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09- Single Factor Model and CAPM

# 09- Single Factor Model and CAPM - Single Factor Models and...

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1 Single Factor Models and the CAPM Marriott School of Management Bus M 410 Winter 2011 Rob Schonlau Last updated Feb 14, 2010

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Lecture 9 Outline l Introduce single factor asset pricing models. Use intuition developed from regression lecture (slide set 8) to understand betas. l Example estimation of the single index model. l Introduce the CAPM l Relate the CAPM and single factor (index) model. Review miscellaneous points regarding the application of the CAPM. 2
What is a “factor model”? l “Factor models are statistical models designed to estimate [systematic and firm-specific] risk for a particular security or portfolio.” -- BKM page 171 l I think of factor models as regression equations where asset returns (the dependent variable) are being modeled as a function of various explanatory variables motivated by financial theory. These regression equations allow the return being modeled to be viewed as function of systematic and firm- specific components. 3

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Intuition for single factor model l Suppose we set out to model asset returns. For simplicity let’s concentrate on stocks for now. The dependent variable in the model will be stock i’s returns. l We know that individual stock prices, and hence returns, are affected by various firm-level and market-wide events (e.g., business cycles, interest rates, war, inflation, new technology, hiring/firing/death of key employees, etc.). For simplicity we will conceptually group industry and region-level events under the “market-wide” category and focus on a single market- wide factor. 4
Single factor model intuition continued… 5

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Single factor model intuition continued… 6
Single factor model  single index model 7

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Single index model (this is the form of the single factor model that can be estimated using real-world data) 8
Intuition from a factor (index) model. Ri = α i + β i Rm + ei Once we have a model we can ask (model-based) questions like: What is the expected return ? E[Ri]= α i + β i E[Rm] What is the variance? Let var2(Rm)= σ2m. Var[Ri] = Var[ α i + β i Rm + ei] = Var[ β i Rm]+Var[ei] = σ2( β iRm) + σ2(ei) = β i2 σ2m + σ2(ei) =systematic risk + firm-specific risk 9

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Lecture 9 Outline l Introduce single factor asset pricing models. Use intuition developed from regression lecture (slide set 8) to understand betas. l Example estimation of the single index model. l Introduce the CAPM l Relate the CAPM and single factor (index) model. Review miscellaneous points regarding the application of the CAPM. 10
11 How to estimate the parameters in an index model?

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12 Steps for setting up the estimation l Decide on an estimation period Services use periods ranging from 2 to 5 years for the regression Longer estimation period provides more data, but firms change. Shorter periods can be affected more easily by significant firm-specific event that occurred during the period (Example: ITT for 1995-1997) l Decide on a return interval - daily, weekly, monthly Shorter intervals yield more observations, but suffer from more noise.
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