Why bond prices fall as rates rise

Bonds have a reputation for being conservative, even boring. But no one ever accused them of being easy to understand. I get a steady stream of emails and blog comments about bonds, and they reveal that many investors are very confused by how bond ETFs work, how they’re affected by changes in interest rates, whether investors can use alternatives to bonds, and even whether it’s OK to abandon them altogether. Let’s dig into one of the most fundamental concepts for bond investors to understand: the inverse relationship between bond prices and interest rates: when one goes up, the other goes down. This is confusing for many people—after all, investors regularly complain that bond yields are low, so shouldn’t higher interest rates be a good thing? And why are we told to stay away from bonds because yields might rise? You never hear people say you should avoid stocks because their dividends might get higher. So what gives?

Yields up, prices down

I’m going to try to explain this important idea using a simplified example. Let’s say Darryl buys a newly issued five-year bond with a face value of $1,000 and an interest rate (or coupon, as it’s called) of 3%, which is the prevailing rate for five-year bonds with similar risk. That bond will pay Darryl $30 in interest each year for the next five years. Let’s also assume that just hours after Darryl buys his bond, interest rates rise sharply. His brother Larry is now able to buy a five-year bond with the same risk but with a 4% coupon. Larry’s bond will pay him $40 in annual interest for every $1,000 in face value.

	Darryl	Larry
Face value	$1,000	$1,000
Maturity	5 years	5 years
Coupon	3%	4%
Annual interest	$30	$40

Enter Lisa, who is looking to buy a bond for her RRSP, so she approaches both Darryl and Larry about making a purchase. As you can guess, if both bonds had the same price, Lisa would obviously choose Larry’s bond because it pays more interest. But although Darryl’s bond pays less than the prevailing rate, it’s not worthless. That 3% coupon and its $30 in annual interest is still worth something, even if you can buy similar bonds yielding 4%. This is where we turn to the elegant mathematics of bond pricing. The value of Darryl’s bond will fall just enough so that its total return will be the same as Larry’s. The calculations are complicated, but a financial calculator or online tool can do it for you easily, as long as you’re careful to use the right inputs. To keep things simple, here’s how the numbers work out in this example, assuming that the bond pays its interest once a year:

Characteristic	Darryl’s bond
Face value	$1,000
Coupon (annual interest rate)	3%
Annual interest payment	$30
Prevailing rate on comparable bonds	4%
Number of years to maturity	5
Market price	$955

Because of the rise in interest rates from 3% to 4%, Darryl’s bond has fallen in value from $1,000 to $955. That is the price at which Darryl’s bond would deliver the same return as Larry’s over the full five years to maturity. This means Lisa could buy Larry’s bond for $1,000 and receive $40 in annual interest for five years, for a total of $200 in interest. Assuming she is able to reinvest those interest payments at the current rate of 4%, her total return on the investment would be 4.3% annually. (It’s a little higher than 4% because of compounding: that is, interest earned on the interest.) On the other hand, Lisa could buy Darryl’s bond for $955. She would receive just $30 in annual interest for five years, for a total of $150, which is $50 less than Larry’s bond paid. But at maturity, Lisa would receive the full $1,000 face value, even though she only paid $955 for the bond. That’s an additional profit of $45. And assuming she is able to reinvest all the interest payments at the prevailing rate, her total return will also be 4.3% annualized over five years:

	Darryl’s bond	Larry’s bond
Initial investment	$955	$1,000
Coupon	3%	4%
Interest received	$150	$200
Face value returned at maturity	$1,000	$1,000
Final value of investment (including compounding)	$1,162	$1,217
Total return over five years	21.7%	21.7%
Annualized return	4.3%	4.3%

Even if you struggle a bit with the math, I hope you now understand the main idea: that is, why bond prices fall when interest rates rise. If the prevailing rate on five-year bonds is 4%, a bond like Darryl’s with a 3% coupon must be worth less than face value. To attract investors like Lisa, Darryl would have to lower the price of his bond just enough to make it equivalent to Larry’s bond with its higher coupon. At a price of $955, investors like Lisa now have no reason to prefer Larry’s bond over Darryl’s .

The other way around

Of course, the opposite is also true: if interest rates fall, older bonds with higher coupons become more valuable. To continue our example above, if rates had fallen from 3% to 2% immediately after Darryl bought his five-year bond, its value would have shot up from $1,000 to about $1,047. That is the price at which both bonds would deliver the same total return:

	Darryl’s bond	Larry’s bond
Initial investment	$1,047	$1,000
Coupon	3%	2%
Interest received	$150	$100
Face value returned at maturity	$1,000	$1,000
Final value of investment (including compounding)	$1,156	$1,104
Total return over five years	10.4%	10.4%
Annualized return	2.1%	2.1%

What about bond funds?

If you’re a Couch Potato investor you’re probably not buying individual bonds: you’re more likely to buy index funds or ETFs that hold hundreds of bonds. But the principle is still the same: when interest rates rise, the value of all these underlying bonds will fall in value, so the price of your fund will decline to reflect that. Now here’s the silver lining in all of this. Because the coupons on existing bonds don’t change when rates move, the interest payments you receive every month likely won’t get any lower. Darryl bought a bond that pays $30 in interest, and he’s still going to get that as long as he owns his bond, whether rates fall to 2% or rise to 4%. Here’s where it pays to think like dividend investors, who seem much more willing to tolerate a decline in the price of their stocks so long as their income stays the same. Indeed, if rates rise gradually, the interest payments on a bond fund will increase as older bonds mature and newer ones are purchased with higher coupons. That means every new dollar you put into your bond fund will have a higher expected return than in the past, because you’re paying less for every dollar of interest. That’s why investors who are still many years from retirement should welcome a modest increase in interest rates: it would cause some short-term pain, but it would also mean higher bond returns over the long term.