Goldman, Sachs & Co. Mortgages Fixed Income Research

1 goldman , Sachs & Co. Mortgages Fixed Income Research valuation and hedging of Inverse IOs As leverage is defined as the ratio of borrowed funds to equity, in the case of the inverse IO this ratio will In a recent mortgage Market Comment article be given by the price of floater (the amount syntheti- ( How To Value and Hedge Inverse Floaters, No- cally borrowed) divided by the price of the inverse vember 19, 1999), we examined in some detail the IO (the amount of equity), as the notional amounts characteristics of inverse floaters, with a particular are the same in the two cases.

2 Therefore, the effec- emphasis on the close similarity between inverses tive multiplier (or leverage) can be written: and repo transactions. In this article, we extend the same analysis to inverse IOs. Inverse IOs are very 1. EM = (Price of Floater / Price of Inverse IO). similar to inverse floaters in the sense that they both employ inherent leverage by carving out a floater = Leverage of Inverse IO. from a Fixed rate and selling the floater. However, an inverse IO is a much more leveraged position in the Many of the formulas and concepts that were devel- underlying Fixed rate CMO class.

3 As a result, the oped in the previous article for inverses are immedi- inverse IO is much more sensitive to the factors that ately applicable to the current case, with the caveat drive inverse valuations. that we can no longer approximate the leverage by the ratio of the floater principal to the inverse princi- A Quick Introduction to Inverse IOs pal, as there is no inverse IO principal. We can ex- An inverse IO can be understood to be the limiting press the duration of the inverse IO in terms of the case of an inverse, as both are a residual side-effect duration of the Fixed rate and floater: of stripping out a floater from a Fixed rate tranche.

4 The difference between the two is in the fraction of 2. Inverse IO Duration = Dur of Fixed +. the principal that is diverted to the floater. EM (Dur of Fixed Dur of Floater). Inverse IOs are created in the following way: Much of the intuition associated with leverage that A Fixed rate tranche of a CMO is broken up into was developed for inverses can be applied with two pieces, an inverse IO and a floater. equal validity to inverse IOs. In particular, we can approximate the yield and OAS of an inverse IO. The floater is backed by all of the principal of with a formula of the form: the Fixed rate, with the coupon given by an index plus a margin.

5 There is an embedded coupon cap 3. Inverse IO Fixed + EM ( Fixed Floater). associated with the floater which corresponds to the case where all of the interest of the underly- ing Fixed rate bond is being diverted to the Typically, as inverse IOs have the maximum syn- floater. thetic leverage possible within the floater/inverse framework, they will also have among the highest The inverse IO is the residual of the Fixed rate OASs, yields, and durations available in the mort- after splitting off the floater. It is a pure notional gage marketplace.

6 Bond with an embedded coupon floor of zero, which implies a LIBOR cap that is struck at the Inverse IOs as Floors underlying Fixed rate less the margin on the Perhaps the easiest way to evaluate inverse IOs is by floater. comparing them with LIBOR floors with the same strike. We will consider as an example GN 99-42. As we discussed in the previous article, inverses and SC, an inverse IO stripped from 1986-87 GNMA 9s inverse IOs are very similar to mortgage repo trans- with a coupon of LIBOR. The corresponding actions, with the corresponding floater representing floater for this bond is GN 99-42 FC, which has a the borrowed funds and the value of the inverse to be coupon of L + 40 bp.

7 Inverse IOs are structured so the equity, or haircut. When viewed in this way, an that the maximum interest that can be received is the inverse IO is the limiting case of an inverse where underlying Fixed rate less the floater margin ( in all of the principal of the Fixed rate is financed by our example) and the minimum is zero. the sale of the floater, achieving the maximum amount of leverage possible in the floater/inverse transaction. 8 December 3, 1999. goldman , Sachs & Co. Mortgages Fixed Income Research Each month, the investor receives: Inverse IOs Are Attractive to Floors FN 98-46 SC Price Pickup Versus Floors at $8-00, Under Various Speed Assumptions (CPRs in %).

8 Coupon = ( LIBOR) + Max(0, LIBOR ). CPR 6 15 20 25 30. Avg. Life = LIBOR when 0 < LIBOR < Floor Val 11-17 11-03 8-13 7-21 6-16. = 0 when LIBOR >= Pickup +113 +99 +45 -11 -48. on the notional balance at that time. (Note that while pricing floors with stated maturities at the average the inverse IO coupon cannot go above , this life of the inverse IO at various speeds. While the corresponds to the case where LIBOR drops below second approach overstates the balance for the first zero. Therefore, while the inverse IO is short a half of the life of the bond and understates it in the LIBOR floor, since it is struck at zero it has no value second half, often this error is small enough to allow and will be ignored.)

9 The above cash flows are qualitative comparison. In the following discussion, equivalent to those of a LIBOR floor struck at we will compare FN 98-46 SC with non-amortizing We can gain further insight into this analogy by de- floors of various maturities, keeping in mind that we composing the above cash flows into two compo- are approximating the amortizing schedule with a nents. Fixed notional and a maturity of the average life. The investor is receiving a Fixed coupon less As FN 98-46 SC is offered at 8-00, one can see from LIBOR on the notional, which is equivalent to a the table at lower left that the inverse IO has value in receiver swap.

10 Comparison with a floor if the average life of the As the coupon on the inverse IO is restricted to bond is longer than approximately years. An- never be negative, the holder of the inverse IO is other way of quantifying this is to compute the also long a LIBOR cap at the Fixed rate strike of breakeven speed for the bond versus the floors mar- the inverse IO. ket. In the table above we calculate the price advan- tage of the inverse IO versus the floor market at We can conclude that an inverse IO is comparable to various realized lifetime speeds.