20-APT_forward rates

20-APT_forward rates - ArbitragePricingTheory...

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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
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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.
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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
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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.
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Key Insights The alpha of the market portfolio is always zero. Alpha =E[r
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20-APT_forward rates - ArbitragePricingTheory...

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