Negative Convexity

What Is Negative Convexity?

Negative convexity exists when the state of a bond's yield curve is inward. A bond's convexity is the rate of change of its duration, and it is measured as the second derivative of the bond's price with respect to its yield. Most mortgage bonds are negatively arched, and callable bonds typically show negative convexity at lower yields.

Grasping Negative Convexity

A bond's duration alludes to the degree to which a bond's price is influenced by the rise and fall of interest rates. Convexity demonstrates how the duration of a bond changes as the interest rate changes. Typically, when interest rates decline, a bond's price increases. In any case, for bonds that have negative convexity, prices decline as interest rates fall.

For instance, with a callable bond, as interest rates fall, the incentive for the issuer to call the bond at par increases; subsequently, its price won't rise as fast as the price of a non-callable bond. The price of a callable bond could really drop as the probability that the bond will be called increases. For this reason the state of a callable bond's curve of price with respect to yield is sunken or negatively raised.

Convexity Calculation Example

Since duration is an imperfect price change assessor, investors, analysts, and traders work out a bond's convexity. Convexity is a helpful risk-the board device and is utilized to measure and deal with a portfolio's exposure to market risk. This assists with expanding the precision of price-development expectations.

While the specific formula for convexity is fairly convoluted, a guess for convexity can be found utilizing the accompanying simplified formula:

Convexity estimate = (P(+) + P(- ) - 2 x P(0))/(2 x P(0) x dy ^2)

Where:

P(+) = bond price when interest rate is diminished

P(- ) = bond price when interest rate is increased

P(0) = bond price

dy = change in interest rate in decimal structure

For instance, expect a bond is at present priced at $1,000. In the event that interest rates are diminished by 1%, the bond's new price is $1,035. Assuming interest rates are increased by 1%, the bond's new price is $970. The surmised convexity would be:

Convexity estimate = ($1,035 + $970 - 2 x $1,000)/(2 x $1,000 x 0.01^2) = $5/$0.2 = 25

While applying this to estimate a bond's price utilizing duration a convexity adjustment must be utilized. The formula for the convexity adjustment is:

Convexity adjustment = convexity x 100 x (dy)^2

In this model, the convexity adjustment would be:

Convexity adjustment = 25 x 100 x (0.01)^2 = 0.25

At last, utilizing duration and convexity to get an estimate of a bond's price for a given change in interest rates, an investor can utilize the accompanying formula:

Bond price change = duration x yield change + convexity adjustment

Features

Surveying a bond's convexity is a great method for estimating and deal with a portfolio's exposure to market risk.
Negative convexity exists when the price of a bond falls as well as interest rates, bringing about an inward yield curve.