Understanding Forex HFT Arbitrage with different counter parties/ Brokers/ ECN

I came across this in a online lecture. But couldn't wrap my head around it.

Lets say I have accounts with two brokers/ECN/STP. Now consider the following scenario for currency pair USD/JPY

Broker1: Bid-110 Offer-111

Broker2: Bid-112 Offer-113

Now we will apply the simultaneous buying of the pair and selling strategy. Lets say I

Buy 500$at 111 from Broker1 and Sell 500$ at 112 to Broker2

Considering no order expiry etc the lecturer says the profit is 500 Yen.

But the account with the Brokers are different.

In the above scenario when I

Buy 500$at 111 from Broker1 --> I bought 500 USDs at 111 rate (opened a position) Sell 500$ at 112 to Broker2 --> I sold 500 USDs at 112 rate (opened a position)

Now since the account isn't one unless I sell the 500USD at Broker1(close position) and Buy 500USD at Broker2(close position) there won't be any gain for me. What I am saying is the rate might not change in my favor in near future when I try to close position. Lets say when I close position the rate is same Broker1 rate is 110 and Broker2 rate is 113 only. So basically I loose 1000Yen.

But in the lecture it says you will gain 500Yen. Shouldn't it consider the closing position thing too? That is the rate at the time of closing position is important.

Is there something I am missing?

Is it to do something with Swap Arbitrage(don't know well).

Or does the position closes automatically or depends on the account type or order type?

Or is there a way to have a single account and link it with different brokers something like single trading account.

I'm interested in hearing other's opinions, but I'll share my thoughts. First, your logic is definitely sound, let's walk through this trade from the perspective of the arbitrageur.

Arbitrageurs play the role of finding mispriced assets and attempting to make a risk free profit by taking both sides of the trade.

In your example, a market participant can buy Yen at broker1 at the ask A and simultaneously go-short Yen at broker 2 by hitting the bid B where there is some kind of spread s = B-A

Typically, and especially in HFT environments, arbitrageurs expect that this spread will typically "narrow" - converge towards a minimum threshold that does not justify either the risk associated or cost of arbitrage.

So, the answer to your question "Did I immediately make 500 Yen?" is twofold - in theory - Yes, because you are holding a net 0 position (you bought and sold the same amount of the same underlying asset, so you have no position and are immune to the idiosyncratic risk of the underlying). But in reality - No, you have not immediately realized this profit because as you point out, you have to somehow capture this spread.

In a HTF environment, you would expect this spread to tighten as other arbitrageurs enter the market, and thus when you unwind your position on both sides, then you will realize the profit. In less liquid markets, you may be able to transfer assets between exchanges and realize the profit that way - ie buy from Broker1 and transfer the asset to Broker 2 where the price is higher. This of course has risks and limitations and is not generally used in HFT in the way that I understand it.

So in summary, your logic is sound, the risk free profit is not immediately realized, but rather the arbitrageur is making a calculated bet that this spread will tighten, and thus they will earn that spread when they unwind their position. As you point out, the spread could continue to widen (maybe temporarily) and you are taking that risk. In a HFT this spread can be very small and the tightening can occur very quickly as other HFT also realize that an arbitrage opportunity exists. This is probably not possible on most liquid exchanges as the exchanges themselves probably run HFT algos that watch for arbitrage and they place themselves at the highest point in the order stack so that by the time others can react, the opportunity has been resolved.

Hope this helps,

• James marks it certainly helps, so basically the arbitrager has to keep track of the tightening or widening of spread, and when it turns in his favor he will close the position on both sides. Its a risk in end and not so called risk free trade as published my every other article about arbitrage on the Internet. – rnv Jul 20 '18 at 16:41
• I should point out, that my comment was mostly in the context arbitrage in the context of HFT. As I pointed out, you could transfer assets between brokers, and yes it would be truly a risk-free trade, but the time it takes to execute might not make it worth it. If you borrow from Broker B at 112 and buy from Broker A at 110, you can pay back Broker B with the shares you hold at Broker A, thus your net 0 position, netting you the difference. If you don't plan to do this, then you are hoping that the spread narrows as others realize the arbitrage opportunity. – Jared Marks Jul 22 '18 at 16:40