The weighted average maturity (WAM) is calculated by considering the different maturities of a bond issue and their respective issue prices. It gives you an average time until the debt will be fully repaid, weighted by how much of the issue matures at each date.
Understanding Weighted Average Maturity
Essentially, WAM is the sum of the products of each maturity's proportion of the total issue price and their time to maturity, according to the reference: "Generally, the Weighted Average Maturity of a Bond Issue is the sum of the product of the Issue Price of each maturity of the Bond Issue multiplied by the number of years from the Closing until that Maturity Date divided by the Issue Price of the entire Bond Issue."
The Formula
Here's how it breaks down mathematically:
WAM = Σ (Issue Price of Maturity * Years to Maturity) / Total Issue Price
Where:
- Σ represents the sum.
- Issue Price of Maturity is the total amount issued for that particular maturity date.
- Years to Maturity is the time from the issue date until that maturity date, expressed in years.
- Total Issue Price is the total amount issued for the entire bond issue.
Step-by-step Calculation
Let's go through the steps to calculate WAM:
- Identify Each Maturity: Determine all the different maturity dates for the bond issue.
- Determine Issue Price for Each Maturity: Note the issue price associated with each maturity date. This is the principal amount at issuance for bonds maturing on each date.
- Calculate Years to Maturity: Find the number of years between the issue date and each maturity date.
- Multiply and Sum: Multiply the issue price for each maturity by its corresponding time to maturity and sum all those results.
- Divide by Total Issue Price: Divide the sum calculated in the previous step by the total issue price of the entire bond issue.
- Result is the Weighted Average Maturity: The resulting value is the Weighted Average Maturity of the bond issue.
Example
Let's say a bond issue has the following characteristics:
| Maturity Date | Issue Price | Years to Maturity |
|---|---|---|
| 2025 | $2,000,000 | 1 |
| 2027 | $3,000,000 | 3 |
| 2030 | $5,000,000 | 6 |
Assume the bond was issued at the end of 2024.
- Sum of (Issue Price * Years to Maturity):
- ($2,000,000 * 1) + ($3,000,000 * 3) + ($5,000,000 * 6) = $2,000,000 + $9,000,000 + $30,000,000 = $41,000,000
- Total Issue Price:
- $2,000,000 + $3,000,000 + $5,000,000 = $10,000,000
- Weighted Average Maturity:
- $41,000,000 / $10,000,000 = 4.1 years
Therefore, the weighted average maturity for this bond issue is 4.1 years.
Practical Insights
- Risk Assessment: WAM is an important metric for investors because it provides insight into a bond's overall sensitivity to interest rate changes. Generally, the longer the WAM, the more sensitive the bond's price will be to changes in interest rates.
- Portfolio Management: WAM allows portfolio managers to evaluate the average duration of their bond portfolio and helps them align it with the institution's objectives and risk tolerance.
- Bond Valuation: Understanding WAM can aid in comparing the value of bond issues with different maturity profiles.
