16 We must determine the percentage of our money to be invested in stocks x and y. Let a percentage of money invested in x and b 1 a percentage of money invested in y. A choice of a and b is called a portfolio. A portfolio is efficient if there exists no other portfolio whose return has a higher mean return and lower variance, or a higher mean return and the same variance, or a lower variance with the same mean return. Let x be the mean return on stock x and y

be the mean return on stock y. The variance of the annual return on one share of stock x is var x, and the variance of the annual return on one share of stock y is var y. Assume that the covariance between the annual return for one share of x and one share of y is cov(x, y). If we invest a% of our

a Show that any solution to this NLP is an efficient portfolio.
b Show that as v* ranges over all non-negative numbers, all efficient portfolios are obtained

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money in stock x and 6% in stock y, the variance of the return is given by a var x+b var y + 2ab cov(x, y) Consider the following NLP: max z = ax + by s.t. a var x + bvar y + 2ab cov(x, y) v*, a+b=1 where * is a given non-negative number.