Lecture2015 - Lecture 15 Empirical Survey and Application:...

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Lecture 15 Empirical Survey and Application: APT Suppose well diversified portfolios X, Y, and Z have expected returns described by the APT E[R n ] = a + b 1n f 1 + b 2n f 2 + b 3n f 3 Where E[R n ] is the expected return of n-th stock. F k = the kth non-diversifiable economy wide risk component a = the risk-free rate The betas of stocks X, Y, Z and a fourth stock, Stock A, can be found in the following table. Stock Expected Return b 1n b 2n b 3n X .1 1 0 0 Y .15 0 1 0 Z .1 0 0 1 A ? -1 1 1 What is the expected return of stock A? To find the expected return of A note that the expected return must satisfy a NO- ARBITRAGE condition. The no-arbitrage condition is that the expected return of stock’s X,Y,Z, and A should satisfy E[R n ] = a + b 1n f 1 + b 2n f 2 + b 3n f 3 and there should be no way to combine X,Y,Z,A into an arbitrage portfolio. Arbitrage Portfolio: A portfolio that has 1) zero cost 2) zero risk 3) positive return. In equilibrium we cannot have expected returns that present arbitrage
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Lecture2015 - Lecture 15 Empirical Survey and Application:...

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