Thursday, April 24, 2008

Risk free FOREX?

Did you know that there is the strategy for trading currencies that is theoretically risk-free? This strategy is called Triangular Arbitrage and it is well described in "Triangular arbitrage as an interaction among foreign exchange rates" by Yukihiro Aibaa, Naomichi Hatanoa, Hideki Takayasub, Kouhei Marumoc, Tokiko Shimizu. The idea is quite the simple: you have account in US dollars - you see the profit opportunity for the following exchange (for example of cource) - convert Dollar to Euro, convert Euro to Yen, then convert back Yen to Dollar. All these conversions are made simultaneously and You get more Dollars at your account.

But how it can be made in terms of your broker trading instruments, i.e. USDJPY, EURUSD, EURJPY?
Michal Kreslik proposed the following idea and it is quite the simple:
Let us imagine three symbols: a, b, c and three fractions: a/b, b/c, c/a.
From the math point of view (a/b)*(b/c)*(c/a) =(constantly) 1.
Let us now replace a,b,c with for example USD,EUR,JPY.
We have (USD/EUR)*(EUR/JPY)*(JPY/USD) = 1 statement now. We got the common tickets for forex trade. Of cource we have no USD/EUR and JPY/USD tickets but we can replace them, so our statement will look like the following:

(1/EURUSD)*(EURJPY)*(1/USDJPY) must constantly equal 1. But this statement is not true. Let's check: (1/EURUSD)*(EURJPY)*(1/USDJPY) = FPI (some variable).

So this FPI (Michal called it because of Fractional Product Inefficiency) never equals 1 but bounces in some range. Even the median point of this range is not unity because of spread.

If we sell EURUSD, buy EURJPY, sell USDJPY (one of the pairs must have fractional lot size) we will not be exposed to any risk related to price movement. If we sell EURUSD, buy EURJPY, sell USDJPY at lower FPI extremum and later (minute, hour, day, week, whatever... because we are perfectly hedged - the same as the we have dummy position) buy EURUSD, sell EURJPY, buy USDJPY at higher FPI extremum - we will get profit. So we have 2 parts of our "trade" - entering the ring and closing the ring. Note again: when we entered the ring we have no risk related to price movement. So it is the same that we are out of the market. Of cource we spent some money to enter the ring (comission).

Quite simple - is not it? Why not try to code it and I did it. I connected my trading robot to my broker's API and went to sleep. When I woke up I was happy and began to imagine how many bags for cash will I need now:

If you do not see the digits: 186 trades, 212 lots (actually minilots in terms of big forex players), comission US$132.06, realised profit US$286,27 and one open ring bouncing near zero (+US$0.02). Note: it is only one ring - EURUSD/USDJPY/EURJPY and only about 3,5 minilots per one hedge. Just imagine how many rings theoretically exist. More than that there may be not only 3 but 4, 5 pairs combination...


(to be continued)


Linuxpower said...


(to be continued)

No news ?

nimzoindy said...

It's been a while since last update. Do this blog still alive?

Linuxpower said...

I think it's a fake :(

Mike said...

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