The Role of Coupons and Duration in a Bond's Total Return
Understanding the calculations involved in determining a bond’s duration can be a very complicated process. However, figuring how that number affects an individual bond and an overall portfolio is quite straightforward.
The rule of thumb is that for every 1% move in interest rates, the price of that bond will move by the duration in percentage terms. In other words, if you hold a bond with a duration of 5 and interest rates move up 1% in a day—that would be a remarkable day—the market value of the bond will drop 5%.
Price movements, however, are only a portion of a bond’s total return. The income component must also be considered. For the aforementioned bond, if the change in interest rates—1%—occurs over the course of a year, and the bond has a 5% coupon, the investor would receive 5% in income while seeing a 5% drop in the value of the bond, resulting in a flat performance for the year.
It’s interesting to look a little deeper into duration. The structure of the bond makes a huge difference in how that duration is calculated, with the coupon of the bond being a primary driver. One of the key duration principles is that as a bond’s coupon increases, its duration decreases, and the bond becomes less sensitive to changes in interest rates, exhibiting lower volatility. The coupon component serves as an offset to a decline in market value brought on by rising rates.
For a real-life example, compare two bonds both maturing on Aug. 15, 2015, one with a 3.8% coupon (Bond A) and the other with a 5.3% coupon (Bond B). At a 3% yield, Bond A has a duration of 6.12, and Bond B 5.92. See below tables to observe how prices change when interest rates are modified in either direction in one year.
A one-percentage point increase in yield brings the price of the two bonds by about 5.4%. Add the impact of the coupons, and the owner of Bond A manages to cap losses at 1.56%, and the owner of Bond B comes away with a -0.16% return. On the flip side, coupons could similarly boost income when rates are falling and bond prices are inching up.
Another way of considering the impact of coupons is to observe a scenario of consecutive rate increases. Below would be a basic representation of the bonds’ experiencing one-percentage point increases in yields for two years:
The second year’s price would reflect about a 5% decrease from the year earlier. Add to that the coupons, and Bond A would post return -1.28%, and Bond B would be able post a positive return of +0.12%, a modest gain but a gain nonetheless. This illustrates that coupons can serve a meaningful purpose in propping up total returns even in a rising-rates environment that puts pressure on bond market values.