Throughout the problems, all interest rates yields are based on the semiannual compounding convention. All coupon bonds pay coupons twice per year with the first payment to be made 6 months from today. All interest rates and yields should be assumed to be strictly positive. Problem 2. Assume that the spot-rate curve is flat at 6%. Consider a portfolio consisting of two par-coupon bonds. (Recall that if the spot-rate curve is flat, then the par-coupon yield curve is also flat at the same value. ) Bond #1 has face value $20,000 and maturity 5 years. Bond #2 has face value $10,000 and maturity 30 years. (a) Find the duration and DV01 for Bond #1 and Bond #2. (b) It 1s desired to purchase a single zero-coupon having the same price and the same DV01 as the portfolio of par-coupon bonds. Find the maturity T of such a bond. (You many assume that zeros of all maturities are available and that discount factors for all maturities are given by d(t) = (1.03)2" ) If you could not do part (a), you may express T in terms of the DVO01 of the portfolio of par-coupon bonds. (c) What parallel shift in the spot rate curve would explain a price decrease of $212.73 in the portfolio?(Use a first-order approximation. Be sure to specify a direction as well as a magnitude of the shift) Problem 4. Given that the annuity yield for maturity 10 years is y,(10) = 0.1 and the par- coupon yield for maturity 10 years is y,.(10) = 0.08, determine the 10-year spot rate #