Kelly isn't (just) about logarithmic utility 2021-02-23T12:12:24.999Z


Comment by simonm on Kelly isn't (just) about logarithmic utility · 2021-02-23T22:25:27.474Z · LW · GW

This was fascinating. Thanks for taking the time to write it. I agree with the vast majority of what you wrote, although I don't think it actually applies to what I was trying to do in this post. I don't disagree that a full-Bayesian finds this whole thing a bit trivial, but I don't believe people are fully Bayesian (to the extent they know their utility function) and therefore I think coming up with heuristics is valuable to help them think about things. 

So, similarly, I see the Peters justification of Kelly as ultimately just a fancy way of saying that taking the logarithm makes the math nice. You're leaning on that argument to a large extent, although you also cite some other properties which I have no beef with.

I don't really think of it as much as an "argument". I'm not trying to "prove" Kelly criterion. I'm trying to help people get some intuition for where it might come from and some other reasons to consider it if they aren't utility maximising.

It's interesting to me that you brought up the exponential St Petersburg paradox, since MacLean, Thorpe, Ziemba claim that Kelly criterion can also handle it although I personally haven't gone through the math.

Comment by simonm on Kelly isn't (just) about logarithmic utility · 2021-02-23T21:51:46.643Z · LW · GW

Yeah, I think I'm about to write a reply to your massive comment, but I think I'm getting closer to understanding. I think what I really need to do is write my "Kelly is Black-Scholes for utility" post.

I think that (roughly) this post isn't aimed at someone who has already decided what their utility is. Most of the examples you didn't like / saw as non-sequitor were explicitly given to help people think about their utility. 

Comment by simonm on Kelly isn't (just) about logarithmic utility · 2021-02-23T19:58:59.719Z · LW · GW

Yes - I cited Peters in the post (and stole one of their images). Personally I don't actually think what they are doing has as much value as they seem to think, although that's a whole other conversation. I basically think something akin to your third bullet point.

Having read your comments on the other post, I think I understand your critique, and I don't think there's much more to be said if you take the utility as axiomatic. However, I guess the larger point I'm trying to make is there are other reasons to care about Kelly other than if you're a log-utility maximiser. (Several of which you mention in your post)

Comment by simonm on Kelly isn't (just) about logarithmic utility · 2021-02-23T17:20:43.887Z · LW · GW

Yeah - I agree, that was what I was trying to get at. I tried to address (the narrower point) here:

Compounding is multiplicative, so it becomes "natural" (in some sense) to transform everything by taking logs.

But I agree giving some examples of where it doesn't apply would probably have been helpful to demonstrate when it is useful

Comment by simonm on Kelly isn't (just) about logarithmic utility · 2021-02-23T17:16:23.939Z · LW · GW

Thanks! That's helpful. I definitely wrote this rather stream of consciousness and I definitely was more amped up about what I was going to say at the start than I was by the time I'd gotten halfway through. EDIT: I've changed the title an added a note at the top

I think the section where I say "it doesn't matter how you think about this" I mean it something in the sense of: "Prices and vols are equivalent in a Black-Scholes world, it doesn't matter if you think in terms of prices of vols, but thinking in terms of vols is usually much more helpful".

I also agree that having a handy version of the formula is useful. I basically think of Kelly in the format you do in your comment I highlighted and I think I would never have written this if someone else hadn't taken that comment butchered it a little but and it became a (somewhat) popular post. (Roughly I started writing a long fairly negative comment on that post, and tried to turn it into something more positive. I see I didn't quite manage to avoid all the anger issues that entails).

Comment by simonm on Kelly isn't (just) about logarithmic utility · 2021-02-23T14:32:09.241Z · LW · GW

I’m not sure what prompted all of this effort,

The comments section here and the post and comments section here. To be completely frank, my post started out as a comment similar to yours in those threads. "I'm not sure what led you to post this". (Especially the Calculating Kelly post which seemed to mostly copy and make worse this comment). 

I’ve rarely heard Kelly described as corresponding to log utility,

I actually agree with you that aside from LW I haven't really seen Kelly discussed in the context of log-utilities, which is why I wanted to address this here rather than anywhere else.

only ever as an aside about mean-variance optimization

Okay, here our experiences differ. I see Kelly coming up in all sorts of contexts, not just relating to mean-variance portfolio optimization for a CRRA-utility or whatever.

