Why do some mutual funds or indexes have an average effective maturity that is way larger (2-4 times larger) than the average effective duration?

Assume there is no interest rate, you loan me 1 dollar and then I give you 0.5 dollar half year and then 1 year later.

The duration of my payment is 0.75 years and maturity is 1 year.

Duration is the average of the time I made the payment and maturity is when I made my last payment.

We can easily proof that maturity is larger or equal to duration, and equality only hold when we have a zero coupon bond

Hard to be too specific when there’s a lot of caveats in both “effective” measures, and their definitions, above :-)

This said, there are two complimentary reasons for maturity>>duration. The first of which is that duration, as a measure of the derivative of price with respect to yield given time, will (almost) always be lower than time. That is just is just a mathematical and a logical given. However I choose to measure “duration”, any cashflows received before maturity, duration > maturity. Simples...

Less trivial become callable corporate bonds, and/or MBS pre-payments. The former allow the borrower to prepay their debt earlier than term. The latter simply allow borrowers to not only repay, but refinance at fixed future long-term rates. Either shortens financial “duration”, compared to legal “maturity”.

In some cases, a portion of the principal can be returned before maturity. Mortgage bonds are one example.