Loading the player...

## What is the 'Macaulay Duration'

The Macaulay duration is the weighted average term to maturity of the cash flows from a bond. The weight of each cash flow is determined by dividing the present value of the cash flow by the price. Macaulay duration is frequently used by portfolio managers who use an immunization strategy.

Macaulay duration can be calculated:

Where:

• t = respective time period
• C = periodic coupon payment
• y = periodic yield
• n = total number of periods
• M = maturity value
• Current Bond Price = Present value of cash flows
Next Up

## BREAKING DOWN 'Macaulay Duration'

The metric is named after its creator, Frederick Macaulay. The Macaulay duration can be viewed as the economic balance point of a group of cash flows. Another way to interpret the statistic is that it is the weighted average number of years an investor must maintain a position in the bond until the present value of the bond's cash flows equals the amount paid for the bond.

## Factors Affecting Duration

A bond's price, maturity, coupon and yield to maturity all factor into the calculation of duration. All else equal, as maturity increases, duration increases. As a bond's coupon increases, its duration decreases. As interest rates increase, duration decreases and the bond's sensitivity to further interest rate increases goes down. Also, sinking fund in place, a scheduled prepayment before maturity and call provisions lower a bond's duration.

## Example Calculation

The calculation of Macaulay duration is straightforward. Assume a \$1,0000 face value bond that pays a 6% coupon and matures in three years. Interest rates are 6% per annum with semi-annual compounding. The bond pays the coupon twice a year, and pays the principal on the final payment. Given this, the following cash flows are expected over the next three years:

Period 1: \$30

Period 2: \$30

Period 3: \$30

Period 4: \$30

Period 5: \$30

Period 6: \$1,030

With the periods and the cash flows known, a discount factor must be calculated for each period. This is calculated as 1 / (1 + r)n, where r is the interest rate and n is the period number in question. The interest rate, r, compounded semi-annually is 6%/2 = 3%. Thus the discount factors would be:

Period 1 Discount Factor = 1 / (1 + 3%)1 = 0.9709

Period 2 Discount Factor = 1 / (1 + 3%)2 = 0.9426

Period 3 Discount Factor = 1 / (1 + 3%)3 = 0.9151

Period 4 Discount Factor = 1 / (1 + 3%)4 = 0.8885

Period 5 Discount Factor = 1 / (1 + 3%)5 = 0.8626

Period 6 Discount Factor = 1 / (1 + 3%)6 = 0.8375

Next, multiply the period's cash flow by the period number and by its corresponding discount factor to find the present value of the cash flow:

Period 1 = 1 x \$30 x 0.9709 = \$29.13

Period 2 = 2 x \$30 x 0.9426 = \$56.56

Period 3 = 3 x \$30 x 0.9151 = \$82.36

Period 4 = 4 x \$30 x 0.8885 = \$106.62

Period 5 = 5 x \$30 x 0.8626 = \$129.39

Period 6 = 6 x \$1,030 x 0.8375 = \$5,175.65

Sum these values = \$5,579.71 = numerator

Current Bond Price = sum of PV Cash Flows = 30/(1 + 3%)1 + 30/(1 + 3%)2 +...+ 1030/(1 + 3%)6 = \$1,000 = denominator

(Note that since the coupon rate and interest rate are the same, the bond will trade at par)

Macaulay duration = \$5,579.71 / \$1,000 = 5.58

A coupon paying bond will always have its duration less than its time to maturity. In the example above, the duration of 5.58 half years is less than the time to maturity of 6 half years. In other words, 5.58/2 = 2.79 years is less than 3 years.

RELATED TERMS
1. ### Dollar Duration

The dollar duration, or DV01 of a bond is a way to analyze the ...
2. ### Interest Rate Sensitivity

Interest rate sensitivity is a measure of how much the price ...
3. ### Bond Valuation

Bond valuation is a technique for determining the theoretical ...
4. ### Discount Bond

A discount bond is a bond that is issued for less than its par ...
5. ### Average Price

The average price is sometimes used in determining a bond's yield ...
6. ### Discounting

Discounting is the process of determining the present value of ...
Related Articles
1. Investing

### Immunization Inoculates Against Interest Rate Risk

Big-money investors can hedge against bond portfolio losses caused by rate fluctuations.
2. Investing

### Simple Math for Fixed-Coupon Corporate Bonds

A guide to help to understand the simple math behind fixed-coupon corporate bonds.
3. Investing

### The Basics Of Bond Duration

Duration tells investors the length of time it will take a bond's cash flows to repay the investor the price he or she paid for the bond. A bond's duration is stated as a number of years and ...
4. Investing

### Why Investors Should Use Duration to Compare Bonds

Duration is a helpful metric that determines a bond's sensitivity to interest rates.
5. Investing

### Comparing Yield To Maturity And The Coupon Rate

Investors base investing decisions and strategies on yield to maturity more so than coupon rates.
6. Investing

### How Rising Interest Rates and Inflation Affect Bonds

Understand bonds better with these four basic factors.
7. Investing

### Why Bond Prices Fall When Interest Rates Rise

Never invest in something you donâ€™t understand. Bonds are no exception.
RELATED FAQS
1. ### How can I use a bond's duration to predict its return?

Learn how the concept of duration is used to determine when future cash flows for a bond will equal the amount paid for the ... Read Answer >>
2. ### Macaulay Duration vs. Modified Duration

Find out more about the Macaulay duration and modified duration, how to calculate them and the difference between the Macaulay ... Read Answer >>
3. ### What are the different types of college savings accounts?

Find out more about the Macaulay duration and zero-coupon bonds and how to calculate the Macaulay duration of a zero-coupon ... Read Answer >>
4. ### What is the difference between yield to maturity and the coupon rate?

A bond's coupon rate is the actual amount of interest income earned on the bond each year based on its face value. Read Answer >>
Hot Definitions
1. ### Capital Asset Pricing Model - CAPM

Capital Asset Pricing Model (CAPM) is a model that describes the relationship between risk and expected return and that is ...
2. ### Return On Equity - ROE

The profitability returned in direct relation to shareholders' investments is called the return on equity.
3. ### Working Capital

Working capital, also known as net working capital is a measure of a company's liquidity and operational efficiency.
4. ### Bond

A bond is a fixed income investment in which an investor loans money to an entity (corporate or governmental) that borrows ...
5. ### Compound Annual Growth Rate - CAGR

The Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer ...
6. ### Net Present Value - NPV

Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows ...
Trading Center