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Lecture 3

# Lecture 3 - Lecture 3 Index Model Motivation Why use a...

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Lecture 3 Index Model

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________________________________________________________________________ Ralitsa Petkova, Krannert School of Management, Purdue University Motivation Why use a model for returns? o A model imposes structure that may reduce the number of parameters that must be estimated. o Even if the model is incorrect, it may provide a reasonable approximation of reality. What is a model? A model is an assumption: o For example, ) R ( E ) R ( E j i = for all i and j . (This model assumes the expected returns of all stocks are the same) o Or t tan cons ) R ( E i = for all i . (This model assumes the expected returns of all stocks are constant)
________________________________________________________________________ Ralitsa Petkova, Krannert School of Management, Purdue University Single-Index Model A single-index model is written as: it mt i i it R R ε + + β β + + α α = , where o it R is the stock return o mt R is the return on a well-diversified market index o it ε is the residual (unexpected) stock return o i β is the stock’s beta (index exposure) We make additional assumptions about the residual (unexpected) stock return: o mean zero 0 ) ( E it = ε and variance 2 i it ) ( V ε σ = ε o independent across time o independent across firms o independent of the market index return ( 0 ) R , ( Corr mt it = ε )

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________________________________________________________________________ Ralitsa Petkova, Krannert School of Management, Purdue University Single-Index Model (cont’d) The single-index model of stock returns decomposes influences on returns into a systematic factor, as measured by the return on the market index ( mt R ), and firm specific factors ( it ε ).
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Lecture 3 - Lecture 3 Index Model Motivation Why use a...

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