Triangle arbitrage lot size calculation

Hi Guys,

I'm trying to work out how to implement a report of triangle arbitrage on a given broker. The language isn't important but the algorithm is driving me batty. All I have to go on is the description on Wikipedia which is not quite the same as the crosses we use (for the purpose of me understanding anyway)

If I have :

AUDUSD <> AUDJPY <> USDJPY

Is this correct?
This means I have 100000USD and 'buy' ~125000AUD. I then buy JPY with AUD, which buys me 10250000JPY. I then buy USD with JPY and get 100000 (in a flat market)

So in lots that would be???
SELL 1/AUDUSD = 1.25lots
BUY AUDJPY = 1 lot
BUY USDJPY = 1 Lot

I'm certain that is incorrect. It seems to me that the location in a symbol of the currencies is important and will be the difference between using it an dividing 1 by that value.

Would someone like to lend me a hand here?

Many thanks,

Chris


(I'm well aware that triangle would be filtered out on a single broker, I'm thinking multiple brokers.)

It's impossible as a retail speculator stop wasting your time.
Even if you could do it you'd fail because because trading lots makes it impossible.
You need to trade singel units.

Yes that is incorrect.
If you have
SELL 1/AUDUSD = 1.25lots
BUY AUDJPY = 1 lot
BUY USDJPY = 1 Lot

you can see that for instance you sell 2 times JPY

The key point is that the lot size is applicable to the first currency of the pair.

So let's make caculations with your numbers (let's use approximation)
So we say that you BUY 1.25 lots of AUDUSD
and then you get 125 000 AUD as Buy and 100 000 USD as Sell
so now you will SELL 1.25 lots AUDJPY and then get 125 000 AUD as Sell and 10 250 000 JPY as Buy (didn't check the exact number for JPY but anyway only the way of calculating it is interesting)
Then at that point you have 10 250 000 JPY as a Buy and 100 000 USD as Sell
So to compensate you will BUY 1 lot USDJPY

In Summary
BUY 1.25 AUDUSD
SELL 1.25 AUDJPY
BUY 1 USDJPY

Same thing changing BUY in SELL and SELL in BUY

I hope it is clear

Dude it IS impossible with lots.

That is wrong. For instance with Oanda you can put any lot size up to 1$ accuracy.

And anyway the point here was to discuss how to make the calculation

That's not a lot. It's a unit.

Firstly, the title should be "Triangle Hedge" or "Three Way Hedge" and not "Triangle Arbitrage". The latter implies that if you do it this way, it will "always" be an arbitrage (which is not always the case and very rarely is).

The actual Lot size is always dynamic. It always changes based on the prevailing market prices of the currencies of interest. Therefore, in all your posts above, it would be wise to include the prevailing market prices of AUDUSD, AUDJPY and USDJPY to give a good Lot size calculation.

STEP 1:
To count/compute for the lot sizes, ALWAYS start off by stating the factual prices first. As of this writing, the prices are:
AUDUSD 0.7965
USDJPY 105.95
AUDJPY 84.44

STEP 2:
Choose your Primary Currency Pair, any Pair; I choose AUDUSD.
I elect to trade 1.00 Lot AUDUSD.
LONG 1 LOT AUDUSD = Buy 100,000 AUD, SELL 79,650 USD
SHORT 1 LOT AUDUSD = Sell 100,000 AUD, BUY 79,650 USD

STEP 3:
Right now, we have AUD and USD monies in our hand.
With the second pair USDJPY we now compute the number of lots needed to equalize/neutralize USD. Since we have 79,650 USD at hand, we go to trade 79,650 USD.
I compute to trade 0.7965 Lot USDJPY
LONG 0.7965 LOT USDJPY = Buy 79,650 USD, Sell 8,438,917 JPY
SHORT 0.7965 LOT USDJPY = Sell 79,650 USD, Buy 8,438,917 JPY

STEP 4:
We now only have AUD and JPY monies in our hand. We currently have 100,000 AUD and 8,438,917 JPY. And to neutralize the most obvious (most rounded number) I suggest to trade:
LONG 1.00 Lot AUDJPY = Buy 100,000 AUD, Sell 8,444,000 JPY
SHORT 1.00 Lot AUDJPY = Sell 100,000 AUD, Buy 8,444,000 JPY

Compare 8,444,000 JPY with 8,438,917 JPY and we get an error margin of 0.07% only. This means that this particular broker has his AUDUSD, USDJPY and USDJPY prices fairly accurate.