If anything, I’d say that the Kelly - log utility connection obviously suggests one point, which is that most people are far too risk-averse (less normatively, most people don’t have log utility functions). The exception is Buffett - empirically he does, subject to leverage constraints.

So I agree with this. I'd quite happily write the "you are too risk averse" post, but I think Putanumonit already did a better job than I could hope to do on that

Comment by simonm on Kelly isn't (just) about logarithmic utility · 2021-02-23T14:21:39.834Z · LW · GW

A couple of reasons:

  1. For whatever reason, people seem to really like Kelly criterion related posts at the moment.
  2. I think Kelly is a good framework for thinking about things
    1. "Kelly is about repeated bets" could easily be "Kelly is about bet sizing"
    2. "Kelly is Black-Scholes for utility"
  3. Kelly is optimal (in some very concrete senses) and fractional-Kelly is optional in some other senses which I think people don't discuss enough
Comment by simonm on Kelly isn't (just) about logarithmic utility · 2021-02-23T12:19:21.878Z · LW · GW

This is my first post, so I would appreciate any feedback. This started out as a comment on one of the other threads but kept on expanding from there.

I'm also tempted to write "Contra Kelly Criterion" or "Kelly is just the start" where I write a rebuttal to using Kelly. (Rough sketch - Kelly is not enough you need to understand your edge, Kelly is too volatile). Or "Fractional Kelly is the true Kelly" (either a piece about how fractional Kelly accounts for your uncertainty vs market uncertainty OR a piece about how fractional Kelly is about power utilities OR a piece about fractional Kelly is optimal in some risk-return sense)

Comment by simonm on Calculating Kelly · 2021-02-23T07:55:04.826Z · LW · GW

Intuitively, if I think something has a ~10% change of happening, I want at least a 10x bet. (Before even worrying about Kelly).

Comment by simonm on Calculating Kelly · 2021-02-22T22:11:13.293Z · LW · GW

This also seems like a better way to intuit approximate answers. If I think an event has a 12% chance, and the potential payoff of a bet is to multiply my investment by 3.7, then I can't immediately tell you what the Kelly bet is. However, I can immediately tell you that  is less than halfway along the distance from 12% to 100%, or that it's more than a tenth of the way. So I know the Kelly bet isn't so much as half the bankroll, but it also isn't so little as 10%. 


1/3.7 ~ 27% >> 12% so you shouldn't be betting anything

Comment by simonm on Calculating Kelly · 2021-02-22T19:56:17.792Z · LW · GW

There is a sense in which fractional Kelly is combining two noisy estimates of the probabilities. (Market probability and your probability). (I say more here). 

Comment by simonm on Calculating Kelly · 2021-02-22T19:20:48.360Z · LW · GW

Edges is p - q (your probability minus the odds implied probability 1/r in your notation).

I don't think pro-gamblers do think in those terms. I think most pro-gamblers fall into several camps:

1. Serious whales. Have more capital than the market can bet. Bet sizing is not an issue, so they bet as much as they can every time.
2. Fixed stake bettors. They usually pick a number 1%, 2% are common and bet this every time. (There are variants of this, eg staking to win a fixed X)
3. (Fractional) Kelly bettors. I think this is closest to your example. A 1/2-Kelly bettor would see 51% vs 49% and say bet  0.5 * (51-49)/(100 - 49) ~ 0.5 * 4% = 2%

Comment by simonm on Reasonable ways for an average LW retail investor to get upside risk? · 2021-02-20T10:07:51.953Z · LW · GW

This isn't quite the right way to think about Kelly betting. Kelly maximises log-wealth after one bet. This isn't quite the same as maximising long-run log-wealth after a series of such bets. In fact, Kelly betting is the optimal betting strategy in some sense (leading to higher wealth than any other strategy).  

