Explanation

This question requires estimating the yield for a 6-year bond using linear interpolation between two known yields at different maturities.

Given data:

• Bond 1: 4 years maturity, YTM = 3.3%
• Bond 2: 7 years maturity, YTM = 5.1%
• Need to estimate: 6-year bond yield

Linear interpolation formula: $\text{Yield}_6 = \text{Yield}_4 + \frac{(6 - 4)}{(7 - 4)} \times (\text{Yield}_7 - \text{Yield}_4)$

Calculation: $\text{Yield}_6 = 3.3\% + \frac{(6 - 4)}{(7 - 4)} \times (5.1\% - 3.3\%)$ $\text{Yield}_6 = 3.3\% + \frac{2}{3} \times 1.8\%$ $\text{Yield}_6 = 3.3\% + 1.2\%$ $\text{Yield}_6 = 4.5\%$

Why this is correct:

1. Linear interpolation is the simplest and most common method for estimating yields between known points on the yield curve.
2. The 6-year maturity is 2/3 of the way between 4 years and 7 years.
3. The yield difference between 4-year and 7-year bonds is 1.8% (5.1% - 3.3%).
4. Adding 2/3 of this difference (1.2%) to the 4-year yield gives 4.5%.

Why other options are incorrect:

• Option A (3.9%): This would be too low and doesn't follow the proper interpolation calculation.
• Option B (4.2%): This might result from incorrect weighting or calculation errors.

Key concept: This question tests understanding of yield curve interpolation, which is fundamental in fixed income analysis for estimating yields at maturities where no bonds are directly quoted.