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**CFA Practice Question**

A 5.25% coupon Treasury security with one year left to maturity is selling for 101.75, and a two-year 5.45% coupon Treasury security is selling at a discount of 0.40% from par. Assume annual discounting. The forward rate for the second year is ______.

A. 5.45%

B. 5.73%

C. 8.07%

**Explanation:**The first year spot rate is computed first from the 1-year bond. It is then substituted in the 2-year bond valuation equation for solving the forward rate for the second year.

Year 1 spot rate based on the 1-year bond: FV = 105.25; N = 1; PV = -101.75; CPT I/Y = 3.44%

2-year bond valuation equation: 99.60 = 5.45/(1.0344) + 105.45/[(1.0344)(1 + f)] => f = 105.45 / [(99.60 - 5.45/1.0344) x 1.0344] - 1 = 0.0807, or 8.07%

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**User Contributed Comments**
15

User |
Comment |
---|---|

octavianus |
100 principal + 5.285 coupon/(1 + spot) = 101.75 Should we assume annual coupons, even though normally we use semi-annual if the problem does not make mention? |

steved333 |
Question says to assume annual |

steved333 |
sum of discounted cfs. First coupon discounted at first year. Second year coupon and fv discounted not at rate^2 b/c the second year's rate is different from the first. So it's discounted by the first year's times the second year's rate. Use algebra to solve for the second year's rate. |

StanleyMo |
good questions. |

scotty21 |
Glad I know how to solve this now, but still dont think I could get this in 1.5 mins! |

aravinda |
Does anyone know why the FV for 1st year should be 105.25? |

cwa4 |
It's including the coupon payment of $5.25 you would receive at maturity. |

boddunah |
good question: expect a question like on the exam. |

jpducros |
DON'T do the following mistake I made : discounting the second cash Flow of the 2 year Bond at (1+X)^2....otherwise you'll find that B is correct. |

mindi |
B is the spot rate for year 2, so in order to get the forward rate = [(1+ .0573)^2]/(1+.0344) -1 = .0807 technically bond valuations should be done CF1/ (1+spot rate1) + CF2/ (1+spot rate2)^2 + ... |

Insipidity |
Thank you mindi! |

NickNT |
I've got the spot for the second bond equal 5.67% - am I wrong? |

Lambo83 |
NickNT I got the same 5.67% for the second bond. I used that in the formula Mindiised and got 7.9% as the forward rate. Mindi I'm curious why you used 5.73% instead. Thanks |

Znanje35 |
jebi ga |

chenyr05 |
how to get the spot rate for year 2 at 5.73%? I got 5.67%, which seems not correct. |