Essay on Homework: Zero Coupon Bond

1503 Words Mar 7th, 2014 7 Pages
E4721

Professor Dastidar

Assignment #1

Question 1
Consider the following data. The column marked  n gives the price today of one dollar delivered in half-year n, i.e., of a zero coupon bond which pays $1 in half-year n. In the next two columns there are the cash flows of two bonds, A and B. Essentially, bond A pays a 20% semi-annual coupon and bond B pays a 10% semi-annual coupon. Both bonds mature in 2.5 years, when each also pays its principal of 100. Assume semi-annual compounding.
Half
Year
1
2
3
4
5

n

Bond A Bond B

.95
.91
.87
.80
.70

10
10
10
10
110

5
5
5
5
105

A. Calculate the price of each bond assuming there are no arbitrage opportunities in the market. (That is, calculate the
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(Hint: the Cashflow Column provides what in class notation is C/2.) Print or write down the spot rates and cashflows.
4. For the rest of the question, you do not need to be in front of the Bloomberg terminal, but you need to have in hand the prices, cashflows and spot rates.
a. Compute yield using the formulas from class with the observed market price.
You are going to recognize an immediate problem: timing of the coupons. To get over this problem, compute the yield under 2 alternative scenarios: rounding back to the last coupon date and rounding forward to the next coupon date. In both cases use the same price. Is the bond yield the same as in part 2? The answer is typically no.
b. Using the cashflows and spot rates, compute the price using semi-annual compounding. Is this the same as the observed price? Again, it probably won’t be. 2

E4721

Professor Dastidar

Assignment #1

Question 4
a) Suppose an investor has access to two bonds, one with a duration of 1.8 and the other with a duration of 4. You are approached to construct a portfolio of these bonds that has a duration of 7. What percentages of the investor’s portfolio should go into bonds 1 and 2 to achieve this target duration? These durations are modified durations.
b) One of these weights is negative. What does this mean in terms of the recommended investment strategy?
What problems might there be in implementing your

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