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3) yes, it can

4) but does it?

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

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...

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!

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.

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.

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.

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.

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.

8:15 AM · Apr 22, 2021Twitter Web App

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?

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?

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?

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?

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.

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.

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.

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!

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?

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.