When interest rates change, bond prices in the secondary market change too. Bonds with longer maturities and lower coupons tend to have the most price volatility.
A bond with a long maturity is usually more sensitive to interest rate changes because you’re locked into its cash flows for a longer time.
Assume you own a 1-year bond and a 20-year bond. If interest rates rise, the market value of both bonds will fall. The 20-year bond’s price will fall more. Here’s why.
When interest rates rise, newly issued bonds come to market with higher yields. That makes existing bonds (with lower coupon rates) less attractive, so their prices drop to compete.
Both the 1-year and the 20-year bond will drop in value, but the 1-year bond typically drops less because:
The 20-year bond has a much longer wait before the investor gets par value back. It’s locked into the lower rate until it matures or is sold, so its price has to adjust more when rates change.
When interest rates fall, long-term bonds tend to rise more in price for the same basic reason. In our comparison:
Bonds with lower coupons tend to have more price volatility than bonds with higher coupons.
Assume you own two 10-year bonds:
When interest rates rise, the value of both bonds will fall. The 2% coupon bond will usually fall further because it pays less interest along the way. With less interest coming in, the bondholder has less cash to reinvest at the new, higher rates.
By contrast, the 10% coupon bond pays more interest each year, giving the bondholder more money to reinvest at the new, higher rates.
Another way to think about it: the lower the coupon, the more likely the bond was sold at a discount. If much of the investor’s return comes from the discount (the difference between the purchase price and par value), the investor has to wait until maturity to realize that part of the return. In a rising-rate environment, that “wait” tends to make the low-coupon bond’s price more sensitive.
When interest rates fall, the value of both bonds will rise. The 2% coupon bond will often rise further because its value is more tied to receiving par value at maturity, and the bondholder isn’t receiving large interest payments that would need to be reinvested at the new, lower rates.
The 10% bond pays much more interest. If the bondholder reinvests those interest payments, they now have to reinvest at lower rates. In this situation, the 10% bond tends to be less valuable than it would be if rates hadn’t fallen, because more of its cash flow arrives early and would be reinvested at lower yields.
Here’s a video breakdown of a practice question regarding price volatility:
The concept of duration is closely related to price volatility. In general, the debt security with the longest maturity and the lowest coupon will have the highest duration.
Duration is unique because it captures two related ideas:
For example, assume we’re analyzing the following bond:
20 year, $1,000 par, 10% debenture trading for 120
This bond pays $100 in annual interest (10% of $1,000) over 20 years. It currently costs $1,200 (120% of $1,000).
If the bond pays $100 per year and costs $1,200, how long does it take to recoup the original $1,200? If we assume the interest is not reinvested*, it takes 12 years:
So, the duration of this debenture is roughly 12 years.
*Duration calculations often assume future cash flows are discounted to present value and reinvested. The details are not important for test purposes, but we’re calling this out because the duration calculation above is very oversimplified. However, test questions tend to focus on the fundamental concepts of duration. Know the basics and you’ll be fine!
Now, assume we’re analyzing this bond:
20-year, $1,000 par, zero coupon bond trading for 45
This bond does not pay interest until maturity (same with all zero coupon bonds), which is in 20 years. It currently costs $450 (45% of $1,000).
Because a zero coupon bond pays no interest until the end, the investor doesn’t receive cash flows along the way. That means it takes the entire life of the bond to recoup the investment. Another way to say this is: a zero coupon bond’s duration equals its maturity.
So, this bond’s duration is 20 years.
Let’s compare the two bonds:
20-year, $1,000 par, 10% debenture trading for 120
20-year, $1,000 par, zero coupon bond trading for 45
Duration and price volatility move together:
These two bonds fit that pattern. Both have 20-year maturities, but the zero coupon bond has greater price volatility and a longer duration.
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