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Explain the concept of convexity. What are the properties of convexity? Consider an 8%, 25-year bond selling to yield 9%. If the yield changes to 10% calculate percent change in price. (a: -9.29%) If the modified duration and convexity of the bond are 10.12 and 172.52 respectively, calculate the percentage change in price due to (1) duration (a: –10.12%), (2) convexity (a: 0.8626%), and (3) the combined effect of duration and convexity.

User Dkz
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Final answer:

Convexity is a concept in finance that measures how sensitive the price of a bond is to changes in interest rates. The properties of convexity include: positive convexity, greater convexity for longer-term bonds and bonds with lower coupon rates, and the relationship between convexity and price change. The percentage change in price due to duration is calculated by multiplying the yield change by the modified duration, while the percentage change in price due to convexity is calculated by multiplying the yield change squared by half the convexity.

Step-by-step explanation:

Convexity is a concept in finance that measures how sensitive the price of a bond is to changes in interest rates. A convex bond has a price-yield relationship that is not linear, meaning that the percentage change in price is not equal to the percentage change in yield. Instead, for a given change in yield, the percentage change in price is higher for lower yields and lower for higher yields.

The properties of convexity include:

  • Convex bonds have a positive convexity, meaning that the price increases more than proportionally when yields decrease, and decreases less than proportionally when yields increase.
  • Convexity is greater for longer-term bonds and bonds with lower coupon rates.
  • The higher the convexity of a bond, the more the bond's price will increase due to a decrease in yield, and the less the price will decrease due to an increase in yield.

To calculate the percentage change in price due to duration, you multiply the yield change by the modified duration. To calculate the percentage change in price due to convexity, you multiply the yield change squared by half the convexity.

User Alepisa
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