I throw the term "expected value" (EV for short) around a lot. What is it, and, more important, why is it the thing that matters?

A thread about the median and the mean.
Let's step back from trading and focus on an idealized situation which is sorta like trading. Say you've got $10 and all you're allowed to do with it is pay $10 to flip a coin which comes up heads 55% of the time, and you win $20 when it does. You can play as much as you want.
The *expected value* (EV) of each flip is

-$10 (cost of playing) + $.55 * 20 = $1

Meaning that each time you play, you're expected to make $1. Pretty good!
You've just got $10, though, and maybe you need to make sure you can buy lunch today, so you *really* don't wanna lose all of it. It's possible to imagine a reasonable utility function which *really* wants lunch and so doesn't want to play this game, even though it's +EV.
Adjusting EV for risk is often a reasonable thing to do, especially when the risks you're taking are high relative to how much $ you have, or if losing would be especially bad for some reason.

This is the source of advice like "don't bet more than you can afford to lose."
This is why, for instance, the insurance industry can succeed. Paying for insurance on your house is -EV -- on average, people pay more than the insurance company ever spends fixing houses. But for most, losing their house would be a giant setback.
Really what's happening here is -- people's utility curves are not linear.

(Something something Kelly Criterion, not re-opening that can of worms, suffice to say many people can rationally discount EV for risk, see below for why Alameda doesn't really.)
In simple terms: how much value does your first $1m give you, as compared to your 10th? Your 100th?

For most people who are just optimizing for their own happiness, utility is *definitely* sub-linear at some point -- $0 -> $1m is great, $99m -> $100m barely matters.
Why doesn't Alameda really have to do this? There are a few reasons.

Day-to-day, the big one is that we have a ton of capital, and it's legit just quite rare that losing a potential bet would cause us real harm.
Using the coin flip analogy, we've got $10000 instead of $10, and we can freely play the game as much as we want without having substantial risk of ruin. It's powerful, and increases our aggregate EV (per time unit since technically the EV is unbounded) since we can't go to $0.
Markets rarely have sufficient liquidity such that our bet sizing is limited by our capital base -- much more often they're limited by how much we can put on without having giant price impact. The only things we can't do because of capital are like, buy half the ETH that exists.
This is powerful! It lets us maximize short-term EV almost all the time, assuming we are trying to maximize overall EV longer-term. And we *are* trying to do that -- @SBF_Alameda has talked extensively about the altruistic goals Alameda operates with.
(This is as opposed to, e.g., a trading firm where everyone's trying to make $15m and then retire -- which exists! and can be true for some Alameda traders -- but which is not true generally for the collective.)
Understanding that our best move is to try to directly maximize EV almost all the time makes a lot of decisions clearer; here are just a few examples, but this is the philosophy underpinning basically every post I have ever made:
Let's say that ca. January, we expect DOGE to move over the next weeks/whatever according to this distribution:
- 10%: up 1000% because Elon keeps going crazy
- 90%: down 75% because he doesn't
This makes the EV

.1 * 1000% + .9 * -75% = +32.5%

So: you're supposed to buy a TON, even though you'll USUALLY lose a lot.

(And, FWIW, I think 10% was a massive under-estimate, but whatever, "not zero" matters most.)
Being EV-maximizing and not having to care about median (etc.) outcomes means we get to do this for big size -- we knew we'd most likely lose, but making 100 similar bets would come out way ahead.

And results aren't the important thing, but ...
Crypto exchanges are known for having these weird errant prints -- so-called "wicks." If you can manage to be on the good side of these wicks, you can actually make a good amount of money!

But should you?
A "typical" giant wick is for something like 50% edge. There are a few per day, on average, and a total of 1000 or so important / liquid markets -- so say that this happens on 1/500 of big markets per day.
Let's say your capital would make .15%/day not tied up (from other trading, or yield farming, or whatever -- you have a better idea of this for your personal strategies). This makes your EV from trying to catch the wick

.002 * 50% + .998 * -.15% = .05%/day -- a loss!
Of course 1/500 is just a guess, and 50% might not be optimal -- it's possible some market dynamics *do* make this worthwhile. But it's not quite as simple as "no-risk way to maybe make a lot" because of opportunity cost.
A personal example: should I abandon my high-paying but safe job to pursue crypto trading?

This choice was easy: I made as much as my "tradfi" bonus in a few weeks trading BTC arbs, and that was that :P "EV" isn't even the word, I demonstrated the value was higher from leaving.
And eventually I joined Alameda because the upside was really just WAY too high working on these things with the best team I'd ever seen - I could run the EV numbers from back then but they're "large."
Most people (young, far from retirement, etc.) have the same kind of luxury we do (on a smaller scale). It's generally way more OK to lose all your $ when you're young than people realize, and I recommend carefully inspecting whether not doing so is capping your potential.
And maximizing EV -- while still quite hard -- is at least an elegant framework to be able to use. It's still important to not let yourself get screwed, but in general betting super big and trying to maximize your expected value is right more often than people think.

