Fixed Income Problem

Chapter 18

1. What is the static spread for a three-year 9% coupon corporate bond selling at 105.58? Choose one from 50, 100, or 120 basis points. Assume semiannual compounding.

|Period |1 |2 |3 |4 |5 |6 |

| Spot Rate (%) |4 |4.2 |4.9 |5.4 |5.7 |6 |

Hint: you should use the trial and error method by calculating the summed-up discounted cash flows.

You can verify your answers in excel, using the “Solver” add-in. (Tools… Add-ins… Tick “Solver Add-in”, and use it).

2. The current on-the-run yields for the Ramsey Corporation are as follows:

|Maturity (years) |Yield to Maturity (%) |Market Value |

|1 |7.5 |100 |

|2 |7.6 |100 |

|3 |7.7 |100 |

Assume that each bond is an annual-pay bond. Each bond is trading at par, so its coupon rate is equal to its yield to maturity. Answer the below questions.

(a) Using the bootstrapping methodology, complete the following table:

|Year |Spot Rate (%) |One-Year Forward Rate (%) |

|1 | | |

|2 | | |

|3 | | |

(b) Using the spot rates or the one-year forward rate, what would be the value of an 8.5% option-free bond of three years maturity?

(c) If σ is assumed to be 10%, how much is the lower one-year forward rate one year from now?

(d) Demonstrate that if σ is assumed to be 10%, the lower one-year forward rate two years from now is approximately 6.437%.

(e) Show the binomial interest-rate...