Lecture_08_09 - Professor Ruslan Goyenko...

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Arbitrage Pricing Theory cont’d Professor Ruslan Goyenko
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Recall: Single Index Model i f M i i f i e ) r r ( ) r r ( + - β + α = - Assume factor is market excess return α i = stock’s expected return if market’s excess return is zero  (we showed alpha should equal zero for fairly priced assets) β i(rM-ri) = the component of return due to market movements ei = the component of return due to unexpected firm-specific events  (mean  zero, uncorrelated across firms, and uncorrelated to market  return)
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Single-index model: decomposing  risk σ i2 =  total variance β i2  σ m2   systematic variance σ 2(e i )   unsystematic variance ) e ( i 2 2 M 2 i 2 i σ + σ β = σ Ri  =  α i + ßiRm + ei 2 2 2 2 i M i square R σ σ β ρ = - = i f M i i f i e ) r r ( ) r r ( + - β + α = -
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Example 1 Consider the two  excess return  index model regressions Which stock has higher firm specific risk? RA  =  .01 + 1.2Rm , R-square = .576,  σ (e i ) = 10.3%    RB  = - .02 + .8Rm , R-square = .436,  σ (e i ) = 9.1%   
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Multifactor Models: Recap Both the ICAPM and multifactor APT imply that  the expected (required)  excess return  on an asset  (or diversified portfolio in the case of the APT) is a  linear function of factor betas E(ri) - rf =  β i,1RP1 +  β i,2RP2 + … Where RPk is the  risk premium  on factor k: the  expected excess return of a portfolio that has a beta of  1 on factor k, and a beta of 0 on all other factors
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Suppose growth in industrial production IP and the  inflation rate IR, drive returns E[IP] = 3%, E[IR] = 5% For stock A:  β A,IP = 1,  β A,IR = 0.5 E[rA] = 12% Suppose IP growth turns out to be 5%, and  inflation growth 8% What is your revised estimate of  E[rA] ? Example 2
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Suppose there are 2 independent risk factors F1  and F2 The risk free rate is 6% Consider 2 well diversified portfolios A and B with E[rA] = 31%,    β A,1 = 1.5,  β A,2 = 2 E[rB] = 27%,  β B,1 = 2.2,  β B,2 = -0.2 What is the expected return beta relationship in  this economy? Example 3
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Consider a 1-factor economy where well-diversified  portfolios A, B and C have expected returns and  betas as follows: E[rA] = 12%, β A = 1.2 E[rB] = 8%, β B = 0.6 E[rC] = 6%, β C = 0 Is there an arbitrage opportunity? What is it? Example 4
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9 FINE441 –Investment management Portfolio Performance Evaluation Portfolio Performance Evaluation Ruslan Goyenko Faculty of Management McGill University
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10 Motivation for Performance Analysis Index funds  simply try to replicate performance of an  index (S&P 500) . An S&P 500 fund effectively holds a  Market Portfolio.
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