Forex Correlation (1)
Many years ago I was introduced to the concept of correlation and its use on Forex. I tried it and frankly had some success with it. Basically I picked a pair whose price actions correlated well with each other and trade them simultaneously as if they were one entity. Most of the time the prices moved together in the same direction, so there wasn’t much gain or loss. Occasionally they differed in direction. If both were gaining, I sold both off and kept the profit. If both were losing, I watched until I felt they had diverged far enough, then I entered more positions. The underlying assumption was since the pair was correlated, eventually they will converge, so entering while they diverge would allow me to have some gain later when they converged. Most of the time the system worked.
But there were times where the divergence was so much that I thought I should cut the loss. Depending on how much you use your margin, you might even get a margin call due to the divergence. I was (and still am) and conservative investor/trader, so it never happened to me, but there were situations that caused me to be quite nervous. On a couple of occasions, the pair didn’t converge after a long time (like a month or more), so I had to cut the loss.
The fact that it could diverge for about a month before converging back suggested that something else was going on instead of the common simple explanation that because each currency was traded in a broad market that sometimes there was a brief period of time where the divergence occurred. A month, to me, is not a “brief period of time.”
In those times I was just starting with about Forex, so I set up a small account to learn. As you know, trading a small account has a significantly different psychological factor than trading a large account even when percent gain/loss is the same. When I started to trade in a bigger amount (what is considered big is quite subjective), I knew I couldn’t just do the feeling-based trading as I did with correlation, so I did a formal study. This article and a few more related to correlation is the result of the study (the figures are generated recently, however).
To be a little more specific, I was using USDJPY and GBPJPY pair. It is easily to understand that they correlate well: they both buy JPY, so the prices usually (but not always) move in the same direction. At first I thought about using a simple arbitage to tell divergence. Arbitage can be expressed by difference or ratio. I could use GBPJPY/USDJPY, for example, and see how the numbers vary. I suspected that the number woulds grow up and down and if Istudied the pattern (long-term and short-term) I could probably see some peaks and valleys and made decisions based of those.
And so I did the calculation of arbitage as defined above, for daily, hourly and 5-min data. I used 300 close prices for each of them, i.e. 300 days, 300 hours (12.5 days), 300 5-mins closes (25 hours). There is no specific reasons for using the same amount of data from daily, hourly and 5-min charts. It is just easier for me to program my spreadsheets the same way for all of them.
Here are the arbitage values that I obtained:
- DAILY: min = 1.433; max = 1.652 (difference = 0.219)
- HOURLY: min = 1.620; max = 1.659 (difference = 0.039)
- 5-MIN: min = 1.645; max = 1.655 (difference = 0.010)
I was a little surprise when I saw the differences between the minimum and maximum values of the arbitage. I was expecting the difference to be smaller with daily data but larger with 5-min data. Afterall, it was how I had been told for a long time: that the data between correlated pairs correlated well in the long run but that we could find divergences in short run and make profit out of it. It looks like the opposite is true. In short-term, the data didn’t show that much difference in movement, but in the long run they showed some divergence.
But the next thing that occurred to me was, “wait a minute, how does that arbitage ratio of GBPJPY / USDJPY really tell me?” If you think about it, each pair is a ratio. When we talk about GPBJPY being 136.48, for example, we are talking about the ratio of Japan Yen over British Pound. So the notation GBPJPY really means JPY/GBP. Likewise, USDJP means JPY/USD. This means that the arbitage that I was going to use, GBPJPY / USDJPY can be written as follows:
(GBPJPY/USDJPY) = (JPY/GBP) / (JPY/USD) = (JPY/GPB) * (USD/JPY) = USD/GBP
But USD/GBP is simply what we normally call GBPUSD!
This realization more or less confirmed what I had suspected in the past: that the divergence or convergence of GBPJPY and USDJPY simply depends on GBPUSD. Actually this makes a lot of sense. If conditions affecting GBPUSD do not change, then of course GBPJPY and USDJPY would move in the same direction since they are both holding JPY. If conditions affecting Japanese Yen do not change, on the other hand, then the fluctuation would depend on conditions affecting GBPUSD. This is just common sense!
But while it is mathematically corrected that arbitage (GBPJPY / USDJPY) is the same as GBPUSD, they are not exactly the same thing because all three are separate pairs that you can buy and sell independently. Maybe there does exist some time where they diverge and we have a window of opportunity. Afterall, that is what the school of correlation investing usually tells you. So the next logical step was to check how closely GBPUSD is related to the arbitage, defined as (GBPJPY / USDJPY).
And so I did the calculation, and the result I got really surprised me (or should I say not surprised me because it had been my suspicion all the time): that arbitage between GBPJPY and USDJPY is high correlated with GBPUSD. In all cases (daily, hourly and 5-min data), the correlations are higher than 0.9!
Here are the correlations between arbitage (GBPJPY / USDJPY) and GBPUSD:
- daily: 0.99999
- hourly: 0.98347
- 5-min: 0.93575
As you can see, the daily correlation is, for our practical purposes, perfect (1 being perfect). Hourly and 5-min correlation are also high. On 5-min intervals, the number is smaller, but a correlation coefficient above 0.9 is still pretty high. That means that if you want to check the divergence and make decision to enter or exit a trade of correlated pairs GBPJPY and USDJPY, you might as well just look at the GBPUSD chart and make decision based on it.
What do all these mean to you
- Correlated pairs sometimes diverge in their chart, but the divergence is not caused by them being sold in different markets (and give you an opportunity to profit). It is caused by the fluctuation of the currency that correlate them in the first place (in this case the the divergence or convergence of USDJPY and GBPJPY pair is caused by GBPUSD).
- If you are doing or trying to do correlation investing/trading, rather than trying to calculate arbitage (in this case GBPJPY/USBJPY), you can simply look at the chart of GBPUSD.
- But if you can trust that you can make correct decision based on the chart of GBPUSD, you might as well trade in GBPUSD. Why bother with trading the GPBJPY and USDJPY pair when the profit/loss is determined by GBPUSD? As we all know, however, it is impossible to always make correct prediction of future price movement based on historical data. This also means that you cannot always trust that a divergence will always be followed by a convergence (especially in the short term).
- Trading in correlated pairs doesn’t seem to offer much advantage, if at all, unless you are doing some kind of hedging and buy and sell each pair at different time, but that is really a concept/strategy in hedging rather that correlation.
- The short-term correlation between arbitage and GBPUSB is high (0.93575) but not perfect (1.0), so there might be some brief period of time where there is true opportunity to trade in the correlated pair (instead of simply trading with GBPUSD); but 0.93575 is pretty high, so those opportunities are rare. Unless you are using computerized trading, you might not even catch them.
The big question is whether the above statements hold true just for the GBPJPY and USDJPY pair or whether they are general truths. In the next article I am going to do the calculations of correlation between arbitage of correlated pairs and the currency that correlate the pairs. Hopefully that will help our understanding of specific correlated pairs.