for the expected return on portfolio V (noting that M 1), you will find that the expected return on V is given by the SML relationship. III. Equilibrium In Capital Markets 11. Arbitrage Pricing Theory The McGraw−Hill Companies, 2001           330 PART III Equilibrium in Capital Markets     11.3 INDIVIDUAL ASSETS AND THE APT   We have demonstrated that if arbitrage opportunities are to be ruled out, each well-diversi- fied portfolios expected excess return must be proportional to its beta. For any two well- diversified portfolios P and Q, this can be written as E(rP) rf   P E(rQ) rf   Q   (11.4)   The question is whether this relationship tells us anything about the expected returns on the component stocks. The answer is that if this relationship is to be satisfied by all well- diversified portfolios, it must be satisfied by almost all individual securities, although the proof of this proposition is somewhat difficult. We note at the outset that, intuitively, we must prove simply that nonsystematic risk does not matter for security returns. The ex- pected return-beta relationship that holds for well-diversified portfolios must also hold for individual securities. First, we show that if individual securities satisfy equation 11.4, so will all portfolios. If for any two stocks, i and j, the same relationship holds exactly, that is, E(ri) rf   i E(rj) rf K j   where K is a constant for all securities, then by cross-multiplying, we can write, for any security i,