Outline-6 - E c 173A FINANCIAL MARKETS L ECTURE OUTLINE...

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Ec 173A – FINANCIAL MARKETS LECTURE OUTLINE Foster, UCSD October 21, 2010 TOPIC 6 – ASSET EQUILIBRIUM PRICING MODELS A. The Capital Asset Pricing Model 1. Introduction: a) One question from MPT. b) The relevant risk. c) The CAPM adds 3 assumptions to MPT: 2. Derivation of the CAPM: a) Starting with market portfolio M, create enlarged portfolio M+ with proportion in asset X and 1 in M. For δ −δ the new portfolio: b) To find the change in return and risk from adding X to M, take the following deriva-tives: c) Now the trick. σ m σ x σ p M Y X μ m μ x r f μ p Fig. Note: μ p = (r μ p ), σ m = (r σ m ), m x m x m m x m , 2 2 2 2 2 ) 1 ( 2 ) 1 ( ) 1 ( σ δ δ σ δ σ δ σ μ δ δμ μ - + - + = - + = + +
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Ec 173A ASSET PRICING MODELS p. 2 of 8 1) We know that in general equilibrium, supply = demand in all markets and excess demand = 0. In financial market equilibrium, excess demand for each asset = 0. 2) Now all of X WAS ALREADY INCLUDED in market portfolio M, so M M+ . Trying to add % of X to M is excess demand for X. So we must δ evaluate the derivatives above at = 0, which δ yields the following: d) The extra return needed on the market portfolio M to compensate for the extra risk from having % of X already in it is: δ e) But all investors diversify by choosing a portfolio along the CML, where their portfolio risk premium = slope of CML = [ μ m r f ]/ σ m . 1) Since X is in the market portfolio M, the risk premium investors are getting for holding X must be the same as the risk premium overall.
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