Asset demand and risk Aversion We often talk about their being a risk-return frontier. One useful utility function for showing this is quadratic utility u(x)=x.5Bx2 We use that fact that E(x-E(x)2=E(x2)-(E(x)2 to get that E(u(x)=E(x)-.5B(E(x-E(x)2+(E(x)2)= E(x)-.5B(E(x)2-.5Bar(x) Of course, you've got this problem that X needs to be a lot less than B to avoid utility falling with incomeAsset Demand and Risk Aversion: We often talk about their being a risk-return frontier. One useful utility function for showing this is quadratic utility ux  x . 5x2 We use that fact that Ex  Ex2  Ex2  Ex2 to get that Eux  Ex . 5Ex  Ex2  Ex2  Ex . 5Ex2 . 5Varx Of course, you’ve got this problem that x needs to be a lot less than  to avoid utility falling with income