(L11)CAPM2(f)2

(L11)CAPM2(f)2 - Lecture #11 The Capital Asset Pricing...

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Primbs/Investment Science 1 Lecture #11 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 - = - or J=0 CAPM Given historical data, we can estimate ) ( and , ), ( f M i f i r r r r - - and compute J . Jensen Index ( J ): ) ( f M i f i r r J r r - + = -
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Primbs/Investment Science 5 Jensen Index J is known as the Jensen Index. r f r β M r β= 1 Security Market Line x J > 0 x J < 0
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Primbs/Investment Science 6 Consequences of Positive J If J > 0 , does this signify a good asset or fund? CAPM says every security should satisfy J=0 ! x i σ r r f M r M M Well…
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Primbs/Investment Science 7 Jensen Index If 0 J this just means that it doesn’t exactly correspond to CAPM. J > 0 means you are rewarded more than CAPM says you should be. (This is good at a security level…see the Harmony Theorem). J < 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.
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Primbs/Investment Science 9 The Sharpe Index 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 J r r - + = - β i f M i i i f i i r r J r r S σ ) ( - + = - = i f M i i i r r J ) ( - + = M i iM M iM i ρ = = 2 M f M iM i i r r J ) ( - + = Therefore: M iM i i i S J S + =
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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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Primbs/Investment Science 12
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(L11)CAPM2(f)2 - Lecture #11 The Capital Asset Pricing...

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