Decomposing a Leveraged LIBOR Swap into Fixed-for-Floating Swaps

Summary

The document asks how to interpret a swap in which one party pays three-month LIBOR while the other pays a rate equal to a fixed percentage minus twice LIBOR. Its proposed simplification is to subtract LIBOR from both sides of the payment comparison. This preserves the net cash flow while expressing the floating-rate exposure as a multiple of a standard LIBOR-versus-fixed swap.

After the transformation, the variable payment is three times the difference between an 8% fixed rate and LIBOR. The quoted arrangement can therefore be understood as three identical swaps, with the payment directions specified in the document. This is an algebraic decomposition of the stated periodic rates, not a separate valuation or risk analysis. The text is framed as a request for clarification and does not discuss notional amounts, payment dates, discounting, or other contract terms that could matter when comparing actual swap agreements.

Key ideas

• Subtracting the same rate from both sides leaves the net payment difference unchanged.
• The resulting floating-rate component is three times the difference between the stated fixed rate and LIBOR.
• The arrangement can be represented as three swaps exchanging LIBOR for the stated fixed rate.
• The algebraic equivalence assumes matching notionals and payment terms for a practical contract comparison.

Tags

# 53094


# Let $L$ denote the three-month US dollar LIBOR rate and an interest rate swap arrangement where fixed rate is $L$ and floating rate is $24\% - 2L$












The following is a question taken from Heard on the Street.

> Let $L$ denote the three-month US dollar LIBOR rate. Consider an interest rate swap arrangement where Party A pays $L$ to Party B, and Party B pays $24\% - 2L$ to Party A. Can you reverse engineer this deal and express it in simpler terms?

The answer given is as follows:

> If you subtract LIBOR, denoted $L$, from both payments, it seems that Party B is paying $24\% − 3L$. This is three times $8\% − L$. The quoted swap is, therefore, equivalent to three swaps, each of which is a swap of LIBOR for $8\%$ fixed (where Party A pays LIBOR, and Party B pays $8\%$).

I do not understand the solution given. Why do we subtract $L$ for both parties? After subtraction, why can we deduce that the quoted swap is equivalent to three swaps and the fixed rate of each swap?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.