About 17 and the EMH. Can’t Scott be just thinking that ETH is sufficiently more risky than BTC so it may have higher expected returns even with the EMH (the EMH allows this, right?). Or even that he might think ETH has some chance of total collapse (like an outlier at 0) so even with equal expected returns it’s much more probable that ETH outperforms BTC than the other way around (?)
Actually this is the other way around. If ETH is less risky than BTC then the median performance of ETH will outperform BTC and his probability could be consistent with EMH
This is neither consistent with historical realised volatility (ETH is more volatile than BTC), nor is it consistent with the options market (ETH implied vols are all higher than the equivalent moneyness BTC implied vols)
If ETH is less risky than BTC then the median performance of ETH will outperform BTC and his probability could be consistent with EMH
Wait. Does this mean that EMH expects less risky investments to have higher performance on average? That sounds shocking enough that I must be confusing something here. Or is this some sort of median vs mean distinction that I’m not seeing
If we’re interested in r = 0 (outperformance of current price) then as vol increases, the probability goes down.
(There’s actually quite a bit of intuitive stuff which drops out of this model (if we’re required to hit a given r, then increasing volatility makes it easier (up until vol = sqrt(2*r)))
So to recap, I was right in that riskier assets can have higher avg returns, but I was missing the usually bigger and opposing effect where as the assets gets riskier, the same avg returns rely more and more on lucky very big gains while doing worse more often (at least if they are sort of lognormal).
My second point I still think was correct, right? -- i.e., that if Scott believed ETH had some chance of total collapse (a mixture distribution), then this skews it to the other side and pushes the median below the mean, and gives some reason to think ETH is more likely to outperform BTC. Does this make sense?
It is possible that Scott believed that ETH is negatively-skewed (ie small chance of collapsing, large chance of small increase) but this would be inconsistent with his probability that ETH is going to 5k.
I think the vast majority of people think crypto is positively-skewed.
About 17 and the EMH. Can’t Scott be just thinking that ETH is sufficiently more risky than BTC so it may have higher expected returns even with the EMH (the EMH allows this, right?). Or even that he might think ETH has some chance of total collapse (like an outlier at 0) so even with equal expected returns it’s much more probable that ETH outperforms BTC than the other way around (?)
Actually this is the other way around. If ETH is less risky than BTC then the median performance of ETH will outperform BTC and his probability could be consistent with EMH
This is neither consistent with historical realised volatility (ETH is more volatile than BTC), nor is it consistent with the options market (ETH implied vols are all higher than the equivalent moneyness BTC implied vols)
Wait. Does this mean that EMH expects less risky investments to have higher performance on average? That sounds shocking enough that I must be confusing something here. Or is this some sort of median vs mean distinction that I’m not seeing
?
tl;dr “some sort of median vs mean distinction”
No, there’s two things going on which act against each other:
Riskier assets have higher returns on average
Riskier assets are more skewed (mean higher than median)
I’ve made the (I think safe) assumption that the skewness of the assets are more important than the relative differences in their expected return.
You can have a play with some toy models for this, for example, fixed Sharpe, lognormal assets you will have something which looks like:
log(X) ~ N(sharpe * vol—vol^2/2, vol)
P(return larger than r) = P( Z*vol + (sharpe*vol—vol^2/2) > r) = P(Z > (-sharpe + vol/2 + r/vol))
If we’re interested in r = 0 (outperformance of current price) then as vol increases, the probability goes down.
(There’s actually quite a bit of intuitive stuff which drops out of this model (if we’re required to hit a given r, then increasing volatility makes it easier (up until vol = sqrt(2*r)))
Niice, it makes sense! Thanks!
So to recap, I was right in that riskier assets can have higher avg returns, but I was missing the usually bigger and opposing effect where as the assets gets riskier, the same avg returns rely more and more on lucky very big gains while doing worse more often (at least if they are sort of lognormal).
My second point I still think was correct, right? -- i.e., that if Scott believed ETH had some chance of total collapse (a mixture distribution), then this skews it to the other side and pushes the median below the mean, and gives some reason to think ETH is more likely to outperform BTC. Does this make sense?
It is possible that Scott believed that ETH is negatively-skewed (ie small chance of collapsing, large chance of small increase) but this would be inconsistent with his probability that ETH is going to 5k.
I think the vast majority of people think crypto is positively-skewed.
Right! My untrained intuition still resists a bit; I should play with the numbers.