When are Investment Projects in the Same Risk Class?

If two investments have the same payoff covariance with the market but one has higher expected payoff, which asset according to the CAPM has most risk? One answer is that as far as risk goes the two assets are the same, because they have the same covariance with the market. The correct answer, pointed out nearly four decades ago by Eugene Fama, but long overlooked, is that investments have the same risk, the same returns beta and the same CAPM discount rate if and only if they have the same ratio of ex ante payoff covariance to payoff mean. This insight clarifies much of the conventional wisdom that surrounds capital budgeting and "risk adjusted" discount rates, while also displaying the mechanics by which information arrival affects the CAPM cost of capital.