Question

Suppose that the annual yield to maturity for the 6-month and 1-year treasury bill is 4.6% and 5.0%, respectively. these yields represent the 6-month and 1-year spot rates. also assume the following treasury yield curve (i.e., the price for each issue is $100) has been estimated for 6-month periods out to a maturity of 3 years:

- Years to Maturity: 1.5, Annual Yield to Maturity (BEY): 5.4%
- Years to Maturity: 2.0, Annual Yield to Maturity (BEY): 5.8%
- Years to Maturity: 2.5, Annual Yield to Maturity (BEY): 6.4%
- Years to Maturity: 3.0, Annual Yield to Maturity (BEY): 7.0%

Compute the 1.5-year spot rate.
A. 5.9870%
B. 6.4665%
C. 5.4146%
D. 5.8297%

Answer 1

The 1.5-year spot rate can be calculated using the given formulas, resulting in a value of 5.9870%. Therefore, the correct option is A.

Step-by-step explanation:

The 1.5-year spot rate can be calculated using the formula:

Spot rate = [(1 + 1-year spot rate)2 / (1 + 6-month spot rate)] - 1

Plugging in the given values:

1-year spot rate = 5% = 0.05

6-month spot rate = 4.6% = 0.046

Spot rate = [(1 + 0.05)2 / (1 + 0.046)] - 1 = (1.1025 / 1.046) - 1 = 5.9870%

Therefore, the 1.5-year spot rate is 5.9870%.