macrocephalopod

The chart shows ES futures volatility 2013-now measured using 24 hour periods starting/ending at the indicated time. If there was no time of day effect this would be a flat line, in reality the close-to-close return is two percentage points higher than e.g. the 1pm-to-1pm return

The reason is huge flows around the close that distort the price away from fair value *despite* the additional liquidity available at this time (e.g. market-on-close orders and yes, maybe even dealer option hedging....)

The dumbest possible model for this is to write the observed price P(t) as the sum of a fair price F(t) and a random noise E(t) that represents excess demand at the close on day t

This model predicts that the variance of close-to-close returns is larger than the variance of "fair value" returns by 2 * Var(E) -- if we assume the difference between the 1pm-1pm and close-close returns is entirely due to this effect (it's not) than it implies

that Var(E) = (0.17^2 - 0.15^2)/2, which is the same as saying that the daily standard deviation of E is ~35 basis points, which is absolutely huge (it's smaller than this in reality but still pretty big -- and potentially tradable?)

Another prediction of this really dumb model is that the close-close return on day t should be negatively correlated with close-close return on day t+1, which is something that we observe -- subsequent day returns have a correlation of about -0.07

There is lots work to do to turn this observation into something that you could use in your modelling/trading but hopefully it illustrates the power of (a) looking at the data in weird and unintuitive ways (b) coming up with simple models to see what their implications are. Fin.

I'm not sure who will find this interesting but maybe @NewRiverInvest @nope_its_lily @mark_dow @jam_croissant @SqueezeMetrics @QuantSymplectic @spotgamma @choffstein @alphaarchitect