Lecture25-2004 - Lecture XXV Refining the Capital Asset...

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1 Lecture XXV Refining the Capital Asset Pricing Model and Introduction of the Arbitrage Pricing Theorem I. Deriving the Capital Asset Pricing Model A. Reconsider the Expected Value-Standard Deviation frontier E t z f r t σ S B. Using the results from the Expected Value-Standard Deviation frontier, we can derive the security market line (SML)
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AEB 6182–Agricultural Risk Analysis and Decision Making Lecture 25 Professor Charles Moss Fall 2004 2 [] i ER 1 i β which is consistent with the standard CAPM relationship ( ) jm Er r r  = +−  See LeRoy and Werner (pp. 145-6). C. Starting with a two-asset portfolio, we construct a portfolio using investment i and asset m . [ ] ( ) [ ] () () () 1 2 2 22 2 1 21 1 pi m i m m a aER Ra a a a σσ σ  =+ + Next, we examine the risk/return relationship based on changes in the share of asset i . [] [ ] 1 2 2 2 2 2 2 1 1 2 2 2 2 4 2 p im p ii m m i m m i m i m a R aa a a a a =− + + + Consider what happens as the share held in asset i becomes small 2 0 2 1 p im m m a im m m m mm R a = ==  The risk/return relationship as the share in asset i becomes small is then computed as
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AEB 6182–Agricultural Risk Analysis and Decision Making Lecture 25 Professor Charles Moss Fall 2004 3 () [] [ ] [] 0 1 1 1 p im m p a m ER a R a βσ σ   = = This relationship then yields [ ] ()[] [] [] 1 1 1 mf m mm m f if r r r r r r r β = −= = −− + ⇒− = II. Empirical Tests of CAPM A. The typical estimation procedure for empirically testing the CAPM is a two step model.
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This note was uploaded on 07/15/2011 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.

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Lecture25-2004 - Lecture XXV Refining the Capital Asset...

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