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
1. To begin, assume that it is now January 1, 1993, and that each bond in Table 1 matures on December 31 of the year listed. Further, assumes that each bond has $1,000 par value, each had a 30-year maturity when it was issued, and the bonds currently have a 10 percent required nominal rate or return.
(d) $1 billion 10 year debenture @ 7.5% with 18.18 warrants at $ 55 exercisable until 1988.
A bond with an annual coupon of $70 and originally sold at par for $1,000. The current market interest rate (yield to maturity) is 8%. This bond will sell at _______. Assuming no change in market interest rates, the bond will present the holder with capital ________ as it matures.
Southlake Corporation issued $900,000 of 8% bonds on March 1, 20X1. The bonds pay interest on March 1 and September 1 and mature in 10 years. Assume the independent cases that follow.
21. Universal Forests current stock price is $154.00 and it is likely to pay a $5.23 dividend next year. Since analysts estimate Universal Forest will have a 13.0% growth rate what is the required return?
14. Global Enterprises has just signed a $3 million contract. The contract calls for a payment of $.5 million today, $.9 million one year from today, and $1.6 million two years from today. What is this contract really worth if Global Enterprises can earn 12 percent on its money?
investor should invest $369.35 in asset A and the remaining $630.65 in asset B. The
At what price will the bonds issue? (Do not round PV factors. Round your answer to the nearest dollar amount. Omit the "$" sign in your
a. What would Mrs. Beach have to deposit if she were to use high quality corporate bonds an earned an average rate of return of 7%.
Complete problem 31 of Chapter 10 (shown below), and submit to your instructor. Show your calculations and the algebraic manipulation of the price equation for the bond. In addition to solving the problem, write a 100 to 200 word essay on the term structure of fixed income securities.
The semi-annual compounded interest rate is 5.2% (a six-month discount rate of 5.2/2 = 2.6%). (15 points)
2. The discount rate for this bond would be 0.70%. I started with an appropriate discount rate to derive my bond purchase price, since I would not purchase a bond without finding out ahead of time what a good price should be.
Q2. Provide a full-page plot of the Capital Allocation Line for the case in Q1. Label the axes and locate cash, D. Equity, D. Bonds, and your optimal complete portfolio clearly on the plot. You may draw this plot by hand.
Coupon bond is one that is below its nominal value. 99.05 It is less than 100 percent of the cash value of the price, which will be traded. Above the face value of the bond premium bond. 101,15 more than 100 percent of the cash value of your price quote. Market interest rates rise above the coupon rate of the bond discount bond when the bond is. Market interest rates, the bond 's coupon rate is below the bonds when the bond underwriters.