You may have run across someone speaking about the duration of their bonds, or you may have listened to your financial advisor talk about the current duration of your portfolio. What exactly did they mean?
Duration, simply put, is the percentage change in price you would expect to see in a bond if there was a 100 basis point yield change. 100 basis points is equivalent to 1%, so what you are ultimately figuring out is what will happen to the price of your bonds, and the price of your bond portfolio, if interest rates moved up or down by 1%. Now with Quantitative Easing (QE) tapering expected to begin as early as September, you may want to know your portfolio duration. If your duration is higher, chances are you will take more of a loss come this Fall and into next year.
Let’s do an example now so that you have an idea of what duration is:
What would the expected percentage price change be for a 30 year bond trading at 110.574 whose duration we’ve found to be 12.50 with an 20 basis point increase in yield (∆y= +0.002)?
So we know the duration is 12.50 and we know the change in the yield to be 20 basis points, or .2% (remember that 100 basis points is equivalent to 1%). Now if duration is terms of a 100 basis point shift, then we must multiply it to find the correct percentage rate to apply at this shift. And since we are finding a negative shock (interest rates are going up) then we must calculate a percentage decrease in price.
-12.50 X (0.002) X 100 = -2.5% approximate percentage price change
Multiply this back into the current value of your bond, which was stated as 110.574 and we get
110.574 X (1 - 0.025) = 107.80965
Now while this may look negative, and it is, duration can also work in your benefit if interest rates fall, especially if your bonds don’t have the option to be called back by the issuer. This is because you can have the percentage price gain of your bond without worrying about the issuer buying said bonds back and then you are stuck having to reinvest in new bonds with lower interest rates.
Now that we have discussed what duration is, let’s now discuss how to calculate duration.
You may have realized a problem with this formula already. How do we calculate the price if yields decline and rise, if we haven’t already solved for duration? There are different methods to solving this challenge, but this will be discussed in another article which covers what Z spread and Spot Rates are, and how they can be used by investors to gain an edge on those who don’t use them.