- CFA Exams
- CFA Level I Exam
- Topic 6. Fixed Income
- Learning Module 29. The Arbitrage-Free Valuation Framework
- Subject 3. Valuing an Option-Free Bond with a Binomial Tree

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**CFA Practice Question**

Assume one year spor rate S

B. 4.153%

C. 5.072%

_{1}is 3%, and 2 year spot rate S_{2}is 3.2%. Interest volatility is 20% for all the years. What is the higher rate at year 1 in the bionomial interest rate tree?A. 3.784%

B. 4.153%

C. 5.072%

Correct Answer: B

In a binomial tree the 1 year spot rate is equal to the forward rate for the first year F

_{0,1}. Since (1 + S_{2})^{2}= (1 + F_{0,1}) (1 + F_{1,2})=> 1.032^{2}= 1.03 x (1 + F_{1,2}) => F_{1,2}= 3.4%. This is the average of higher and lower interest rates. F_{1,2H}= 0.034 e^{1 x σ}= 0.034 e^{0.2}= 4.153%###
**User Contributed Comments**
2

User |
Comment |
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berns23 |
Shouldn't the answer be C? 5.072% i.e 0.034e*(2x0.2) |

berns23 |
Nvm..I finally got it. Page 287 is clear enough. |