( portfolio must be on the line in Figure 11.3 and the beta of the market portfolio is 1, we can determine the equation describing that line. As Figure 11.4 shows, the intercept is rf and the slope is E(rM) - rf [rise E(rM) - rf; run 1], implying that the equation of the line is

E(rP) rf [E(rM) - rf] P (11.3) Hence, Figures 11.3 and 11.4 are identical to the SML relation of the CAPM.3

We have used the no-arbitrage condition to obtain an expected return-beta relationship identical to that of the CAPM, without the restrictive assumptions of the CAPM. This sug- gests that despite its restrictive assumptions the main conclusion of the CAPM, namely, the SML expected return-beta relationship, should be at least approximately valid.

It is worth noting that in contrast to the CAPM, the APT does not require that the benchmark portfolio in the SML relationship be the true market portfolio. Any well-diver- sified portfolio lying on the SML of Figure 11.4 may serve as the benchmark portfolio. For example, one might define the benchmark portfolio as the well-diversified portfolio most highly correlated with whatever systematic factor is thought to affect stock returns. Ac- cordingly, the APT has more flexibility than does the CAPM because problems associated with an unobservable market portfolio are not a concern.

In addition, the APT provides further justification for use of the index model in the prac- tical implementation of the SML relationship. Even if the index portfolio is not a precise proxy for the true market portfolio, which is a cause of considerable concern in the context of the CAPM, we now know that if the index portfolio is sufficiently well diversified, the SML relationship should still hold true according to the APT.

So far we have demonstrated the APT relationship for well-diversified portfolios only. The CAPM expected return-beta relationship applies to single assets, as well as to portfo- lios. In the next section we generalize the APT result one step further.