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Bond Duration and Convexity: Practical Application

Now imagine that each bucket is filled to a level representing the present value of that payment. The further out the plank you go, the smaller the present value of that payment. This represents the time value of money: $30 tomorrow is worth more than $30 five years from now, assuming normal economic conditions.

The plank is essentially a timeline, and duration is the point along the plank where a fulcrum would go to balance the whole system. (The buckets themselves, for argument's sake, don't weigh anything.) Can you see why the duration of a zero-coupon bond would be equal to its maturity? Because the payment stream from a zero-coupon bond consists entirely of a single payment at maturity, that's where the fulcrum would have to go.

So, what's the use of knowing a bond's duration? If you know a bond's duration, you can estimate how much its price will change if its yield changes. Note that there are different types of duration. The one described above is Macaulay duration, defined by Frederick Macaulay in his 1938 study of U.S. financial markets. To easily estimate how much a bond's price will change if its yield changes, you need its modified duration, which you get by dividing the Macaulay duration by one plus half the yield. Once you know the modified duration, you can multiply it by a change in yield to calculate the approximate change in price. For example, a bond with a duration of 6.4 will go up about 6.4% in price if its yield drops by 1% (100 basis points), and down about 6.4% if its yield rises by 100 basis points.

Just a couple more points about duration.

Why it's useful: Duration gives investors a way to compare bonds with different maturities and coupons. A recent Fund Forum talked about the fact that bonds with big coupons are less interest-rate sensitive than bonds with small coupons, all things being equal. Using the Salomon analogy, you can see why. The more that's in those small buckets, relative to the amount in the big bucket, the further to the left the fulcrum will go to balance the system. In other words, the shorter the duration.

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