STEP 5:
In all Three-Way Hedge, you get Two (2) sets of hedge.
Set #1:
Long 1.00 Lot AUDUSD
Long 0.7965 Lot USDJPY
Short 1.00 Lot AUDJPY

Set #2
Short 1.00 Lot AUDUSD
Short 0.7965 Lot USDJPY
Long1.00 Lot AUDJPY

Of course you dont get to trade 0.7965 lots; you can trade 0.79 lots if your broker allows 1K lot sizes, or choose to trade 0.8 lot only. Likewise, you can choose to scale up and trade 10 Lots on AUDUSD, 7.96 Lots USDJPY and 10 Lots AUDJPY. etc...

Now, to verify jlpi's computations:
His ratio of 1.25 : 1 is approximate equal to my above ratio of 1.00 : 0.7965
So I verify his computation is good.

BTW: Our computations today is accurate; but they will be wrong next month or a day from now. So compute as shown above.



SIDE NOTE

Another application of this 3 Way hedge or more accurately this hedge ration computation is to divulge the truth behind alot ot those hedging guru's technique.

We all have heard alot about the EURUSD and USDCHF hedging trades. Most if not all claims that EURUSD and USDCHF has an inverse correlation. This is true. Whenever EURUSD go up, USDCHF go down. However, this (correlation) is not a Mathemathical fact, but rather a pnenomenon (something that happened yesterday but is not guaranteed to happen today/tomorrow).

One particular idiotic trade system is the FreedomRock wherein you are told to go Long EURUSD and Long USDCHF. The lot ratio is fairly about 1.00 EURUSD and 1.10 on USDCHF. The lot sizes changes but there is no mathematical computation to it. Basically/Mathematically, you are told to go Long 1.00 Lot EURCHF and go short 0.1 Lot USDCHF and aggressively trade as much as 50% of your equity into margin (ie if you have $100K 100:1 leverage in your account, trade as much as 20Lots on EURUSD and 25 Lots on USDCHF and not fearing about DRAWDOWNS!

We all know that in 2006 to H1 2008, EURCHF is very very bullish. Sure FreedomRock members were making HUGE money but whenever EURCHF takes a dip (and I do mean very big dip during Feb 2007, Aug 2007, Mar 2008), your account is wiped dry with margin calls. Many traded at IBFX; IBFX has Credit Card Funding, very convenient to top-up a dwindling account, and many where drawn to fund non-stop their accounts till they lost more than they could chew!

To the next idiot system that tells me Opening (EURUSD + USDCHF) Simultaneously and Closing those positions Simultaneously (of course at later time either in Profit or in Loss), isnt same with EURCHF, show me the money. You were all Lucky that EURCHF was simply in a huge train ride uphill. Now watch Thomas and his Friends take the downhill express

The point is that it is absolutely possible to perform the calculation and put the trades with the accurate size.

Thanks a lot guys for the help. I'm writing out he first cut of the code now. The two AHA's I needed were that BUYing AUDUSD implicitly sold USD, etc, etc. (I've never needed to think about that before) The second thing I sort of suspected but didn't completely comprehend was that in calculating sizes I had to account for the location in direction of the pair (AUD vs USD). I was looking for some kind of simple Put a SELL here and then multiply the other two elements by the first.

Again, thanks a lot. With my thought patterns as they were I don' think I would have solved it any time soon

Is there any calculator or formula if i want to buy and sell in equal value lot with base currency of USD if I take random pair.
For I want to go Short on AUDUSD Long=AUDCHF/AUDJPY

How many lot i need to go SHORT if i go .01 LOT size for AUDCHF/AUDJPY