Understanding Weighted Average Life (WAL) vs Duration: Explained

Introduction

When it comes to investing in bonds or other fixed-income securities, two important concepts to understand are Weighted Average Life (WAL) and Duration. These measures play a crucial role in evaluating interest-rate risk and making informed investment decisions. In this article, we will explore the differences between WAL and Duration, how they are calculated, and their significance in bond investing.

What is Weighted Average Life (WAL)?

Weighted Average Life (WAL) is a metric used to determine the average number of years for which each dollar of unpaid principal on a loan or mortgage remains outstanding. It takes into account the timing and amount of principal repayments and provides a measure of the average time it takes for the principal to be repaid.

WAL is calculated by multiplying the outstanding principal balance at each point in time by the time remaining until maturity, and then summing up these values. The result is divided by the total outstanding principal balance to arrive at the weighted average life.

For example, let's say we have a mortgage with an outstanding principal balance of $100,000. The mortgage has two repayment periods - one after 5 years and another after 10 years. The outstanding principal balance after 5 years is $80,000, and after 10 years, it is $60,000. The calculation of WAL would be:

($80,000 * 5 + $60,000 * 10) / ($80,000 + $60,000) = 7.5 years

What is Duration?

Duration is a measure of the sensitivity of a bond's price to changes in interest rates. It indicates how much the price of a bond is expected to change for a 1% change in interest rates. Duration takes into account the timing and amount of cash flows from a bond, including coupon payments and the repayment of principal at maturity.

Duration is calculated as the weighted average of the present values of all the cash flows from the bond, with the weights being the proportion of each cash flow to the total present value of all cash flows. The result is divided by the bond's current market price to arrive at the duration.

For example, let's consider a bond with a current market price of $1,000, a coupon payment of $50 per year, and a maturity of 5 years. The present value of each cash flow is calculated based on the prevailing interest rate, and the weighted average is determined. The calculation of duration would be:

((PV of $50 at year 1 * 1) + (PV of $50 at year 2 * 2) + (PV of $50 at year 3 * 3) + (PV of $50 at year 4 * 4) + (PV of $1,050 at year 5 * 5)) / $1,000 = x years

Differences between Weighted Average Life (WAL) and Duration

While both Weighted Average Life (WAL) and Duration are measures used in bond investing, they differ in their calculations and interpretations.

Calculation

WAL takes into account the timing and amount of principal repayments, while Duration considers the timing and amount of all cash flows (including coupon payments) from a bond. The formulas used to calculate WAL and Duration are different, as discussed earlier.

Interpretation

WAL represents the average time it takes for the principal to be repaid, while Duration indicates the sensitivity of a bond's price to changes in interest rates. WAL focuses on the repayment of principal, whereas Duration considers both the principal and coupon payments.

Application

WAL is often used to assess the credit risk of a loan or mortgage, as it provides an estimate of the average time it takes for the principal to be repaid. Duration, on the other hand, is primarily used to evaluate interest-rate risk and make investment decisions in the bond market. Duration helps investors understand how changes in interest rates can impact the price of a bond.

Conclusion

In summary, Weighted Average Life (WAL) and Duration are important measures in bond investing. While WAL focuses on the repayment of principal and provides an average time for repayment, Duration takes into account all cash flows and indicates the sensitivity of a bond's price to changes in interest rates. Understanding these concepts can help investors make informed decisions and manage interest-rate risk effectively.