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Week 4_Single Index Model

# Week 4_Single Index Model - Risk and Return Single Index...

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Risk and Return Single Index and Multi-factor Models

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2 Last Time Introduced the CAPM Limits to diversification Certain types of risk are priced Role of the market portfolio Expected return on an asset is related to its risk relative to a very well-diversified portfolio What is the market portfolio? www.moneychimp.com/articles/valuation/ capm.htm For MSFT
3 Expected Return and Risk The CAPM says the market portfolio is the tangency portfolio: Expected return = Risk-free rate + (Reward to per unit of market risk) × (Amount of market risk) Expected return = Price of time + (Price of market risk) × (Amount of market risk) The CAPM equation: = = + σ σ i f M f 2 i M M f i f i M 2 M M E(r ) r E( E(r) r E(r ) r cov(r, r) r cov(r r ,r ) ) = β β = σ i M i f i M f i 2 M Cov(r,r ) E(r) r [E(r ) r] where

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4 β as a Measure of Risk β is a measure of stock i’s market risk: The contribution of stock i to total market risk σ M . The co-movement between stock i and the market portfolio. The characteristic line: R i,t = α i + β i R M,t + e i,t R M R i The characteristic line * * * * * * * * * * * α i β i
5 SML for Stock Selection E(r A ) β M r f E(r M ) 1 E(r) SML α A β A A E(r A ) - r f = α A + [E(r M ) - r f ] β A

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6 Text reference This week lecture: Chapter 8 Tutorial problems due this week: Ch9: 1-17, CFA: 1-12 Next week lecture: Chapter 10 Tutorial problems due next week: Ch8: 1-17, CFA: 1-5
7 Today Index models The Single Index Model Risk decomposition Covariance Multi-index models Risk factors

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8 Single Factor Model Start with expected FIRM SPECIFIC changes for the variable Assume a single indicator (factor) accounts for all unexpected changes common to different variables Assume all other unexpected changes are variable specific Determine/estimate the sensitivity of the variable to the indicator for example, if the variable is returns on a security: r i = E(r i ) + m i + ε i β i
9 Single Index Model Specific single factor model The factor is an observable market index All return not captured by the factor is attributable to firm specific events r i - r f = α i + β i (r M - r f ) + e i

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10 The Single-Index Model The firm-specific effects are given by α i +e i with α i
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