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

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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
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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 - = - β or α = 0 CAPM Given historical data, we can estimate ) ( and , ), ( f M i f i r r r r - - β and compute α . Jensen Index ( alpha ): ) ( f M i i f i r r r r - + = - β α
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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 α < 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 α = 0 ! x x i σ r r f M r M σ M Well…
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Primbs/Investment Science 7 Jensen Index (alpha) If 0 α this just means that it doesn’t exactly correspond to CAPM. α > 0 means you are rewarded more than CAPM says you should be. (This is good at a security level…see the Harmony Theorem). α < 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 x x i β r r f M r 00 . 1 M Slope of this line Treynor Index: i f i r r β - = Security Market Line The Treynor index is appropriate for securities, but not portfolios Compute excess return per unit of risk taken.
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Primbs/Investment Science 9 The Sharpe Ratio x x i σ r r f M r M σ M Slope of this line Sharpe Index (Ratio) i f i r r σ - = 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 β α σ ) ( - + = - = i f M i i i r r σ β σ α ) ( - + = M i iM M iM i σ σ ρ σ σ β = = 2 M f M iM i i r r σ ρ σ α ) ( - + = Therefore: M iM i i i S S ρ σ α + =
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Primbs/Investment Science 11 CAPM 2 Investment Implications The Harmony Theorem Other uses of CAPM CAPM as a pricing formula
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