Optimal Hedge Ratio, h

[Falak Soomro]

I have a question regarding optimal hedge ratio, as stated on pg 28, ST5-C11:

h = rho * sigma_s/sigma_f
where :
sigma_s is the change in spot prices over the life of the hedge
sigma_f is the change in future price over the life of the hedge
rho is the correlation coefficient between sigma_s and sigma_f

The change in spot prices and the future price is S_T - S_t and F_T - F_t

We know the S_t and F_t from the market, but how do we know S_T and F_T.

Are these are estimates calculated by some other way? If so, the optimal hedge ratio is prospectively estimated.

If we wait until the life of the hedge expires, optimal hedge ratio would be calculated prospectively, which would be useless to know in order to protect your position of portfolio.

Can anyone be kind enough to clarify?

Regards and good luck for exam!

 

[Simon James]

sigma_s is the change in spot prices over the life of the hedge
sigma_f is the change in future price over the life of the hedge

You are right we must use an estimate of the expected volatility (as we can't know the actual). The "over the life of the hedge" refers to the duration - ie for a three month contract we should use the 3mo volatility.

 

[Falak Soomro]

You are right we must use an estimate of the expected volatility (as we can't know the actual). The "over the life of the hedge" refers to the duration - ie for a three month contract we should use the 3mo volatility.

Many thanks for clarification James!

 

[him27jan]

Equity sigma can be calculated from implied volatility in option prices whereas futures sigma can be calculated from historical data.

Cheers!