Explanation

The price/yield relationship for option-free bonds is convex. This means that:

1. Convexity describes how the duration of a bond changes as interest rates change
2. For option-free bonds, as yields increase, bond prices decrease at a decreasing rate
3. As yields decrease, bond prices increase at an increasing rate

Key points:

• Linear relationship (Option A) is incorrect because bond prices don't change at a constant rate with yield changes
• Concave relationship (Option C) is incorrect - this would describe bonds with embedded options (like callable bonds)
• Convex relationship (Option B) is correct because:
  • When yields rise, the price decline is less than what would be predicted by duration alone
  • When yields fall, the price increase is more than what would be predicted by duration alone

Mathematical representation:

The price-yield relationship can be expressed as: $P = \sum_{t=1}^{n} \frac{C}{(1+y)^t} + \frac{F}{(1+y)^n}$ Where:

• P = bond price
• C = coupon payment
• F = face value
• y = yield to maturity
• n = number of periods

This relationship produces a convex curve when graphed, with the curve bending toward the origin.