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Suppose that it is impractical to use all the assets that are incorporated into a specified...

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Advance Math

Suppose that it is impractical to use all the assets that areincorporated into a specified portfolio (such as a given efficientportfolio). One alternative is to find the portfolio, made up of agiven set of n stocks, that tracks the specified portfolio mostclosely—in the sense of minimizing the variance of the differentreturns. Specifically, suppose that the target portfolio has(random) rate of return rM. Suppose that there are n assets with(random) rates of return r1, r2, … rn. We wish to find theportfolio rate of return: r = ?1r1+ ?2r2 + … + ?nrn (with?_(i=1)^n??I = 1) minimizing var(r - rM) Find a set of equationsfor the ?n’s Although this portfolio tracks the desired portfoliomost closely in terms of variance, it may sacrifice the mean. Hencea logical approach is to minimize the variance of the trackingerror subject to achieving a given mean return. As the mean isvaried, this results in a family of portfolios that are efficientin a new sense, say tracking efficient. Find the equations of the?i’sthat are tracking efficient.

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