A reader writes in, asking:

“I know that interest rates and bond prices move in opposite directions, but I don’t honestly understand

whythat is the case. And while we’re at it, why do bond funds with a long duration have bigger price fluctuations than bond funds with a short duration?”

Imagine that you buy a $1,000, 10-year Treasury bond, with a 2% coupon rate. (That is, it pays $20 of interest per year.) And you hold that bond for five years, such that it is now effectively a 5-year Treasury bond with a 2% coupon rate.

And imagine that, over those five years, interest rates have risen, and newly-issued 5-year Treasury bonds are now paying 3% interest.

In such a scenario, if you wanted to sell your bond for $1,000, you’d have a very difficult (i.e., impossible) time. Nobody would want to buy your bond with its 2% interest rate, when they could just buy new 5-year bonds with a 3% interest rate instead. In order to sell your bond, you’d have to sell it for less than $1,000. That is, its price has gone down because interest rates have gone up. (Specifically, you would have to sell your bond at a sufficient discount that it would offer the same yield to maturity as newly-issued bonds of the same duration.)

And the same sort of thing happens in reverse. Imagine instead that rates on 5-year Treasury bonds had *fallen* to just 1%. In that case, people would be willing to pay *more* than $1,000 for your bond with its 2% coupon rate. That is, interest rates fell, so the value of your bond went up.

### Why Do Longer-Term Bonds Have More Interest Rate Risk?

When interest rates change, the price of a bond fund will move (in the opposite direction) by an amount approximately equal to the average duration of the fund, multiplied by the percentage change in applicable interest rates. For example, if the whole Treasury yield curve were to rise by 2%, a Treasury bond fund with a 3-year average duration would fall in price by roughly 6%, and a Treasury bond fund with a 7-year average duration would fall in value by roughly 14%.

But *why* do longer-duration bonds experience more severe price fluctuations? Without getting into the underlying math*, I think the concept is most easily understood with an example.

Imagine that on a given day you purchase a 1-year Treasury bond and a 20-year Treasury bond, both of which you plan to hold until maturity. Then, on the very next day, the entire Treasury yield curve moves upward by 1%.

- Holding the 1-year bond to maturity means you’ll be collecting a subpar interest rate (i.e., missing out on an additional 1% yield, relative to new bonds) over the next year.
- Holding the 20-year bond to maturity means you’ll be collecting a subpar interest rate each year for the next
*twenty*years.

Missing out on an additional 1% yield for a year isn’t great of course. But missing out on 1% per year for twenty years is a *much* bigger deal. And that is essentially why longer-duration bonds have larger price fluctuations when current interest rates change.

*For those who are interested in the technical explanation: The market value of a bond at any point in time is equal to the sum of the present values (i.e., discounted values) of each of the future cash flows the bond holder will receive. When market interest rates change, the discount rate we use to calculate present value changes. And a given change in discount rate (e.g., 1% higher or lower) has a much greater effect on cash flows far in the future (such as you would receive with a long-term bond) than cash flows in the near future.