor­rect. It is not pos­si­ble with pre­dic­tion mar­kets in their cur­rent state for them to make money from that knowl­edge. If you dis­miss this per­son be­cause they haven’t bet on pre­dic­tion mar­kets, you are ac­tively wrong, you are mak­ing me and a sys­tem I be­lieve is a good idea look bad by as­so­ci­a­tion, and I would like you to stop talk­ing about this.