Friday, December 15, 2017

Bitcoin Future-Spot Divergence



As of last night’s close, the price for a January bitcoin future was $1,171.21 higher than the price for a bitcoin. That means anyone could:
  • Buy one bitcoin for about $16,500
  • Sell a bitcoin future for about $17,500
  • Wait until January
  • Sell off the bitcoin and pay off the future contract
  • Pocket over $1,000.
That’s a return of ~6% in just one month, and you can lock it in instantly - once the bitcoin is bought and the future sold, their values will move in tandem, so there’s no risk of losing money. Normally, we expect these kinds of arbitrage opportunities to disappear quickly - especially for assets like bitcoin, which are easy to acquire and cost nothing to store. So why haven’t the prices converged?


If you want to know why an apparent arbitrage opportunity hasn’t disappeared, an easy way to find out is to try to exploit it, and see what stops you.


In this case, the main issue is that a bitcoin future is a future. Futures require both parties to hold margin: money available to cover their side of the contract as prices move. Usually, margin on a future isn’t huge, since prices aren’t too volatile. But bitcoin? Very volatile. That means very high margin requirements.


As usual, Interactive Brokers has everything you need to know on one page: margin requirement to sell a single bitcoin future is $40,000. Now, that margin can still earn interest while it’s sitting around, so it isn’t a “cost” per se. You don’t need to spend it in order to take advantage of the arbitrage opportunity. But you do need to have it available, and you can only arbitrage one bitcoin per $40,000 available.


This is still a pretty good opportunity, but you can only put so much money into it. That explains why small traders aren’t wiping out this arbitrage opportunity. So, next question: why aren’t the usual big institutions arbitraging away that price difference?


Usually, here’s how the situation would play out. A trader would buy a bitcoin and sell a future. Now, the trader would like to repeat this trade in order to make more money. So, the trader would go to a banker and say “hey, I have this low-risk arbitrage opportunity, I’d like to take out a loan collateralized by my one bitcoin in order to leverage my position.” Banks love collateral, so they’d give the trader a loan, and the trader would make the same trade again. Now the trader has another bitcoin, gets another loan, rinse, lather, repeat. In actual practice, many of the middle steps happen automatically, and the whole process is called “leveraging”.


With bitcoin, this is not so easy. Good luck finding a banker who will make a loan collateralized by bitcoin (i.e., look for a margin account which allows direct bitcoin trading). Even setting aside that issue, a trader would also have to borrow for the futures’ margin requirement. Now, the whole arbitrage together is actually very low risk, so it should be possible in theory to get a loan to do this… but it would require a personal relationship with a banker who understands the nitty-gritty and is willing to dip their toe in untested waters.

Put it all together, and we have a beautiful, persistent arbitrage opportunity limited by liquidity. It will disappear eventually, but it’s going to take time for the bankers to warm up.

Tuesday, December 5, 2017

Lemons, In-Group Signals and Marketing

Professor Quirrell didn't care what your expression looked like, he cared which states of mind made it likely.” - Harry Potter and the Methods of Rationality, chapter 26


Quick, which slogan will yield more sales:
  • “Be smart, buy X!”
  • “Not Your Grandma’s X”
Got a guess? Good, remember it.


This post is going to present some background game theory on signalling, and then talk about what that theory predicts for the slogans above.


The Lemons Game

What can a used car dealer say to convince you it's not a lemon? (image source)

Consider a game with two players: a prospective car buyer, and a seller. The seller begins with either a working car or a broken car - a “lemon” - at random (50% chance for each). The seller knows whether or not the car is a lemon, and considers a working car more valuable. So, for instance, maybe the seller is willing to sell only above $10k if the car is working, but will sell a lemon as low as $5k. On the other side, the buyer is willing to pay up to $12k for a working car, or up to $6k for a lemon.


One little wrinkle: the buyer has no way to check whether or not the car is a lemon before deciding whether to buy. Mechanical problems may not be immediately obvious during a test drive.


What happens?


Well, think it through from the borrower’s perspective. The car has a 50% chance of being a lemon, a priori. Ignoring risk aversion, a buyer would pay $9k for a 50/50 chance of a working car… but at that price, the seller wouldn’t be willing to part with a working car. So if the buyer offers $9k, then she will only end up with either no sale or a lemon! So, the borrower will only bid somewhere between $5k and $6k in the first place - since she’s only going to get lemons anyway, she only offers enough to buy a lemon.


The sad thing is, you may have an honest seller on one side trying to sell a working car for $11k, and a buyer on the other side who would love to buy a working car for $11k… but the deal won’t happen, because there’s no way for the seller to convince the buyer that the car isn’t a lemon. Anything the seller could say which would convince the buyer, a dishonest seller with a lemon could also say.


Cheap Talk vs Signalling
The lemons game illustrates a key concept: even when you let two people communicate freely, it may be impossible to convey relevant information between them.


