In the above section, it states the following:
"Comparing equation (3.5) with equation (3.3), we see that they imply h hat = beta. This is not surprising. The hedge ratio h hat is the slope of the best-fit line when percentage one day changes in the portfolio are regressed against percentage one-day changes in the futures price of the index. Beta is the slope of the best-fit line when the return from the portfolio is regressed against the return for the index."
I think there is a subtle point here.
- h hat is change in portfolio (to be hedged) against change in future price.
- beta is change in portfolio (to be hedged) against change in index value (change in spot index price instead of future price).