How to compute the intersection point of the indifference curve and the cml curve?

How to compute the intersection point of the indifference curve and the cml curve?

The utility indifference curve's function is: U=Annu_rf +y.*(Annu_ret_pf-Annu_rf )-0.5*A*y.^2*Annuvola_pf ^2

The cml curve's function is: cml = Annu_rf + ((orpReturn - Annu_rf) / orpVola) * cmlVola;

Answer 1

[Matt J]

You've negelected to tell us what the independent variable is. If I assume it is Annu_rf, then one way would be,

U=@(Annu_rf) Annu_rf +y.*(Annu_ret_pf-Annu_rf )-0.5*A*y.^2*Annuvola_pf ^2;

cml = @(Annu_rf) Annu_rf + ((orpReturn - Annu_rf) / orpVola) * cmlVola;  

intersection = fzero(@(x)  U(x)-xml(x)  , something)