Comment by simonm on The Kelly Criterion in 3D · 2021-02-20T09:26:57.547Z · LW · GW

Rather than talking about p and b (your probability and net fractional odds*) doing things in terms of p and q = 1/(b+1) (your probability and implied odds probability) makes calculations easier and lots of the things you didn't expect more intuitive. Specifically:

This means:

1. It is easy to see the fraction is piecewise linear
2. The answer to Q5 is obvious.

* aside: who talks in net fractional odds? None of the 3 major odds styles use it

Comment by simonm on Reasonable ways for an average LW retail investor to get upside risk? · 2021-02-17T09:31:43.796Z · LW · GW

TL;DR Leverage

"Upside risk" I am going to divide into two categories:

  1. Skewed returns - "Bets with a payoff which is either very large and positive; or small and negative"
  2. Outsized returns - "Bets with a higher mean return"

It seems to me that you're mostly thinking in terms 1. There are plenty of ways to do this systematically; 

  • buying options [Buying SPACs slightly above NAV is roughly equivalent to buying options]
  • buying insurance
  • buying early-stage growth stocks
  • buying lottery tickets
  • betting on dogs

They all have a range of distributions but largely they are money-losing (on average). The reasons for this are fairly straightforward. Everyone likes lots of upside, with limited downside, so those bets get bid up and their expected returns fall. Personally I think these are a bad thing to do systematically*. You need to be deriving some value from the "excitement" for these strategies to be compensating you for the average loss you're taking. 
* Where you're hedging some personal risk and paying over the odds to do it (health/home insurance) then you should do it systematically. 

More interesting to me is how can retail investors achieve 2. without losing their shirts. (You mentioned a few of these (selling options, EM equity)). Off the top of my head there are a few different ways to boost your returns systematically (roughly in order of how "good" I think they are for retail):

  • Leverage
  • Equity factors (momentum, value, etc)
  • Vol risk premium
  • FX/Rates carry, CDS premia, ...
  • "Alpha"

People have already mentioned vol risk premium. (Mostly expounding it's virtues). To give a bear case on this. This strategy can definitely become crowded. Even before the March '20 sell-off, vol sellers had had a terrible run from 2018-2020. Personally I believe that VRP exists, but it's not a premium I'd want to collect as a retail account. The market is pretty sophisticated and most of the ways to express that trade are full of nasty gotchas. 

There have also been a few discussions of alpha. (Or at least the idea that LW-ers can beat the market in some risk-adjusted sense). For someone uninterested in finance, I think this is extremely unlikely - and probably going to end badly.

I think leverage is broadly underrated by retail. Margin accounts are getting cheaper and cheaper, and running a leveraged (say) 60/40 portfolio is becoming increasingly viable. This will increase risk and returns. You will pay some cost for the leverage, but this is by far the cleanest way to boost your returns in my option.

Equity factors - momentum, value etc. There's hundreds of these factors now all with a range of "acceptance" within the finance community. Access to them is becoming much easier (factor ETFs are a thing).

Carry etc - ... There's a bunch of different strategies which fall into this bucket. I'm not going to say a huge amount about them because I think this is something which is really worth doing your own research on. They are accessible to smart retail investors, but you will need to think carefully about what your strategy is,

Comment by simonm on Reasonable ways for an average LW retail investor to get upside risk? · 2021-02-17T08:43:50.746Z · LW · GW

As always, don't bet over Kelly. [...] without betting over Kelly

You mention Kelly twice in the context of selling options on indices, but it's not clear to me how a "average LW retail investor" is supposed to calculate their edge.

Comment by simonm on Reasonable ways for an average LW retail investor to get upside risk? · 2021-02-17T08:38:49.471Z · LW · GW

Kudos on your great returns. I don't have any particular quibbles with your strategy although I would caution other people to think hard about whether or not they have a good sense of what is "cheap" or "expensive" when it comes to single stock vol. Ending up on the wrong side of the next GME will be very painful.

In general, I believe the average less wronger to be more intelligent than the average trader (possibly even the average professional trader) and thus capable of achieving steady returns which beat the market. Maybe this is just survivorship bias talking, though.

The "average trader" is not a particularly good benchmark. Performance is very skewed, and the vast majority lose money. I am assuming by "average" you are referring to median. The mean trader breaks-even (mechanically) as we're talking about a zero-sum game.

 "Intelligence" isn't the only relevant skill. The difficult parts of trading are not usually "being smarter than the market" but things like: 

  • Having high quality information
  • Having high quality execution
  • Temperament


Comment by simonm on Build Your Number Sense · 2021-01-28T14:09:12.884Z · LW · GW

This example by Tom Scott is excellent imo

Comment by simonm on Number-guessing protocol? · 2020-12-07T16:54:30.521Z · LW · GW

Or, we could give confidence intervals. But how should they be scored?


