How Risky are Your Bonds?

Bond prices go up and down every day just like stock prices, but for different reasons.

It is important to understand that bond prices move inversely to interest rates.  In other words, if interest rates go up on bonds or bond funds like the one you own, the price of existing bonds go down and vice versa when interest rates go down.  Understanding the “Duration” of your bond or bond mutual fund will tell you how much a change in interest rates should affect the price of your bond investment.

By definition, duration is the change in the value of a fixed income security (bond). That will result from a 1% change in interest rates.

Duration is stated in years. For example, a 5 year duration means the bond will decrease in value by 5% if interest rates rise 1% and increase in value by 5% if interest rates fall 1%. Duration is a weighted measure of the length of time the bond will pay out. Unlike maturity, duration takes into account interest payments that occur throughout the course of holding the bond. Duration is a weighted average of the maturity of all the income streams from a bond or portfolio of bonds.

Consider a vanilla bond that pays coupons annually and matures in five years. Its cash flow consist of five annual coupon payments. The last payment includes the face value of the bond.

The money bags represent the cash flows you will receive over the five-year period. Balance the red lever at the point where total cash flows equal the amount paid for the bond. The fulcrum must be farther to the left, at a point before maturity. Unlike the zero-coupon bond, the straight bond pays coupon payments throughout its life and therefore repays the full amount paid for the bond sooner.

Factors Affecting Duration

It is important to note, however, that duration does change as the coupons are paid to the bondholder. The bondholder receives a coupon payment, the amount of the cash flow is no longer on the time line. Which means it is no longer counted as a future cash flow, that goes towards repaying the bondholder. The model of the fulcrum demonstrates this: as the first coupon payment is removed from the red lever and paid to the bondholder, the lever is no longer in balance because the coupon payment is no longer counted as a future cash flow.

The fulcrum must now move to the right in order to balance the lever again:

Duration increases immediately on the day a coupon is paid, but throughout the life of the bond. The duration is continually decreasing as time to the bond’s maturity decreases. The movement of time is represented above as the shortening of the red lever. Notice how the first diagram had five payment periods and the above diagram has only four. This shortening of the time line, however, occurs gradually, and as it does, duration continually decreases. So, in summary, duration is decreasing as time moves closer to maturity, but duration also increases momentarily on the day a coupon is paid and removed from the series of future cash flows. All this occurs until duration, eventually converges with the bond’s maturity. The same is true for a zero-coupon bond

Duration: Other factors

Besides the movement of time and the payment of coupons, there are other factors that affect a bond’s duration: The coupon rate and its yield. Bonds with high coupon rates and, in turn, high yields will tend to have lower durations than bonds that pay low coupon rates or offer low yields. This makes empirical sense, because when a bond pays a higher coupon rate or has a high yield, the holder of the security receives repayment for the security at a faster rate. The diagram below summarizes how duration changes with coupon rate and yield.