- CFA Exams
- CFA Level I Exam
- Topic 6. Fixed Income
- Learning Module 6. Fixed-Income Bond Valuation: Prices and Yields
- Subject 3. Relationships between Bond Price and Bond Characteristics

###
**CFA Practice Question**

Given the following spot rates, the arbitrage-free value of a 5%, 2.5-year Treasury would be closest to ______.

B. $96.61

C. $100.00

A. $86.10

B. $96.61

C. $100.00

Correct Answer: A

Arbitrage-free value = 2.5/(1.05)

^{1}+ 2.5/(1.052)^{2}+ 2.5/(1.054115)^{3}+ 2.5/(1.056174)^{4}+ 102.5/(1.058)^{5}= 86.10###
**User Contributed Comments**
21

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

kalps |
interest each 1/2 year = 2.5 Spot rate / 2 = denominator (discount factor semi annual) Could split in to 6 different compenets if required |

o123 |
*better off using the formula for a question like this! |

Rotigga |
You better know how to make love to your HP-12C for a question like this. |

octavianus |
o123: what formula are you referring to that would make this simpler? |

steved333 |
Hey, Rotigga, I think my TI-BAII will be giving it to me rough with no rewards on this one!!! |

raida |
any one with any ideas on how to calculate it on BA II? I doubt will have enough time to calculate it manually |

thekapila |
on TA BA11: FOR FIRST 3 CALCULATIONS USE FV = 2.5 1/Y = SPOT RATE/2 N = PERIOD MENTIONED FOR LAST USE FV = 100+2.5 = 102.5 SPOT RATE = 1/Y = 5.8 N = 5 PV = 86.100 |

jwebbs |
^ so you use the length of the entire treasury as the present value all the time? or did u just get lucky? |

capitalpirate |
gr8 work thekapila... genius! |

Richie188 |
use a spreadsheet.... |

IvanTG |
unfortunately you can't use a spreadsheet at the exam... |

8thlegend |
Arbitrage-free value = 2.5/(1.05)1 + 2.5/(1.052)2 + 2.5/(1.054115)3 + 2.5/(1.056174)4 + 102.5/(1.058)5= 86.10 Where did the 2.5 come from? is it the 5% coupon 5/2? How did they get the discount rate? |

Mutsa |
Treasury bonds pay coupon semi annually. Annual coupon is 5% of 100 i.e 5. Semi annualis 5/2 i.e 2.5. Alos forgot and used coupon of 5%. Got a wong answer. Will keep it in mind for next time |

Saxonomy |
I prefer... 2.5 / 1.1000^(0.5) + 2.5 / 1.1040^(1.0) + 2.5 / 1.1082^(1.5) + 2.5 / 1.1123^(2.0) + 102.5 / 1.1160^(2.5) Just much more cleaner. Call me weird. |

akils |
I agree with Saxonomy |

jonan203 |
i have to figure out a way to do this on a 12c without having to write anything down. |

davcer |
2.38+2.25+2.13+2.0+77.3 and thats it |

ascruggs92 |
If you know basic math you would see immediately that the stated rate and discount rate differential is too large for B. to be the answer (if maturity was 1 year away PV would be about 95). C. is obviously wrong which leaves only A. |

ashish100 |
this is CFA, not basic math. we dont know basic math! |

Logaritmus |
listed bond price <= price of 5 yr semi with YTM = 10% = 89.176 < B,C that easily eliminate B and C. |

ZETA |
okay guys, the whole point of buying the notes is because we dont have the time right why on earth are these notes full of manual calculations instead of finacial calculations, I mean where is the common sense here. |