where So is the price of the security at the time the hedge is created. The
quantity V satisfies the Black-Scholes equation since C and S separately
do, and the equation is linear. Thus it reasonable to contemplate Delta for
the portfolio. The partial derivative of the entire portfolio with respect to
S represents the sensitivity of the value of the portfolio to changes in S.
Differentiating both sides of Eq. (9.1) with respect to S produces