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Evaluating an IRS and Bond Carry Trade Presented as Arbitrage

Article Quant Q&A · Author: Kran
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Summary

The exercise describes a proposed trade using interest rate swaps, short selling a coupon bond, and rolling deposit funding. It bootstraps discount factors from swap rates, then compares the bond’s discounted cash flows with swap-related receipts to claim a small positive value at inception. The author notices a cash-flow gap at intermediate coupon dates and asks how borrowing and additional swaps might cover it.

The response questions whether the trade qualifies as arbitrage and suggests that using the other swaps would make it a carry trade. This distinction matters: the displayed present-value comparison does not by itself show that all dated cash flows can be funded without risk. The document gives no complete hedge, financing schedule, or proof of guaranteed profit, and its own answer is tentative. Readers should treat the calculation as an incomplete exercise in cash-flow matching and carry, not as evidence of a risk-free arbitrage opportunity.

Key ideas

  • The proposed position combines a short bond, rolling deposits, and a receive-fixed interest rate swap.
  • Discount factors are bootstrapped from the stated swap rates to compare discounted cash flows.
  • The author identifies a funding shortfall on intermediate bond coupon dates.
  • A positive present-value calculation alone does not prove that a strategy is risk-free or self-financing.
  • The response characterizes use of additional swaps as a possible carry trade rather than a clear arbitrage.

Tags

Fixed incomeArbitrageCarryRisk management
Full text
# Basic arbitrage exercise


# Basic arbitrage exercise












In the exercise we are given, possible contracts to buy/sell and possibility to take credits / make deposits money with current market rates. We are asked if its possible to make profit at time T=0 and if yes then we should describe the strategy that guarantees this profit.

Instruments:

1Y IRS @ 4.5% (fixed leg paid yearly) vs 3month market rate (eg. LIBOR)

2Y IRS @ 4.7% (as above) vs as above

3Y IRS @ 4.8% as above vs as above

Bond 6% (yearly) with Nominal: 100, costs 103

I calculated discount factors using IRS bootstrapping method. DF(1Y)=0.957, DF(2Y)=0.912, DF(3Y)=0.863

And I found out that indeed one can make money, If one sells short the bond and allocates the 103 (income from the short sell) on the 3 months deposits according to current market rate, rolling it for 3 years, and secure this with 3Y IRS (receiving fixed leg), such that one would receive 5% each year (instead of LIBOR*103*3/12 every 3 months)

We have the following at T=0: $$103(DF(1Y)5\%+DF(2Y)5\%+DF(3Y)(1+5\%))-100(DF(3Y)(1+6\%)+DF(2Y)5\%+DF(1Y)5\%\approx0.26$$

The only problem is that in my cash flows I am missing money at T=1Y and T=2Y to pay the part of the coupon that exceeds what gets covered by the IRS's 103*5% of the short sold bond. My lecturer told me that I apparently I can solve this by taking credits and securing it with the "remaining" IRS contracts, unfortunately I cannot really see how.

## Answer by demully (score 1)

https://quant.stackexchange.com/a/50881

I don't know where to begin with the potential problems calling this an "arbitrage", but here then below is the kind of "answer" I suspect your lecturer is looking for:

If you're supposed to use the 2y or 3y in any way, the "arb" becomes a "carry trade", as played by many a carry-and-roll junkie ;-)

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.