Do Longer Duration Bonds Have More Convexity?
Original post by Victoria Duff of Demand Media
Duration and convexity in bonds describe very simple concepts, but to understand them you must first understand some bond basics. When a bond is to be issued, it has a set maturity date, and the bond syndicate manager assigns a coupon and dollar price based on the prevailing market interest rates. Duration and convexity describe the price behavior of the bond in different interest-rate environments.
The coupon indicates the amount of interest the bond will pay each year. If a bond coupon is 4.75 percent, it will always pay $47.50 per $1,000 face value bond. Through up and down markets, the price of the bond in dollars will change, but the coupon rate will remain the same. The benchmark in the bond market is the prevailing interest rate on each maturity of U.S. Treasury bonds -- the highest-rated credit in the bond market. All corporate and municipal bonds trade at a spread to similar-maturity Treasurys, depending on their credit rating. Since Treasurys are rated AAA, a AA corporate bond may trade at a yield 10 basis points higher than the similar maturity Treasury bond, but an A-rated corporate will trade at a yield spread of perhaps 20 basis points higher. The same with municipals.
The yield curve is a graphic representation of prevailing market yield rates on the 2-year, 5-year, 7-year, 10-year, 20-year and 30-year Treasury bonds. Normally, the shorter the maturity, the lower the market interest rate. As the Federal Reserve manipulates interest rates to suit its monetary policy, the yield curve changes shape. When the economy is in transition, the yield curve is relatively flat, with yields on short bonds only slightly lower than the yields on long bonds. When the Fed signals a rise in interest rates, the short end of the curve rises, with yields on 2- through 5-year bonds higher than those on the longer bonds. This is called an inverted yield curve. In a few days, or a few weeks, yields on the long end of the yield curve will rise higher than yields on the short end, and the yield curve will return to a normal slope.
The goal of a professional bond portfolio manager is to maintain or grow the dollar value of the portfolio and increase the return on investment, which includes interest rate yields plus trading profits. Bond prices fall when interest rates rise, so the portfolio manager will move in on the yield curve by selling longer bonds before their yields rise and buying shorter bonds. Once rates have peaked, the portfolio manager sells the short maturities and buys the higher-yielding longer maturities, moving out on the yield curve.
Duration shows how much the value of a bond declines with every percentage change in interest rates. For example, an investment with a modified (stated as a percentage) duration of five years will rise 5 percent in value for every 1 percent decline in interest rates and fall 5 percent in value for every 1 percent increase in interest rates. When a portfolio manager moves out on the yield curve, he is increasing average duration to optimize return on investment. Moving in on the yield curve decreases average duration. The longer the bond, the longer the duration. For an 8 percent coupon, the duration of a 5-year note is 4.0 years, and that of a 30-year bond is 11.3 years. The higher the coupon, the shorter the duration. High-coupon bonds decline in price at a lower rate, as interest rates rise, than do low coupon bonds.
Bond convexity represents the rate of change of the duration of a bond expressed in dollars rather than percentages. Callable bonds and mortgage-backed securities have negative convexity, meaning the graph of the relationship between their price and yield is convex rather than concave. This means that as interest rates fall, callable bonds will be called and refinanced at lower coupon rates and mortgage backed bonds will pay off sooner as the underlying mortgages get refinanced to lower rates. Calling the bond or paying it off sooner shortens the duration. When rates rise, there is no risk of your bonds being called away and little risk of your mortgage-backed bonds paying off early. This extends the duration of your bonds. Longer duration has positive convexity. Shorter duration results in negative convexity.
- Philippe Jorion; "Philippe Jorion's Orange County Case: 2.1 Duration;" The Paul Merage School of Business
- Morningstar; Bond Fund Basics; Sue Stevens, CFA, CFP, CPA; August 2006
- Securities Industry and Financial Markets Association; Risks of Investing in Bonds
- Western Washington University College of Business and Economics; Valuation of Bonds
About the Author
Victoria Duff specializes in entrepreneurial subjects, drawing on her experience as an acclaimed start-up facilitator, venture catalyst and investor relations manager. Since 1995 she has written many articles for e-zines and was a regular columnist for "Digital Coast Reporter" and "Developments Magazine." She holds a Bachelor of Arts in public administration from the University of California at Berkeley.
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