Why you need to understand duration.

Why you need to understand duration

The concept of duration was developed more than five decades ago to show that maturity length is not necessarily the best measure of time in judging a fixed-income investment. Rather, an investor must consider the timing and relative size of all of the

Despite its relative advantages both in measuring price volatility and in providing assistance for reducing the interest rate risk of a fixed-income portfolio, duration receives little coverage. Given increasingly volatile interest rates and an unstable yield curve, however, an understanding of this measure of interest rate-induced price volatility is quite relevant to chief financial officers, whether functioning in the capacity of fund raisers or investment managers.

The concept of duration is generally presented from the viewpoint of the investor or the portfolio manager. Because duration is superior to maturity length for judging the price volatility of a fixed-income security, the concept has important applications for financial officers managing investment portfolios. Duration also incorporates both changing market values and changing returns from the reinvestment of cash to provide a better measure of the return an investor will earn on a fixed-income security.

Price volatility

It is well known that rising interest rates force bond values downward, while falling interest rates generate price increases for fixed-income securities. The longer the maturity of a security, the greater the change in price for a given change in interest rates. Bonds with long maturities are thus considered to have significantly more interest rate risk than do bonds with relatively short maturities.

The change in a security's price caused by a given change in interest rates is also a function of the security's coupon size. Fixed-income securities with large coupons tend to be affected to a lesser extent by interest rate changes than are low-coupon securities. Many investors have discovered to their sorrow that zero-coupon bonds, securities that make only a single cash payment at maturity, are subject to substantial fluctuations in market values whenever even relatively modest changes in interest rates occur.

Thus, there are really two interacting factors - maturity length and coupon size - that cause a bond's price to change in response to a change in market interest rates. Owners of long maturity bonds find that interest rate changes have a lesser effect upon the market value of the bonds if the coupons are relatively high. On the other hand, long maturity bonds with low coupons are subject to great price volatility because of interest rate changes.

Duration incorporates both coupon size and maturity length in approximating the degree to which a bond's market price will be affected by interest rate changes. For relatively small changes in interest rates, the percentage change in a bond's price is approximately equal to the bond's duration times the percentage change in interest rates. If interest rates climb from 10 percent to 10.25 percent (a change of 25 basis points or 0.25 percentage points), a bond with a duration of 15 years will decline in price by approximately 15 times 0.25, or 3.75 percent. A slight revision in this formula permits a more accurate computation for larger changes in interest rates. Regardless of which measure of price volatility is utilized, however, it is clear that the longer a bond's duration, the greater the price variation caused by interest rate changes.

An understanding of duration lets a financial manager select securities that can provide the best returns for a given scenario of interest rates. An expectation of falling rates favors the purchase of securities with long durations that will provide an investment portfolio with maximum capital gains. An outlook for rising interest rates would make the financial manager favor the conservative approach of acquiring securities with short durations in order to minimize potential losses. It is important to note that there are a number of maturity and coupon combinations that produce the same duration. Thus, the financial manager has some flexibility in selecting among the securities that are available to attain a given investment posture.

Assuring a return for a

given investment period

Duration can also help an investment manager to meet a goal that requires earning a specific return. Again, duration is successful at this task because it incorporates both maturity length and the reinvestment rate in its calculation.

Purchasing a fixed-income security with a maturity that matches the date when funds are required to meet a specific need can produce a return that is higher or lower than expected because of a changing return that will be earned on the reinvestment of cash payments prior to maturity. Thus, an investment manager may purchase a 10-year, 10-percent coupon bond in order to meet an obligation in 10 years only to find that soon after the security is purchased, market rates decline and the return earned from the reinvestment of interest payments is considerably less than originally anticipated. The result is that the principal will be returned on the maturity date as expected, but the additional income derived from reinvested cash flows will be substantially less than had been anticipated at the time the bond was purchased. The bottom line is that there will be insufficient funds to meet the obligation at the end of 10 years.

