Key Properties of Duration flow in Measuring Bond Interest Rate Risk

Duration is a key financial metric used to measure a bond’s sensitivity to interest rate changes, also reflecting the risk of retirement liabilities. In investing, duration represents the number of years required to recover a bond’s true cost, calculated based on the present value of all future coupon and principal payments.

Key Properties of Duration in Measuring Bond Interest Rate Risk

1. Coupon Rate: Duration decreases as the bond’s coupon rate increases. Bonds with lower coupon rates exhibit higher durations because their cash flows are weighted more toward the future, resulting in greater interest rate risk.
2. Yield to Maturity (YTM): Duration decreases as the yield to maturity rises. Lower yields increase a bond’s duration by emphasizing the weight of future cash flows, particularly the maturity payment.
3. Interest Rate Elasticity: Duration provides an accurate measure of a bond’s price sensitivity to interest rate changes.

Relationships between Bond Features and Duration

• Coupon Rate (c): An inverse relationship exists between the coupon rate and duration. Higher coupon payments reduce duration because more cash is returned earlier. Lower-coupon bonds face greater interest rate risk due to their longer duration.
• Yield to Maturity (r): There is an inverse relationship between yield to maturity and duration. A lower YTM extends duration by increasing the weight of later cash flows.
• Time to Maturity: Generally, a longer time to maturity leads to a higher duration, reflecting increased interest rate risk. However, deep-discount bonds can exhibit decreasing Macaulay duration beyond a certain maturity point.
• Zero-Coupon Bonds: For zero-coupon bonds, duration equals the bond’s time to maturity because all cash flows occur at maturity.
• Interest Rate Risk: Duration quantifies a bond’s sensitivity to interest rate changes. As rates rise, duration decreases.
• Linear Approximation: Duration serves as a linear estimate for price sensitivity, performing best with small interest rate movements.
• Fraction of Current Coupon Period Elapsed (t/T): As the fraction of the current coupon period (t/T) increases, duration slightly decreases due to approaching the next coupon payment. Once a coupon is paid, the duration increases slightly, creating a saw-tooth pattern.

Modified Duration

Modified duration highlights the inverse relationship between interest rates and bond prices. It measures how much a bond’s price is expected to change in response to a 1% change in interest rates. This formula provides a practical way to quantify a bond’s sensitivity to interest rate fluctuations.

Macaulay duration calculates the weighted average time before a bondholder receives the bond’s cash flows. In order to calculate modified duration, the Macaulay duration must first be calculated.

Read: WHAT IS DURATION OR MACAULAY DURATION?

Modified duration is an extension of the Macaulay duration, which allows investors to measure the sensitivity of a bond to changes in interest rates.

Modified Duration= Macaulay Duration ÷ (1+Yield to maturity) ÷ number of coupon periods per year

Where,

Macaulay Duration=Weighted average term to maturity of the cash flows from a bond

Read: WHAT IS MODIFIED DURATION?

Calculating face value :

To calculate the final face value payment, you can divide the face value by (1+r) ^t

Where, r is yield to maturity and t is time in years