Calculating a Bond's Effective Duration

Effective duration is a calculation of the cash flow on a bond with an embedded option that may alter its profits. Some bonds are slightly more complicated than those with a standard "modified duration" that accounts for only one interest rate. This kind of bond, often called a structured note, has underlying options that can be executed during the bond's lifetime. If they are not executed, the bond's modified duration will equal its effective duration. If they are executed, effective duration must be calculated separately. 

Embedded Option Example

You purchase a bond from Company A. This debt note has an interest rate of 7 percent. At the time of purchase, Company A also embeds an option to call the bond in the future at current interest rate levels. This way, if Company A's bonds begin to fall in interest rate, it can decrease the interest rate it is paying you and other investors. In return for embedding this option, Company A offers the high interest rate of 7 percent for the time being. When you purchase this bond, you are betting the interest rate will not drop below this level. In the future, Company A's existing bond interest rates are 10 percent. It will not execute the option to call your bonds and reissue them at the 10 percent rate. Therefore, the bond's effective duration in this case would be the same as the modified duration because the interest rate never changed on the bond.

Interest Rate Fluctuation

Now imagine Company A's current bonds offer an interest rate of 6 percent. Company A would execute the option, reissuing your bond at 6 percent, changing the interest rate you receive on the bond partway through the bond's life cycle. The bond would no longer behave like an option-free bond. Instead, the interest rate for part of the bond's life cycle would be different from the interest rate on the remainder of the bond's life. Therefore, the duration of the bond would change, and the effective duration calculation would result in a different interest rate than a modified duration calculation.

Using Effective Duration

Before purchasing a bond with an embedded option, you may complete two calculations on the bond's potential profitability. In one calculation, determine your earnings if the option is not executed. Then, determine the profitability if the option is executed at several different levels. The difference between the first calculation and the subsequent calculations shows you how risky the embedded option on the bond truly is. If the two calculations are relatively similar, then the risk level of the embedded option is not significant. If they are widely different, the embedded option presents great risk. Make sure you are taking this risk only if the potential for reward is also very great. For example, in the above scenario, Company A has an embedded option that makes its bonds riskier than others without an option. However, if the bonds are issued several points above the average coupon rates on the market, the risk may be worth the potential earnings.

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