Average life, also known as the weighted average life (WAL), is a measure used in finance to compare bonds of different durations and repayment schedules. It considers both the timing and amount of cash flows, providing an average duration that is weighted by these cash flows.
This page now absorbs the longer Weighted Average Life (WAL) explainer, so the core concept and the worked example live in one place.
Types/Categories of Bonds and Average Life
- Fixed-rate Bonds: Bonds with a fixed coupon rate and specified maturity date.
- Floating-rate Bonds: Bonds with variable interest rates that adjust periodically.
- Amortizing Bonds: Bonds that have periodic principal repayments over their term.
- Zero-Coupon Bonds: Bonds that pay no interest but are issued at a discount to par value and mature at face value.
Key Events in the Development of Average Life
- Introduction of Structured Financial Products: The need for average life became more pronounced with the advent of mortgage-backed securities (MBS) and asset-backed securities (ABS).
- Advancements in Financial Mathematics: The development of sophisticated financial models enabled the precise calculation of average life.
Detailed Explanation
Average life is calculated using the following formula:
$$ \text{Average Life} = \sum \left( \frac{CF_t \times t}{\sum CF_t} \right) $$
Where:
- \( CF_t \) = Cash flow at time \( t \)
- \( t \) = Period in which the cash flow is received
Importance
- Investment Decisions: Provides investors with a clearer understanding of the time frame over which they can expect to receive cash flows from a bond.
- Risk Management: Helps in assessing the interest rate risk and reinvestment risk associated with different bonds.
Example Calculation
Consider a bond with the following cash flows:
$$
\begin{aligned}
& \text{Year 1: } \$100 \\
& \text{Year 2: } \$100 \\
& \text{Year 3: } \$100 \\
& \text{Year 4: } \$100 \\
& \text{Year 5: } \$100 \\
\end{aligned}
$$
The average life would be:
$$
\begin{aligned}
& \text{Average Life} = \frac{100 \times 1 + 100 \times 2 + 100 \times 3 + 100 \times 4 + 100 \times 5}{500} \\
& = \frac{100 + 200 + 300 + 400 + 500}{500} \\
& = \frac{1500}{500} \\
& = 3 \text{ years}
\end{aligned}
$$
- Duration: A measure of the sensitivity of the price of a bond to changes in interest rates.
- Maturity: The date on which the principal amount of a bond is to be paid back in full.
FAQs
-
What is the difference between average life and duration?
- Average life considers the weighted average time to receive cash flows, while duration measures price sensitivity to interest rate changes.
-
Why is average life important in bond investment?
- It helps investors understand the timing of cash flows and manage interest rate and reinvestment risks.
-
Is average life the same as weighted average life (WAL)?
- In most bond and mortgage contexts, yes. WAL is simply the more formal label for average life.