1) Suppose thatyouaregiventhefollowinginformationonbondprices: Bond Time-to-Maturity CouponRate Price A 0.5 5% 100.45 B 1.0 6% 100.79 C 1.5...
Question:
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.
- 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%.
- Compute the prices and the yields to maturity of these coupon bonds.
- 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?
- What happens to the prices of these bonds if
- (a) the whole yield curve shifts uniformly upward by 50 basis points,
- (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)
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill