Week 5_APT

# Week 5_APT - Next week Midsession exam No formula sheet...

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1 Next week: Midsession exam ± No formula sheet ± Bring only pens, pencils, eraser, CALCULATOR ² None will be provided, and you will need them! ± Material covered: Weeks 1-5 ² Risk and return (expected, averaging) for assets and portfolios ² Markowitz Portfolio Optimization ² CAPM ² SIM ² APT ± Multiple choice and short answer/problems

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Risk and Return Arbitrage Pricing Theory
3 Last Time ± SIM ± Risk decomposition ± Multi- factor models

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4 The Single-Index Model ± Motivation: to simplify the Markowitz model ± The excess return is assumed to have two independent components: one that is driven by the market (macro events), and the other driven by firm-specific events: r i -r f = α i + β i (r M f ) + e i
5 Security Characteristic Lines R Stock Individual Security The characteristic line: R i = a i + b i R M + e i , where R i = r i -r f , R M = r M - r f . R M R M R Port Portfolio

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6 Risk Decomposition ± Variance: σ i 2 = β i 2 σ M 2 + σ ε 2 ² Systematic risk = β i 2 σ M 2 ² Firm-specific risk = σ ε 2 ² Systematic risk/total risk = ß i 2 σ M 2 / σ i 2 = ( ρ i,M ) 2 = R-sqr ± Covariance: ² No industry effects: Cov(e i ,e j ) = 0 for all i and j. ² Cov(r i , r j ) = Cov( β i r M , β j r M ) = β i β j σ M 2 ² Accurate? ± Parameters for 100 stocks = 100 means+100 variances+100 β ’s +3(r f , E(r M ), σ M 2 )=±303
7 Text reference ± This week lecture: Chapter 10 ² Tutorial problems due this week: ± Ch8: 1-17, CFA: 1-5 ± Next week BREAK ± Week 6 MIDSESSION EXAM ± Week 7 lecture: Chapters 11, 24 ² Tutorial problems due week 7: ± Ch10: 1-3,5-11, CFA: 1-8

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8 Today ± Arbitrage and arbitrage pricing theory ± APT equations ² The factor model ² The pricing equation ± Proof/intuition ± An example
9 Tracking Portfolios and (risky) Arbitrage ± A tracking portfolio T for a target asset i is designed to match the systematic component of i’s return: ² Same risk exposures: β T,j = β i,j for factor j.

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Week 5_APT - Next week Midsession exam No formula sheet...

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