Adjusted Vs. Effective Duration

Named after Frederic Macaulay, this type of duration measures the number of years it takes investors to recover the cost of a bond. Thus, a bond might have a maturity of 10 years -- the time until the principal is returned -- but a shorter duration such as 8.5 years if the bond makes quarterly interest payments. Like all duration metrics, Macaulay's duration recasts the bond's interest and principal payments in terms of their present value. Macaulay's duration is calculated by adding up the present value of the bond's cash flows, multiplying them by the time to receipt and dividing the sum by the market price of the bond.

Modified duration takes Macaulay's duration one step further, adjusting it to express a bond's sensitivity to changes in interest rates. Specifically, modified duration indicates by how much a bond's price will change if interest rates rise or fall by exactly 1 percent, or 100 basis points. To calculate modified duration, divide Macaulay's duration by one plus the yield to maturity divided by the number of coupon periods per year. For example, a bond with a modified duration of 5.3 would be expected to increase in price by 5.3 percent if interest rates fall by 1 percent or fall by 5.3 percent if interest rates rise by 1 percent.

Some bonds contain call features, meaning that the issuer can redeem the bond ahead of schedule on specific dates. Callable bonds may be redeemed when interest rates fall, because issuers can refinance their debt more cheaply. Investors generally don't like having their capital returned in these situations as they're stuck reinvesting it at lower prevailing rates. Through complex modeling, effective duration refines modified duration by incorporating the probability of issuers exercising their call options.

Duration is fundamental to bond investing for many reasons. It provides a measure of a bond's interest rate risk that complements other risk criteria, such as credit and liquidity risk. Duration also enables comparison of interest rate risk across different bonds of similar maturities, and it can be applied across entire bond portfolios as an average weighted duration to provide an overall measure of risk. Most importantly, duration is used by investment managers to maximize their future profits -- if their predictions are correct. For example, an asset management firm that is bullish on bonds, meaning that it believes interest rates will fall, can maximize gains for its investors by constructing a high duration portfolio.