It is possible that Scott believed that ETH is negatively-skewed (ie small chance of collapsing, large chance of small increase) but this would be inconsistent with his probability that ETH is going to 5k.
I think the vast majority of people think crypto is positively-skewed.
because any participant in the options market can hedge their position against the underlying asset.
Right, but then the underlying asset is telling you something and if you disagree with that, then you can trade the underlying asset. There’s nothing special about options here. The difference comes from the fact that the underlying asset can have a return. (In the same way that a bond have a price different from par doesn’t (necessarily) mean that the market is forecasting default—they are discounting the value of a future cash flow).
What evidence do you have that this is true? Your post is taking risk neutral probabilites from the market + your own opinion that risk neutral is similar to real world, then presenting that as the “market probability”, which is very misleading.
The evidence would be something akin to “the historic sharpe for risk assets is <1” so the order magnitude of risk premia is “small enough” relative to the volatility.
I don’t think there is anything misleading about taking the market prices, constructing a bet and presenting that as a market probability, any more than taking showing betting odds and saying that’s the betting market probability. Sure, there might be some subtleties depending on the market (eg long-shot bias, fees, etc), but fundamentally that’s the price the market is offering. If you disagree, BET.
Edit: Maybe a better framing is that in order for option probabilities to give us a ~real world pdf of asset price at a given time, the asset needs to be approximately a martingale from now to the time in question. Many people would strongly disagree that BTC/ETH are even approximately a martingale on this time scale (they think there’s large positive drift).
I agree with this, all I’m saying is that the degree to which those assets fail to be a martingale is small relative to their volatility.
You are making a strong claim that is contrary to the view of many or most of the top crypto traders in the market, and yet you don’t make this clear but instead claim it’s a “market probability”, with the implication that people should defer to it unless they have strong domain knowledge.
I assume all those people are long crypto, which fundamentally means they disagree with the underling price and are long… I don’t see any inconsistency between that and what I’m saying. I would be more interested if you could find me someone who thinks both that
option prices are wrong
they shouldn’t have a position in options
they shouldn’t have a position in the underlying
because of some kind of risk-neutral vs real-world probability considerations.
tl;dr “some sort of median vs mean distinction”
No, there’s two things going on which act against each other:
Riskier assets have higher returns on average
Riskier assets are more skewed (mean higher than median)
I’ve made the (I think safe) assumption that the skewness of the assets are more important than the relative differences in their expected return.
You can have a play with some toy models for this, for example, fixed Sharpe, lognormal assets you will have something which looks like:
log(X) ~ N(sharpe * vol—vol^2/2, vol)
P(return larger than r) = P( Z*vol + (sharpe*vol—vol^2/2) > r) = P(Z > (-sharpe + vol/2 + r/vol))If we’re interested in r = 0 (outperformance of current price) then as vol increases, the probability goes down.
(There’s actually quite a bit of intuitive stuff which drops out of this model (if we’re required to hit a given r, then increasing volatility makes it easier (up until vol = sqrt(2*r)))
Actually this is the other way around. If ETH is less risky than BTC then the median performance of ETH will outperform BTC and his probability could be consistent with EMH
This is neither consistent with historical realised volatility (ETH is more volatile than BTC), nor is it consistent with the options market (ETH implied vols are all higher than the equivalent moneyness BTC implied vols)
I detailed a few of them which are already on Metaculus here. If there are others which you are particularly keen to see added I’m sure they could be written
I just ball-parked the numbers from a the tightest call spread currently tradable in the market. If precision was important I’d do something more sophisticated.
Yeah not really sure why you’d divide the option price by current spot?
I’m now confused as to what you mean by “real world” in this context?
Zvi is giving a credence for the event (p_zvi).
The market is offering a bet which implies some probability for the event (p_market).
All I am noting is p_zvi is different from p_market. I don’t think there’s anything special about the fact that options are involved here. (Unless I’m the one inferring you were specifically talking about options when you talk about “risk neutral measures”. All market probabilities are in some sense in risk neutral probabilities. If you’re complaint is about me talking about market probabilities then I guess this post wasn’t really for you?)
EDIT: To be more concrete about this, the places where “risk neutral” vs “real world” probabilities end up mattering is places where there is a concrete risk premium. (ie what the options market implies about stocks in 1y’s time doesn’t account for the fact that “stocks tend to go up over time”). In all the examples we’re talking about, those risk premiums are tiny relative to the numbers involved so they don’t make a significant difference to how we should be calculating the “market implied” odds.
