9 (This problem requires some knowledge of regression.)

In Table 17, you are given the annual returns on three different types of assets (T-bills, stocks, and gold) (file Invest68.xls) during the years 1968–1988. For example, $1 invested in T-bills at the beginning of 1978 grew to $1.07 by the end of 1978. You have $1,000 to invest in these three investments. Your goal is to minimize the variance of the annual dollar return of your portfolio subject to the constraint that the expected return on the portfolio for a one-year period be at least 10%. Determine how much money should be invested in each investment. Use a spreadsheet to compute the mean, standard deviation, and variance of the return on each asset. To compute the covariance between each pair of assets, remember that an estimate of the covariance of T-bills and gold is given by cov(T, G)  sTsGrTG (where sT  standard deviation of return on T-bills; sG  standard deviation of return on gold).

Note that rTG  (R2)1/2, where the sign of r is the same as the slope of the least squares line.

In addition to determining the amount to be invested in each asset, answer the following two questions.

a I am 95% sure that the increase in the value of my assets during the next year will be between ______ and ______ .

b I am 95% sure that the percentage annual return on my portfolio will be between ______ and ______ .