Which of the following statement(s) is(are) false regarding the selection of a portfolio from those that lie on the capital allocation line?

(I) Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more risk-averse investors.

(II) More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors.

(III) Investors choose the portfolio that maximizes their expected utility.