QuestionQuestion

1. Consider the following government securities: Security A pays $1 in years 1, 2 & 3 and has a current value of $2.24. Security B pays $1 in years 1 & 3 and pays nothing in year two. The current market value of security B is $160. Security C pays $1 in year 2 and has a current price of 0.74. Assume all three securities can be held long or short. Formulate an arbitrage strategy that generates a profit of $2 today with no future net liabilities.
Use the term structure for problems 2 – 7:
2. Calculate the discount function for the above term structure.
3. A bond pays $100 in year 1, 2, 3 and pays $1,100 in year 4. What is the price of the bond today (year zero)? What is the YTM?
4. You are offered an annuity where you pay $12,000 today and receive $5,000 in year 1, $6,000 in year 2, $1,000 in years 3-6. Do you purchase the annuity?
5. You have three bonds with the cash flows as shown in the table below. Construct a synthetic 1-year zero coupon bond with a face value of $100 using the three bonds (in other words find the number of each of the bonds needed to create a $100 cash flow in year 1. Use the term structure above to price the three bonds and the synthetic 1-year zero. Compare the price of synthetic 1-year zero to the 1-year discount factor.
Bond          Year 1             Year 2         Year 3
1                   10                   20                30
2                   10                   20               210
3                   210                  220                0

6. Construct a synthetic 2-year zero coupon bond with a face value of $100 using the three bonds (in other words find the number of each of the bonds needed to create a $100 cash flow in year 2. Use the term structure above to price the three bonds and the synthetic 2-year zero. Compare the price of synthetic 2- year zero to the 2-year discount factor.
7. Construct a synthetic 3-year zero coupon bond with a face value of $100 using the three bonds (in other words find the number of each of the bonds needed to create a $100 cash flow in year 3. Use the term structure above to price the three bonds and the synthetic 3-year zero. Compare the price of synthetic 3- year zero to the 3-year discount factor.
8. You need $200,000 for an anticipated outflow eight years from today. The prevailing interest rate is 7% (there is a flat yield curve). You have identified two coupon bonds that both mature in eight years and have face values of $1,000. One bond pays annual coupons of 6.20%, the other pays annual coupons of 8.70%.
Assuming that rates remain at 7% find the future value you would have in eight years for investing in both bonds. Based on these terminal values, how many of each type of bond will you need to buy to accumulate the required $200,000.
9. Coupons for the on the run par bonds for the following maturities are shown in the table below. Using the bootstrapping method, determine the yields for a 1-year zero, 2-year zero, 3-year zero and 4-year zero coupon bonds.

Maturity                Coupon for OTR Par
(years)                           Bonds
1                                       6%
2                                     6.5%
3                                       7%
4                                     7.5%

10. Assume you have 3 bonds as shown in the table below with prices, coupons and yield to maturities as shown. The maturity of these bonds is 6 years.

BOND    COUPON          PRICE YIELD TO MATURITY          YIELD
A                12%                              $1,219.70                         7.342%
B                  9%                               $1,074.26                         7.422%
C                  3%                               $790.90                            7.448%

Evaluate each of these bonds to determine which should be added to your portfolio. The criteria for evaluation includes coupon, yield to maturity, yield, total return for a coupon reinvestment rate (assumed to be 7%), and relative valuation based on component value. For each criteria, state which bond or bonds you would recommend. (Hint: for component value analysis find the price of Bond B based on the components as determined using Bonds A & B).

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Strategy: Sell 20 units of Security A short and Buy 20 units of Securities B & C.
Cash Flow today: + 20(2.24) = 44.80 {Security A}
- 20(1.60) = 32.00{Security B}
- 20(0.74) = 14.80{Security C}
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