Consider three bonds, each promising to pay $100 in 10 years. The first bond is X bond that always pays. The other two are Y bond and Z bond, which may pay the full $100 dollars, or may default and only pay $0, The corresponding probabilities of these events occurring are:

	Z pays 100	Z pays 0
Y pays 100	0.4	0.1
Y pays 0	0.1	0.4

Throughout this problem assume that the present value discounting between today and tomorrow is negligible.

(a) What are the expected values of the X bond, Y bond, and Z bond?

(b) What are the variances of the X bond, Y bond, and Z bond?

(c) What is the covariance of the Y bond, and Z bond?

(d) What is the correlation of the Y bond, and Z bond?

(e) Deciding to diversify, you buy 50% of the X bond, 25% of the Y bond and 25% of the Z bond. What is the expected value and variance of this portfolio?