# 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.

• Notwithstanding some potentially ambitious assumptions made about unchanged swap spreads and yield curves, what LIBOR are you assuming? – demully Jan 27 '20 at 22:36
• @demully No explicit number is given. 3month LIBOR that's it. It fluctuates and the point of this exercise is to secure your profit with IRS contract ( same nominal you allocate in deposits for the 3moth LIBOR, rolling these deposits for 3 years) and receive fixed leg of the contract. – Kran Jan 28 '20 at 8:40

## 1 Answer

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 ;-)