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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 investorspecific result just derived used the following assumptions:
1. Investor preferences display risk aversion and nonsatiation, and are
quadratic; or, if preferences are not quadratic, asset returns are multivariate
elliptically distributed
2. Oneperiod 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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