A steepening of the yield curve means that the yields of longer-maturity bonds increase more than the yields of shorter-maturity bonds. A parallel shift of the yield curve means that yields on bonds of all maturities change by the same amount. You believe the yield curve will steepen and you want to construct a trade that makes a profit if this view is correct. This is called a steepener trade. Describe how you would construct a steepener trade from the following pairs of bonds. In so doing, you must construct the trade so it is unaffected by (i.e., hedged to) small parallel shifts in the yield curve, since you don't have a view on whether yields will on average shift up or down. Describe your trade in terms of the dollar values bought or shorted in each bond. To normalize things, assume you invest $ 1000 in your long bond position. (Hint: this problem involves computing the durations of the bonds.)

(a) A 2-year zero coupon bond with a yield to maturity of 2% and a 10-year zero coupon bond with a yield of 3%

(b) A 2-year zero coupon bond with a yield to maturity of 2% and a 5-year annual- paying coupon bond with a 2.5% coupon and a yield of 2.5%.