- CFA Exams
- CFA Level I Exam
- Topic 6. Fixed Income
- Learning Module 44. Introduction to Fixed-Income Valuation
- Subject 7. The Maturity Structure of Interest Rates

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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 spot rate for the second year is ______.

A. 5.67%

B. 5.45%

C. 5.73%

**Explanation:**The first year spot rate is computed first from the one-year bond. FV = 105.25; N = 1; PV = -101.75; CPT I/Y = 3.44%

It is then used in the valuation of the two-year bond, without the forward rate. 99.60 = 5.45/(1.0344) + 105.45/(1 + s

_{2})

^{2}

s

_{2}= [105.45 / (99.60 - 5.45/1.0344)]

^{1/2}- 1= 0.0573, or 5.73%

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**User Contributed Comments**
11

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

george2006 |
The spot rate for 2nd year == the spot rate from t=0 to t=2. Don't confuse it with the expected future spot rate == forward rate from t=1 to t=2. Spot rate is always for the rate at time zero. |

tanyak |
where do they get 1o5.25 and 3.44% in the same calculation? |

Shelton |
clear explanation S=5.7293% |

Janey |
I think the 105.25 came from the one year treasury $100 principal plus the $5.25 for the coupon payment |

ehc0791 |
The coupon treasury should make coupon payment every 6 month, not every year, right ? I don't get this question. |

rkrazib |
"assume annual discounting" has been mentioned here. |

tonytough |
shelton,i agree with janey, since spot rate is ytm for zero coupon bond, for 1yr coupn pmt conviniently coincides with maturitry (hence principal of no interim pymts b4 maturity upheld). |

mountaingoat |
i don't understand why s1 was used in calculation and not just solve using s2. afterall only C2 coupon was used in association with first cashflow. any insight? |

LordHux |
is there an easier way to do this? |

shann680 |
folks it doesn't matter if you use fv=105=25 or fv=100 and pmt=5.25. you still get the i/y. |

michaeloa3 |
This doesn't make sense to me. Isn't the YTM on the 2 year treasury they mention the spot rate? |