What it means
Most bonds repay their principal in one go at maturity, but some repay in instalments over time. A sinking fund bond requires the issuer to retire part of the issue each year, and mortgage-backed bonds pass through principal as homeowners repay their loans.
For these bonds, the final maturity can be far later than the date when most of the money comes back. Average life is the weighted average time until the principal is repaid.
Each repayment is weighted by the amount repaid, so a bond that returns most of its principal early has a short average life. This is more informative than the final maturity date, which only tells you when the last payment falls due.
Yield to average life then treats the bond as if all the principal were repaid on the average life date. This is a shortcut, and it gives a single yield figure that can be compared with other bonds.
It is not as precise as a full cash flow yield, which uses each payment on its own date. The measure is useful for comparing amortising bonds with ordinary bullet bonds.
A sinking fund bond with a thirty-year final maturity but an average life of ten years behaves more like a ten-year bond in terms of interest rate sensitivity. Using the final maturity would overstate how long the investor's money is tied up.
Analysts should remember that average life can change. For mortgage-backed bonds, faster homeowner repayments shorten the average life, while slower repayments lengthen it.
The yield to average life is therefore only as reliable as the repayment assumptions behind it.
In practice
Real-world examples.
Example
A bond analyst compares a sinking fund bond with a final maturity of 20 years against an ordinary 8-year bond. The sinking fund bond has an average life of 8 years, so the analyst compares it with the 8-year bond. The yield to average life shows which offers the better return.
Example
A portfolio manager buys a mortgage-backed security and assumes a certain pace of homeowner repayments. The assumption gives an average life of 6 years, and the yield is calculated on that basis. When rates fall and homeowners refinance, the average life shortens and the manager reviews the position.
Example
A corporate treasurer issues a bond with an annual sinking fund and wants to describe the cost of borrowing. She uses the average life to describe how long the money will be outstanding on average. The board can see that the effective borrowing period is shorter than the final maturity.
Formula
Calculation
Average life = sum of (time of each repayment x amount repaid) / total amount repaid
Approximate yield = [annual coupon + (face value - price) / average life] / [(face value + price) / 2]
Suppose a $1,000 bond repays $250 of principal at the end of each of years 1, 2, 3 and 4. Average life = (1 x 250 + 2 x 250 + 3 x 250 + 4 x 250) / 1,000 = 2,500 / 1,000 = 2.5 years. If the bond has a 6% coupon ($60) and a price of $980, the approximate yield = [60 + (1,000 - 980) / 2.5] / [(1,000 + 980) / 2] = (60 + 8) / 990 = 6.87%.Case study
Seen in the real world.
Northgate Utilities is an illustrative, fictional company that issued a $100,000,000 bond with a 25-year final maturity and a sinking fund requiring equal annual repayments from year 6 onwards. Investors asked how the bond should be compared with ordinary bonds.
The financial analyst calculated the average life by weighting each year's repayment by the time until it was paid, and found it was about 15.5 years rather than 25. She then calculated the yield to average life and compared it with 15-year bonds from similar issuers.
The comparison showed that the bond was fairly priced against 15-year bonds but looked cheap against 25-year bonds. The illustrative lesson is that choosing the right comparison date matters as much as the yield itself.
Watch out
Common mistakes.
- Using final maturity to compare amortising bonds, when most of the principal comes back earlier.
- Treating average life as fixed for mortgage-backed bonds, when it changes with repayment speeds.
- Using yield to average life as an exact return, when it is a simplified measure that differs from a full cash flow yield.
Questions
People also ask.
What is yield to average life?
It is the yield of a bond calculated as if all the principal were repaid on the bond's average life date.
How is average life calculated?
It is the weighted average of the dates of principal repayments, with each date weighted by the amount repaid.
When is it most useful?
It is useful for bonds that repay principal gradually, such as sinking fund bonds and mortgage-backed securities.
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