A relatively simply way to do this would be rather than CI, you give "location and scale" and are scored according to:

Comment by simonm on 12 Rules for Life · 2020-12-03T21:28:22.007Z · LW · GW

I strongly disagree with that too. If someone says "x is true" when x is not true, then saying "x is not true" does have value. Assuming you're talking to a reasonable person

I think the subtext of you asking that is you are saying that I am not "refuting the central point". (I also disagree with that, but ymmv)

Comment by simonm on 12 Rules for Life · 2020-12-03T21:02:12.705Z · LW · GW

Consuming media created by others is a passive activity

I think I just fundamentally disagree with this. Reading can be passive, but it can be active as well. Reading doesn't just mean "looking at words".

You are running someone else's thoughts through your brain.

I don't really accept that this is what reading is like. I read your post, but I didn't mindlessly accept what you had to say.

Comment by simonm on 12 Rules for Life · 2020-12-03T14:06:39.348Z · LW · GW

I strongly disagree. It seems to assume that everything is read as often as it's written which is not true. The best writing is written once and read millions or billions of times. Maybe it should be write 1/100th or 1/1000th of what you read. (But even this assumes that what you're writing is worthwhile, which for lots of people I think is not true).

Comment by simonm on Are index funds still a good investment? · 2020-12-03T13:56:57.046Z · LW · GW

Some other things which I didn't mention here, but really are somewhat important stories

1/ Active trading (as opposed to active investing). Market making, stat arb, etc

2/ The rise of private investments. There's a decent case that the best listed companies get taken private, leaving the public markets with only the very largest companies which no-one can take private, and the companies which no private equity firms want to take public

3/ Semi-active investing / factor investing. I find it quite hard to ignore the evidence that there are factors which outperform broad market indices (Momentum, Value, Large Cap, Low Vol, etc). Should you misweight your investment away from cap-weights to capture some of this additional value?

Comment by simonm on Are index funds still a good investment? · 2020-12-03T13:52:21.148Z · LW · GW


TL;DR In my opinion, yes, still a good investment, if only because the alternative is not great

I think there's several things to tease out:

1/ What do we mean by "Index Funds"? Are we talking about the platonic global cap-weighted fund which owns the entire investible universe? Are we talking about country specific cap-weighted funds? Sector specific? Cap-weighted but only the biggest n (S&P500, etc)? Cap-weighted, but also only if they meet certain governance / financial standards?

I find it quite hard to find fault with the platonic ideal of an index fund (although I will attempt to talk latter a little about some issues with it). Unfortunately, it's pretty much impossible to create for any number of reasons.

There are definitely potential issues with individual indices.

a/ Index inclusion - it's clear that being added / removed from the index can have massive impact on a company's valuation. Recent examples include Tesla and [these guys front running index inclusion](

b/ Governance - as more and more of stocks are owned by non-voting, passive owners it's easier for management to get away with shadier dealings

c/ Anti-competitiveness - [Matt Levine has written extensively about this idea]( I don't take it too seriously, and I don't think it harms investors as much as the broader market

d/ Missing the "good" investments - if assets revalue when they join an index, you are definitely missing out if all you are doing is buying the index. (At which point the assets will already have revalued). I think there is a similar phenomenon here related to where stocks are listed. The same stock can trade at vastly different valuations based on the stock market which its listed on. (Not at the same time, I mean here re-listing can be a big catalyst for stock price growth).

2/ What if index funds are overvalued in general?

"if index funds were overvalued, the active traders should make a killing on that inefficiency"

I don't think this is quite right. If our platonic index funds are overvalued then the entire market is overvalued and there's not really anything you can do about that as an active trader. (Except perhaps bet that it's going to go down, and that's a very tough bet to make). If you think that individual index funds are overvalued, that's still a tough trade, since you have to wait for company cash flows to prove you right, and you might be waiting a long time / find yourself squeezed out by weight of money long before then.

3/ What are our alternatives?

Perhaps this is a lack of imagination on my part, but I see roughly 7 areas where you can "invest" your capital. (Separate from "using capital as collateral for running a trading strategy").

a/ Cash
b/ Equities
c/ Real Estate
d/ Bonds
e/ Commodities
f/ Precious metals 
g/ Cryptocurrencies

There's a case (I think best made by Mike Green) which suggests the world is divided into "Cash" and "Non-Cash" (which we can proxy with equities and bonds) and that the use of index funds is causing the amount of cash held in the world to decline which causes non-cash assets to revalue higher and higher (especially when valued in cash terms). I don't think this story is completely true (I don't think all buyers of index funds are entirely price insensitive) but I think it has enough merit which is worth thinking about.

