11102012 p kolm 10 so similar to our calculation

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Unformatted text preview: O MANAGEMENT WITH ECONOMETRICS, VER. 11/10/2012. © P. KOLM. 10 So similar to our calculation above, ei ¢Sw M = siM = L (mi - rf ) (w )¢ Sw M M 2 = sM = L (mM - rf ) And, therefore we conclude that for the entire market it must hold that mi - rf = siM 2 M s (m M - rf ) for any asset i. This model is called the capital asset pricing model (CAPM) RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/10/2012. © P. KOLM. 11 CAPM is valid for a market that satisfy the following assumptions The investor-specific result just derived used the following assumptions: 1. Investor preferences display risk aversion and non-satiation, and are quadratic; or, if preferences are not quadratic, asset returns are multivariate elliptically distributed 2. One-period model: The investor is myopic, considering only the current period 3. Perfect competition: the investor takes the asset’s price as given 4. Absence of frictions: no taxes, no transaction, no regulations, no short sales restrictions 5. All assets owned by the investor are marketable 6. Information on any asset, if available, can be obtained without cost 7. The types of assets are given exogenously 8. Assets are perfectly divisible 9. A riskless asset exists 10. Homogeneous availability and interpretation of information RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/10/2012. © P. KOLM. 12 11. Homogeneous access to investment opportunities So far the assumptions have no bearing on equilibrium asset pricing. The derived results follow from: the rational portfolio choices of individual investors. The return on any asset i, as perceived by an individual investor, can be related to the risk free rate and the perceived return on any perceived frontier portfolio The key assumption needed to deriv...
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