Question

A related problem with duration analysis revolves around the concept of convexity . Please provide more information on convexity and suggest two ways a way of reducing the impact of this limitation.

Answer 1

Convexity describes relationship between bond price and bond yields that tells how duration of bond changes due to change in interest rates.It is used to measure and control market risk of portfolio.

example-SecurityX: if interest rate increases, bond yield increases and bond price falls

Security Y: if interest rate decreases, bond yield decreases and bond price rises.

here, Security X has higher convexity than Security Y.

Convexity is a better measure for determining impact on bond price, when there are large and more fluctuations in interest rates.As convexity increases, systematic rate of portfolio increases and vice-versa.

Higher the coupan rate of security, lower will be its convexity.

Convexity is a better measure of interest rate risk than duration as duration assumes interest rate and bond price have linear relationship.

Positive convexity- when bond duration rises and bond yield falls.

Negative convexity- when bond duration increases and bond yield rises.therefore when interest rate rises, prices increases.

Reduce limitation of duration: duration does not account accurately for more changes in interest rates.therefore, convexity measure is also included in its calculation.

Modified duration and convexity considered as best for calculation of sensitivity of bond price to interest rate changes.

But major disadvantage is assuming parallel shift in yields curve.

Convexity is used for bonds with low credit risk. THerfore it should not be used for high credit risk bonds.

Convexity assumes cash flow of a bond does not change with change in interest rates

to reduce this limitation- Effective convexity is being used.it consider cash flow changes in relation to change in yield.