Bond Duration Analysis

What is Duration of the bond?

The very first thing to remember is, duration of the bond is not maturity of the bond as both are different.

• Duration is defined as a weighted average of the maturities of the individual payments
• It is a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows
• It is an important measure for investors to consider, as bonds with higher durations carry more risk and have higher price volatility than bonds with lower durations
• Duration is also a point where the investor faces no interest rate risk

Terminology:

Zero coupon Bond: Issued at discount to face value and redeemed at par. Does not pay any interest

Vanilla bond/Straight: A normal interest bearing bond

 

Macaulay Duration:
The formula usually used to calculate a bond’s basic duration is the Macaulay duration

Where,

n = number of cash flows
t = time to maturity
C = cash flow
r = required yield (YTM)
M = maturity (par) value

Alternate Equation:

Lets understand the same with an illustration:

Consider a 12.5% bond with annual coupons, redeemable after 5 years at a premium of 5%. If the current interest rate is 15%, calculate duration of the bond.

Hence Duration of the bond = 375.11/94.11 = 3.99 Years

Remember duration of a zero coupon bond is equal to its maturity.

Duration and Bond Characteristics:

 

•   The lower the coupon, the higher the duration.

•   The higher the coupon, the lower the duration.

•   The longer the term to maturity, the higher the duration.

•   The shorter the term to maturity, the lower the duration.

•   The smaller the duration, the smaller the price volatility of the bond.

•   The greater the duration, the greater the price volatility of the bond.