Read on Twitter
1/ Having lots of fun convos in the DM’s about positioning of systematic players (and how that positioning changes w.r.t. spot, realized volatility, and time).
I think an important equation to keep in mind is:
dL/dV = -T / V^2
I think an important equation to keep in mind is:
dL/dV = -T / V^2
2/ If we assume leverage (L) is simply equal to target volatility (T) divided by realized volatility (V) (i.e. L = T / V), then we find that the change in leverage w.r.t changes in volatility is equal to the equation above.
3/ What does this mean?
Since T is pretty much constant, it tells us that leverage changes (i.e. buying / selling pressure) will be due to changes in realized volatility (duh).
Since T is pretty much constant, it tells us that leverage changes (i.e. buying / selling pressure) will be due to changes in realized volatility (duh).
4/ But I think the important point is to consider how that sensitivity changes as a function of the realized volatility level.
For a target volatility of 12%, if V=10%, then for every 1% change in realized volatility, leverage will change by 12%.
At V=25%, it’s 1.92%.
For a target volatility of 12%, if V=10%, then for every 1% change in realized volatility, leverage will change by 12%.
At V=25%, it’s 1.92%.
5/ So as volatility goes up, the leverage in these strategies becomes desensitized to smaller changes in volatility.
6/ Consider a simple S&P 500 target volatility index. Today, realized vol is ~21.6%.
That tells me the sensitivity is -2.55% for a 1% change in realized volatility.
That tells me the sensitivity is -2.55% for a 1% change in realized volatility.
7/ For buying/selling pressure, we care about how the leverage changes.
For a 12% target vol strategy, once realized vol is north of 25%, there isn’t a lot of change happening.
Rapid change is in the 5-to-20% region.
For a 12% target vol strategy, once realized vol is north of 25%, there isn’t a lot of change happening.
Rapid change is in the 5-to-20% region.
8/ Now, if short-term realized volatility quadruples from here back to March levels we will certainly see meaningful de-risking.
But realized volatility starts to slide down from 20% to 15% to 10% would to some really meaningful re-risking as well.
But realized volatility starts to slide down from 20% to 15% to 10% would to some really meaningful re-risking as well.
9/ This obviously gets more complicated when you start talking about multi-asset strategies (where there are correlation considerations), but the overall point remains:
As realized volatility goes up, sensitivity to changes in volatility goes down.
FIN.
As realized volatility goes up, sensitivity to changes in volatility goes down.
FIN.
