The basic idea is that the arbitrageur takes a position in the forwards market and covers the risk by lending or borrowing the currencies involved at different interest rates. With the exchange rate risk covered, this leaves the trader free to exploit an interest rate gap.
To understand this strategy, we first need to understand how forwards and futures are priced.
Why Are Spot and Forward Prices Different?
If you look at a quote for a forward or futures contract, you’ll notice it’s nearly always different to the spot rate. It holds for many asset types that forwards trade at either a premium or a discount to the spot rate.
It’s often thought that this must be because the market is “pricing in” assumptions about the future.
Although this seems like a logical explanation, it’s not correct. The spot price already reflects all known information about the future. The difference is in the value date.
If a future or forward does include a discount or premium that is not reflected in the underlying market or in interest rates, we can arbitrage against that and make a profit.
To prove this, take a very simple example. Take the Australian dollar and the Japanese yen. The spot rate for AUDJPY is currently 82.90 / 83.0. But suppose some bank, let’s call it Bank ABC is quoting 12-month forwards for the same as the spot rate. That is, AUDJPY at 82.90 / 83.0. Each contract is for 1000 units.
If I buy one contract from them, Bank ABC will have to sell me 1000 AUD in 12 months’ time at a price of 83,000 yen. If I short one contract from them, Bank ABC is committed to buy 1000 AUD in 12 months at a cost of 82,900 yen. The short is simply the same as a forward contract on JPYAUD.
To check the prices we do the following calculation. Suppose the 12-month interest rate on the Australian dollar is 3.5% and the 12-month interest on Japanese yen is 0.12%. These rates are fixed at 12 months maturity, the duration of the deal.
We now check the cost of buying/selling these currencies today and holding the position for 12-months. To do this we need to:
Borrow 83,000 x JPY for 12 months at 0.12%
~ Convert 83,000 x JPY to AUD at today’s spot rate 83.0
~ Gives 1000 AUD
Lend 1000 AUD at 3.5% for 12-months
In 12 months:
I receive AUD interest at 1000 x 3.5 % = AUD 1035
I pay JPY interest at 83,000 x 0.12% = 83,100 JPY
This gives an effective 12-month exchange rate of 80.29.
Covered Interest Arbitrage
The above shows that Bank ABC is offering to sell forwards at which the interest rates are not in parity. That means there’s a riskless profit opportunity to be made because the no-arbitrage condition does not hold.
We can create a covered interest rate trade to exploit this gap. The above shows we could create our own 12-month AUDJPY forward contract today and sell it at 80.28. This would make zero profit with zero risk.
With this knowledge, we know that Bank ABC is quoting too high by offering to do a forward at the spot rate. We can set up the following arbitrage trade that covers exchange rate risk and possible interest rate changes:
Short 1 x Bank ABC’s contract @ 82.90
Borrow 80,193 x JPY for 12 months at 0.12%
~ convert to 966.18 AUD at spot rate
Lend 966.18 AUD at 3.5% for 12-months
In 12 months’ time my AUD is worth 1000 and ABC is obliged to buy from me 1000 x AUD at 82.9 yen. My synthetic forward that I create today allows me to convert AUD in 12-months’ time at 80.28 yen. Therefore, I can buy 12 month AUDJPY at 80.29 and immediately sell to ABC at 82.9 making a riskless profit of 2.61 yen.
Since the contract was for 1000 AUD, I would make a riskless profit of 2610 yen on the deal after the 12-months. See the cash flow diagram.
To do the above without the cash payments, I could simply have bought an AUDJPY forward from another dealer, assuming it was priced somewhere around the 80.28 mark and enough to make a profit.
Locking in Interest Rates
The different pricing in forwards and futures is down to interest rates and value dates.
In the arbitrage example, both sides of the trade lock in at today’s interest rates, and exchange rates. There was no need to predict the future at any time. The only knowledge we needed were today’s 12-month interest rates and today’s exchange rates.
If there were no other variables impacting the currencies other than interest rates, then the forward/future price would always reflect the future value. This is why forwards are referred to as unbiased estimators of future exchange rates.
Uncovered Interest Arbitrage
We could also have done the above trade without direct lending or borrowing by using the spot market. This is known as uncovered interest arbitrage.
But this technically wouldn’t be an arbitrage deal at all since the outcome would depend on the path of interest rates over the next 12 months. In other words it isn’t riskless. This would have been a carry trade with forward hedging.
