Why effective duration impacts interest-rate risk

Davidson, Steve

The volatile interest-rate environment of the past year intensifies community bankers’ focus on interest-rate risk measurement.

Declining rates throughout 2001 had the positive effect of generating record levels of mortgage origination volume for the industry. It also led to more prepayments and refinancing of mortgages at lower rates.

For instance, the 2002 ACB Real Estate Lending Survey found that refinancings accounted for 55 percent of community banks’ loan production last year.

From the bank’s perspective, lower mortgage rates create reinvestment risk-that is, whether institutions can find ways to invest the proceeds from prepaid mortgages and generate comparable returns.

Duration-a frequently cited interestrate measurement tool-was originally developed to analyze bond and fixed-income securities. Today it is broadly used in the community banking industry to estimate the impact of interest rate changes on a bond’s price. It assumes that interest rates affect market value of a bond’s contractual cash flows and does not account for the impact of interest rates on a financial instrument’s actual cash flows.

Effective duration refines the modified duration calculation by considering changes in cash flows of a fixed-income security (including mortgage assets) as interest rates change. It also helps illustrate reinvestment risk issues.

What is Effective Duration?

According to a recent article entitled “An Example of How to Use and Compute Effective Duration and Effective Convexity,” duration is defined as “the weighted average life of a fixed-income financial instrument’s contracted cash flows.”

Cash flows are generally considered as interest and principal payments required under the terms of the fixed-income instrument’s agreement. Fixed-income analysts consider duration a better measure than the stated maturity of a bond, because duration takes into account intermediate cash flows.

Duration differentiates the timing of contracted cash flows between a zero-coupon bond and a periodic interest-payment bond, even if both have the same stated maturity. Modified duration measures the percentage change in the price of a financial instrument for a change in market interest rates.

For some financial instruments, cash flows can change dramatically in different interest-rate environments.

The difference is especially meaningful for mortgages and mortgage-backed securities due to the embedded prepayment option that the borrower may exercise at any time but is more likely to exercise as mortgage rates fall.

A fixed-income financial instrument without any option properties will produce results similar to a modified and effective duration. Even when there is an explicit or implicit call (or put) option on the financial instrument, the difference is not dramatic over certain ranges of interest rates-especially when the option is far “out of the money.

At higher interest rates, the homeowner’s implicit call option is not important. After all, consumers are not likely to refinance a mortgage at higher rates. As rates come down, and the homeowner’s prepayment option is more likely to be exercised. This is when the results of effective and modified duration become meaningful.

Effective duration is used to estimate the price change for a given change in interest rates and is mathematically calculated as the price of the financial instrument (for example, a bond) given a general decline in interest rates (a parallel downward shift in the yield curve) minus the bond price given a general increase in interest rates (an upward parallel shift in the yield curve) divided by twice the current price times the shift in basis points of the yield curve.

The Callable Bond

Consider two bonds, one that has no option and the other that has a call option beginning in the second year.

Table 1 demonstrates the effective duration measured percentage price change of Bond A and Bond B under different interest rate environments. In the case of Bond A, the price would change by 4.21 percent for a given change in the bond yield under the hypothetical current yield-curve environment.

If the yield curve moves down by 500 basis points, the same yield change would generate a 4.4 percent bond price change. In the case of Bond B, under the hypothetical current yield curve environment, there would be a 3.08 percent price change. If the yield curve declines by 500 basis points, there would be only 1.91 percent price change.

Table 1 shows that there is much less of a price impact in the case of the callable bond than the bond without the call option as rates decline. This is what we would expect, because the call option would be more likely to be exercised as market rates decline.

Conversely, in higher yield curve environments, the effective duration calculated price change differentials between the two bonds are minimal, because the call option is less likely to be exercised.

Effective Duration and the Investor

We can apply the callable bond example to residential mortgage loans and mortgagebacked securities. As indicated at the outset, the mortgage borrower’s ability to prepay a mortgage is similar to a call option.

As the effective duration calculation takes into account the impact of interest rates on cash flows, effective duration can enhance a community banker’s financial management toolbox. It can help us understand and anticipate mortgage asset-pricing behavior in different interest rate environment.

Effective duration formalizes something that lenders intuitively understand: interest rates have a profound effect on financial and mortgage markets.

At the same time, similar to other financial valuation measurements, community bankers should keep in mind the assumptions underlying the effective duration calculation.

Steve Davidson is senior financial economist for America’s Community Bankers and editor of the monthly newsletter Economic Outlook. His e-mail address is sdavidson@acbankers.org.

Copyright America’s Community Bankers Apr 2002

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