I think there’s ~80-85% chance the Olympics happen on time. I think there’s a ~90% chance that the Olympics go ahead this year.
I think the case against them going ahead this year is roughly:
Current state of COVID in Japan, potential for it getting worse
“Cancellation is possible” statements from government
Public opinion is against the games
I don’t think it’s very likely, but do I think there’s a ~15-20% chance that COVID flares up in Japan in the next 3 months in a particularly bad way? Doesn’t seem crazy to me.
(FWIW, I don’t think betting on the Olympics at the FTX odds is a bad bet, I just don’t think it’s a sure thing)
Risk neutral vs Real world measure isn’t really a meaningful distinction the way you think it is. You can construct a binary bet in terms of options, and the price is the market price for that bet and that’s the market probability. It’s no different than betting on any other event. If you don’t like market pricing, then sure, ignore everything I’ve written here, but don’t think “risk neutral measure” is some magic phrase which lets you ignore the options market. If you think the odds are different, you can always place that bet.
I’m not saying Zvi is wildly wrong. Indeed he says he wouldn’t trade with anything in 40-60% (and the market being at 60% means he’s technically not “off” it), but I given it’s close to what he’d consider trading, I think that’s an interesting difference worth noting.
I’ve copied this, but only taking the market forecasts. Doing this meant I’ve spotted a couple of things which I think Zvi missed:
8. Olympics going ahead on schedule
Zvi cites the Metaculus forecast, but it actually isn’t specific to the schedule. Other prediction markets are half-way between his forecast and Scott’s. (Although my personal forecast is the ~same as Zvi)
12. Netayahu. I’m not sure if Zvi meant to, but he missed that PredictIt does have an end of year market.
14. Zvi seems somewhat off the option market forecast. (Judging him slightly on hard mode as I think he’s pretty skilled)
17. I’m not sure this was quite his “biggest” fuck you to EMH. The Dow predictions and ETH to 5k both seem significantly worse
Right, so the back of the envelope calculation for what I think you are calling volatility drag is:
geometric return = arithmetic return—volatility^2 / 2
If you have constant leverage (for example like most constant-leverage ETFs) then you effectively multiply your arithmetic return by a constant and your volatility by the same constant so your new geometric return is:
leverage * arithmetic return—leverage^2 *volatility^2 / 2
Your example is correct.
There is a sense in which all three (leveraged-ETFs, margin, futures) are all equivalent, the main difference is in how active you need to be to maintain you need to maintain your strategy. In terms of “closest to buy-and-hold” I think they go in this order:
Margin (buy less than your broker allows you too, maintain cash in your brokerage, periodically adjust)
Futures (make sure you hold significantly more cash than your brokerage, roll your futures appropriately)
Leveraged-ETFs (hold cash to rebalance, you will need to do so regularly)
There is a sense in which they also go in the opposite order in terms of effort. (For example, if you do want to maintain constant leverage (which is of course the concrete recommendation for juicing returns) then leveraged ETFs are the way forward as tryactions explained)
Leverage is not more complicated than it looks. “Borrow money to invest”. (Or more usually in finance “borrow money using your investments as collateral to invest more”).
Futures aren’t the only way to invest with leverage. Probably the easiest way for a retail investor would be something along the lines of owning ETFs on margin.
Treasury futures and cash treasuries are pretty much exactly the same amount of volatile. Even when the cash/futures basis blows up, we are talking tiny amounts relative to the volatility of the underlying. You can absolutely leverage treasuries via treasury futures and assuming that treasuries outperform your cost of funding then you will “juice” your returns.
Futures prices are priced so there is no arbitrage—nothing more, nothing less
The price of the futures account for this. (Otherwise there would be an arbitrage, see 2.)
I don’t really understand your question here?
Yes, you definitely can let your leverage ratio float around a bit, in fact I would strongly recommend this. Just because someone will offer you X amount of leverage, doesn’t mean you should take it all. In practice you should be able to avoid margin calls in a well managed position, although it is a risk you are taking with leverage, and you need to appreciate that before going down this path.
The traditional finance theory way to acquire more risk would be to increase leverage in your portfolio
(I explain more here and that thread is full of other ideas you might like)
You’ve given an example which is already 10x what I asked for, and you could have plausibly done another 5x your size… I’m glad you made some money, but I don’t think this is what I’m talking about
I also looked into this after that discussion. At the time I thought that this might have been something special about Kelly, but when I did some calculations afterwards I found that I couldn’t get this to work in the other direction. I haven’t fully parsed what you mean by:
(And since payoffs of the bet-against-yourself strategy are exactly identical to Kelly betting payoffs, a bunch of Kelly bets at house odds rearrange money in exactly the same way as this.)But this is clearly equivalent to how hypotheses redistribute weight during Bayesian updates!So, a market of Kelly betters re-distributes money according to Bayesian updates.
