(Our thanks to Nils Hakannson, University of California, Berkeley, for providing this problem.) Two securities have the following joint distribution of returns, r1 and r2:
P{r1 = - 1.0 and r2 = .15} = .1,
P{r1 = .5 and r2 = .15} = .8,
P{r1 = .5 and r2 = 1.65) = .1.
(a) Compute the means, variances, and covariance of returns for the two securities.
(b) Plot the feasible mean-standard deviation [E(R), σ] 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 the possibility of lending, but not borrowing, at 5% (without risk) is added to the previous opportunities. Draw the new set of [E(R), σ] combinations. Which portfolios are now efficient?