The Average Life of a Mortgage Loan
The average life of a mortgage loan is the average time it takes for any one dollar of principal to be returned, or paid. A loan's monthly payment is constant, but it includes both principal and interest, and the ratio of principal to interest gets larger each month. The average life will therefore pass the loan's midpoint, since more principal dollars are paid then. Average life is also known as weighted average life, or WAL, since each time period is weighted by its principal dollar amount.
Other People Are Reading
-
Bonds
-
Bonds have a face value; a coupon, or interest rate; and a maturity date. You might pay the bond's face value, get the interest payments over time and get back the face value at maturity. A premium bond costs more than face value to compensate for a lower than face value yield, while a discount bond costs less than face value to compensate for a higher than face value yield. Mortgage-backed securities, similar to bonds, can also sell at value, at a premium or at a discount.
Bonds Vs. MBS
-
When you purchase a bond at face value, the yield to maturity and purchase price stay the same no matter how long it takes to get there. This is not true with premium or discount bonds. Here, the time to maturity plays a role. The longer it takes until maturity, the more the premium bonds cost for the same yield (or less yield for the same price) and the less the discount bonds cost for the same yield (or more yield for the same price). Mortgage-backed securities are basically the same (as bonds), but you can't go by the length until maturity, because the principal is paid though that time. That's why you have to know its average life (as well as prepayment risk).
-
Average Life Formula
-
Multiply each month's number by that month's principal payback amount. Sum the amounts, and divide the sum by the loan amount. The result is WAL months. Divide by 12 to convert into years. A more intuitive formula follows: Divide each month's principal payback by the loan amount. This tells you the month's principal payback proportion of the loan. The more dollars it has, the more it is recognized (excuse the pun). Multiply each month by its proportional strength, and sum the results for WAL months. Divide by 12 to convert into years.
An Example
-
Say you borrowed $10 and paid it back over three months, $2 on month 1, $3 on month 2, and $5 dollars on month 3. For the first method, the sum of months times dollars (2+6+15) is 23. 23 divided by 10 (the loan amount) is 2.3. For the second method, the first month has 20 percent of the loan, the second month 30 percent and the 3rd month 50 percent. Reduce each month's waiting time by multiplying it by its proportion. 20 percent of one month (.2) + 30 percent of 2 months (.6) + 50 percent of 3 months (1.5) is 2.3 months, same as before. In this example, you have to wait 2.3 months on average to get back any one dollar.
-