On the other hand, if the financial manager had purchased a bond with a duration of 10 years (in contrast to a maturity of 10 years), the return from holding the bond would approximate the anticipated return regardless of what happened to the rates of return earned on reinvested funds. Remembering that duration is shorter than maturity length for all except zero-coupon bonds, the change in the market value of the security at the target date will be offset by changes in the return earned by cash distributions.

If the market rate of interest falls between the date the bond is purchased and the target date when funds are needed such that a reduced return is earned on reinvested interest payments, the increase in the market value of the bond will approximately offset the reduced return from reinvested funds. Essentially, one part of interest rate risk, a change in the market value of the security, is offset by the other part of interest rate risk, a change in the return that is earned on reinvested funds. Thus, an increase in the market rate of interest will allow the investor to earn a higher return on reinvested funds at the same time that the market value of a fixed-income investment will be adversely affected.

In choosing a bond or a portfolio of bonds according to duration rather than maturity, a financial manager is admitting to the difficulty (some would say the impossibility) of forecasting interest rate changes. Regardless of what occurs with respect to the market rate of interest following the assembly of a portfolio of bonds, the firm locks in an approximate rate of return to the target date. Thus, the financial manager immunizes the firm's investments from changes in the market rate of interest. Of course, if the executive's goals change and it is necessary to liquidate an investment position at some time other than the target date, the outcome may be quite different.

Financing decisions

Because the returns that are required by investors to get them to part with their funds are the flip side of financing costs to the firm, anything that affects the actions of investors must affect the financial manager's cost of raising funds. Thus, if portfolio managers and individual investors consider duration rather than maturity in selecting bonds for purchase, it is duration that should concern the financial manager in making financing decisions. If duration becomes the prime consideration of fixed-income investors, then the maturity of a new issue becomes important only because it is one of the factors that influence the issue's duration.

Because duration is superior to maturity length in judging the appropriateness of a bond, there is every reason to expect that duration will become an increasingly important consideration in the minds of investors deciding upon a bond issue's desirability. This desirability applies to new issues of bonds as well as to issues traded in the secondary market. Thus, while financial managers are now more likely to consider maturity length in structuring a new bond issue for sale, it can be expected that duration will gradually supplant maturity as a consideration.

To a limited extent, duration has already manifested itself. During the 1980s, an increasing number of deep-discount and zero-coupon bonds were part of the new issue market. In addition, there were numerous issues structured as combinations of zero-coupon and interest-bearing debt. Issues with zero coupons are unique in that their durations and maturity lengths are equal. Thus, large bond issues frequently include at least a moderate amount of zeros as a way of meeting the needs of limited segments of the investing public. Even here, however, it appears that the zeros are frequently being offered more on the basis of their maturity so that the relationship with duration was considered of secondary importance by issuers. As the concept of duration is utilized by a greater proportion of the investment community in the future, there will be an increasing demand for bond issues that offer the most sought-after durations.

For many investors, the major disadvantage of owning corporate zero-coupon bonds and original issue discount bonds stems from a negative cash flow. Taxes that must be paid annually in interest that remains unpaid until a bond matures or is sold can produce a significant cash flow problem for many individual investors. However, for individual retirement accounts and institutional investors where taxes are not a consideration, zero-coupon bonds with maturity lengths equal to durations offer significant advantages in accumulating funds for known obligations.

A matter of time

Duration is generally considered superior to maturity length as a measure of the economic life of a bond. Despite its advantages and the fact that duration is certainly not a new concept, it remains more theory than reality among many individuals who could benefit from knowledge of its implications. As the dissemination of financial data continues to improve and the types of data available to the investment community continue to expand, there is every reason to expect that the concept of duration will become a consideration for an ever greater proportion of the investment community. As this occurs it will become increasingly important for financial executives to develop both financing and investment strategies that will take advantage of the trend.

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