Average Life of MBS

Can someone help me understand what the Average Life calculation means? For example, quesitons 13.d on page 474 asks for the average life for tranche A, the Answer is 0.30.

Is this .30 years? How do I interrupt this number provided there are ~7 payments left for Tranche A

The stated maturity of CMOs is not a very useful measure of the expected life of the bond given the receipt of prepayments as principal return. Instead, the average life is more frequently used as a measure of expected bond life and represents the average time to receipt of principal payments (scheduled principal repayments and projected prepayments). In practice, Average Life is one proxy for risk exposure that is better than using stated maturity because the impact of principal return through the life of the bond (as oppose to bullet maturities on Treasury Notes or most corporate bonds).

I haven’t looked at this example specifically, but if there are 7 payments left and an average life of 0.30 years, this basically means that “on average” I get my principal back in 0.30 years. This is because I get some return of principal in each of those 7 payments (as opposed to all my principal back in period 7). It would be misleading to think of my full principal return exposure to be 7 payment periods because my exposure is actually amortizing down through that time.

For example, if I lent you $100 for 10 years, and each year you pay me back $10 (ignore interest), I would say the “average life” of my loan to you is 5 years. I wouldn’t say the life of the loan (as a proxy for risk exposure) is 10 years, because at that point in time, your last payment to me is only $10 in order to repay me in full. So, average life on amortizing bonds provides for a better measure of exposure than maturity of the bonds.

Awesome explanation. Thanks for this.