20-APT_forward rates

20-APT_forward rates - YieldCurve&ForwardRates...

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Arbitrage Pricing Theory  BKM 7.5 and 10.6

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Arbitrage Pricing Theory APT: Ross (1976) Makes minimal assumptions: In equilibrium, no arbitrage opportunities Conclusion: alphas should be near zero
Measuring Alpha: Review Notation: Alpha is measured as the intercept in the following regression: f m e m f i e i r r r r r r - = - = i e m e i e br r + + = α

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Arbitrage Pricing Theory Suppose we measure the alpha of a “well diversified” portfolio. Most of the variation is systematic Variance of e i is small To an approximation, we can ignore e i in our regression for well diversified portfolios.
Examples Y variables: returns on different stocks X variable: return on market Asset 1: Lot’s of variation in e 11% of variation is systematic R-squared=0.11 89% of variation is unsystematic Asset 2: Not a lot of variation in e 82% of variation is systematic R-squared=0.82 18% of variation is unsystematic

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Extreme Example Asset 3: All error terms are 0 100% of variation is systematic R-squared=1 0% of variation is unsystematic
Examples For the “extreme example” there is no error term: For example 2 (well diversified portfolio): Error terms are small Most variation is systematic e m e r a r 3 3 β + = e m i e i r r α+

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Arbitrage APT: Assume: In equilibrium there are no arbitrage opportunities (chance to make free money) Claim: for well diversified portfolios, alpha must be approximately zero, or in other words, CAPM view of equilibrium is approximately correct.
Key Insights The alpha of the market portfolio is always zero. Alpha =E[r

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This note was uploaded on 03/01/2012 for the course BUS M 410 taught by Professor Brianboyer during the Fall '10 term at BYU.

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20-APT_forward rates - YieldCurve&ForwardRates...

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