Question 1
– And here are the questions:
Using the spreadsheet “Term Structure Template.xlsx” please complete the following exercises.
1. Calculate the prices for the first two bonds (.5 and 1 yr to maturity)
2. Calculate the spot rates, discount factors, and forward rates for the curve. State these rates both on a semi-annual and a BEY basis.
3. Use the spot rates to price a 6-year semi-annual pay 6% coupon bond. (Note: You will want to do this in an extra column in your excel spreadsheet).
4. Use the spot rates to price a 5-year semi-annual pay 9% coupon bond. (Note: You will want to do this in an extra column in your excel spreadsheet).
5. Use the spot rates to price a 4-year 7% semi-annual pay coupon bond. (Note: You will want to do this in an extra column in your excel spreadsheet).
Problem: Assume that you wish to take a bet on the yield spread between two bonds: a 10-year corporate bond rated BB and a 10-year Treasury bond. Information about both bonds follows:
10 year Treasury bond 10 year BB corporate bond
Maturity 10 years 10 years
Coupon rate 5% 7%
YTM 5.5% 7.5%
Current price $96.193 $96.526
DV01 $0.0744 $0.0680
Assume that you believe the economy is going to get much worse in the future, and you wish to make your bet based on this premise. Also assume that you will buy 1000 units of the bond that you are going to hold “long.” Finally, ignore margin requirements, interest on cash proceeds, and any intervening coupon payments of the long and short bonds. Answer the following questions in a Word document:
1. Are you betting that rates are going to converge or diverge? Why?
2. Which bond will you buy and which bond will you short-sell?
3. What is the DV01 ratio? Round to exactly 4 decimal places.
4. Using the DV01 ratio, calculate the number of units of the bond you will short-sell.
5. State your initial balance sheet assuming you implement the trade. Assume that you come up with the cash to fund the long position out of your pocket. Be sure to clearly label each column and describe each entry. Also be sure to include the totals.
6.Assume that in 1 month, the following is the information about the two bonds
10 year Treasury bond 10 year BB corporate bond
Maturity 10 years 10 years
Coupon rate 5% 7%
YTM 6% 7%
Current price $92.561 $100 7.
7.Restate your balance sheet using the above information. Be sure to clearly label each column and describe each entry. Also be sure to include the totals.
8. What is your gain or loss on equity in dollars?
9. What is your percentage gain or loss on equity as a holding period return?–
Time in Years Time in Periods Coupon Rate YTM Price Discount Factor Sum of current and prior period discount factors Theoretical Semi-Annual Spot Rate Theoretical Annual Spot Rate Implied Semi-Annual Forward Rates Implied Annual Forward Rates
0.5 1 0.00% 5.25% 0.97442 0.974421 2.62500% 5.25000% 2.87515% 5.75030%
1 2 0.00% 5.50% 0.94719 1.921610 2.75000% 5.50000%
1.5 3 5.75% 5.75% $100.00
2 4 6.00% 6.00% $100.00
2.5 5 6.25% 6.25% $100.00
3 6 6.50% 6.50% $100.00
3.5 7 6.75% 6.75% $100.00
4 8 6.80% 6.80% $100.00
4.5 9 7.00% 7.00% $100.00
5 10 7.10% 7.10% $100.00
5.5 11 7.15% 7.15% $100.00
6 12 7.20% 7.20% $100.00
6.5 13 7.30% 7.30% $100.00
7 14 7.35% 7.35% $100.00
7.5 15 7.40% 7.40% $100.00
8 16 7.50% 7.50% $100.00
Assume that par = 100
Given
Calculated