My general view is from an asset allocation point of view there is very little to encourage bonds, commodities, precious metals and crypto. (Safe) bonds have negative real yields. Hoarding commodities seems to have little utility so why should it have positive returns. Gold / Precious metals / Crypto only seems to derive it's value from some sort of Keynesian beauty contest which I feel I have no edge in so I tend to steer clear. That said, I still think it's worthwhile holding some of all of them if only to benefit from their lack of correlation, store of value properties which enable you to rebalance.

So we're left with Equities and Real Estate. I'm going to dump real estate into equities on the grounds that you can hold real estate via REITs, but I think RE has properties much more similar to inflation linked bonds than companies.

The next question, now we've established our asset allocation, is "How do I own my equities?". Again (lack of imagination on my part) I see roughly two choices here: Own index funds. Buy individual stocks.

Owning index funds has a lot to recommend it - cheap, easy to do, getting information from the whole market etc

Buying individual stocks has a lot of problems - how do you find them? how do you value them? what makes you think you're better at it than the market at large?  

My general advice to people who can't solve those problems is "Own Index Funds".

Comment by simonm on 2020 Election: Prediction Markets versus Polling/Modeling Assessment and Postmortem · 2020-11-19T14:41:40.939Z · LW · GW

I think Zvi would also bet against the market if that happened. If he thinks the probability is 50% and the market is offering 38%, that's a great bet

He's completely consistent in that he puts the probabilities of these events between the markets and Nate (which inevitably means betting against the market in the direction of the models) 

Comment by simonm on Covid 11/12: The Winds of Winter · 2020-11-14T14:23:34.334Z · LW · GW

As far as I can tell the exchange settled:

 - Nominee markets

 - State markets, excluding (AZ, GA, MI, NV, PA, WI)

They haven't settled the big market (Next President) nor any of the key states which are "contested" (for whatever definition of contested you're interested in) (or any of the vote percentage, EC handicap markets etc).

It's possible the sportsbook settled the presidential market, but that's a very different beast to the exchange. (Lots of "normal" bookies have already settled the presidential market)

Comment by simonm on Did anybody calculate the Briers score for per-state election forecasts? · 2020-11-14T10:06:52.808Z · LW · GW

That paper doesn't actually justify why 538's probabilities don't form a martingale. (In fact it's plausible that they do - to demonstrate they aren't I'd want to see someone show a strategy which is successfully arbitraging the probabilities). Since 538's model isn't open source, it's pretty difficult to say whether or not it is a true martingale, but that paper definitely doesn't show it.

If we were to take a similar model which is open source (specifically The Economist's model) we can see that it is not far from being a martingale. Specifically if they added forecasting for their [fundamentals model]( (not difficult, just painful). I don't think the difference made by the fundamentals model is that significant so I think it would have been fairly difficult for anyone to arbitrage those odds. (Not that they were correct, just that they were broadly time-consistent)

Comment by simonm on What is a probability? · 2020-11-13T17:54:47.779Z · LW · GW

In which case, isn't there a much shorter argument. "Given an uncertain event there is some probability that event occurs and that probability depends on the information you have about the event". That doesn't seem very interesting to me? 

Comment by simonm on What is a probability? · 2020-11-13T16:46:34.012Z · LW · GW

To make this framework even less helpful (in the instance of markets) - we can't know what information they contain. (We can perhaps know a little more in the instance of the presidential markets because we can look at the margin and state markets - BUT they were inconsistent with the main market and also don't tell you what information they were using).

Comment by simonm on What is a probability? · 2020-11-13T16:39:26.489Z · LW · GW

One thing that falls out of this post's framework is that it makes sense to say that one prediction (and in extension, one probability) is better than another, but it doesn't make sense to talk about the correct probability – unless 'correct' is defined as the point of full information, in which case it is usually unattainable.


This is all well and good, but I feel you've just rephrased the problem rather than resolving it. Specifically I think you're saying the better prediction is the one which contains more information. But how can we tell (in your framework) which model contained more information.

If I had to make my complaint more concrete, it would be to ask you to resolve which of "Story 1" and "Story 2" is more accurate? You seem to claim that we can tell which is better, but you don't seem to actually do so. (At least based on my reading).

