When interest rates change, bond prices in the 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 its cash flows are spread out over 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 coupon rates) less attractive, so their prices must drop to compete.
Both bonds decline in value, but the 1 year bond usually declines less because:
The 20 year bond doesn’t have that quick reset. The investor is effectively locked into the lower coupon for much longer (unless the bond is sold), so the price has to adjust more to make the bond competitive in the new, higher-rate environment.
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 issues) 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 typically fall further because it pays less interest along the way. With smaller coupon payments, the investor has less cash flow to reinvest at the new, higher interest rates.
The 10% coupon bond pays more interest each year, giving the bondholder more money to reinvest at the new, higher rates. That extra cash flow 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 discount (the price moving up to par at maturity), the investor has to wait until maturity to realize that part of the return.
When interest rates fall, the value of both bonds will rise. The 2% coupon bond will typically rise further because more of its value is tied to receiving par value at maturity rather than receiving large coupon payments along the way. With smaller coupon payments, the investor is less exposed to having to reinvest those payments at the new, lower rates.
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 in a falling-rate environment, so it tends to rise less than a 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.
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) for 20 years. It currently costs $1,200 (trading at 120% of $1,000)*.
*Bonds are typically quoted on a percentage of par basis. Meaning, a quote of 120 means a bond is trading for 120% of par ($1,000). For test purposes, you can simply add a zero to the end of the bond quote to find its price. You should not expect to see detailed questions related to bond quotes on the Series 6 exam.
If this bond pays $100 in annual interest and currently costs $1,200, how long will it take an investor to recoup the original investment? If we assume the interest is not reinvested*, it will take 12 years ($1,200 ÷ $100 per year). 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 (trading at 45% of $1,000).
Zero coupon bonds don’t pay interest until the end, so 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 move together: the longer the maturity and the lower the coupon, the higher the price volatility and the longer the duration. These two bonds fit that pattern. Both have 20 year maturities, but the zero coupon bond is more price-sensitive and has the longer duration.
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