Hull.21.05:

[CarlosB]

Hi, for this question:

21.5b. If the actual volatility exhibits “mean reversion in returns,” (Linda Allen’s phrase) how
does our calculated daily volatility compare to the actual?

Could please someone explain why or better:
21.5b. The square root rule overstates when there is mean reversion in returns (i.e.,
negative autocorrelation). Therefore, the actual daily volatility is greater than (>) 4.89%.

 

[ShaktiRathore]

Hi
Square root rule assumes iid returns that is returns are uncorrelated no autocorrelation at all. If sigma is estimated daily volatility then over next T days volatility just scales to square root of time under SRR so vol(T) under srr is sqrt(T)*sigma. While if we assume mean reversion of returns or negative autocorrelation the volatility over T days is sqrt(sigma^2..T times-2Cov....T(T-1)/2 terms)=sqrt(T*sigma^2-T(T-1)*Cov)<sigma*sqrt(T),thus volatility estimated using negative autocorrelation is less than estimated under srr.
Thanks.