This problem comes up whenever someone might be motivated to bluff. In the lemon game, a seller with a lemon is motivated to bluff - whatever a seller with a working car might say to sell for $11k, the seller with a lemon will also say in an attempt to get $11k for their lemon. Thus the phrase “cheap talk”: talking can’t actually convey any useful information here.


In the real world, we have various ways around this.


Among the simplest is Carfax: a trusted third party which can tell the buyer whether the car is a lemon. A seller with a working car will happily pay Carfax $50 to certify it. The certified car will then sell somewhere around $11k.


But barring trusted third parties (Carfax isn’t perfect), how else can a seller signal that their car is not a lemon? Remember, the key here is that it must be something which a seller with a lemon could not, or would not, do!


Another simple answer: offer to cover the cost of any mechanical issues for some time after the sale. That would be expensive for lemon-sellers, so they won’t agree to it. Any seller willing to cover mechanical costs must be selling a working car. This is useful, but it creates a new problem: the buyer will be incentivized not to take very good care of the car, since the seller is covering repair costs anyway.


Here’s a more interesting answer: whenever the car needs repairs, the buyer pays for the repairs and then sends the receipt to the seller. The seller takes enough money out of their bank account to cover the repairs, puts the money in a fireplace, and burns it. As before, this is a bad deal for lemon-sellers, so they won’t agree to it. Only sellers with working cars, expecting few mechanical issues, will agree - ideally, this means little or no money will actually need to be burned! What matters is the seller’s willingness to bet on the quality of the car, which signals the car’s quality to the buyer.


Marketing and In-Group Signalling
In the lemons game, the key to effective signalling is that the signal - whether a carfax report, a contract to cover breakdowns, or a contract to burn money in the event of breakdowns - must be very expensive for a lemon-seller, but not very expensive for the seller of a working car. This is critical. Anything which a dishonest lemon-seller could afford to say is cheap talk, and buyers won’t buy cheap talk.


This has interesting implications for in-group signalling.


Suppose I want to signal to my goth friends that I’m in their boat. So, I put on the most over-the-top outfit I can manage, chains and black makeup, the whole shebang - the key being that such an outfit would definitely not fit in any non-goth social circle. (Politics offers better examples, but I don’t want to derail this post.)


If someone wants to signal their membership in a group, then the best way to do that is with something which would be prohibitively expensive for someone outside the group. In these situations, we’re not usually talking about monetary expense. Instead, the “cost” is in social capital with other groups. In other words: the best way to signal membership in an in-group, is to do something which completely ruins one’s chance with the out-group.


Which brings us to marketing.


Truism: it’s better to have 10% of the population 100% interested in your product than to have 100% of the population 10% interested. Nice heuristic, but the model which usually underlies it in practice is in-group signalling. If you can signal that your product is affiliated with some group, then group members will buy your brand religiously. Apple, converse, starbucks… many a household name has made a fortune on this principle. But the all-important key to an in-group product is that it must not target everyone. Like the lemons game, if anyone can send the signal, if the signal is no more expensive for the out-group than for the in-group, then the signal is not a signal at all - it’s just cheap talk. Signals must cost something.


If you want to signal that your product is great for <in-group>, then the best way to do that is to offend <out-group>. The more blatant, the better. “Duck Dynasty” figured this out better than most, and gathered a truly ridiculous following for a show which could generously have been called a non-entity. Part of the key to Starbucks’ success, is all the people who hate it and hate everything a $5 coffee stands for. That’s the beauty of it: offend the out-group’s sensibilities, and you send a strong signal of in-group status. It’s the equivalent of offering to burn money if the car breaks down. (Just make sure to pick an actual in-group first; offending random people is no more useful than randomly burning money!)


Let’s say, hypothetically, you want to get young people to use product X. Easy tagline: “Not Your Grandma’s X”. Conversely, for targeting less-young people, “X for Grownups”, ideally delivered with an ad making fun of teenagers for being idiots (I remember a great Old Spice campaign along these lines). Humans have great intuition for this sort of thing: we see our outgroup mocked, and automatically assume that the mocker is “on our side”.


A few other ideas, to convey the flavor:
  • “Moms love X!”
  • “The X for people who like trucks”
  • “X: for true <sports team> fans only”
Note that these don’t always “offend” the outgroup per se; but they do all but guarantee that nobody in the out-group will ever buy your product. Indeed, the more they discourage out-group members from buying the product, the better they work. Non-moms will almost never buy “X for moms”. By way of contrast, consider a useless slogan like “Be smart, buy X!”. Everyone wants to be smart! Unless your advertising manages to convey a very group-identity-loaded concept of “smart”, enough to actually turn away non-”smart” consumers, it’s going to come off as generic cheap talk and fail to tap into any identity at all.


The takeaway:

  • Signalling should be costly to fake; otherwise it’s just cheap talk.
  • In the case of in-group signalling, the “cost” is usually to push away out-group members.
  • Humans have strong intuition for this stuff.
  • In-group-specific marketing should push away people not in the group.
  • More generally, in marketing, any signal which costs only ad spend dollars will be seen as cheap talk - ad spend is cheap for fakers.