LectureXII - Lecture XII: Market Evaluation of Investment...

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Lecture XII: Market Evaluation of Investment Risk Part III: CAPM and APT I. Derivation of the Capital Asset Pricing Model A. Some of the Theory 1. Tobin Revisited ( 29 ( 29 ( 29 1 11 P fM P M PP R x R xR x xx d d dx d R d x dR s s ss = +- = - + =- = a. The last term is the slope of the Expected Value- Standard Deviation frontier. Note that we have changed the space from Expected Value-Variance frontier. Most of the financial discussions are actually in E-S space, but this raises some complications particularly with respect to covariance terms. b. Next, we solve for x. ( 29 1 P fmM Pm fMm PfM R x RR xR x RRRx dx d RRR = +- - = - + ⇒= - ⇒= - c. Returning to the variance equation: P m d dx s s d. Combining both results: P P fMMf d d R RR RR sss - == -- e. Since the expected rate of return on the market portfolio is greater than the risk free interest rate, the slope of the capital market is positive. 2. Next, we develop the conditions for the asset not in the market portfolio. ( 29 ( 29 ( 29 2 2 2 22 2 2 2 1 2 1 21 A j j jm A j j m m A j j j m j j R x R x x s s = =++ = + - +- a. In this case, we are creating a portfolio of the asset
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LectureXII - Lecture XII: Market Evaluation of Investment...

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