(And since payoffs of the bet-against-yourself strategy are exactly identical to Kelly betting payoffs, a bunch of Kelly bets at house odds rearrange money in exactly the same way as this.)
But this is clearly equivalent to how hypotheses redistribute weight during Bayesian updates!
So, a market of Kelly betters re-distributes money according to Bayesian updates.
So take the following with a (large) grain of salt before I can recheck my reasoning, but:
Everything you’ve written (as I currently understand it) also applies for many other betting strategies. eg if everyone was betting (the same constant) fractional Kelly.
Specifically the market will clear at the same price (weighted average probability) and “everyone who put money on the winning side picks up a fraction of money proportional to the fraction they originally contributed to that side”.
The reason that I think articulating why strategies might exist is that I’m a dogmatic EMH fundamentalist. When a person gives investment advice, I have historically ignored it, the same why I ignore it when somebody makes an argument for why I should consider using heroin, or committing suicide. Those behaviors are on my “no” list. I don’t intellectually engage with arguments in favor of them, and short-circuit the updating of my priorsLikewise, the EMH has put investment advice (aside from “invest in index funds”) on my “no” list. I follow an iron law of not engaging with investment advice.
The reason that I think articulating why strategies might exist is that I’m a dogmatic EMH fundamentalist. When a person gives investment advice, I have historically ignored it, the same why I ignore it when somebody makes an argument for why I should consider using heroin, or committing suicide. Those behaviors are on my “no” list. I don’t intellectually engage with arguments in favor of them, and short-circuit the updating of my priors
Likewise, the EMH has put investment advice (aside from “invest in index funds”) on my “no” list. I follow an iron law of not engaging with investment advice.
I would highly recommend reading the full introduction to Section 20 of Cochrane’s “Asset Pricing”. (The whole course is excellent) Roughly he takes you through the progress academic finance has made since the 1970s, whilst not repudiating EMH, finding reasons why “invest in index funds” isn’t necessarily the whole story for investors.
Are there investment strategies, besides index fund investing, that make the amount of money you have, your level of political access, and your accumulated knowledge infrastructure, relatively unhelpful, or even actively harmful, for evaluating certain specific types of investments—even if those resources are also extremely helpful for accessing and evaluating other trades?
I don’t understand this sentence?
In other words, are there investment strategies where individual, ‘one-off episodes’ of rational thought—as opposed to accumulated rational reflection over long periods of time—is more important than any other factor for accurately predicting price change for a subset of possible trades?
… still lost
In other other words, are there investment strategies that are unattractive to hedge funds, but work well for small, smart, creative, and hard-working analyst-investors?
Fine, interesting question, I don’t really see how it links to what you wrote in your post? You seem to posit reasons why strategies might exist, but really this is a concrete problem. “Name some strategies”.
And in addition (I try to give a tentative guess to establish plausibility):If these investment strategies exist, can we identify them?How easy is it to end up with a compelling, yet wrong answer?You’re proposing a third, important question (this I don’t know the answer to):If we can identify such a strategy, how many such opportunities can we expect to find, and how much competition will we face from other investors in our reference class?
And in addition (I try to give a tentative guess to establish plausibility):
If these investment strategies exist, can we identify them?
How easy is it to end up with a compelling, yet wrong answer?
You’re proposing a third, important question (this I don’t know the answer to):
If we can identify such a strategy, how many such opportunities can we expect to find, and how much competition will we face from other investors in our reference class?
I don’t really see where you ask how to identify strategies? Nor whether or not you could delude yourself?
I don’t really think LW is short of people suggesting strategies for small investors:
Extrapolate across the employees in the whole fund, and that amounts to something a bit like “inertia.” Another way of putting it is that smaller investors face lower opportunity costs by exploring novel investment types.
Right, but then my point is individual funds don’t matter. What matters is the ecosystem. Are there funds in your area? Another way of of putting your argument is: “Individual investors have an advantage because they can scan across all investments” but my counter to this is:
You already accept LARGE FIRMS can’t cover the space of all investments—how can an individual investor manage?
You aren’t competing with one firm, you’re competing with ALL FIRMS
This doesn’t quite make sense to me, taken alone. Any $1mm opportunity is also a $10 opportunity, but not all $10 opportunities are $1mm opportunities. There must be more, say, $1,000 opportunities. Hard to give a firm reason to explain what the ratio would be.
