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**CFA Practice Question**

Given the following table of spot rates, calculate a zero-volatility spread for a three-period instrument with a 7.5% coupon priced at $100.70.

B. 330 basis points

C. 250 basis points

A. 350 basis points

B. 330 basis points

C. 250 basis points

Correct Answer: A

Using trial and error, the value of zs = 350 basis points.

$100.70 = 3.75/(1+(.03+zs)/2)

^{1}+ 3.75/(1+(.033+zs)/2)^{2}+ 103.75/(1+(.035053+zs)/2)^{3}Using trial and error, the value of zs = 350 basis points.

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**User Contributed Comments**
19

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

quincy |
How to use Calculator for this one? |

cuong |
pick one option and then put into the equation. Using trial and error to get the final result. |

haarlemmer |
The problem here is the tech is so much advanced that using computer would be much easier. Maybe someday, we will have our exam on computer rather with calculator. |

danlan |
Suppose it's semiannual coupon, so the coupon for a period is 3.75 instead of 7.5 |

myanmar |
but the spot rates are on an annual basis, right? don't we have to devide the spotrates by 2 |

myanmar |
ok silly question, i've not seen the "/2" |

cwrolfe |
Calculation of z-spread is not in the LOS |

valeris |
Computing using calculator: 1. For each of the three periods determine PV of cash flow using spot rates (coupon=3.75) : a) Period 1 - 3.69458 b) Period 2 - 3.62925 c) Period 3 - 98.4807 Sum them up to get PV = 105.80448 Calculate the rate using PV above, FV =100, PMT = 3.75, N = 3. Rate = 1.747 x 2 = 3.5% |

Bevin |
I just put in PV = -100.7 FV = 100 N = 3 PMT = 3.75 Then CPT I/Y = 3.5 |

thanks |
I think valeris way of calculating rate is ok.. not sure abt Bevin's... esp because u used semi-annual rate for pmt and so technically 1/Y would also be semi-annual. Thus if you multiply 3.5*2, then the rate is no longer correct. |

MFTIOA |
Bevin - need to calculate the cash flow for each spot rate... that's the definition of the z-spread |

mishis |
valeris has N wrong, it should be 6 periods in calc. How to calculate this without using trial and error? |

TheHTrader |
The trial and error approach is conceptually better understood but time-consuming. I agree to valeris - easier to calculate but need a little adjustment in thinking it through - the last step integrates bootstrapping in PV = "purchase price", and the yield generated should be the z-spread. |

alallstar |
Valeris seems to have it right. mishis: Why would you use 6 periods? It says 3 periods, not 3 years. |

hardig |
Help - how did valeris get the pv cashflows - I can't get it to work out on BA ii+ |

gulfa99 |
guys its a simple question. You can answer it by looking at the options. Look at the term structure of spot rates, they are upward slopping. As we have learned earlier in a upward slopping spot curve, z rates are always higher than spot rates. By this logic answer is A, all other options are lower. |

johntan1979 |
Ignore gulfa99's comment. A is not higher than period 3's spot rate of 3.5053%. Follow valeris' way. That's the fastest and correct way. |

Shaan23 |
Valeris -- Impressive Would not have thought of that. |

MrFortei |
Please can someone tell how Valeris got his period a,b, and c answer using the ba ii plus calculator? |