FBE441_06_TestingCAPM_APT

FBE441_06_TestingCAP - FBE 441 Investments Prof David Solomon Lecture 6 Testing the CAPM and the APT Model Tests of the CAPM The Value and Size

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FBE 441 Investments Prof. David Solomon Lecture 6: Testing the CAPM and the APT Model Tests of the CAPM The Value and Size Anomalies The Fama-French 3 Factor Model The APT Model Readings: BKM chapters 9 and 10
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2 - Lecture 5 : - Markets in Equilibrium - The Capital Asset Pricing Model (CAPM) - Lecture 6 (today): - Tests of the CAPM - The Value and Size Anomalies: The Fama-French 3 Factor Model - The APT Model Lecture Outline:
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3 CAPM vs. The Real World (1) What is the market portfolio anyway? . [Roll’s Critique]: can we ever test the CAPM? (2) Anomalies: small & “value” stocks outperform . Is Beta dead? (3) Another anomaly: the momentum effect . Yet another reason to look at multi-factor models! -> THIS LECTURE !
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4 Testable Predictions of the CAPM According to the Roll critique, the main testable prediction of the CAPM is: -The market portfolio is mean-variance efficient -The market portfolio has the highest possible Sharpe Ratio -When a security’s excess returns are regressed on market excess returns, there should not be a significant alpha. i.e. α=0 ]) [ ( ] [ i f m i i f r r E r r E - + = - β α
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5 Testable Predictions of the CAPM -We could compare Sharpe Ratios directly, but in practice it’s easier to run regressions t-tests for alpha give easy evaluation of statistical significance. -Do negative alphas violate the CAPM, or only positive alphas? Both are violations! A negative alpha means the stock has returns that are too low relative to its risk. Short the stock, and invest in a higher expected return stock with the same risk
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6 Testable Predictions of the CAPM -So significant positive or negative alphas indicate violations of the CAPM. Between 1986 and 1990, Microsoft had an alpha of 4.23% per month(!!). r msft - r f = 0.0423 + 1.425[r m – r f ] + ε Does this violate the CAPM?
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8 Testable Predictions of the CAPM -Not necessarily! Need to focus on the difference between realized returns and expected returns. -The CAPM is a statement about expected returns and expected alphas What we measure is realized returns and alphas: First of all, we need to know whether the results are statistically significant. t i t f t m i i t f r r r r , , , , t i, ) ( ε β α + - + = - ]) [ ( ] [ i f m i i f r r E r r E - + = -
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9 Testable Predictions of the CAPM -Measurement error is the difference between the true alpha and the measured alpha -A t-test tells us how likely the result would have been by chance alone. So a statistically significant alpha would seem to violate the CAPM. -The t-statistic for Microsoft’s α is 2.72. This gives a p-value of 0.008. So is the CAPM is rejected then?
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10 Testable Predictions of the CAPM -Depends how many regressions you ran! A 5% significance level means that ‘if the true alpha were zero, you would only observe a realized alpha this large 5% of the time. -What if you ran 100 regressions? You would expected 5 significant alphas at a 5% level by chance alone!
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This note was uploaded on 02/23/2011 for the course FBE 441 taught by Professor Callahan during the Spring '07 term at USC.

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FBE441_06_TestingCAP - FBE 441 Investments Prof David Solomon Lecture 6 Testing the CAPM and the APT Model Tests of the CAPM The Value and Size

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