Mayers and Rice conjecture that an investor with better information will on average plot above the security market line as drawn by uninformed investors. This paper demonstrates that this conjecture is false in general, by constructing a counterexample. However, the Mayers-Rice conjecture is really part of a much broader hypothesis concerning whether increases in expected returns correspond to increases in expected utilities. It is shown that this latter hypothesis is true when the investor has an exponential or logarithmic utility function.