n sum our results support the important testable implications of the two- parameter model. Given that the market portfolio is efficient-or, more specifically, given that our proxy for the market portfolio is at least ap- proximately efficient-we cannot reject the hypothesis that average returns on hTew York Stock Exchange common stocks reflect the attempts of risk- averse investors to hold efficient portfolios. Specifically, on average there seems to be a positive tradeoff between return and risk, with risk mea- sured from the portfolio viewpoint. In addition, although there are "sto- chastic nonlinearities" from period to period, we cannot reject the hy- pothesis that on average their effects are zero and unpredictably different from zero from one period to the next. Thus, we cannot reject the hy- pothesis that in making a portfolio decision, an investor should assume that the relationship between a security's portfolio risk and its expected return is linear, as implied by the two-parameter model. We also cannot reject the hypothesis of the two-parameter model that no measure of risk, in addition to portfolio risk, systematically affects average returns. Finally, the observed fair game properties of the coefficients and residuals of the