Suppose that the zero-coupon yield curve is upward sloping. In particular we have r(t + .5) r(t) for t = .5, 1, . . . , 10. Consider the following securities

A: a zero-coupon bond with maturity 10 years.

B: an annuity with maturity 5 years.

C: an annuity with maturity 10 years.

D: a coupon bond with maturity 10 years

If possible, order these securities by yield to maturity from lowest to highest. Give a BRIEF explanation of your ordering. If it is not possible to order the yields (or if more information is needed), give an explanation why not (including what additional assumptions you may need to provide an ordering).

Assume that the spot curve is flat at some level y > 0. Let denote the Macauley duration of a 10 year par-coupon bond ( is assumed to be a multiple of six months). Consider the following securities:

A: a 10 year premium bond.

B: a zero-coupon bond with maturity 10.

C: a zero-coupon bond with maturity .

If possible, order these securities by their Macauley duration from largest to smallest. Given a brief explanation of your reasoning. If it is not possible to order the securities by duration based upon the given information, please explain why not, including any additional assumptions you would need to provide the ordering