Easiest Fixed Income Midterm exam ever
March 7, 2006 (30 points)
1. (6 points) Today is March 7th 2006. You borrow $1MM (1,00,000 USD) for 18 months
and decide to invest it for 15 months at the current market rates shown below :
6 month: 5.00% / 5.10% 15 month: 5.20% / 5.30% 18 month: 5.40% / 5.50%
You wish to hedge the mismatched position. Use the adequate Eurodollar contract quotes from exhibit 1 to determine which FRA to use and its price (use last trade quote)
What amount to you deal for a complete hedge ?
When it comes to fixing the FRA after 15 months, the 3-month rate is 6.09% / 6.19%.
What is the settlement amount?
2. (6 points) Use a binomial interest tree to determine the option price of a 3-year 8% bond that pays interest annually, if it’s a callable in one year at 101.
Use the following zero rates for the problem: 6 month: 5%
1 year: 5.30% 2 year: 5.40% 3 year: 5.50%
Assume the lowest 1-year forward rate to be 5.70% and 1-year volatility = 10%. The bond after 3 years trade at 103.25.
3. (3 points)Today is March 7, 2006. IBM 7% October 15, 2026 bond trades at 101 and pays semi annually.
What is the YTM of the bond using the approximation formula only?
What is the dirty price?
What is my total cost including accrued interest if I wish to purchase 120 bonds?
---4. (3 points)What is the modified duration of a 5-year 5% coupon bond paying annually? Assume a flat yield curve at 5.5%.
This bond has a convexity of 120. What is the bond’s new price for a 50BP increase in yield using duration and convexity?
5. (2 points)Here are the following bids on the $70 billion face value of the 10-year Treasury bond auction. The Fed requested $20 billion.
JPM : 20 billion @4.65%
Merrill :15 billion @4.68%
Goldman Sachs: 15 billion @4.63%
Morgan Stanley : 22 billion @4.66%
Who gets what and what is the Fed’s bid on its share ?
---6. (10 points)
B. What is this trade betting on ?
7. Rate the difficulty of this exam from 1 to 5 (1 = easy)
