You assume limit orders are linear in dollars instead of shares. With CARA/normal and common volatility, limit orders are linear in shares and prices are beliefs weighted by reciprocal risk-aversion.
Paradoxically the surge of interest and depth of the markets can be bad for prediction accuracy. At the risk of using a tired analogy, only a fairly small number of traders and analysts were actively trading or covering Gamestop stock in January 2019. Two years later, both the absolute number of traders and volume had increased by orders of magnitude, but clearly the resulting "prediction" was not more correct as a result.
In a similar fashion, moving political prediction markets from a fairly niche interest of politics obsessives to the much wider world of crypto, where large positions, aggressive manipulation, and huge PnL swings are de rigeur, might change the accuracy from what it has been in previous cycles.
“there is a very liquid optionable US midcap which enables people to express the exact same view as a Kamala Yes contract with significantly superior payoff structures and tax consequences“
I am too ideologically and emotionally committed with prediction markets to agree with you, even though I am a no-coiner and crypto skeptic, but nonetheless great text.
As some other people have pointed out, electionbettingodds.com and Manifold have very decent Brier Scores. I don't know PolyMarket's Brier Score, but I predict it's probably decent.
I have been trading the Harris contract with a full Kelly at my fun-money account. My trading plan has been Nate Silver + 2%. It seems obvious to me that the market has been manipulated some weeks ago, but right now, the moves are consistent with Silver Bulletin moves. Funnily enough, I think it was Kris Abdelmessih that posted in his blog that even if you have an edge, new information that changes the market and changes your own view, according to some assumptions, make so that the new market price is also Kelly optimal. And indeed, I have been barely changing my exposure since after Fredi9999 started his position.
What is interesting to me is that no one seems to be extracting the "true probabilities" from PolyMarket order book, as the paper you suggested says it would. It seems it'd be very value added!!
The intro implicitly claims that Harris has a >50% chance of winning, and is currently priced at 38, which puts the expected return of a Harris bet at (at least) 11,500% annualized, if I did the math right (= (50/38)^(52/3) - 1). I can buy that there are limits to arbitrage, but surely the limits to arbitrage aren't that big? Like it's plausible that a single whale could move the market that much, but surely you personally should be betting the other side?
You can't eat annualized returns, unless they had a new presidential election every 3 weeks for a year and the betting markets were similarly mispriced every time.
Per Polymarket's market depth calculator, it would only take a $3mm mkt buy of Harris to move the price back to 50/50, which isn't a tremendous amount of size to get a 25% price impact. You could sell $3mm of DJT equity for a 1-2% price impact, 20x lower.
So if you think the correct price is >50 and it takes $3M to move the price up to 50, why haven't you personally invested like $30K or $300K?
Edit: Like I know you said in the post that the reason you haven't invested is "limits to arbitrage" but I feel like you haven't adequately explained why you think those limits are prohibitive, and to my reckoning it looks like they aren't.
I don't have a strong ideological commitment to the price on Polymarket accurately reflect Kamala's chances. If this asset is mispriced, a natural question might be "what other financial assets are functions of the winner of the Presidental election, and are those assets mispriced in an even more egregious way?". The answer to that question is that there are, and that I have invested significantly more than $30k or $300k betting on *those*.
I'm not sure I buy the premise of this, nor do I buy the conclusions.
-People who view the market prob. to be too high should buy NO. People who believe the market prob. to be too low should buy YES. Depending on their confidence and bankroll, they may buy more or less shares, pushing the prob. higher or lower.
-People who are consistently wrong will lose their bankroll, people who are consistently accurate will grow their bankroll, thus improving the predictive power of the market. The more obviously mispriced the market is, the more it will attract smart money.
I think the key aspect of prediction markets that you're overlooking is that unlike the vast majority of market-traded assets, they literally RESOLVE to 0 or 100 and pay out accordingly! This outcome incentivizes trading grounded in some "truth" or whatever.
>everybody in this model is betting precisely their optimal Kelly fraction, given their own subjective probability assessments and the market prices
How do you get that?
Your "Buy Qty ($)" graphs are linear and go to 100% of wealth at the edges, which is how Kelly would act if the x axis were believed propability, but you have it as price.
Indeed, using the alternative formulation of Kelly as betting a fraction of your wealth on each outcome equal to the respective propabilities, we get:
total long (shares): w_x*x/p+w_y*y/p
total short (shares): w_x*(1-x)/(1-p)+w_y*(1-y)/(1-p)
with wealths w_x, w_y, believed propabilities x, y, and price p. Setting them equal gives us exactly that the price is the wealth-weighted average propabilitiy.
That said, Im not sure this averaging is really necessary? I think the idea behind prediction markets is that people update on the fact of others trading, in spherical cow land they could do that until they aumann agree, and in real *very high volume* markets, each trader is only staking an infinitessimal fraction of their wealth, so they can also trade until they aumann agree.
i see how the described dynamic moves the "odds" of a 0% probability to >0%, but I don't see how it move a 50% probability to 40%. How would the non-linear bias push something away from 50/50?
You assume limit orders are linear in dollars instead of shares. With CARA/normal and common volatility, limit orders are linear in shares and prices are beliefs weighted by reciprocal risk-aversion.
If this is all true then why do we see a good "track record" of these markets?
> https://electionbettingodds.com/TrackRecord.html
> There is also a decent correlation with other models (ie Nate Silver). and polls
Based on this doesn't it seem like by the time the election comes market prices are probabilities?
Paradoxically the surge of interest and depth of the markets can be bad for prediction accuracy. At the risk of using a tired analogy, only a fairly small number of traders and analysts were actively trading or covering Gamestop stock in January 2019. Two years later, both the absolute number of traders and volume had increased by orders of magnitude, but clearly the resulting "prediction" was not more correct as a result.