Lots of investments are $1mm investments and aren’t $10 investments. (Try and see if you can get a $10 allocation in an IPO / VC / PE type investment).
Humans might differentiate themselves from such algorithms by focusing on an approach to investing that considers it more along the lines of “superforecasting”-style questions. Figuring out how to ask and answer questions with good judgment, and determine how the answers bear on the market, is something that an algorithm is not cut out for.
And you think hedge funds aren’t doing this? I’m not sure exactly what edge you’re ascribing to small investors here.
No (I’m assuming you’re talking about 20% gains on a low-volume stock). But I have modest confidence that these opportunities might exist, and that I’d discover historical examples if I took the time to look. Right now, I’m trying to focus more on “how the EMH could be wrong (enough) under not-too-unreasonable assumptions to justify doing more research to verify or falsify the model,” rather than making an argument that the model is valid or that the EMH is right or wrong. As I said, this is highly speculative, and I am inexperienced but trying to learn.
I like the way of framing EMH as “Is EMH true for you?” and there may or may not be reasons to believe it’s true for you. Personally I have rather dim views of people who claim that EMH is not true in some generality. If you want to convince me EMH isn’t true for you, develop a track record.
(Also to be clear a 20% gain on even the lowest volume stock wouldn’t count for me—very low volume stocks would still allow investors to invest many times more than $1000...)
And this is my key point. Within this class of opportunity, you’re not competing with hedge funds. You’re competing with other small investors. One thing I really don’t understand is what fraction of small investor wealth is tied up in things like index funds and managed retirement funds. Of small investor wealth, what fraction is people actively trying to play the small-cap low-volume weird-investment stock market? What level of sophistication does their thinking rise to?
I would recommend you spend some time on [insert any online investing forum]. There are loads of people doing it. I’m not sure the “fraction” is particularly meaningful. One thing which I think is mechanically true is more of the investments in small caps are active (since fewer indices invest in small caps).
I think this section makes two arguments:
The investment universe is very large; it’s hard for one fund to cover all of it
Large investment funds have inertia associated with any large company
I think both points are ~wrong / unimportant for EMH.
Whilst the investment universe is large, so are the number of eyeballs on it. There are many funds all specialising so whilst you might not be competing with Bridgewater in your microstock world, you may be competing with some other funds.
Whilst each fund is structured differently, typically individual portfolio managers have a lot of autonomy within their mandate. If they change their mind about a position they can move very quickly. (Ignoring the size issue from the next paragraph). Bureaucracy can be a factor in some funds, but that’s typically not what limits people.
I think the argument (as you’ve written it) doesn’t really make a huge amount of sense. (Saying that each person needs to find $x/per hour etc). Whilst not all trades scale, lots do, so finding a $10 opportunity is not necessarily easier or harder for a large fund than a $1mm opportunity. Some other advantages of scale which you’re glossing over:
Access to investments not available to smaller investors (allocations in issuance, private deals, products unavailable to retail investors, co-location etc)
Execution edge—your trade is typically being managed by hand, theirs can be managed by algos written by professionals; they can watch the market 24⁄7 to find the small edge in some weird basis you know nothing about.
A seat at the table—don’t like the way the board is handling a company you own? Phone them up / get your own board seat. Want to understand something about a company you might invest in? Have a chat with the head of IR / CEO etc
Small edges being meaningful—squeezing out another basis point on a big investment makes a big difference in $ terms. (You sort of address this later)
meaning that they’d need to be 20x as efficient as you in identifying them.
Consider the HFT—they are trying to place trades to earn pennies and they are much more than 20x as efficient as you at identifying those opportunities. (I don’t think HFTs are particularly interesting to consider when thinking about “competition” in an EMH sense, but I think it’s a good illustration about how much more efficient funds can be than you).
To be sure, a small investor still must compete against other smart, small investors for whatever edge there is to be found. But now we’re basing the EMH, with respect to these small-time and strange investments, on the intelligence of people more or less like you and me.
I don’t think this is quite the right interpretation. Can you describe to me a concrete trade which looks like: 20% return on $1000. (All the ones I can think of tend to be just as amenable to professionals). The other issue of playing in the “micro-investment” pool, is typically liquidity is much lower, so costs are higher.
EDIT: To be clear viz-a-vis your title “Are there opportunities for small investors unavailable to big ones?” I think the answer is “Yes, but there are lots more small investors”