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JOURNAL OF POLITICAL ECONOMY In the portfolio model the investor looks at individual assets only in erms of their contributions to the expected value and dispersion, or risk of his portfolio return. With normal return distributions the risk of port- folio p is measured by the standard deviation, G(R,), of its return, R, and the risk of an asset for an investor who holds p is the contribution of the asset to o(R,). If x is the proportion of portfolio funds invested in asset i, Gy=cov(R,, R,)is the covariance between the returns on assets i and j, and N is the number of assets, then cov(Ri, Rp) Cip g(R RP) Thus, the contribution of asset i to o(Rp)-that is, the risk of asset i in the portfolio p-is proportional to x10/((2)=cov(R,R)/(R Note that since the weights xip vary from portfolio to portfolio, the risk of an asset is different for different portfolios For an individual investor the relationship between the risk of an asset ind its expected return is implied by the fact that the investors optimal portfolio is efficient. Thus, if he chooses the portfolio m, the fact that m is efficient means that the weights xim, i=1, 2, .., N, maximize ex portfolio return E(Rm) E(R1) subject to the constraints is common when return distributions are assumed to be normal. whereas an inter fractile range is usually suggested when returns are generated from some other symmetric stable distribution It is well known that the mean-standard deviation version of the two-parameter portfolio model can be derived from the assumption that investors have quadratic case, the empirical evidence of Fama (1965a) (1970),Roll(1970),K, Millet (1971), and Officer (1971)provides support for the "distribution"approach to the model. For a discussion of the issues and a detailed treatment of the two-parameter model, see Fama and Miller (1972, chaps. 6-8) 'e also concentrate on the special case of the two-parameter model obtained witl the assumption of normally distributed returns. As shown in Fama(1971)or Fama metric stable model are the same as those of the normal model tIldes (-)are used to denote random variables. And the one-period percentage eturn is most often referred to just as the return
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