Comment by simonm on Limits of Current US Prediction Markets (PredictIt Case Study) · 2020-07-18T11:21:17.145Z · LW · GW

You were the one making the claims about crypto. FTX isn't accessible to US or UK based bettors for the Trump election. (So not a grey area, just not an area you can use at all).

(I also refused to believe that liquidity is real. Whenever I see orders like that in an order book I am usually fairly confident that there is something subtle going on which means they have a technological way to avoid being filled.

Looking into FTX, the subtlty is that you can't submit orders 2% thru' the order book, which means you can safely leave gigantic orders off-market to maintain queue spot or for other technical reasons).

Comment by simonm on Limits of Current US Prediction Markets (PredictIt Case Study) · 2020-07-17T07:23:19.819Z · LW · GW

Fair enough, for a one off it might work, although that wouldn't be the case for someone who is regularly active in prediction markets.

Theoretically on the 28th, but that doesn't answer my question about where you can currently get serious money down down in crypto?

Comment by simonm on Limits of Current US Prediction Markets (PredictIt Case Study) · 2020-07-16T07:31:36.883Z · LW · GW

1. I don't agree that the prices are fairly similar. PredictIt,, Omen, and FTX (let me know any other crypto exchanges you want considered) all have Trump ~40%. Betfair has him ~35%. I think that's materially different. (Also, the volumes on those exchanges are all pretty limited, so I'd be impressed if you could get $1mm down that way). I agree you could potentially get some risk down via P2P betting, but I don't think it's fair to describe that as a "prediction market". (Although it does nuke his point of excusing people from not putting their money where their mouth is).

2. I don't think you can get $1mm of risk down on Betfair. (Because of the Premium Charge issue I mentioned). I think the only way I can see that being done at the moment is P2P, and I'm not sure I'd be comfortable with the counterparty risk involved.

Comment by simonm on Limits of Current US Prediction Markets (PredictIt Case Study) · 2020-07-14T14:19:18.006Z · LW · GW

Agreed - 4/ is solved by allowing margin.

(Although margin is trickier if the event can suddenly resolve to 0 or 1 at any time, I think there are even solutions to this)

Comment by simonm on Limits of Current US Prediction Markets (PredictIt Case Study) · 2020-07-14T14:06:04.490Z · LW · GW

I don't think that "lots of the informed people" being elsewhere should make much difference. The main metric for how seriously to consider data from prediction markets (in my mind) is open interest (or volume / liquidity if open interest isn't available).

Yes - well, there are taxes on gambling profits, but on the betting companies, but not the individual gamblers.

Comment by simonm on Limits of Current US Prediction Markets (PredictIt Case Study) · 2020-07-14T13:12:23.209Z · LW · GW

I feel this is more "limits of PredictIt" rather than "limits of prediction markets". Doing the equivalent analysis for Betfair for someone in the UK. (2% charge on profits, no fee for withdrawing).

Right now the market for Trump to win is (£1200) 2.78 / 2.80 (£7421)

Those imply probabilities of 35.97% and 35.71%

After fees, 36.44% and 35.00%.

That's not a bad spread, and you can do this in much more size. (If you're willing to work a bit, you can comfortably get on £10,000s at prevailing levels).

We pay no taxes on gambling, so there's none of Section III to worry about.

(Admittedly, once we start talking about even more serious size we run into Betfair's Premium Charge, but for your average UK based rationalist, I don't think Betfair is as bad a prediction market as you're making out).

Comment by simonm on Six economics misconceptions of mine which I've resolved over the last few years · 2020-07-14T12:58:41.691Z · LW · GW

I think it would be extremely material for the 2020 Presidential Election. Lets say for sake of argument that Biden winning means the TCJA gets partially reversed and corporate tax rates go up 2%. That would have an extremely large (downward) impact on stock prices.

The market cap for stocks is huge O(10^13) compared to amounts wagered on the Presidential Election O(10^8), so any effect is going to swamp prediction markets.

However, I don't believe that this effect is material to prediction markets at the moment.

1/ Prediction markets just aren't super efficient. Compare PredictIt (41%), Betfair (36%) and various other venues to see the kind of differences out there in estimates for the odds of Trump winning re-election.

2/ Volumes aren't super high, so this sort of hedging the author talks about is a long time away.

3/ Financial actors have much more liquid ways of hedging election risk than hedging in thin prediction markets.