CitiFX Risk Advisory Group Trend Models can simple trend strategies work long term Dr Jessica James Investor Risk Advisory Group CitiFX Risk Advisory Group Overview 2 Trend models general overview In and out of sample testing Trend model enhancements CitiFX Risk Advisory Group Trend models overview CitiFX Risk Advisory Group Trend is popular 4 85 of CTA returns are explained by simple trend following The figure rises to almost 100 when carry and option trading are included They are without doubt the most popular systematic rule based strategies used by overlay managers and currency alpha funds They may be backtested relatively easily CitiFX Risk Advisory Group Trend models The idea of a trend is intimately connected with that of momentum if a currency moves in one direction in one period it is likely to continue that direction in the next However there will be reversals within larger trends and the key to successful trend following is to discover when a trend starts and ends and not be taken in by false signals Moving average models are historically very successful at capturing trends and they have many different variations simple MA multiple MA exponential Garch fade in out We use the simplest possible a simple single MA for research purposes further complexity may be added if a principle is established 5 CitiFX Risk Advisory Group Historical returns to trend models 6 Historically long term trends are displayed in currency pairs which are the exchange rates between disparate economies USD JPY EUR USD etc Interestingly those pairs which do display a marked tendency to trend all have their optimal moving average at about 70 days Those currencies which historically have not trended are the pairs which are the exchange rates between closely linked economies EUR CHF GBP USD etc The majority of trend models give very similar results CitiFX Risk Advisory Group Trending or not 7 We sought to establish which currencies trend or not by looking at the results of the simplest possible trend following strategy that of a single moving average By buying when the rate was above a simple arithmetic moving average and selling when it was below we obtained a P L curve for the trading strategy since the start of the data set in 1992 We looked at every length of moving average strategy from 5 to 130 days We use USD JPY and USD CAD as opposite examples Forwards are not included but tests with full MTM calculations indicate that they make little difference even to USD JPY CitiFX Risk Advisory Group Two very different currencies The behaviour of the two currencies is utterly different USD JPY makes money and has a positive IR for almost any length of moving average So strong is the trending behaviour of the JPY that similar all encompassing positive results are obtained for most of its crosses USD CAD stubbornly refuses to rise above zero under any circumstances It is not difficult to draw the conclusion that USD JPY trends and USD CAD does not Annual Returns and IR as a function of moving average length for USD JPY 15 10 0 4 5 0 2 0 0 0 0 2 0 20 40 60 80 100 120 Days in moving average Information Ratio Annual Return 5 140 Inform ation Ratio 0 6 0 4 Annual return Inform ation Ratio 0 8 8 Annual Returns and IR as a function of moving average length for USD CAD 0 2 0 0 0 2 0 4 0 6 0 8 0 20 40 60 80 100 120 Days in moving average Information Ratio Annual Return 10 8 6 4 2 0 2 4 6 140 Annual return CitiFX Risk Advisory Group More currencies 0 0 0 2 5 0 0 4 0 6 5 0 8 1 0 20 40 60 80 100 120 0 2 0 0 0 2 0 4 0 6 10 140 0 20 0 2 0 0 0 2 0 4 0 6 60 80 100 120 Days in moving average Information Ratio 9 Annual Return 10 8 6 4 2 0 2 4 6 140 Information Ratio 0 4 40 100 120 Annual Return Annual Returns and IR as a function of moving average length for EUR JPY Annual return Information Ratio 0 6 20 80 Information Ratio Annual Return Annual Returns and IR as a function of moving average length for EUR USD 0 60 Days in moving average Days in moving average Information Ratio 40 10 8 6 4 2 0 2 4 6 140 0 6 0 5 10 0 4 0 3 6 0 2 0 1 2 8 4 0 0 0 0 1 0 20 40 60 80 100 120 Days in moving average Information Ratio Annual Return 2 140 Annual return 0 0 4 Inform ation Ratio 10 Annual return Information Ratio 0 4 0 2 Annual return Annual Returns and IR as a function of moving average length for USD AUD Annual Returns and IR as a function of moving average length for USD CHF Note that the past about 40 days there is extraordinary stability of performance with respect to the moving average CitiFX Risk Advisory Group Stability of returns and IR We tested out the stability of the strategy with respect to the number of days in the moving average We find that in fact there is a large range of moving averages which deliver similar returns for the average portfolio Date 100 day returns 40 day returns 10 80 day returns 20 day returns 60 day returns 02 01 00 99 98 97 96 95 94 93 92 91 90 89 45 40 35 30 25 20 15 10 5 0 5 88 returns in face Cumulative returns for various moving average strategies for the average portfolio CitiFX Risk Advisory Group The best moving average It is interesting to find the best moving average obviously this is an optimisation but only of a single parameter 11 Accordingly we repeated the analysis with finer granularity creating returns and information ratios for moving averages between 20 and 100 days with steps of 5 days The following graphs reveal the optimal region CitiFX Risk Advisory Group Optimal region for annual return Variation of Annual Return with days in moving avarage 10 00 USD JPY 8 00 USD CHF Annual return EUR USD 6 00 EUR JPY 4 00 GBP JPY EUR GBP CHF JPY USD AUD USD CAD 2 00 EUR CHF 95 100 90 85 GBP USD GBP CHF 2 00 Average 4 00 Days in moving average 12 80 75 70 65 60 55 50 45 40 35 30 25 20 0 00 There is a best region around 70 days but in general results are not sensitive to the number of days There is a clear picture of the degree of trend activity in each currency CitiFX Risk Advisory Group Optimal region for information ratio The best region is the same as is the lack of sensitivity to the moving average Variation of Information Ratio with days in moving avarage 1 00 USD JPY 0 80 Annual return USD CHF 0 60 EUR USD …