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SBF
@SBF_FTX
Replying to
@SBF_FTX
3) Let's pretend that EUR, GBP, and USD all had 0 interest rates and you didn't have opinions on any of them. Let's also pretend they are all worth they same now. Then you see contracts for EUR/GBP and GBP/EUR, where you can trade one for the other. They settle in 10 years.
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SBF
@SBF_FTX
4) What should you do--buy/sell/neither? Well, what's the expected value (EV), or mean outcome, of EUR/GBP? By (3), the EV of EUR, GBP, and USD is all that they won't move on average. so EV of EUR/USD is $1 and EV of GBP/USD is $1.
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SBF
@SBF_FTX
5) This would make it seem like EV of GBP/EUR and EV of EUR/GBP are also 1. But is that _really_ true?
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SBF
@SBF_FTX
6) Well, let's say that GBP hyperinflates and goes away. Maybe the UK adopts EUR. Sure, it's unlikely. But if it happened, then EUR/GBP = ....infinity? Even if the odds are only 0.01% of this, EV of EUR/GBP = infinity! Even though EUR=GBP=EV of EUR = EV of GBP = 1.
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SBF
@SBF_FTX
7) Whoa. So I guess you should buy a lot of EUR/GBP, even though GBP's EV is just as high as EUR's. Except: what if the EU gets rid of EUR with 0.01% chance? Then EV of GBP/EUR = infinity!
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SBF
@SBF_FTX
8) In fact, even though right now EUR = GBP, EV of EUR/GBP and EV of GBP/EUR could both be > 1! So does that mean you should... sell all your GBP for EUR, and then also sell all your EUR for GBP? Obviously not, somehow.
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SBF
@SBF_FTX
9) Ok, here's what's _really_ going on. The world isn't measured in EUR or GBP or even USD. It's measured in Bread, and Houses, and Teddy Bears. Let's just stick with bread for now.
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SBF
@SBF_FTX
10) If GBP --> 0 then EUR/GBP --> infinity. But that doesn't mean buying EUR/GBP is that great! EUR/bread -- the amount of amount of bread you can get per EUR -- is still like 1 loaf per euro, even if GBP --> 0. EUR goes to infinite GBP, each GBP being worth 0 bread.
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SBF
@SBF_FTX
11) So, in fact: EV of GBP/EUR > 1, EV of EUR/GBP > 1 BUT, neither buying GBP nor buying EUR is particularly good. The EV isn't in the numerator--it's in the denominator, and the nonlinearity of it.
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SBF
@SBF_FTX
Replying to
@SBF_FTX
14) So even if you don't have views on ETH, USD, or BTC, EV of ETH/USD * BTC > current value! So the BitMEX contract should trade at a premium, and in fact it does. It's called a quanto contract.
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