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**CFA Practice Question**

Suppose the spot rates (annualized) for Treasuries are given as:

1 year = 1.92% (1/2 of annualized 1 year spot rate)

1.5 years = 2.37% (1/2 of annualized 1.5 year spot rate)

2 years = 2.96% (1/2 of annualized 2 year spot rate)

6 months = 1.31% (1/2 of annualized 6 month spot rate)

1 year = 1.92% (1/2 of annualized 1 year spot rate)

1.5 years = 2.37% (1/2 of annualized 1.5 year spot rate)

2 years = 2.96% (1/2 of annualized 2 year spot rate)

The Z-spread (annualized) is 1.24% for a 2 year maturity, 4% coupon (paid semi-annually) bond with face value of $1,000. (Remember, these rates are calculated using 6-month periods.) The price of the bond is:

A. $1,001.86

B. $1,021.86

C. $1,024.25

**Explanation:**You have to divide the Z-spread by 2 (to get the 6-month rate) and then add it to the spot rates.

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**User Contributed Comments**
6

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

chantal |
can anyone explain pls ? |

cwest020 |
I keep getting 996.72 |

jjhigdon |
I am also confused. 20/(1.0131+.0062) + 20/(1.0192+.0062)^2 + 20/(1.0237+.0062)^3 + 1020/(1.0296+.0062)^4 = 943.08. Why is that not right? The 6 month spot rates, even before adding the spread are less than the 1/2 year coupon rate, so the bond should be trading at a discount, right? |

praj24 |
I'm really struggling with this, I've tried to calculate this price and I'm not getting the answer. Can anyone provide the right workings? From my calculations I have: Z-Spread/2 = 0.62 (Add to spot rates) 6 mths = 1.31 + 0.62 = 1.93 1 Year = 1.92 + 0.62 = 2.54 1.5 Year = 2.37 + 0.62 = 2.99 2 Year = 2.96 + 0.62 = 3.58 Therefore PV of CFs: 20/(1.0193)^0.5 = 19.81 20/(1.0254) = 19.50 20/(1.0299)^1.5 = 19.14 1020/(1.0358)^2 = 950.71 Price = 1,009.16??? Also tried the same as JJ above but no luck. |

Bedee |
Guess 1.009,16 is closest to the offered results, therefore Choice A is the correct one. Praj24's calc is the only feasible I am aware of. Don't forget u got many traps on the exam! |

ConnerVP1 |
I had: Z-Spread= .62 .5 Year = 1.31/2+.62 = 1.275% 1 Year = 1.92/2+.62 = 1.58% 1.5 year = 2.37/2+.62 = 1.805% 2 Year = 2.96/2+.62 = 2.10% PV Yr .5 = 20/1.01275 = 19.748 Yr 1 = 20/(1.0158)^2 = 19.38 Yr 1.5 = 20/(1.01805)^3 = 18.96 Yr 2 = 1020/(1.0210)^4 = 938.60 PV= 996.69 I don't see where I went wrong, pretty sure analyst notes is off. |