Duration & volatility

Price volatility

When interest rates change, bond market values fluctuate in the market. Bonds with longer maturities and lower coupons tend to see the most price volatility.

Long maturities

When a bond has a long maturity, it tends to be more sensitive to interest rate changes. Time has a compounding effect on market values. Assume you own a 1-year bond and a 20-year bond in your portfolio. When interest rates rise, market values for both bonds will fall. The 20-year bond’s price will fall more in price. Let’s talk about why.

When interest rates rise, it makes current bonds less valuable. Existing bond values are dependent on the interest rates of new bonds. When interest rates rise, new bonds become more valuable (they’re being issued with higher rates than before), leading to existing bonds falling in value.

While both the 1-year and the 20-year bond will fall in value, the 1-year bond won’t fall as much. Within one year, the investor will receive their par value back. At that point in time, the investor can reinvest their money back into a new bond with a higher rate of interest.

The other bond has a 20-year wait until that can happen. It’s locked in at the lower rate of interest until it matures or is sold. This is why bonds with longer maturities fall further in price when interest rates rise.

When interest rates fall, long-term bonds rise further in price for the same reasons. Going back to our comparison, the 1-year bond will rise in price, but not by much. It matures within one year; if the investor decides to reinvest their money back in the market, they will be buying a bond with a lower rate of return.

The other bond has a higher interest rate that’s locked in for the next 20 years. Because of this, the market value of the 20-year bond will rise much further than the 1-year bond.

Low coupons

Bonds with lower coupons have more price volatility than bonds with higher coupons. To understand this, assume you own two 10-year bonds. One has a 2% coupon and the other has a 10% coupon.

When interest rates rise, the value of both bonds will fall. The 2% coupon bond will fall further in price because it has less interest to reinvest back into the market at the new, higher rate of interest. The 10% coupon bond pays much more interest and gives more money to the bondholder to reinvest back into the market at the new, higher rate of interest.

The lower the coupon of a bond, the more likely it was sold at a discount. If a bond’s value is mostly from its discount, the investor must wait until maturity to make money from the bond’s discount. The 10% bond is more valuable in this situation because the 10% bond pays more interest that can be reinvested at higher rates right now.

When interest rates fall, the value of both bonds will rise. The 2% coupon bond will rise further in price because its value is likely tied to a discount. Remember, the lower the coupon, the more likely the bond was sold at a discount. When much of the bond’s value is achieved at maturity when the investor receives the par value of the bond, it is not required to reinvest large sums of money at lower rates of return.

The 10% bond pays much more interest to its bondholder. If the bondholder decides to reinvest their interest back into the market, they are forced to now buy bonds with lower rates of return as interest rates fell. The 10% bond is less valuable in this situation because the 10% bond pays more interest that would be reinvested at lower rates right now.

Here’s a video breakdown of a practice question regarding price volatility:

Duration

The concept of duration is part of the same “family of ideas” as price volatility. In fact, the debt security with the longest maturity and the lowest coupon will maintain the highest duration.

So, how is duration unique? In addition to measuring how quickly a security responds to interest rate changes, it also measures the amount of time necessary for an investor to recoup their original investment. For example, let’s assume we’re analyzing the following bond:

20 year, $1,000 par, 10% debenture trading for 120

This bond will pay $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 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, let’s 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 do not pay interest until the very end of the bond, therefore it will take the entire length of the bond for the investor to recoup their original investment. Or, another way of saying a zero coupon bond’s duration is equal to its maturity. Therefore, this bond’s duration is 20 years.

Let’s now compare the two bonds:

20-year, $1,000 par, 10% debenture trading for 120

• Duration = 12 years

20-year, $1,000 par, zero coupon bond trading for 45

• Duration = 20 years

As we discussed at the beginning of this section, duration and price volatility both measure price volatility on a bond. The longer the maturity and the lower the coupon of the bond, the higher the price volatility and the longer the duration. These two bonds align with this concept. Both are 20-year bonds, but the zero coupon bond’s market price is more volatile and reflects a longer duration.