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4) but does it?

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5) Well, in general, the answer is "meh". Say that the S&P500 had momentum: that is to say, if it went up yesterday, it'll go up today on average. Let that "beta" from historical returns to future returns be x%. I.e., if it was up 20% last year, you'd predict +20%*x% next year

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6) How big could x reasonably be? Well say x=80%. The S&P was up ~16% in 2020. That would predict +13% in 2021. So if you could borrow USD @ << 13% and use it to buy S&P, that would be a good trade. Well, ignoring risk...

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7) But the real risk here isn't that huge. S&P volatility is about 15-20%. If you could borrow USD @ 1%, make 16% in EV, and have a risk standard deviation of 15%, then... your mean outcome is +12%, your stdev is 15% (per year). That's pretty good for just being long!

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8) But, inflation adjust it, etc. If there really were 80% beta/correlation, *lots* of people should borrow USD to get longer S&P. People do buy stocks! But not *that* much. And USD borrows are pretty cheap on wall st right now.

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9) There's a limit here. That beta *can't* be 500%, or else the world would expect +80% this year and everyone would get leveraged long borrowing cheap USD, until it had already realized that gain.

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10) But it's way more extreme on a day timescale. If the day-to-day beta was 80%, then after a 1% up-day, you'd expect 0.80% price increases the *next* day. That's insane! *everyone* on wall st would get as long the S&P as they could if that were true. 0.80%/day ~ 300%/year.

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11) So prices would immediately jump +0.80% without waiting. Ok, but what if I claimed the day-to-day (D2D) beta was 1.2%. If the S&P was up 1% yesterday, that would imply +0.012% today. that's...... possible.

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12) If lots of smart quants knew that the S&P was expected to go up 0.012% in the next day, they could... well they couldn't really do all that much. _maybe_ they could pay 0.003% to borrow USD and buy $100m of S&P, moving it 0.012%, making 0.0045% on the average buy, or $4.5k.

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13) Could an inefficiency of $4.5k per day for wall st last? Yup! No real reason to think the industry would compete it away to that precision.

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14) Ok, so we know momentum can't be 80% day-to-day for S&P, and it *could* be 1.2% (or -1.2%--maybe there's mean reversion, who knows!). 3% beta D2D is more iffy: a 0.03% price prediction is actionable on the S&P! So that's roughly the cutoff. ....How about crypto?

8:15 AM · Apr 22, 2021Twitter Web App

Replying to

15) Lots of people seem to believe in momentum in crypto. What is a "bull market" if not the expectation that positive returns yesterday predict positive returns today?

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16) How bullish could the market really be? Well, BTC moves about 3%/day. (D2D) beta of 1 --> 3% price predictions; beta of 1% --> 0.03% predictions. What's plausible?

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17) If the beta were 10, then you'd expect BTC to go down 24% tomorrow, and everyone would short the shit out of it. So that's not plausible. How do we find the line here?

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18) Well, how expensive is it to trade crypto? Getting 100% long is close to free. But sure, lots of people already are 100% long. How about 200%? That varies! But during "bull markets", USD borrows often trade at ~100% interest annualized, or 0.30%/day. Same with perps.

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19) So, if predicted price increases were 1%/day, you could make money getting margin long. If they were 0.10% per day, you might not be able to. The breakeven is around 0.30%/day. With ~3%/day vol, that means 10% D2D beta: if BTC is up 1% today you'd expect 0.10% tomorrow.

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20) To be clear that doesn't mean there *is* momentum. But there could be! There could be up to ~10% daily momentum (or mean reversion!) in BTC without implying everyone should be leveraged long.

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21) How about annual? Annual BTC vol ~50%. But interest rates are often > 50%, so even betas above 1 are possible from last year --> this year during bull markets!

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22) Anyway, what prompted this was a bunch of tweets that were bullish, because of momentum, on ETH and SOL. And I was wondering--is that possible? Or is that saying everyone else is crazy not to buy more?

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23) Well maybe everyone is crazy! But if they move ~5%/day and borrow rates/perps are often 0.30%/day, you could imagine a D2D beta of up to ~0.2 or so without being too crazy. Which would mean if they were up 3% yesterday, you could have a model predict + (or -!) 0.6% today.

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24) And again--this isn't to say momentum *does* exist. Instead maybe things mean revert, or maybe there isn't any of either! But day-to-day betas of up to +-0.1 in BTC and +-0.2 in alts aren't out of the question. (Fixed typo from 1 --> 0.1)

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