Chartered Financial Analyst Level 1

Chartered Financial Analyst Level 1

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A bond portfolio consists of the following option-free annual-pay coupon bonds: Bond 1 Bond 2 Par value 300,000300,000 450,000 Market value 200,000200,000 400,000 Yield to maturity 4% 3% Macaulay duration 7.5 5.4 The modified duration of this portfolio is closest to:

Explanation:

The correct answer is A because the modified duration of the portfolio is calculated as the weighted average of the modified durations of the individual bonds, using market values as weights. Here's the step-by-step breakdown:

  1. Calculate Modified Duration for Each Bond:

    • Modified Duration (ModDur) = Macaulay Duration / (1 + Yield to Maturity)
    • ModDur of Bond 1 = 7.5 / (1 + 4%) = 7.211538
    • ModDur of Bond 2 = 5.4 / (1 + 3%) = 5.242718

  2. Determine Weights Based on Market Values:

    • Weight for Bond 1 = 200,000/(200,000 / (200,000 + $400,000) = 0.333333
    • Weight for Bond 2 = 400,000/(400,000 / (200,000 + $400,000) = 0.666667

  3. Calculate Portfolio Modified Duration:

    • Portfolio ModDur = (Weight for Bond 1 × ModDur of Bond 1) + (Weight for Bond 2 × ModDur of Bond 2)
    • Portfolio ModDur = (0.333333 × 7.211538) + (0.666667 × 5.242718) = 5.898992 ≈ 5.9

Why Not B or C?

  • B is incorrect because it uses par values instead of market values for weights, leading to a miscalculation.
  • C is incorrect because it mistakenly uses Macaulay duration instead of modified duration for the portfolio calculation.
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