(L12)CAPM2_ns

# (L12)CAPM2_ns - Topic #12 The Capital Asset Pricing Model...

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Primbs/Investment Science 1 Topic #12 The Capital Asset Pricing Model (CAPM 2) Reading: Luenberger Chapter 7, Section 5 – 9

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Primbs/Investment Science 2 CAPM 2 Investment Implications The Harmony Theorem Other uses of CAPM CAPM as a pricing formula
Primbs/Investment Science 3 Investment Implications of CAPM One fund theorem: Buy the market plus treasury securities . Can CAPM help me evaluate the performance of assets and funds?

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Primbs/Investment Science 4 Example: Evaluating the performance of a fund CAPM: ) ( f M i f i r r r r - + = β ) ( f M i f i r r r r - = - or α = 0 CAPM Given historical data, we can estimate ) ( and , ), ( f M i f i r r r r - - and compute . Jensen Index ( alpha ): ) ( f M i i f i r r r r - + = -
Primbs/Investment Science 5 Jensen Index α is known as the Jensen Index in a CAPM context. However, it is also commonly referred to as “alpha”. r f r β M r β= 1 Security Market Line x α > 0 x < 0

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Primbs/Investment Science 6 Consequences of Positive α If α > 0 , does this signify a good asset or fund? CAPM says every security should satisfy = 0 ! x i σ r r f M r M M Well…
Primbs/Investment Science 7 Jensen Index (alpha) If 0 α this just means that it doesn’t exactly correspond to CAPM. > 0 means you are rewarded more than CAPM says you should be. (This is good at a security level…see the Harmony Theorem). < 0 says you are rewarded less. But, it doesn’t mean that the asset or fund is efficient. The Jensen index is appropriate for securities, but not portfolios

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Primbs/Investment Science 8 The Treynor Index β r r f M r 00 . 1 M Slope of this line Treynor Index: i f i r r - = Security Market Line The Treynor index is appropriate for securities, but not portfolios Compute excess return per unit of risk taken.
Primbs/Investment Science 9 The Sharpe Ratio i σ r r f M r M M Slope of this line Sharpe Index (Ratio) i f i r r - = If a fund is efficient, it has the same slope as the capital market line. The Sharpe index is appropriate for portfolios.

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Primbs/Investment Science 10 Connection between Jensen and Sharpe ) ( f M i i f i r r r r - + = - β α i f M i i i f i i r r r r S σ ) ( - + = - = i f M i i i r r ) ( - + = M i iM M iM i ρ = = 2 M f M iM i i r r ) ( - + = Therefore: M iM i i i S S + =
Primbs/Investment Science 11 CAPM 2 Investment Implications The Harmony Theorem Other uses of CAPM CAPM as a pricing formula

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Primbs/Investment Science 12 CAPM as a Pricing Formula P Q CAPM: ) ( f M i f i r r r r - + = β
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## This note was uploaded on 01/24/2009 for the course MS&E 242 taught by Professor Primbs during the Fall '06 term at Stanford.

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(L12)CAPM2_ns - Topic #12 The Capital Asset Pricing Model...

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