Interest rates are expressed as annualized rates for the term specified. Report your interest rate answers as fractional numbers like 0.11 for 11% per year.
Problem A.
Construct a Replicating Portfolio (RP) to replicate a 1.5-year Bond-0 that pays A1 percent of coupon per year. The available bonds for replication are:
a one year zero coupon Bond-1, a 1.5-year Bond-2 that pays A2 percent coupon per year, and a 1-year Bond-3 which pays A3 percent coupon per year.
All the bonds (Bond-0, Bond-1, Bond-2, and Bond-3) have the same face value of $100 and pay their annual coupons two times a year.
Compute an arbitrage trading strategy to generate profits, if any, when the current market prices of the four bonds, respectively, are A4, A5, A6 and A7.
1. What is the dollar face value of Bond-1 in the RP?
2. What is the dollar face value of Bond-2 in the RP?
3. What is the dollar face value of Bond-3 in the RP?
4. What is the cost of the RP?
5. What is the arbitrage fair price of Bond-0?
6. Write 1 if Bond-0 is to be held long and 0 if Bond-0 is to be held short in arbitrage trading strategy.
7. Write 1 if Bond-1 is to be held long and 0 if Bond-1 is to be held short in an arbitrage trading strategy.
8. Write 1 if Bond-2 is to be held long and 0 if Bond-2 is to be held short in an arbitrage trading strategy.
9. Write 1 if Bond-3 is to be held long and 0 if Bond-3 is to be held short in an arbitrage trading strategy.