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a stocks value is 1.2. If GDP increases by only 3%, then the value of F would be 1%, representing a 1% disappointment in actual growth


versus expected growth. Given the stocks beta value, this disappointment would translate into a return on the stock that is 1.2% lower than previously expected. This macro surprise together with the firm-specific disturbance, ei, determine the total departure of the stocks return from its originally ex- pected value.   Well-Diversified Portfolios   Now we look at the risk of a portfolio of stocks. We first show that if a portfolio is well di- versified, its firm-specific or nonfactor risk can be diversified away. Only factor (or sys- tematic) risk remains. If we construct an n-stock portfolio with weights wi, wi 1, then the rate of return on this portfolio is as follows:   rP E(rP) PF eP (11.1) where     P wi i   is the weighted average of the i of the n securities. The portfolio nonsystematic compo- nent (which is uncorrelated with F) is   eP wiei   which similarly is a weighted average of the ei of the n securities.     2 Stephen A. Ross, "Return, Risk and Arbitrage," in I. Friend and J. Bicksler, eds., Risk and Return in Finance (Cambridge, Mass.: Ballinger, 1976). III. Equilibrium In Capital Markets 11. Arbitrage Pricing Theory The McGraw−Hill Companies, 2001           CHAPTER 11 Arbitrage Pricing Theory 325     We can divide the variance of this portfolio into systematic and nonsystematic sources, as we saw in Chapter 10. The portfolio variance is   2 2 2 2 P P F (eP)