How to Calculate the Weighted Average Life for Bonds

Image Credit: opolja/iStock/GettyImages

The weighted average life for a bond or another interest-bearing investment refers to the average amount of time for a dollar of principal to be repaid. Bonds with higher weighted average life values may be more risky. Keep in mind that the weighted average life is generally less than the maturity time, which measures how long it takes a bond to finish paying out entirely.

Bonds Repaying Principal

While people often think about a bond as an investment that you can buy and sell on the open market similar to a stock, it's also often useful to think about a bond as a loan. After all, companies and government agencies issue bonds in order to borrow money, often to pay for short-term projects over a long period of time.

Over the course of the bond's existence, the bond pays back money on a set schedule, including principal and interest. Unlike many loans that individuals take out, bonds may not pay back fixed amounts over time and may make larger payments at certain times of the life of the bond.

It's often useful for investors to figure out roughly when the principal, or the initial loan amount of the bond, will be paid back. Bonds that take longer to do that may be more risky than those that pay back principal more quickly, taking into account other considerations like the issuer's credit ratings and overall economic situations.

Weighted Average Life

The amount of time that the average dollar of principal on a loan remains outstanding is called the weighted average life. You can use the weighted average amortization period calculation formula to find this value.

To do so, look at the bond's issuing documents or other documentation to find out when and how much the bond pays back over its lifetime. Sum up the payback amounts to find the total amount the bond pays back. Then, for each payback amount, multiply that amount by how far into the future it is, and sum up those numbers. Divide that larger sum by the smaller sum of the payback amounts to get the weighted average life of the bond.

For instance, consider a bond that pays back $5,000 in one year, $10,000 in two years and $20,000 in four years. Its total payback amount is $35,000. The weighted sum is $5,000 * 1 + $10,000 * 2 + $20,000 * 4 = $105,000. Divide $105,000 by $35,000 to get the weighted average life of 3 years. Note that you can use another unit of time, such as months or days, if that is more convenient, as long as you make sure that all periods of time are expressed in the same units.

Factors Affecting Weighted Average Life

Bonds that pay back more money sooner will have shorter weighted average life. For instance, consider the above example, but imagine that the $20,000 payment and $5,000 payments are swapped.

Then, the weighted average life = ($20,000 * 1 + $10,000 * 2 + $5,000 * 4) / $35,000 = $60,000 / $35,000 or roughly 1.71 years. Because the big payback comes sooner, the weighted average life is shorter.

Weighted Average Life and Maturity

When a bond has paid back everything that it is going to pay, it is said to have matured. The maturity date is often further away than the weighted average life, which makes sense, because it takes into account when the bond is paying back interest as well as principal. The weighted average life can be a more useful measure of a bond's payback periods than maturity for many purposes.

references