Question

Which of the following statements about convexity are true?

I. Convexity accounts for the curvilinear function of bond rates
II. A bond with a very low coupon and a long maturity will have low convexity III. A bond investor would seek to avoid bonds with high convexity.
IV. Convexity is defined as the rate of change of the slope of the price/yield curve
V. There is an inverse relationship between maturity and convexity
a. I.
b. II. III. IV.
c. I. IV.
d. II. IV. V.
e. I. II. IV. V.

Answer 1

Among the statements provided, only statements I and IV about convexity are true. Convexity reflects the curvilinear relationship of bond prices with interest rates and is the rate of change of the slope of the price/yield curve.

Step-by-step explanation:

Among the statements about convexity presented, the correct ones are:

• Convexity accounts for the curvilinear relationship between bond prices and interest rates. (Statement I)
• Convexity is defined as the rate of change of the slope of the price/yield curve. (Statement IV)

Now, to clarify the incorrect ones:

• A bond with a very low coupon and a long maturity will generally have high convexity, not low. (Statement II is false)
• Bond investors often prefer bonds with high convexity, especially in a stable or falling interest rate environment, as they tend to increase in price more than they decrease for a given change in yield. (Statement III is generally false)
• There is generally a direct relationship between maturity and convexity; longer maturity bonds tend to have higher convexity. (Statement V is false)

The correct answer to the question is c. I. IV.