(Our thanks to Nils Hakansson, University of California, Berkeley, for providing this problem.) Two securities have the following joint distribution of returns, r1 and r2:
a) Compute the means, variances, and covariance of returns for the two securities.
b) Plot the feasible mean-standard deviation [E(R), a] combinations, assuming that the two securities are the only investment vehicles available.
c) Which portfolios belong to the mean-variance efficient set?
d) Show that security 2 is mean-variance dominated by security 1, yet enters all efficient portfolios but one. How do you explain this?
e) Suppose that the possibility of lending, but not borrowing, at 5% (without risk) is added to the previous opportunities. Draw the new set of [E(R), o - ] combinations. Which portfolios are now efficient?