A thread about tails -- or, bullshitting about things that no one can really know for sure. https://twitter.com/python_trade/status/1329057120160014339?s=20

Something you’ll hear people talk about in trading a lot is “tails.” What are they, and why do they matter so much? To discuss, I think it’s worth delving into some examples, and why they often come down to making your best guesses about things it’s basically impossible to know.

Technically, tails refer to the sections of a distribution graph that are off to the sides -- see the attached graphs. A distribution is called “fat-tailed” if it’s relatively “flat” -- that is, if the probability one of its outcomes is far from the mean is relatively high.

An example of a fat-tailed distribution might be a uniform one -- that is, where the chances of any event are equally likely. Of course the tails here are “fat” (compared to, say, a normal distribution) because they’re just as likely as the mean!

On the other hand, an extreme version of a “skinny-tailed” distribution might be a constant distribution -- that is, one where there’s actually just one possible value. Those tails don’t even exist.

This comes up in real life a lot -- insurance is a viable business because some combination of: people are bad at estimating tails for many events (losing a house in a fire, e.g.) and so overpay for it, and others can't afford the total loss, so willingly overpay.

And in finance you see it too -- super out of the money options will often trade at really high premia, exactly because people actually *over-estimate* the probability of an idiosyncratic big move, in a very “it’ll happen or it won’t so it’s 50/50” way.

So, why does all this matter for crypto trading? It turns out that evaluating tails properly has HUGE implications for the expected value of all kinds of trades. Some examples:

Let’s say two identical (or nearly so) products are trading at different prices -- maybe two BTC futures with really similar indices are trading 15bp apart and expiring in a week. How good is this trade?

Well, depends on how much you can lever up -- let’s evaluate how good it is with different leverages. If you can put the spread on for 5x your collateral on each account, you’re making 5 * 15bp / 7 = 11bp/day on your capital. Not bad, by many metrics!

But this is not *actually* riskless -- because if BTC moves enough that one of the accounts gets liquidated (let’s pretend this would need to be a 10% move, for now -- the exact amount depends on a few factors, and also on which exchanges we’re talking about). How likely is that?

Depends! This is equivalent to the question of “how big are the tails in BTC’s distribution over the next week.” You could look at previous weeks to make a guess, but maybe you expect the next week to be more or less volatile than typical.

You could look at options to determine what the market thinks about this week’s tails, but then you’d also want to look at how accurately-priced *those* have been in the past. And even still, maybe this week is weird somehow! It’s hard to ever know.

Let’s say you lose 5% in total on the trade if one of the legs gets liquidated (the loss depends on lots of things -- liquidity if this happens, how much capital it is, etc.). If it has a 5% chance to occur, your EV is now .95 * 75bp +.05 * -500bp = 46bp, or about 6.5bp/day.

A good amount worse! And replace 5% with 15%, and suddenly you’re *losing* money in EV -- and both of those seem plausible to me depending on different market conditions! So you can see that getting tails right can have HUGE implications for what spreads are good.

(Also, insert something about 100x leverage being almost always bad because then your tails are like, 95% of the relevant distribution and you’re just gonna get liquidated almost every time :P).

How about: I recognize that some product has a ton of prints REALLY far from BBO, let’s say because of giant liquidations that happen from time to time when the market moves a lot. I want to place big scales far from BBO to try and scoop those up. Seems good?!?

Maybe! Let’s say you’re placing these scales 1.5% away from BBO, and those scales are gonna get hit once a month or so, and each time the product will get back into line within a few minutes. If you can lever this up 5x, you’re gonna make 150bp / 30 * 5 = 25bp/day from this.

Seems great in EV! But if this is happening -- isn’t it possible that there are sometimes *really* errant prints? What if I get filled 1.5% away but the liquidations drive the price even further away right away? Might *you* get liquidated?

Let’s say that it needs to move an additional 10% for that to happen (as usual, this depends on actual platform specifics). If this does happen, you’re gonna end up losing 10% or so (since the product will get back in line) -- more, since you get liquidated at a *worse* price.

If that has a 3% chance to happen each time you get filled, suddenly your EV from the trade is 5 * (.97 * 1.5% + .03 * -12% (or so)) = 5%/month = 17bp/day. Still quite good!

But if it’s actually 15% and not 3%? Suddenly this trade is a loser, just like the other one. And you’re only getting one data point per month, so how can you make a good decision here?! It’ll pretty much all depend on intuition, and rational people can differ.

(This is similar to something Alameda has done in the past, and the real numbers at play *did* in fact make it such that two traders’ estimates for the tails made the decision for what size / BBO distance to do it for really different -- we still don’t know what was right!)

Now, why did I write this as a RT of a question about TRUMPFEB? Well, pricing TRUMPFEB correctly is *exactly* an application of these concepts -- Trump being president in February seems to represent a tail event, one which is pretty unlikely, but like, who knows HOW unlikely.

If you told me two experts believed the chances were 1% and 30%, I don’t think I’d be especially *shocked*. Certainly you can find plenty of people on the internet who believe the chances are either 0% or 100% -- I think both of those are certainly wrong and colored by bias.

But between 1% and 30%? I couldn’t tell you for sure which is a “better” guess. I (and Alameda) have thoughts on this, of course -- we are in the business of trying to estimate tails, and we think we’ve learned a lot about that from the crypto trading we do all the time.

But we’re never *sure* we’re right, and we’re not *sure* about TRUMPFEB, either. Looking into precedent, asking legal and political experts, trying to construct narratives around how likely even people like the Trump team thinks they are to win -- all valid heuristics.

As important as getting good at estimating tails is getting good at knowing when to be super confident about tails -- most people are WAY too confident about them, and I’d recommend all the 0% and 100% people on this one could benefit from a little sanity-checking.