If you did the same EUR amounts in your EUR/JPY and EUR/AUD and set it so that the AUD amount satisfied the size requirements for your AUD/JPY position you are 100% fully hedged mate - just have some P/L sitting in JPY depending on where you did all the legs.
Rather than ask you to do all the work and explain through a specific example, how about…
Say I want to hedge a long AUDJPY $100K position. I decide to do a Long EURAUD and a Short EURJPY.
The EURAUD and EURJPY synthetic need to be bought and sold in quantities which will match the primary pair, pip for pip, in total.
A 1 pip plus move in the primary will provide a +$10.12 move in the primary position value. So I need to ensure I buy/sell USDCHF/GBPCHF so that their combined move of -1 pip equates to a -$10.12 move in the synthetic position value. Yielding a net move for the entire hedge of Zero. A position size of $68K for EURAUD and $50K for the EURJPY will provide the theoretically perfect hedge. Yes?
If I had done this at 08:15:46 this morning (which is when I time-stamped the data), as I write (15:40) the primary Long AUDJPY is standing right now at +77.1 pips. The synthetic short is standing at -106.7. An overall -29.6 loss on the position. Had I taken the opposite strategy, obviously this would have yielded a +29.6 profit. But this is beside the point. If my thinking and calculations are correct (which is where I suspect the problem lays), a theoretical hedge such as this does not perform as the simple math transform suggests it should.
I think you are over-complicating it a bit.
Generally a sign of the lack of total comprehension or the confusion which precedes it. LOL.
GJ there is a discrepancy with what I thought I would have expected from a hedge like this, what everyone else thinks we will get from a hedge like this, and the actual results I’m getting. I’m trying to find where my error is.
The attached shows two tables. The upper is the multiplier I’m using for each of the synthetic pairs (row 4) for any given primary pair (column B) based upon the current $/pip/$100K move. The second table shows the position size required for to hedge a nominal $100K size on the primary.
Where am I going wrong?