1) Suppose that you are given the following information on bond prices:

Bond	Time-to-Maturity	Coupon Rate	Price
A	0.5	5%	100.45
B	1.0	6%	100.79
C	1.5	8%	104.30
D	2.0	9%	107.12

 

Assume that all of the bonds pay coupons semi-annually, with $100 face value.

 From the information above, calculate the zero-coupon yield curve in terms of semi- annually compounded yields, using the bootstrap methodology.

1. Calculate the price of a bond with the following terms (bond E):

   a. 2 years-to-maturity

    b. Semi-annual coupons with a coupon rate of 7%

    c. Face value of $100.

    What is the yield-to-maturity of the bond from the previous part? (use Excel or any mathematical solver for this question)

  Construct a portfolio using bonds A, B, C, and D that replicates the payoffs to bond E. Hint: Start by using bond D to match the payoff at t = 2. Then include the right amount of bond C so that the portfolio of C and D matches the payoff at t = 1.5. Continue similarly for bonds B and A. Note: there is no restriction on the sign of the weights: e.g. the weights can be negative if the strategy requires to sell some bonds. What is the price of this portfolio? Does this price make sense?

 2) Consider the zero-yield curve reported in the following table. Consider two bonds, both with 5 years to maturity, but with different coupon rates. Let the two coupon rates be 5% and 8%.

1. Compute the prices and the yields to maturity of these coupon bonds.
2. How do the yields to maturity compare to each other? If they are different, why are they different? Would the difference in yields imply that one is a better 'buy' than the other?
3. What happens to the prices of these bonds if 
4. (a) the whole yield curve shifts uniformly upward by 50 basis points, 
5. (b) the yields for the maturities between 6 and 7.5 move downward by 25 basis point (while the rest of the curve remains unchanged)?

 

Maturity	Yield(% p.a.)	Maturity	Yield(% p.a.)
0.25	6.33	4.00	6.67
0.50	6.49	4.25	6.62
0.75	6.62	4.50	6.57
1.00	6.71	4.75	6.51
1.25	6.79	5.00	6.45
1.50	6.84	5.25	6.39
1.75	6.87	5.50	6.31
2.00	6.88	5.75	6.24
2.25	6.89	6.00	6.15
2.50	6.88	6.25	6.05
2.75	6.86	6.50	5.94
3.00	6.83	6.75	5.81
3.25	6.80	7.00	5.67
3.50	6.76	7.25	5.50
3.75	6.72	7.50	5.31

 

Table1: Zero-yield curve (semi-annually compounded)