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What Bond Duration do?
One fundamental concept in bond valuation is the inverse relationship between interest rates and bond prices. When market interest rates fall, the value of existing bonds rises. Conversely, when interest rates rise, bond values decline. This fluctuation introduces what’s known as interest rate risk—a risk inherent in all bonds, whether issued by the government or private entities. So, how can investors protect themselves against this risk? The answer lies in understanding bond duration.
What is Bond Duration? (And Why It Matters)
The concept of duration was introduced in 1938 by Canadian economist Frederick Macaulay, which is why it’s often referred to as Macaulay Duration. Duration essentially measures a bond's sensitivity to interest rate changes and provides insight into the time structure of cash flows. In simpler terms, it tells us how long it will take, on average, to recover the bond’s cost through its interest payments and principal—much like a payback period or a break-even point.
Duration is expressed in years, and the longer the duration, the more interest the bond may offer—but also the more sensitive it is to changes in interest rates. That means higher risk. For example, if you compare two bonds—one with a 5-year maturity and another with a 10-year maturity—the 10-year bond will generally have a longer duration and greater exposure to interest rate fluctuations. Over a 10-year period, market rates are more likely to shift, increasing the bond’s volatility.
How to Calculate Bond Duration (A Step-by-Step Example)
Example:
A bond with a face value of $100 has a coupon rate of 10% per annum, a time to maturity of 5 years, and a yield to maturity (YTM) of 14%. Let's calculate the duration of this bond.
Step 1: Determine the cash flows
Since the bond pays a 10% annual coupon on a $100 face value, the annual payment is $10.
So, the cash flows for each year will be:
• Year 1: $10
• Year 2: $10
• Year 3: $10
• Year 4: $10
• Year 5: $10 (coupon) + $100 (principal repayment) = $110
Step 2: Calculate the present value (PV) of each cash flow using 14% YTM
Use the formula:
PV = 1/(1+0.14)^n, where n = Year number
Calculations:
• Year 1: PV = 1 / (1 + 0.14)^1 = 0.877 → 10 × 0.877 = $8.77
• Year 2: PV = 1 / (1 + 0.14)^2 = 0.769 → 10 × 0.769 = $7.69
• Year 3: PV = 1 / (1 + 0.14)^3 = 0.675 → 10 × 0.675 = $6.75
• Year 4: PV = 1 / (1 + 0.14)^4 = 0.592 → 10 × 0.592 = $5.92
• Year 5: PV = 1 / (1 + 0.14)^5 = 0.519 → 110 × 0.519 = $57.09
Step 3: Add up the present values to get the bond's value
Total bond value = 8.77 + 7.69 + 6.75 + 5.92 + 57.09 = $86.22
Step 4: Multiply each year's present value by its time period
• Year 1: 1 × 8.77 = 8.77
• Year 2: 2 × 7.69 = 15.38
• Year 3: 3 × 6.75 = 20.25
• Year 4: 4 × 5.92 = 23.68
• Year 5: 5 × 57.09 = 285.45
Total of these weighted values = 8.77 + 15.38 + 20.25 + 23.68 + 285.45 = $353.53
Step 5: Calculate the bond’s duration
Duration = Total weighted value / Bond value
= 353.53 / 86.22
≈ 4.10 years
The bond’s duration of 4.10 years means that if you hold this bond for at least 4.10 years, the interest rate risk (i.e., potential loss in value due to rising interest rates) will be offset by the reinvestment income earned during that time. In simple terms:
Loss in bond value due to rate increase = Gain from reinvesting coupon payments.
4 Key Properties of Bond Duration
• Higher Coupon Rate = Shorter Duration:
Bonds with higher coupon rates generally have shorter durations. For instance, if you compare two bonds—one with a 5% annual coupon and another with 10%—their durations might be 2.87 years and 2.68 years, respectively. This illustrates a negative relationship between coupon rate and duration.
• Longer Maturity = Longer Duration:
The longer a bond’s maturity, the longer its duration. For example, a bond maturing in 5 years may have a duration of 4.17 years, while one with a 10-year maturity might have a duration of 9.1 years.
• Higher Yield to Maturity = Shorter Duration:
As the yield to maturity (YTM) increases, the bond’s duration decreases. For instance, a bond with an 8% YTM may have a duration of 4.10 years, while one with a 12% YTM could have a slightly shorter duration of 4.02 years.
• Zero-Coupon Bonds: Duration Equals Maturity:
In the case of zero-coupon bonds, the duration is equal to the time to maturity. Since these bonds don’t offer periodic interest payments, there’s no reinvestment risk—the entire return is received at maturity in a single payment.
About the Author: Abhishek Lohar
B.Com Graduate and the Founder of Free Online Financial Calculator. I specialize in simplifying complex financial calculations and investment strategies. My mission is to ensure you can make confident financial decisions using our research-backed content and accurate calculators.
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Disclaimer: The information provided in this article is for educational purposes only and should not be considered financial advice. Please consult with a qualified professional before making any investment decisions.