Ok so for completeness, assuming Black-Scholes and an example portfolio of 100 long $C_1$, 100 long $C_2$ (both on the same underlying), and 10 shares of the same underlying, $S$. **Portfolio delta:** $$\frac{\partial}{\partial S} (100C_1 + 100C_2 + 10S) = 100\frac{\partial C_1}{\partial S} + 100\frac{\partial C_2}{\partial S} + 10\frac{\partial S}{\partial S}$$ Where $10\frac{\partial S}{\partial S}$ term is 10. **Portfolio gamma:** $$\frac{\partial^2}{\partial S^{2}} (100C_1 + 100C_2 + 10S) = 100\frac{\partial^2 C_1}{\partial S^2} + 100\frac{\partial^2 C_2}{\partial S^2} + 10\frac{\partial^2 S}{\partial S^2}$$ Where $10\frac{\partial^2 S}{\partial S^2}$ term is 10 **Portfolio theta:** $$-\frac{\partial}{\partial \tau} (100C_1 + 100C_2 + 10S) = -100\frac{\partial C_1}{\partial \tau} - 100\frac{\partial C_2}{\partial \tau} - 10\frac{\partial S}{\partial \tau}$$ Where $10\frac{\partial S}{\partial \tau}$ term is 0 **Portfolio vega:** $$\frac{\partial}{\partial \sigma} (100C_1 + 100C_2 + 10S) = 100\frac{\partial C_1}{\partial \sigma} + 100\frac{\partial C_2}{\partial \sigma} + 10\frac{\partial S}{\partial \sigma}$$ The $10\frac{\partial S}{\partial \sigma}$ term is 0. **Portfolio rho:** $$\frac{\partial}{\partial r} (100C_1 + 100C_2 + 10S) = 100\frac{\partial C_1}{\partial r} + 100\frac{\partial C_2}{\partial r} + 10\frac{\partial S}{\partial r}$$ The $10\frac{\partial S}{\partial r}$ term is 0. Note this assumes the options are on the same underlying. This is important because the partials assume a small (or at least constant) change in the underlying across the portfolio. If $C_1$ and $C_2$ were on different underlyings, we cannot necessarily assume that a small change in the underlying of $C_1$ will be the same small change in the underlying of $C_2$