Suppose that a tranche from which an inverse floater is created has an average life of five years. What will the average life of the inverse floaterbe?

What will be an ideal response?

The coupon rate on the tranche from which two classes (floater and inverse floater) are created can support the aggregate interest payments that must be made to them. As in the case of the floater, the principal pay-down of an inverse floater will be a proportionate amount of the principal pay-down of bond class that created it. Thus, the floater and inverse floater will have a weighted average life equal to the average life of the tranche from which it is created. In equation form, we have:

Average life = 5 years = (inverse floater's weight)(X years) + (floater's weight)(Y years) where X equals inverse floater's average life in years and Y equals floater's average life in years. Solving for X, we get:

X years = .

Let's illustrate. Suppose that the floater and inverse floater are equally-weighted (each weight = ½). If so, then, we have:

X years = = ?

(1/2)X years = 5 years – (1/2)(Y years) ? (1/2)X years + (1/2)Y years = 5 years. Thus, the average life of the inverse floater would be 5 years.

Now assume that the average life for the floater and inverse floater are equal (X = Y). Further solving gives: (1/2)X + (1/2)X = 5 years ? X = 5 years and Y = 5years.

If we assume that 2X = Y, then we have: (1/2)X + (1/2)(2X) = 5 ? (3/2)X = 5 ? X = 3.33 years and Y = 6.67 years. Thus, the average life of the inverse floater would be 3.33 years. Similarly, we could show that if X = 2Y, then the average life of the inverse floater would be 6.67 years.