Assignment
1. You have been hired by a small pension fund to help them design a bond portfolio to fund a $10 million obligation that will come due in 4 years. The managers of the fund would like to use 2 year zero coupon bond along with their existing bond portfolio A that includes following three zero coupon bonds with the corresponding portfolio weight:
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Security
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5 year zeros
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7 year zeros
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10 year zeros
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Portfolio weight
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25%
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25%
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50%
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Suppose that the yield to maturity on all bonds is 5% (in other words, the yield curve is ?at at 5%).
a) How much money do you have to invest today in the bond market to entirely fund your obligation?
b) What is the durations of current existing bond portfolio A and the obligation (due in 4 years).
c) How would you structure your holdings of the 2 year zero coupon bond and their existing portfolio A so that you are protected against the risk of interest rate ?uctuations? Please indicate the dollar amount you would invest in each security.
2. You will be paying $10,000 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%.
a) What is the present value and duration of your obligation?
b) What maturity zero coupon bond would immunize your obligation?
c) Suppose you buy a zero coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 9%. What happens to your net position (difference between the value of bond and that of your tuition obligation)? What if rates fall to 7% (instead of 9%)?
3. A 20-year maturity bond pays interest of $90 once per year and has a face value of $1,000. Its yield to maturity is 10%. You expect that interest rates will decline over the upcoming year and that the yield to maturity on this bond will be only 8% a year from now. What is the return you expect to earn by holding this bond over the upcoming year?
4. In the bond market, we find the following Treasury bonds and their prices.
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Bond price
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$980
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$98
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$96
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Maturity
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2 years
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1 year
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2 years
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Face value
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$1,000
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$100
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$100
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Coupon rate
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10%
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0%
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0%
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a) Compute the YTMs for the above three bonds.
b) Using the two zero coupon bonds, compute the forward rate that is applied for the period from the end of Year 1 to the end of Year 2.
c) Suppose that we need the above coupon bond for your cash requirements. However, due to some reasons, we cannot buy the coupon bond. Therefore, instead of the coupon bond, we decide to buy 1 year and 2 year zero coupon bond. If this alternative investment has the same cash flows as the coupon bond, how many bonds we need to buy (i.e., XX 1 year bonds and OO 2 year bonds)? What is the cost for this alternative bond investment?
d) Using your work in question 3), is there an arbitrage opportunity? If any, how can we transact for arbitrage? Compute the arbitrage profits. (for this question, we can assume that we can transact the coupon bond.)
5. You are in charge of the bond trading and forward loan department of a large investment bank. You have the following YTM's for ?ve default-free pure discount bonds as displayed on your computer terminal:
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Years to Maturity
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1
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2
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3
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4
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5
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YTMj
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0.06
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0.065
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0.07
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0.065
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0.08
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Where YTMj denotes the yield to maturity of a default free pure discount bond (zero coupon bond) maturing at year j.
a) A new summer intern from Harvard has just told you that he thinks that 3 year treasury notes with annual coupons of $100 and face value of $1,000 are trading for $1,000. Would you ask the intern to recheck the price of this coupon bond? If so, why? If there is one actually traded for $1,000, how would you take this opportunity?
b) A client approaches you looking for an annualized quote on a forward loan of $5 million dollars to be received by the customer at the end of the third year and she will repay the loan at the end of the ?fth year. How would you structure your holdings of pure discount bonds so you can exactly match the future cash ?ows of this loan? Please indicate the number of bonds to be purchased or sold and the involved cost/benefit in dollar terms. What is the corresponding annualized forward interest rate you quote for your client?
c) Suppose that you purchased the bond in part 1(a) at the price you calculated. It is now one year later and you just received the ?rst coupon payment on the bond. At this time, the yield to maturities up to 3 year pure discount bonds are
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Years to Maturity
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1
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2
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3
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4
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5
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YTMj
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0.08
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0.095
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0.09
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0.075
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0.06
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If you were to sell the bond now, what rate of return would you realize on your investment in the bond?
6. Florida Enterprise has bonds on the market making annual payments, with the eight-year maturity, a par value of $1,000, and selling for $948. At this price, the bonds yield 5.9%. What must the coupon rate be on the bond?
7. Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 8.5%, has a YTM of 7%, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 7%, has a YTM of 8.5%, and has 13 years to maturity. What is the price of each bond today? If interest rates are unchanged, what do you expect the price of these bonds to be one year from now? In three years? In eight years? In 12 years? In 13 years? Illustrate your answers by graphing bond prices versus time to maturity.
8. Winter Time Adventures is going to pay an annual dividend of $2.60 a share on its common stock a year from now. Yesterday, the company paid a dividend of $2.50 a share. The company adheres to a constant rate of growth dividend policy. What will one share of this common stock be worth 11 years from now if the applicable discount rate is 8.0 percent?
9. Panther Corp. stock currently sells for $68 per share. The market requires a returns of 11% on the company's stock. If the company maintains a constant 3.75% growth rate in dividends, what was the most recent dividend per share paid on the stock?
10. International Corp. currently has an EPS of $4.04, and the benchmark PE for the company is 21 (the benchmark PE can be the PE ratio of comparable companies). Earnings are expected to grow at 5.5% per year.
a) What is your estimate of the current stock price?
b) What is the target stock price (i.e., forecasted stock price) in one year?
c) Assuming the company pays no dividend, what is the implied return on the company's stock over the next year? What does this tell you about the implicit stock return using PE valuation?
Format your assignment according to the following formatting requirements:
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