Buy 1000 AUDJPY @ spot rate 83.00
Sell 1000 AUDJPY @ forward rate 82.9
The interest rate differential was 3.5% – 0.12%=3.38%
If AUD interest rises to 4% in 6 months, the differential is then 3.88%. Assuming this is the overnight swap rate, the total interest would be:
1000 x (½ x 3.38 + ½ x 3.88) = 36 AUD
Exchange = 1000 x (82.9 – 83.0) = -100 yen
Total profit in 12 months = 36 AUD – 100 yen
On the other hand if AUD interest falls to 2% in 6 months, the differential is then 1.88%. The profit would then be:
1000 x (½ x 3.38 + ½ x 1.88) = 26 AUD
Exchange = 1000 x (82.9 – 83.0) = -100 yen
Total profit in 12 months = 26 AUD – 100 yen
With the spot trade, the rollover interest will be realized daily and that can be reinvested. In a real scenario the nightly rollover interest would be lower to account for this reinvestment possibility. Swap rates would have broker markups added to them as well.
Finding Interest Rate Arbitrage Opportunities
In today’s digital world, financial markets are more efficient than ever and foreign exchange is no exception to this trend. The act of arbitrage itself tends to reduce the opportunity and lead to more efficiency. That is, arbitrage is “self-eradicating”. The more arbitrageurs there are, the fewer gaps there will be.
However the sprawling, non-centralized over the counter forex market does create some unique opportunities that don’t exist elsewhere. There’s now a myriad of forex broker-dealers and the industry is highly competitive.
Interest rate arbitrage opportunities do exist in the spot market. You can see these by checking swap rate tables. But the potential profits in the spot market are small compared to the forwards market and the risks are higher.
This is because spot trades are rolled over each night at the current interest rate – usually the overnight LIBOR or cash rate. That means the interest rate gap can close after just a few days, which means the deal can be in loss after adding other trading costs.
Brokers typically offer different rates of rollover interest on spot trades. To capitalize on day traders, some brokers will charge higher spreads but lower swap rates. While some do the opposite. For that reason interest arbitrage between brokers can sometimes be found.
Which Fees Can Impact Arbitrage Trading?
In arbitrage trading the profits are usually slim and so all of the costs have to be taken into the calculation. For example, in the above, the upfront cost of the deal was zero. But to open the forward contract we would have to hold some cash in margin. A few brokers do pay interest on margin deposits, but not all of them. So the opportunity cost of the margin deposit needs to be included as a cost.
The other significant cost in covered interest arbitrage is that of lending and borrowing. In the example the deal required lending and borrowing at close to interbank rates. Any markup on lending and borrowing therefore also needs to be added in. It can be a deciding factor if you can’t access competitive rates. If the markup is too high it will almost certainly negate any profits on the arbitrage deal.
Finally, most online forex brokers are simply not geared towards the needs of arbitrage traders. So to become an arbitrageur the retail trader usually needs to open an account with a bank or specialist brokerage firm. The advantage with this is that other assets held such as stocks or bonds can be used as collateral towards margin and so reduce overall cost. Collateral can also allow you to access more competitive lending/borrowing rates through the use of repos or secured borrowing.
Interesting examples. So at what rate would arbitrage be zero?
I am taking a finance class and need a tutor to better understand.
What does it mean by the daily swap will be lower because of reinvestment possibility? Why then it’s not the same as the yearly?
For one thing there’s the reinvestment possibility but also longer maturity carries a higher premium. The steeper the yield curve, the less the daily rate would be in comparison to the 12 month. So 1-day “overnight” interest is nearly always lower than 12 month interest except in some situations where the yield curve is inverted. If 12-month interest is 3.5% daily interest would probably be 3.4% or less. That’s why the amount accumulated in daily swap is going to be quite a bit lower.
Hi and thanks for the nice ideas. Can you explain something please? I don’t understand why in the example Uncovered Interest Arbitrage that use daily swaps the profit is different to example 1.
If I make the interest to same as example 1 I get a bigger profit in the second one than in the first. Should the profit be the same or am I missing something?
The profit is not different its the same when the interest is the same. The difference you get is because of the difference in trade sizes between those two examples. In the first example the amount that the interest accumulates on was AUD 966.18. That was used since it becomes AUD 1000 after 12 months with interest added. That was chosen so that it matches the contract size of 1000 units when it matures.
In the uncovered example the interest accumulates on 1000 right from the start so the profit is a bit higher. When it’s changed to 966.18, it comes out exactly the same.
966.18 x ( 3.5 % – 0.12 % ) x 83 = 2710.5 yen
Minus 100 yen for the spread between spot and forward = 2610.5 yen