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Chartered Financial Analyst Level 1

Chartered Financial Analyst Level 1

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Two-year and three-year government benchmark zero-coupon bonds are priced at 96 and 93 (per 100 face value), respectively. The implied one-year forward rate in two years' time is closest to:

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Explanation:

The correct answer is B (3.23%). The implied forward rate is derived from the relationship between the spot rates of the two- and three-year zero-coupon bonds. The discount factors for the two-year and three-year bonds are calculated as follows:

  • Two-year bond: DF₂ = 0.96 = 1 / (1 + Z₂)² → Z₂ = 2.0621%
  • Three-year bond: DF₃ = 0.93 = 1 / (1 + Z₃)³ → Z₃ = 2.4485%

The implied forward rate (IFR₂,₁) between the second and third year is calculated using the formula:

(1 + Z₂)² × (1 + IFR₂,₁) = (1 + Z₃)³

Substituting the values:

(1.020621)² × (1 + IFR₂,₁) = (1.024485)³

Solving for IFR₂,₁:

(1 + IFR₂,₁) = (1.024485)³ / (1.020621)² = 1.032258

IFR₂,₁ = 1.032258 - 1 = 3.2258% ≈ 3.23%.

This calculation aligns with the principles of forward rate determination in fixed-income securities, where the forward rate is inferred from the term structure of interest rates.

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