Introduction Currency fund and currency overlay programs have become the flavor of the month for investors. These products both utilize bespoke and often confidential trading models to take advantage of the volatile currency markets. Funds use models to predict when spot, forward or sometimes option trades should be placed to generate return, while overlay programs use the same models to make hedging decisions. The fund products can, at their best, generate healthy annual returns (in some cases 7%-10% of the face value of the trades), while good overlay programs offer option-like protection and the possibility of 1%-3% return enhancement. These are the results from the best, of course. Choosing the right overlay provider or currency fund is a critically important decision.
Most if not all of these currency products rely at least in part on trading models. Trend following, range trading, technical--there is no end to the variety of models which are seen. One promising class of models, which are popularly supposed to work, are periodic models, relying on a seasonal ebb and flow of cash driven by regular needs to square up accounts at certain dates. We investigate this class of model here, and show that just because a phenomenon is often assumed to exist, it is useful to test it out before going ahead and risking money on it.
It has often been suspected that some currencies exhibit periodic behaviour--for example, in dollar/yen, there is often an end-of-month settlement when Japanese companies need to square up accounts. If it were true, then it would be a useful and easily managed addition to a currency trading portfolio, as trade directions and amounts would be known well in advance. However, while some strategies claim to exploit just such a phenomenon, there has been little empirical investigation as to whether periodic strategies actually exist, or whether assiduous data mining has just thrown up an outlier.
Dollar/Yen Periodic Model
In order to first establish whether there is any possibility of finding such a model, we used dollar/yen as a test bed. We looked at the results of buying and selling once per period, and also allowed the length of the actual period to vary. Thus we had three variables;
* Period length * Buy day * Sell day
which we wished to optimize to find the combination with the best information ratio.
The problem with optimizing such a set of parameters is that the surface which we need to search has many local maxima and minima, and in general it is difficult to say that one has found the best combination of parameters. Accordingly, we decided to search the whole space, allowing the period to be up to 65 days long, and allowing the buy and sell days to have any values within this. Obviously, this leaves us with a pile of data to analyze, so for each period length up to 65 days, we just recorded the buy and sell days which gave the best information ratios. We then selected the best of these 65 information ratios, and came up with the following:
* Sell on day 12 * Buy on day 37 * Period has 60 days
Our data set started on 1t July 1988, so these numbers take day one of the first period as that day, but obviously any other start date would have left us with the same period length and different start and end dates to pick up on the same trades.
The statistics on this optimized strategy are as follows:
Annual return on face: 12.0%
Information ratio: 1.05
The cumulative returns during the backtesting period are shown in Figure 1.
As can be seen, although there are some drawdowns, in general the returns are excellent. The trading strategy, if real, is a desirable addition to any portfolio.
Testing With Distribution Of Information Ratios
In order to determine if this is a genuine result or just a data 'feature', we wish to know what kind of returns might be expected from such a strategy. We would expect that there are maybe one or two combinations of parameters which give very good results, and the rest give results which are essentially random centered roughly on zero. However, to look at the whole spectrum of results would involve a huge number of records, so instead we just look at those information ratios obtained from a period of 65 days, with all possible variation of buy and sell days within the period. This provides over 4,000 points which is statistically adequate.
We find that the mean of the information ratios obtained for the distribution is zero, as expected, with a standard deviation of 0.20. This means that the information ratio of 1.05 is 5.1 standard deviations away from the mean, a result we would not expect to see with less than 31 million points in the distribution if the distribution is normal. Taking into consideration that the total number of strategies within the space is of the order of 200,000 we may say that this result is very significant and likely to be real.
Testing With Randomised Data
The above analysis does make the assumption that the distribution of information ratios is normal. If it is fat tailed instead, then the information ratio of 1.05 may still be just a data feature. Financial markets and trading strategies are not exactly famed for sticking to the normal distribution--in general they are pretty non-linear systems which can have significant fat tails. Thus a more stringent test is needed to ascertain if the strategy is tradable.
If our information ratio is way higher than the best one might reasonably get by looking at all possible variations of period and trading days with a randomly generated rate, then we may have some level of confidence that the strategy is real. However, normally generated random numbers will not duplicate a lot of the fat-tailed features of the FX rates, so instead we randomly re-ordered the daily returns of the actual USD/JPY series. Then we repeated the search of the whole strategy space, finding the very best information ratio for all combinations of period length, buy and sell days.
The first random re-ordering gave a best IR of 0.84, 4.2 deviations away from the mean. One would expect a result about this good from the randomization, so we are confirmed in our optimism that the strategy is real. However, a second randomization gave a best IR of 1.12, which rather blows the strategy out of the water. We must conclude that the distribution of information ratios expected from such a strategy is very fat tailed, and the results we found are nothing but data mining. We do not expect that the trading strategy will have any future predictive power (although we may monitor it for a few months, just in case!).
Conclusion
Periodicities in currencies are often suspected to exist, and thus investigating periodic trading strategies seems promising. A search of all possible periodic strategies finds a possible candidate with and information ratio of 1.05 for a period of 60 days, selling on day 12 and buying on day 37. The fact that this is a quarterly strategy is cause for optimism that some kind of trade flow may be responsible for the currency behaviour.
If we assumed that the distribution of information ratios is normal, then our result is very significant. However, a more stringent test is to randomize the daily returns and to repeat the strategy search. We would not expect it to work on such randomized data. However, on only the second set of randomized data, we find a 'best' information ratio of 1.12 which is better than that found on the real rate! We must regretfully accept the fact that, at least in dollar/yen, periodic trading strategies are unlikely to be real.
As dollar/yen was the most promising of the currency candidates, it is unlikely that a similarly exhaustive search using another currency will throw up any more useful results. Periodic trading models--though they may look impressive in backtesting--are best omitted from currency funds and overlay programs.
This week's Learning Curve was written by Dr.Jessica James, v.p. in the Risk Advisory Group of CitiFX. The views expressed are the author's own and are not necessarily shared by Citigroup or any of its affiliates.
