1. Market Commentary FX alpha modelling June 2008 Dr. Jessica James Managing Director, Citi

2. 2 Market Commentary 2 Overview Introduction to FX alpha modelling FX models – an example –Trend –The art of model combination –Trend + Option selling

3. 3 Market Commentary 3 Model metrics Leave to start a hedge fund Information Ratio The information ratio is defined as annualised return divided by annualised risk (standard deviation of monthly return) All other quantities are given in percentages of the face amount (this is unambiguous) Ann. return = 7.04% IR=0.70 Max drawdown=17.5% Ann. return=13.04% IR=1.40 Max drawdown=11.3% Tell the spot desk Sell the idea Bring it to a conference Annual return Maximum Drawdown

4. Market Commentary Trend-option model Example of a switch model

5. 5 Market Commentary 5 Average Information Ratio It seems reasonable to use the average IR over all moving average lengths as a metric for the degree of trend following behaviour which exists in a currency –This precise figure will vary somewhat according to the range of moving average strategies which are tested, but it should be possible to see which currencies ‘trend’ and which do not On the right we tabulate the average IR for a number of different major currencies and crosses Trading costs were included for all currencies.

6. 6 Market Commentary 6 Option selling in certain currencies Option selling also seems to apply to a subset of currencies We seek a general metric which will indicate how successful a particular The deciding factor for whether option selling is profitable or not is usually the particular currency, not the particular delta We therefore averaged the results of the option selling strategies at three different deltas – ATMF, 25 delta and 10 delta - to obtain information ratios for these average selling strategies for all the currencies Trading costs were included which varied with the currency.

7. 7 Market Commentary 7 Comparing option selling and trend following It can be seen that the better a trend follower a currency is, the worst it is for option selling, and vice versa! The only currency which gives acceptable returns in both is EUR/USD.

8. 8 Market Commentary 8 The best of trends and options It seems that these strategy types are mutual opposites but.... some currencies which are in general non trending have trending ‘periods’ some currencies which don’t do well overall selling vol have profitable option selling periods. We wish to find a ‘switch’ to go from one strategy type to the other An obvious one to try is volatility

9. 9 Market Commentary 9 Which options? Which vol switch? Which trend? We do not wish to get hurt by the switch to trend when holding written options Thus short options are best Weekly options are those which we have the best data for Weekly vol however is too date-affected to use as a switch But we find that all of 1, 2, 3, 6 month vols work well! Overall, the exact trend strategy has little impact on results. We selected an 80 day moving average strategy for all ccys The results hardly change for other days

10. 10 Market Commentary 10 Trend only results... mediocre As expected, these results are overall mediocre, with only the very strong trending currencies like USD/JPY delivering good returns.

11. 11 Market Commentary 11 Weekly straddle writing - poor This is not a particularly inspiring result, and the risks of systematic option selling are high. To successfully combine two different strategies, they need to have comparable levels of returns. The straddle writing strategy returns are small compared with the trend following, so we introduced a leverage factor of 2.

12. 12 Market Commentary 12 Simple addition of the two Returns for trend following and straddle writing strategies -20% -10% 0% 10% 20% 30% 40% 50% Jun-92Jun-93Jun-94Jun-95Jun-96Jun-97Jun-98Jun-99Jun-00Jun-01Jun-02 Date Return in % of face 80 day trend Weekly straddle writing x2 Adding trend and straddle It is clear that they are anticorrelated; in fact the correlation between the monthly returns is –0.24. The graph shows the 2x leveraged results for the option selling Note that these results are for the average portfolios for all the currencies. The IR for the trend and straddle writing strategies are 0.63 and 0.23 respectively. The portfolio formed by the addition of the two has a much healthier IR of 0.91 However, a switching rule which intelligently chooses which strategy is currently likely to do best should better this result again.

13. 13 Market Commentary 13 Detailed strategy rules for switching 1.Is 1m ATM volatility above the trailing 5 year average? 2.If yes, sell a 1 week straddle every day with notional 2/5P (the factor of 2 comes from the leverage, the factor of 1/5 from the fact that we are dealing a 5 day product every day and need to normalise) 3.If no, check whether the FX spot rate is above its 80 day trailing moving average 4.If it is above, take a long position with notional amount P 5.If it is below, take a short position with notional amount P 6.If the 1m ATM volatility is initially below and rises above its trailing 5 year average, neutralise the spot position and sell a straddle 7.If the 1m ATM volatility is initially above and falls below its trailing 5 year average, do not cut out the option position but allow it to expire. However, immediately put on a long or a short spot position to trend follow with the 80 day moving average.

14. 14 Market Commentary 14 Results In nearly every currency the IR has improved dramatically The IR of the average portfolio has leaped to 1.49 We can see above that the switching rule has enabled the combination of two strategies, which yielded 2.94% and 1.19% annual returns, to reach a substantial 6.76% per annum Given that the identical strategy is applied to each currency without change, there can be little doubt that this is a real and useful effect.

15. 15 Market Commentary 15 Results

16. 16 Market Commentary 16 Single Currency Illustrations The pale blue regions indicate the high vol periods where straddle writing was the selected strategy, and the white regions similarly are the trend following periods The strategy is very successfully indicating which periods are best for the different strategies Note that as this is monthly data, not quite every ‘switching’ period is represented, as these can vary on a sub-monthly level. Switching model for GBP/USD -40% -20% 0% 20% 40% 60% 80% 100% 120% 9293949596979899000102 Date Return in % of face switchtrendstraddle writecombination

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