# Principal payments for floating and inverse floating tranches

When allocating principal prepayments, is it always done in terms of weighting? For example, suppose you have a 20 million inverse floating tranche and 80 million floating tranche, would you allocate repayments proportionately, 20:80 ?

As far as I know, yes.

I don’t know why you’d do it any other way.

Thanks again for the quick response

You’re welcome.

I never understood the concept of inverse floating. Magician - can you please explain the concept.

Thanks.

Essentially when interest rates increase, you receive less coupon payments. Hence ‘inverse’

If you look at the equation, you will see the coupon payment is deducted and then multiplied by LIBOR. Therefore, as the coupon payment increases, you receive less payments.

Piece of cake.

A floating rate bond will pay a coupon such as LIBOR + 100bp: its coupon will increase when LIBOR increases (1:1) and decrease when LIBOR decreases. If the increase is greater than 1:1 – for example, the coupon is 2×LIBOR – 500bp – then it is called a leveraged floater, and if the increase is less than 1:1 – for example, the coupon is ½×LIBOR + 300bp – then it is called a deleveraged floater,

An inverse floater behaves the opposite: when LIBOR increases, its coupon decreases, and vice versa. An inverse floater will have a coupon such as 9% – LIBOR. Note that the coefficient on LIBOR needn’t be 1; if the coupon were, say, 15% – 2×LIBOR, it would called a leveraged inverse floater, and if the coupon were, say, 7% – ½×LIBOR, it would be called a deleveraged inverse floater.

Suppose that you have a \$60,000,000 pool of 10-year, fixed-rate bonds, paying an average coupon of 6.25% (from which you take your 25bp fee, leaving 6% for the bondholders). You create a CMO with two tranches: one has a floating rate of LIBOR (capped at 12%), the other is an inverse floater. If you have \$30,000,000 par in each tranche, then the inverse floater will have a coupon of 12% – LIBOR (with a floor of 0%). The total coupon, then, is:

(\$30,000,000/\$60,000,000)(LIBOR) + (\$30,000,000/\$60,000,000)(12% – LIBOR)

= ½×LIBOR + 6% – ½×LIBOR

= 6%

If the floating-rate tranche is \$45,000,000 par, then the inverse floater will be \$15,000,000 par and have a coupon of 24% – 3×LIBOR; once again, the total coupon is:

(\$45,000,000/\$60,000,000)(LIBOR) + (\$15,000,000/\$60,000,000)(24% – 3×LIBOR)

= ¾×LIBOR + 6% – ¼×3×LIBOR

= 6%

If the floating rate tranche is \$20,000,000 par, then the inverse floater will be \$40,000,000 par and have a coupon of 9% – ½×LIBOR; you guessed it: the total coupon is still 6%.

One interesting characteristic of inverse floaters is their extremely long effective duration. The effective duration of a portfolio is the (market value) weighted average of its constituent bonds. The above pool will have an effective duration of, say, 9 years, and the effective duration of the floater is near zero, so all of the effective duration has to come from the inverse floater. If it were 50/50 floater/inverse floater, then the effective duration of the inverse floater would be about 18 years, 1.8 times the maturity. If it were 75/25 floater/inverse, then the effective duration of the inverse floater would be about 36 years, and if it were 33.3/66.7, then the effective duration of the inverse floater would be about 13.5 years.

You’re welcome.

Thanks. You are magic!

You’re quite welcome.

S2000magician - I couldnt understand why 3x LIBOR is used as highlighted below… You have three times the par value in the floater as in the inverse floater, so a 1% increase in LIBOR will have three times the effect on the floater as on the inverse floater. For them to cancel (so that the total coupon paid is constant at 6%), the inverse floater has to react three times as much as the floater.

Try some numbers: suppose that LIBOR starts at 3% and increases to 4%, _ a 1% increase _. The (annual) coupon on the \$45,000,000 floater starts at \$1,350,000 (= 3% × \$45,000,000), then increases to \$1,800,000 (= 4% × \$45,000,000). The total coupon on the \$60,000,000 pool is \$3,600,000 (= 6% × \$60,000,000), so the coupon on the inverse floater has to fall from \$2,250,000 (= \$3,600,000 – \$1,350,000) to \$1,800,000 (= \$3,600,000 \$1,800,000). This, the coupon on the inverse floater drops from 15% (= \$2,250,000 ÷ \$15,000,000) to 12% (= \$1,800,000 ÷ \$15,000,000): _ a 3% decrease _.