Why use single index model? (Instead of projecting full matrix of covariances) 1.Less information requirements 2.It fits better!

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Presentation transcript:

Why use single index model? (Instead of projecting full matrix of covariances) 1.Less information requirements 2.It fits better!

If we only knew α !

Maybe we do know α ! Two approaches: (i) security analysis (ii) efficient market theory (e.g. CAPM)

CAPM - Assumptions Lots of small investors (none dominant) All have same holding period All assets publicly traded No taxes or transactions costs All investors are MV optimizers –(e.g. optimizing U = μ – ½Aσ 2 ) Everyone shares same information (homogeneous beliefs)

CAPM - Implications All investors hold risky assets in the same proportion (“market portfolio”) The Capital Market Line is the best attainable capital allocation frontier Risk premium on the market portfolio is proportionate to risk and degree of risk aversion Risk premium on individual assets proportional to risk premium on the market portfolio and the beta of the security relative to market portfolio

CAPM - Implications Implies that α i = 0 all I in the index model CAPM: Index model

CAPM: Does it fit the data? Jensen, 1968

Private information and the security market line (SML) Expected return (market and private) SML Beta,  i Q (buy) S (sell) P actual return expected return T (sell) M (The larger is  i, the larger is ER i ) r R

Measures of portfolio performance

More generally: