IX Explaining Relative Prices 1 Explaining Relative Prices

Explaining Relative Prices 1. CAPM – Capital Asset Pricing Model 2. Non Standard Forms

Assumptions behind the CAPM 1. 2. 3. 4. 5. No transaction costs Assets are

Sharpe – Lintner – Mossine (CAPM) Two Approaches to deriving 1. Economic intuition 2.

A more rigorous proof Lintner Equation 7

Must hold for all securities and portfolios 9

Non standard forms of the CAPM If the CAPM does a good job of

Modification of assumptions 1. Short sales 2. Riskless lending and borrowing 3. Personal taxes

Short Sales Since under the standard CAPM nobody short sells in equilibrium 12

Is a rate – such that if we could lend or borrow at it

is greater than 0 and smaller than 1 Global minimum variance involves positive investment

Non Marketable Assets CAPM With nonmarketable assets (H) Price of risk * amount of

Test of Equilibrium Models Expectations (1) Test with realizations – expectations are an average

Fama and Mac Beth 1. 2. 3. Auto correlation of , , and ,

Rolls Critique Mathematically can show for any efficient portfolio “Unfortunately it has never been

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IX. Explaining Relative Prices 1

Explaining Relative Prices 1. CAPM – Capital Asset Pricing Model 2. Non Standard Forms of the CAPM 3. APT – Arbitrage Pricing Theory 2

Assumptions behind the CAPM 1. 2. 3. 4. 5. No transaction costs Assets are infinitely divisible No personal taxes Price Takers Investors look only at expected return and variances of their portfolio 6. Unlimited short sales 7. Unlimited lending and borrowing at the riskless Rate 8. Homogenous Expectations about time horizon 9. Homogenous expectations of expected return, variance, and covariance 10. All assets are marketable 3

Sharpe – Lintner – Mossine (CAPM) Two Approaches to deriving 1. Economic intuition 2. Rigorous analysis 4

A more rigorous proof Lintner Equation 7

Homogenous Expectations 8

Must hold for all securities and portfolios 9

Non standard forms of the CAPM If the CAPM does a good job of explaining return why bother 1. May do a better job 2. Even if the CAPM explains return; macro behavior might not explain micro behavior – e. g. , everybody does not hold market portfolio 3. If we don’t include influences in the model, e. g. , taxes we can’t study the impact of their influences on the model 10

Modification of assumptions 1. Short sales 2. Riskless lending and borrowing 3. Personal taxes 4. Non marketable assets 5. Heterogeneous expectations 6. Non price taking behavior 7. Multi period analysis 8. Consumption CAPM Rolls critique 11

Short Sales Since under the standard CAPM nobody short sells in equilibrium 12

Is a rate – such that if we could lend or borrow at it we would hold the market portfolio Lintner Equation But for zero beta so 15

by convexity of efficient frontier 17

is greater than 0 and smaller than 1 Global minimum variance involves positive investment in market and zero beta portfolios and therefore, expected return must be in between. 18

Non Marketable Assets CAPM With nonmarketable assets (H) Price of risk * amount of risk 24

Test of Equilibrium Models Expectations (1) Test with realizations – expectations are an average and on the whole correct Market Model Substitution 25

Fama and Mac Beth 1. 2. 3. Auto correlation of , , and , 31

Rolls Critique Mathematically can show for any efficient portfolio “Unfortunately it has never been subject to an unambiguous empirical test. There is considerable doubt…that it will be. ” 35

POST TAX CAPM 36