Duration

Based on the bond pricing equation:

It is evident that the factors affecting the price of a bond are the time to maturity (n), coupon rate, and the interest rate (i) which is used to discount the cash-flows of the bond to determine its price today.

Duration is a measure of the sensitivity of the price of a bond to a change in interest rates. It is the weighted average of the maturities of all cash-flows of a bond. It is expressed as a number of years, and represents the focal point of a bond’s cash-flows. A 5-year duration, for example, means that a bond will decrease (increase) in value by 5% if interest rates rise (fall) by 1%.

Rising interest rates cause a fall in bond prices, whereas falling interest rates cause a rise in bond prices. When interest rates go up (down), cash-flows are discounted at a higher (lower) rate, and thus the present value of a bond’s cash-flows falls (rises).

Investors use duration to measure the volatility of a bond. The longer the duration, the longer an investor has to wait to receive the bulk of the payments, and the more its price will drop as the interest rate goes up. This also means that, because of the additional risk, a higher duration bond will also have a higher expected return or yield.