I denote by $W_0$ and $W_1$ the wealth of an investor at $t=0$ and $t=1$, respectively. Let $r_f$ be the risk free rate, $r$ the vector of returns of the risky assets in excess of the risk free rate, and $w$ the vector of weights of the risky assets. Here is the classical mean-variance optimization problem: $$\max_{w} E(W_1)-\frac{\gamma}{2}Var(W_1)$$ $$\textrm{st.}\hspace{0.5cm} W_1=W_0(1+r_f+w'r)$$
Injecting the constraint into the optimization problem, the first order condition is thus written as follows: $$\frac{1}{\gamma} E(r)=W_0Var(r)w$$
My point is that I would like to end up with the classical mean-variance first-order condition: $$\frac{1}{\gamma} E(r)=Var(r)w$$
But I still have this $W_0$ in the equation... Did I miss something? Could someone please help me? Thanks