In a similar fashion, moving political prediction markets from a fairly niche interest of politics obsessives to the much wider world of crypto, where large positions, aggressive manipulation, and huge PnL swings are de rigeur, might change the accuracy from what it has been in previous cycles.
“there is a very liquid optionable US midcap which enables people to express the exact same view as a Kamala Yes contract with significantly superior payoff structures and tax consequences“
🤔🤔🤔🤔🤔
DJT isn’t real so can’t figure this one out 😔
How dare you enter my comments section and sully the name of beautiful, perfect BQNT. Begone, foul troll.
I am living in your walls plugged into your BBG tunnel to make you exceed your data limit
I am too ideologically and emotionally committed with prediction markets to agree with you, even though I am a no-coiner and crypto skeptic, but nonetheless great text.
As some other people have pointed out, electionbettingodds.com and Manifold have very decent Brier Scores. I don't know PolyMarket's Brier Score, but I predict it's probably decent.
I have been trading the Harris contract with a full Kelly at my fun-money account. My trading plan has been Nate Silver + 2%. It seems obvious to me that the market has been manipulated some weeks ago, but right now, the moves are consistent with Silver Bulletin moves. Funnily enough, I think it was Kris Abdelmessih that posted in his blog that even if you have an edge, new information that changes the market and changes your own view, according to some assumptions, make so that the new market price is also Kelly optimal. And indeed, I have been barely changing my exposure since after Fredi9999 started his position.
What is interesting to me is that no one seems to be extracting the "true probabilities" from PolyMarket order book, as the paper you suggested says it would. It seems it'd be very value added!!
the Kris post you are referring too is my prior blog post! Truly we are a one-stop shop for your prediction market gambling services: https://quantian.substack.com/p/losers-average-losers
The intro implicitly claims that Harris has a >50% chance of winning, and is currently priced at 38, which puts the expected return of a Harris bet at (at least) 11,500% annualized, if I did the math right (= (50/38)^(52/3) - 1). I can buy that there are limits to arbitrage, but surely the limits to arbitrage aren't that big? Like it's plausible that a single whale could move the market that much, but surely you personally should be betting the other side?
You can't eat annualized returns, unless they had a new presidential election every 3 weeks for a year and the betting markets were similarly mispriced every time.
Per Polymarket's market depth calculator, it would only take a $3mm mkt buy of Harris to move the price back to 50/50, which isn't a tremendous amount of size to get a 25% price impact. You could sell $3mm of DJT equity for a 1-2% price impact, 20x lower.
So if you think the correct price is >50 and it takes $3M to move the price up to 50, why haven't you personally invested like $30K or $300K?
Edit: Like I know you said in the post that the reason you haven't invested is "limits to arbitrage" but I feel like you haven't adequately explained why you think those limits are prohibitive, and to my reckoning it looks like they aren't.
I don't have a strong ideological commitment to the price on Polymarket accurately reflect Kamala's chances. If this asset is mispriced, a natural question might be "what other financial assets are functions of the winner of the Presidental election, and are those assets mispriced in an even more egregious way?". The answer to that question is that there are, and that I have invested significantly more than $30k or $300k betting on *those*.
This was brilliant! Thank you!
I'm not sure I buy the premise of this, nor do I buy the conclusions.
-People who view the market prob. to be too high should buy NO. People who believe the market prob. to be too low should buy YES. Depending on their confidence and bankroll, they may buy more or less shares, pushing the prob. higher or lower.
-People who are consistently wrong will lose their bankroll, people who are consistently accurate will grow their bankroll, thus improving the predictive power of the market. The more obviously mispriced the market is, the more it will attract smart money.
I think the key aspect of prediction markets that you're overlooking is that unlike the vast majority of market-traded assets, they literally RESOLVE to 0 or 100 and pay out accordingly! This outcome incentivizes trading grounded in some "truth" or whatever.
There should be a million dollar-plus incentive to bring the odds back to reality then, right? Are you getting in on the action?
Kalshi has Trump at 62%. They have professional market makers, SIG, providing liquidity through limit orders. There are no fees.
This profit opportunity should draw in traders. There are hedge funds with lots of money to take bets like this.
Do you really think that Smart Capital looks at that and decides:
1. the probabilities are wrong by a lot, and
2. they don't want to bet?
That seems very unlikely.
the Wolfers paper you link to states "prediction market prices appear to be quite accurate predictors of probabilities"
>everybody in this model is betting precisely their optimal Kelly fraction, given their own subjective probability assessments and the market prices
How do you get that?
Your "Buy Qty ($)" graphs are linear and go to 100% of wealth at the edges, which is how Kelly would act if the x axis were believed propability, but you have it as price.
Indeed, using the alternative formulation of Kelly as betting a fraction of your wealth on each outcome equal to the respective propabilities, we get:
total long (shares): w_x*x/p+w_y*y/p
total short (shares): w_x*(1-x)/(1-p)+w_y*(1-y)/(1-p)
with wealths w_x, w_y, believed propabilities x, y, and price p. Setting them equal gives us exactly that the price is the wealth-weighted average propabilitiy.
That said, Im not sure this averaging is really necessary? I think the idea behind prediction markets is that people update on the fact of others trading, in spherical cow land they could do that until they aumann agree, and in real *very high volume* markets, each trader is only staking an infinitessimal fraction of their wealth, so they can also trade until they aumann agree.
i see how the described dynamic moves the "odds" of a 0% probability to >0%, but I don't see how it move a 50% probability to 40%. How would the non-linear bias push something away from 50/50?
Enjoyed the post, thanks!
Sorry, I'm terribly ignorant re: footnote 1. What's the very liquid optional midcap you're referring to? Thanks!
Oh, I just finished reading the comments. DJT 😂