Figure out the value of the equity position (or the cost of it if you're doing a leverage play), then figure out what that is in Yen.
Realize here that you aren't in any way, shape, or form doing a carry trade here. If you were, you'd be borrowing in Yen, swapping to another currency, and investing in an instrument denominated in that, the idea being you make much higher rate in the latter. For example, borrowing Yen, swapping to Aussie, and buying Aussie bonds. The hope is that AUD/JPY stays relatively stable so as not to wipe out your carry trade profits.
If you're just looking to match an equity market position against the likes of AUD/JPY you're just doing a spread trade. You playing the equity performance against that of a currency pair viewed as being closely tied (via the carry trade) to how stocks perform.
The carry trade is about borrowing cheap and investing elsewhere for the higher return. You could borrow yen, convert to dollars, and put that money to use in the ES. That would be USD/JPY. You could borrow yen, convert to pounds, and put it into the FTSE. That would be GBP/JPY. You could borrow yen, convert to aussie, and put it into Australian stocks. That would be AUD/JPY.
But that's not what you're looking to do. You want the carry trade via the retail FX market. The best spread there is AUD/JPY. If you also have an equity position, then that is either a hedge against the AUD/JPY position (if you short the index), or a twofer bet on economic improvement as both AUD/JPY and the index will tend to move in the same direction (at least in the current cycle). If you are looking to run a hedge, then you need to look at correlations from a GBP value perspective, as that is your account currency.
Like I noted before, the AUD/JPY vs. S&P correlation is a function of both reacting to the same basic fundamentals. The carry trade, as represented by AUD/JPY, is on the rise (greater demand to borrow and convert out of the yen, higher demand for higher interest rate currencies) becomes more popular when the economic backdrop is good because it increases the prospective returns of the strategy and reduces the risks. Same with stocks.
Look at the yield curves of the two. People are borrowing yen and buying aussie for the carry on rate differential as well as borrowing yen to but up indexed stock. I think that the money flowing into both is the reason for the correlation. Thats what I was trying to say before.
But wouldn't you expect that when the ES was bought (even with leverage), that the AUDJPY correlation would change?
Borrow yen, convert to AUD, then convert to US to buy the ES.
That's the same as borrowing yen to convert to US directly but the USDJPY has no such direct correlation with the stock market.
I can understand that yen would be borriws and converted into both AUD or US to get the carry but any conversion to US would immediately change the AUDJPY cross rate therefore throwing off the correlation?
But if people are borrowing the yen to buy the ES, I don't really follow why the AUDJPY is so closely correlated. The link between ES and AUDJPY is showing that people are borrowing yen and converting them into aussie dollars, no? What happens after that point for them to buy the ES< they have to convert into US dollars but that means the USDJPY should be more closely correlated with the ES :|
Overall, the JPY is pretty well correlated (inversely) to the stock market. Folks are borrowing yen to convert to all sorts of currencies to invest in a whole array of markets (stocks, bonds, commodities, etc.). This is not strictly an ES trade. In fact, I'd argue the ES part of it is relatively small. This is why I keep saying it's not about people specifically borrowing yen to tradet he ES. It's about how the same things drive the carry trade currencies and stock prices.
What are some of the "same things"
I mean, I guess people could be borrowing yen to convert into bonds.
Traditionally bonds move opposite to stocks although recently they've been moving the same way.
If it was computers realigning the stock markets to fair value with the yen, you;d expect the process to be a lot quicker yet the correlations always seem to have some delay in them.
On the other hand, if it wasn't computers and the "tings" driving the currency trades, why would the correlation be so perfect?