Question

Explain the concept of duration and describe how it is used in hedging interest rate futures. Be sure to discuss the limitations of duration.

Answer 1

Duration is the degree of sensitivity of the price of an underlying to one basis point change in the intrerst rates. Mathematically, it is the 1st differential of the price w.r.t. the interest rates. Over time there have been several ways of calculating duration such as Modified duration, Macaulay Duration and the most recently Effective duration. ED is the most common method presently being used and is calculated as follows:

As in the case of bonds, the price of the bond falls with the rise in interest rates and vice versa, the ED cant be negative for bonds.

Limitations of Duration are as follows:

1. Inaccurate for large changes: As it is only the first differential of the price yield curve, it doesnt incorporate for the curvature od the curve and is only the tangent of the curve. So as the changes in terest rate become of high magnitude, the distance between the tangent line and the curve increases leading to inaccuracies. Because of this reason the concept of convexity came up

2. Interest rate: Duration considers risk only related to interest rates and ignores risks pertaining to factors such as credit risk, changes in the market value or defalut risk

3. Mixed portfolio: Duration is more appropriate for single asset portfolios expecially bonds and in case of a diversified portfolio, comprising stock bonds and other instruments, duration is not a complete measure and rather difficult to estimate.

Use of durate in hedging interest rate futures:

Interest rate futures are entered into to safeguard against the rising interest rates which would cause the price of the underlying to fall. If the expectation is such that the interest rate will rise, the party that wants to hedge would enter into a future contract to buy an interest bearing underlyingat a future date and at a specified price. The counter party obviouls expects the interest rates to fall and enters into the future for a specualtive purpose.

As explained earlier, duration is the measure of movement in price wrt to the movement in the interest rate risk so once the duration is estimated, we know how much will the price move and in which direction with and exoected change in the interest rate. Using this information, the contrated price is determined for the IRF