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SBF
@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
13) Since ETH and BTC are correlated, if ETH goes up then longs make money but also the contract is worth more (because BTC is probably up). And if ETH goes down longs lose money, but the contract is worth less (because 0.0024 BTC is worth less, probably).
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SBF
@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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