Why Are Lower Coupon Bonds More Volatile?

A bond represents a loan made by an investor to a borrower, which can be a corporation or a government entity. This loan involves the borrower paying fixed interest payments over a set period, with the principal repaid at the end of this period. The price of a bond can fluctuate, and this sensitivity to changes in market interest rates is known as bond price volatility. Understanding this volatility is important for investors. This article explains why bonds with lower coupon rates generally exhibit greater price volatility when market interest rates change compared to bonds with higher coupon rates.

Fundamentals of Bond Pricing

Bonds possess several characteristics, including a face value (the principal repaid at maturity) and a specific maturity date. They also have a coupon rate, which determines the fixed interest payment received periodically, usually semi-annually.

A bond’s market price is determined by calculating the present value of its future cash flows. These cash flows include regular coupon payments and the final repayment of the face value at maturity. Investors discount these future cash flows using prevailing market interest rates.

Market interest rates and bond prices move in opposite directions. When market interest rates rise, the present value of a bond’s fixed future cash flows decreases, causing the bond’s price to fall. Conversely, if market interest rates decline, fixed future cash flows become more valuable, leading to a rise in the bond’s market price. This inverse relationship is foundational to understanding how bond prices react to changes in the broader economic environment.

Introducing Bond Duration

Bond duration measures a bond’s price sensitivity to interest rate changes. It quantifies how much a bond’s price is expected to change for a given change in market interest rates. A higher duration indicates a bond’s price will be more responsive to interest rate movements.

Duration represents the weighted average time until a bond’s cash flows are received. Each cash flow is weighted by its present value relative to the bond’s total present value, reflecting the timing of its overall cash flow stream.

A bond with higher duration carries greater interest rate risk, meaning its price will experience larger fluctuations for any given change in market rates. This increased sensitivity translates directly into higher volatility. Investors use duration to assess the interest rate risk of their bond holdings.

Duration is distinct from a bond’s maturity date. While maturity is the fixed date when principal is repaid, duration considers the timing of all cash flows, including coupon payments.

How Coupon Rates Influence Duration

The coupon rate directly affects a bond’s duration by influencing the timing of its cash flow receipts. Bonds with lower coupon rates provide smaller periodic interest payments. Consequently, a larger proportion of the bond’s total return relies on the final principal repayment at maturity.

This structure means a significant portion of the bond’s value is realized further in the future. As a result, the weighted average time until all cash flows are received is pushed further out. The smaller early payments contribute less to the overall present value, making the later principal repayment more impactful on the duration calculation.

Conversely, bonds with higher coupon rates distribute a larger share of their total return through more substantial periodic interest payments. These larger, earlier cash flows mean a greater portion of the bond’s value is returned sooner.

This earlier receipt of cash flows shortens the weighted average time until all payments are received. Therefore, higher coupon bonds have a lower duration compared to lower coupon bonds with similar maturities. The more frequent and larger coupon payments reduce the bond’s overall sensitivity to interest rate changes.

Connecting Duration to Price Volatility

Duration serves as the primary gauge of a bond’s sensitivity to shifts in interest rates. A higher duration signifies a bond’s price will react more significantly to changes in market yields. This relationship is central to understanding bond price movements.

Because lower coupon bonds inherently possess a higher duration, they are more sensitive to fluctuations in market interest rates. Their cash flows are more heavily weighted towards the distant future, making their present value calculations more susceptible to changes in the discount rate.

Consequently, even a small adjustment in market interest rates results in a larger percentage change in the price of a lower coupon bond. This greater price movement, both upwards when rates fall and downwards when rates rise, means they exhibit higher volatility. In contrast, higher coupon bonds, with lower duration, experience smaller price swings for the same interest rate change.

The interplay among coupon rates, bond duration, and interest rate movements explains the difference in volatility. Lower coupon bonds have a longer duration because their cash flows are received later, translating into greater price sensitivity and higher volatility.