Practice Question
The convex shape of the bond price-yield curve shows:
I. The curve is always downward sloping.
II. The curve is flatter when the yield is high.
III. For 1% changes in the interest rate, the decreases in the bond price when the interest rate increases are greater than increases in the bond price when the interest rate decreases.
Select one:
Statement I: The bond price-yield curve is always downward sloping because as the yield (interest rate) increases, the present value of the bond’s future cash flows decreases, leading to a lower bond price. This is a fundamental characteristic of the bond price-yield relationship.
Statement II: The curve is flatter when the yield is high because at higher yields, the bond price becomes less sensitive to changes in yield. This results in a less steep (flatter) curve. This is a direct result of the convexity of the price-yield curve.
Statement III: This is incorrect. Convexity actually means that for equal changes in yield (e.g., ±1%), the bond price increases more when yields fall than it decreases when yields rise. In other words, bond prices gain more for a drop in yield than they lose for a similar increase.
Conclusion: Statements I and II are correct. Statement III misrepresents convexity. Therefore, the correct answer is:
B) Both I and II are correct.