10 (Refer to Problem 9 data.) Suppose that the return on the ith asset may be estimated as mi biM ei, where M is the return on the market. Assume that the ei are independent and that the standard deviation of ei may be estimated by the standard error of the estimate from the regression, with the return on the market as independent variable and the return on the ith asset as the dependent variable. Now you can express the variance of the portfolio without calculating the covariance between each pair of investments. (Hint: The variance of the market will enter into your equation). Use the estimated regression equation to estimate the mean return on the ith asset as a function of the return on the market.

For the data in Problem 9, formulate an NLP that can be used to find the minimum variance portfolio yielding an expected return of at least 10%. Why is this method useful when many potential investments are available?

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TABLE 17 Annual Returns on Assets Year Stocks Gold T-Bills 1968 11 11 1969 -9 8 1970 4 -14 577 1971 14 14 4 1972 19 44 1973 -15 66 1974 -27 64 1975 37 0 1976 24 -22 1977 -7 18. 1978 7 31 1979 19 59 10 49865570O 1980 33 99 11 1981 -5 1982 32 -25 15 22 4 11 1983 23 -11 9 1984 6 -15 10 1985 32 1986 19 1987 1988 17 2257 -12 16 22 -2 8658