A bond market investor is considering the choice between a mortgage-backed security (MBS) index with an expected return of 9.75% and a standard deviation of 10%, and a Treasury bond index with an expected return of 5% and a standard deviation of 10%. The two indices tend to move together, with a correlation of 0.9.

a. Write formulas for the expected return and variance of the return on a portfolio that puts weight w on the MBS index, and (1-w) on the Treasury bond index.

b. Draw a diagram to show the set of mean-variance portfolios.

c. Show that the minimum-variance combination of the two indices puts an equal weight on each. What feature of this example is responsible for this result? What are the mean and variance of the return on the minimum-variance portfolio?