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 period of 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 - but the 20-year bond’s price will typically fall more. Here’s why.
When interest rates rise, newly issued bonds come to market with higher yields. That makes existing bonds (with lower coupons) less attractive, so their prices drop to offer a competitive yield.
Both the 1-year and the 20-year bond will decline in value, but the 1-year bond usually declines less because:
The 20-year bond doesn’t have that flexibility. The investor must wait much longer to get par value back, and the bond is effectively “stuck” paying the lower coupon unless it’s sold. That longer wait is why long-maturity bonds tend to fall further when rates rise.
When interest rates fall, the same logic works in reverse. Long-term bonds usually rise more in price because their higher coupon payments (relative to new, lower-rate bonds) are locked in for many years. In our comparison:
Bonds with lower coupons tend to have more price volatility than bonds with higher coupons.
To see why, 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 coupon income coming in, the investor has less cash to reinvest at the new, higher rates.
The 10% coupon bond pays more interest each year, giving the bondholder more money to reinvest at the higher prevailing rates. That higher coupon income helps reduce the bond’s sensitivity to rising 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 bond moving from a discount price up to par at maturity, the investor has to wait longer to realize that return.
When interest rates fall, the value of both bonds will rise. The 2% coupon bond will typically rise further because:
By contrast, the 10% bond pays much more interest. If the bondholder reinvests those coupon payments, they’ll now be reinvesting at lower rates. That reinvestment effect makes the high-coupon bond relatively less valuable when rates fall, so its price tends to rise less than the low-coupon bond.
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.
So what makes duration different? Duration is commonly used to describe:
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 a 20-year period. It currently costs $1,200 (trading at 120% of $1,000)*.
*If the bond quote above is confusing, please revisit this chapter to review.
If this bond pays $100 in annual interest and currently costs $1,200, how long will it take an investor to recoup their original investment? If we assume the interest is not reinvested*, it will take 12 years (12 years x $100 annual interest). Therefore, 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 (trading at 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 full life of the bond to recoup the investment. Another way to say this is: a zero coupon bond’s duration is equal to its maturity. Therefore, 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 point in the same direction: longer maturities and lower coupons generally mean greater sensitivity to interest rate changes. These two bonds fit that pattern. Both have 20-year maturities, but the zero coupon bond typically has more price volatility and a longer duration.
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