This paper corrects errors in two earlier attempts in this journal [Ha
wawini (1986) and Sun (1990)] to analyze a simple portfolio model geom
etrically. It also points out that the general approach taken by these
authors has serious shortcomings. For example, an unmodified use of t
heir technique does not permit one to derive the result that optimal r
isky investment is inversely related to risk if the utility function i
s quadratic.