A reader writes in, asking:

“I am aware that bonds and bond funds with longer duration have greater price changes in response to interest rate moves than shorter-term bonds do. And given that, I understand that longer-term bonds generally have higher yields because of that higher risk. That makes perfect sense.

What I have never been able to wrap my head around is

whydo the prices of longer duration bonds fluctuate more severely?”

A bond’s market price is really just the result of a net present value calculation. That is, the price of a bond at any given time is the sum of the present values of each of the cash flows from the bond (i.e., the present value of each interest payment plus the present value of the payment upon maturity).

(See this article if you haven’t encountered the concept of present value before. It’s worth a read, as it’s one of the most fundamental concepts in finance.)

As a reminder, the present value of a given cash flow is calculated as follows:

PV = FV / (1 + r)^n

where:

PV = present value

FV = future value (i.e., the dollar amount of the cash flow in question)

r = annual discount rate

n = number of years before the cash flow is received

The greater the number of years, the greater the impact of the discount rate. Compare the two following examples.

**Example 1:** Given a discount rate of 2%, the present value of a $1,000 cash flow to be received **one** year from now is $980. If we raise the discount rate to 3%, the present value falls to $971, a change of $9.

**Example 2:** Given a discount rate of 2%, the present value of a $1,000 cash flow to be received **five** years from now is $906. If we raise the discount rate to 3%, the present value falls to $863, a change of $43.

Point being, a 1% increase in the discount rate had a much larger effect on the cash flow that was further in the future.

When we’re calculating the present value of a bond, the discount rate is the return that investors could expect to earn from other bonds with similar risk (i.e., other bonds with the same credit rating and same duration).

So when interest rates change, the discount rate changes. And the further in the future the cash flow is to be received, the greater the change in present value (i.e., market price).

So, the longer the duration of a bond (i.e., the further in the future its cash flows will be received, on average), the greater the change in present value (i.e., market price) when interest rates change.