# Average Life

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## Average life is a concept that aids analysts and investors in calculating the risk and return of debt assets like bonds, loans, and securities backed by mortgages.Â

It is the typical period of time for which each unit of unpaid principal is anticipated to stay outstanding. It relies on the debt issue's repayment plan, which might be either a lump sum at maturity or payments over the duration.

To calculate the average life of a bond, one can use the following formula:

Average life = Sum of (t * C / F)

Where:
• t = time to each payment
• C = principal payment at time t
• F = face value of the bond

For example, suppose a four-year bond has a face value of \$1,000 and pays annual principal payments of \$400, \$300, \$200, and \$100 each year. The average life of this bond is:

Average life = (1 * 400 / 1000) + (2 * 300 / 1000) + (3 * 200 / 1000) + (4 * 100 / 1000)

Average life = 0.4 + 0.6 + 0.6 + 0.4

Average life = 2 years

The bond's average life indicates how soon its principal will be repaid. Because they receive their gains sooner and are exposed to less risk from interest rates, investors tend to favor shorter average lifespan.Â

The possibility that changes in interest rates will affect a bond's market value is known as interest rate risk. A bond's price volatility and exposure to interest rate changes will both be greater the longer its average life is.

Prepayment risk is another element that influences the typical life of a bond. Prepayment risk is the possibility that the borrower will pay down the principal ahead of time, shortening the bond's typical life and lowering the amount of income the investor will receive.Â

Mortgage-backed securities, which are supported by collections of mortgages that can be refinanced or paid off by homeowners, frequently carry a prepayment risk. Analysts evaluate the prepayment speed using various models, then change the average life to account for the risk of prepayment.

The Public Securities Association (PSA) model is one such example, which presupposes that prepayment rates begin low and steadily rise to a steady level after 30 months. The PSA model employs a reference point known as 100% PSA, which denotes a prepayment rate of 0.2% in month one, increasing by 0.2% each month until it reaches 6% in month 30, and remaining at 6% thereafter.Â

For instance, a mortgage-backed asset with a 10-year original average life would have a 7.19-year adjusted average life under a 100% PSA.

Using multiples of 100% PSA allows the PSA model to be modified to account for various prepayment scenarios. For instance, 50% PSA denotes a prepayment rate that is half that of 100% PSA, while 150% PSA denotes a prepayment rate that is 1.5 times that of 100% PSA. The average life of the mortgage-backed securities decreases with increasing PSA %.

For comparing various debt instruments and evaluating their risk and return characteristics, average life is a relevant statistic. It can assist investors in selecting the optimal investment option based on their tastes and expectations.Â

However, the average life is not a set value and can vary over time as a result of elements like interest rates and prepayments. As a result, investors should constantly review their debt securities and modify their strategies as necessary.
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