# Measuring a Bond's Interest-Rate Sensitivity

*What is the difference between duration and average life? -- Kevin Hwang*

Kevin,

Bond duration

and average life are different ways of measuring the interest-rate sensitivity of a debt security.

Duration, measured in years, is the amount of time it will take for a bond investor to receive half of the present value of all future cash flows (coupon payments and principal repayment) from the bond. The discount rate for calculating the present value of the cash flows is the

bond's yield

.

Duration gives you an indication of approximately how much a bond's price will change in the event its yield shifts by a full percentage point (100 basis points). A bond with a duration of 6 years will increase in price by about 6% if its yield sheds 100 basis points, and decrease in price by about 6% if its yield rises by 100 basis points.

Duration is a fine measure of interest-rate sensitivity for a regular, noncallable bond with future cash flows that are thoroughly predictable. The trouble is, in the vast world of debt securities, many, many of them are callable, meaning that the issuer retains the option to either retire the bond early or accelerate repayment of principal if interest rates fall. Investors get compensated for this with higher yields on callable bonds than on noncallables. But the bottom line is, the future cash flows from a callable bond are unpredictable, because they depend on what happens with interest rates.

So bond wizards developed a more complicated measure of interest-rate sensitivity for callable bonds called effective duration. Effective duration takes into account the fact that as interest rates change, cash flows will change as well. Obviously, it involves assumptions about how much a given change in interest rates will affect cash flows, and as such, it's part science, part art.

Average life, the subject of your question, is a predecessor of effective duration that was developed for analyzing mortgage-backed securities, explains Evan Firestone, director of mortgage research at

**Merrill Lynch**

.

Mortgage-backed securities, discussed at greater length in an earlier

Fixed-Income Forum, have unpredictable cash flows because homeowners -- the effective issuers of the bonds -- have the option to prepay all or part of their loans at any time. That makes them some of the most complicated income securities to analyze.

In addition, because every mortgage payment a homeowner makes is part interest, part principal, mortgage investors receive payments that are part interest, part principal.

The average life of a mortgage-backed security is the amount of time it takes for the weighted average of principal payments to come back to the investor, assuming a certain rate of prepayments. A pool of 30-year mortgages can have an average life ranging from less than five years to more than 20, depending on how fast a rate of prepayments is assumed.

Neither effective duration nor average life tells you exactly how much a security's price will change as its interest rate changes for the simple reason that that is not knowable. But effective duration is the best tool that's been developed so far for comparing the interest-rate sensitivity of callable securities to noncallable ones.

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TSC Fixed-Income Forum aims to provide general bond information. Under no circumstances does the information in this column represent a recommendation to buy or sell bonds, funds or other securities.