involves the simultaneous purchase and sale of equivalent securities in order to profit from discrepancies in their price re- lationship. The concept of arbitrage is central to the theory of capital markets. This chapter discusses the nature and use of arbitrage opportunities. We show how to identify arbitrage opportunities and why investors will take the largest possible po- sitions in arbitrage portfolios. Perhaps the most basic principle of capital market theory is that equilibrium market prices are rational in that they rule out (risk-free) arbitrage opportunities. Pricing rela- tionships that guarantee the absence of arbitrage possibilities are extremely powerful. If actual security prices al- low for arbitrage, the result will be strong pressure to restore equilibrium. Only a few investors need be aware of arbitrage opportunities to bring about a large volume of trades, and these trades will bring prices back into balance. The CAPM gave us the security market line, a relationship between expected return and risk as measured by beta. Arbitrage pricing theory, or APT, also stipulates a relationship between ex- pected return and risk, but it uses dif- ferent assumptions and techniques. We explore this relationship using well- diversified portfolios, showing in a one-factor setting that these portfolios are priced to satisfy the CAPM expected return-beta relationship. Because all well- diversified portfolios have to satisfy that relationship, we show that all individual securities almost certainly satisfy this same relationship. This reasoning leads to an SML relationship that avoids reliance on the unobservable, theoretical market       320 III. Equilibrium In Capital Markets 11. Arbitrage Pricing Theory The McGraw−Hill Companies, 2001           CHAPTER 11 Arbitrage Pricing Theory 321     portfolio that is central to the CAPM. Next we show how the single-factor APT (just like the CAPM) can easily be generalized to a richer multifactor version. Fi- nally, we discuss the similarities and differences between the APT, the CAPM, and the index model.           11.1 ARBITRAGE OPPORTUNITIES AND PROFITS