Solution
= Solution
Differentiate expected utility at the optimum $X_0$ in each portfolio direction:
$$
0=E[U'(X_0)(S_1-(1+r)S_0)].
$$
Rearranging gives the claimed <vector> identity.
= Solution
Differentiate expected utility at the optimum $X_0$ in each portfolio direction:
$$
0=E[U'(X_0)(S_1-(1+r)S_0)].
$$
Rearranging gives the claimed <vector> identity.