Yo Man

Duration and Convexity - The Basics

During the last twelve months the 2-Year U. S. Treasury Note yield has fallen from a high of 6.45% in July to

a low of 3.90% in June. As a result many fixed income portfolios have had their duration shorten

significantly. This was due to many of the embedded options being priced in-the-money or to the call date. As

a result of the lower rates, callable securities began to be called away and principal prepayments on mortgagerelated

products began to increase. This resulted in higher cash balances and shorter duration fixed income

portfolios.

Moving forward, when and if interest rates begin to rise, embedded options will shift out-of-the-money. This

shift will cause the bond’s duration to lengthen, as it will be priced based on its yield to maturity instead of on

the shorter call date. Keeping these interest rate changes in mind, when analyzing individual bonds or fixed

income portfolios, duration and convexity are two sensitivity measures that help illustrate exposure to parallel

changes in interest rates.

Duration

Starting with duration. Duration is a measure of the price volatility of a bond or portfolio equal to the

weighted average term to maturity of the bond or portfolio’s cash flows. The weights are the present values of

each cash flow as a percentage of the present value of all cash flows. The higher the duration of a bond or

portfolio, the higher it’s percentage price volatility. Example, suppose a portfolio has a duration equivalent to

4%. Then that portfolio’s market value will decline 4% for each 1% increase in interest rates or increase 4%

for each 1% decline in interest rates.

Exhibit 1 illustrates how the price of a fixed income portfolio might respond to a parallel shift in the yield

curve.

Here, r represents a parallel shift in

interest rates, measured in percentages.

For example, r = 1.0-%, would

correspond to a 1.0-% (or 100 basis point)

rise in interest rates. The variable p is

the...