Try it!

• • •

Missing some Tweet in this thread? You can try to force a refresh

Keep Current with Sam Trabucco

Sam Trabucco Profile picture

Stay in touch and get notified when new unrolls are available from this author!

Read all threads

This Thread may be Removed Anytime!


Twitter may remove this content at anytime! Save it as PDF for later use!

Try unrolling a thread yourself!

how to unroll video
  1. Follow @ThreadReaderApp to mention us!

  2. From a Twitter thread mention us with a keyword "unroll"
@threadreaderapp unroll

Practice here first or read more on our help page!

More from @AlamedaTrabucco

28 Apr
I often talk here about decisions I/Alameda made that went well. Sometimes people ask for examples of the opposite -- times when I made a mistake and lost a lot, or even times I lost a lot by doing the right thing. Both happen a lot!

A thread about melted wings.
Alameda uses "March 12" in a Voldemort-like way -- it invokes dread like not much else, and it comes up a lot in mean vs. median discussions ("sure this usually works but it loses $5m on March 12," etc.)

Before March 12, though, there was another Terrible Day: September 25.
September 25, 2019 was -- at the time -- the scariest day I'd ever had trading, and I think it was maybe Alameda's worst potential vs. realized PNL day ever (we *could* have made a TON -- we, uh, didn't).
Read 21 tweets
22 Apr
2 years ago, Alameda maintained pretty strict delta neutrality most of the time, generally trying quite hard to make sure our PNL was from spreads and arbs. Today, not so much -- we got ... uh, really long in winter 2020, for instance. What changed?

A thread about super powers.
Let's back up a little: why does Alameda trade crypto? Why don't we do something else, like equities options trading? Or sports betting? Or competitive Scrabble?

(Incidentally, these are all things various team members have done or still do :P)
The basic answer: it's where the money is. We could make a bunch of sports betting models -- likely some of the world's best! -- but the money in crypto just makes it better. And sadly (for me), the money in competitive Scrabble is nothing to write home about.
Read 27 tweets
18 Apr
Haven't done one of these in a while: what happened in the crypto markets today?

A thread about the past and the future.
For the past week or so, crypto has been on a tear. It's risen slowly but steadily from the mid-$50s to new highs over $65k, seemingly without a ton of fanfare. Amidst excitement over the COIN direct listing, parts of this seemed almost inevitable.
The COIN listing came and went. And it's hard to say that it was anything but a pretty big disappointment vs. the market's hopes (and, certainly, amidst the market's hype-driven rally).

Read 25 tweets
14 Apr
So far, auction indications have been a bit lower than I think the market was expecting (e.g. where it was trading on FTX earlier).

On FTX, it's fallen to close to that indic price:
The crypto market is reacting broadly basically how I thought -- the world is all watching this, the world all expects BTC to be correlated to COIN right now (since Coinbase's success is seen as something of a proxy for success of BTC in the US), so crypto is crashing.
And the worst performers of all? The likes of BNB and other exchange tokens, who are seen as *especially* correlated with COIN and Coinbase more generally. When the indics first started crashing, BNB *really* underperformed -- it's recovered some but not totally vs. BTC.
Read 4 tweets
14 Apr
Heading into Coinbase's hotly anticipated listing, markets have been volatile, and there's been a lot of great trading to do if you know where to look.

Honestly, the trading has seemed almost ... *too* great? And pretty easy to predict.

A thread about efficiency.
Let me first discuss this notion more generally -- efficiency. A market is called *efficient* if prices in the market consistently reflect some true fair value, based on all possible data at the time -- trade history, blockchain data, news, etc.

How efficient are crypto markets?
This shouldn't be a *giant* surprise, but the answer is: not really :P

A priori this might not be totally clear, but we've seen time and again the markets just not move in the obvious direction for what seems like an eternity:
Read 25 tweets
12 Mar
March 12, 2020 was the hardest* day** of my life. A year later, it sticks out more clearly as the most interesting situation I've ever been faced with -- and one from which I've learned a ton. Here are a few lessons I learned directly from March 12:
*tied with the time in 9th grade when I was forced to play on a baseball team and managed to strike out vs. a pitcher who walked everyone else and would have walked me 4-0 if I had not swung once

**really the 3ish days around then, but it felt like a month so IDK

Pre-COVID, crypto was its own thing. Mostly divorced from the traditional markets, BTC (for instance) really did not have a beta to SPY, for instance -- it was totally its own thing.
Read 32 tweets

Did Thread Reader help you today?

Support us! We are indie developers!

This site is made by just two indie developers on a laptop doing marketing, support and development! Read more about the story.

Become a Premium Member ($3/month or $30/year) and get exclusive features!

Become Premium

Too expensive? Make a small donation by buying us coffee ($5) or help with server cost ($10)

Donate via Paypal Become our Patreon

Thank you for your support!

Follow Us on Twitter!