Process Driven, Limited Risk FX Trading 08 April 2008
The Theory FX Markets trend approximately 15% of the time. The key is to avoid non-trending markets and focus on the currency pairs that are trending. However, there is always an FX market that is trending. The decision to enter a trade is made up of three factors: A technical trend signal is essential. Implied volatility must be close to or below actual volatility. Supporting macro factors. A portfolio of positions is highly dependent on hourly and daily correlation matrices. Once a trade is entered, it is expressed with a delta neutral long option position. Once a trade is entered, gamma hedging is strongly process driven. 2
The Process Examine Daily and 10 Minute bar charts with the same two indicators, using the same variables to reduce curve fitting. Use daily data to determine if a market is trending. Both daily indicators must agree a trend exists to consider a position. If both daily indicators do not agree then there is no position. On average, there is a trend approximately 15% of the time (i.e. no position in a particular asset 85% of the time). 3
The Process Assuming a daily trend exists, then own gamma in that currency pair as long as implied volatility is not at a large premium to actual volatility. Close out the long gamma position as soon as a strong trend signal disappears. There are tradable up moves and down moves in a trending market that make rebalancing a long gamma position a more structurally sound process. Use the correlation matrix of trending currency pairs to enter trades with lower correlation in the underlying currency pair. 4
Option Trade Characteristics Option maturities in the 4 week area provide a trade-off between gamma and time decay. Initial option strikes will normally be approximately 25-30 delta in the direction of the primary trend so initial premium per trade is limited. (The caveat is when there is extreme skew in that direction). Normally, if delta reaches 60%, the strike will be rolled down to 25-30% again and size adjusted for the market conditions. 5
Gamma Management Use 10 minute data to determine when to rebalance delta positions. In short term uptrends net delta is only flat or long up to 10% of option notional. In short term down-trends net delta is only flat or short up to 10% of option notional. When there is no short term trend signal, rebalance frequently with net delta of +/- 5% around short term technical levels particularly out of liquid time zones. The aim is to avoid using any stop loss orders and improve the average on the delta. The offset to not using stop losses on the delta is the daily time decay expense. Time decay is a more stable cost than stop losses on outlier moves in markets. 6
Liquid Time zones vs. Illiquid Time Zones FX markets have two kinds of behaviour depending on when they have liquidity. Liquidity is correlated to when the dominant currency pair s country is active (e.g. USD/CAD is most liquid during Toronto daylight hours) Delta management is different depending on liquidity. Trending behaviour is more robust when FX markets are most liquid. This can be predetermined by back testing short term trend following models that switch on and off at different times of the day. Trend needs to be given more benefit of the doubt when markets are liquid. More active delta management is required in less liquid time zones. This means leaving looping limit orders in illiquid times at predefined fractions of Average True Ranges. 7
Volatility Components At times implied volatility may look expensive relative to actual volatility or a GARCH equivalent. This filter also needs to have some impact on the currency pair selection process. I have defined implied volatility as relatively cheap when one month at-the-money implied is less than 20 day actual volatility. I have defined implied volatility as expensive when one month at-the-money implied is more than two vols over 20 day actual volatility. However, given a maturity profile of a maximum of 4 weeks, this process is less impacted by vega rather efficient management of gamma exposure. 8
Current Daily and Hourly FX Correlations. An important part of Currency Portfolio Selection. AUDJPY AUDUSD AUDNZD AUDCAD CHFJPY EURAUD EURCAD EURCHF EURUSD EURJPY EURGBP GBPCHF GBPJPY GBPUSD NZDUSD NZDJPY CADJPY USDCAD USDCHF USDJPY AUDJPY AUDUSD 27% AUDNZD 11% 62% AUDCAD -22% 53% 36% CHFJPY -23% 59% 70% 64% EURAUD -93% -12% 10% 43% 53% EURCAD -81% 9% 20% 70% 65% 95% EURCHF 88% -11% -16% -29% -41% -81% -74% EURUSD -72% 39% 41% 66% 79% 86% 92% -80% EURJPY 61% 44% 50% 31% 53% -27% -10% 56% -3% EURGBP -73% 23% 34% 71% 74% 89% 96% -72% 94% 0% GBPCHF 84% -21% -30% -61% -67% -92% -95% 88% -96% 21% -96% GBPJPY 94% 2% -5% -46% -37% -91% -88% 91% -83% 51% -86% 94% GBPUSD -47% 57% 40% 35% 64% 53% 54% -71% 78% -7% 53% -64% -50% NZDUSD 27% 81% 4% 41% 22% -23% -3% -2% 19% 19% 4% -4% 6% 43% NZDJPY 96% 11% -16% -32% -42% -95% -86% 92% -82% 48% -81% 91% 95% -57% 25% CADJPY 94% 6% -3% -53% -42% -95% -94% 87% -85% 43% -87% 93% 97% -52% 9% 94% USDCAD -51% -61% -36% 35% -6% 54% 55% -16% 19% -21% 41% -33% -45% -30% -51% -42% -56% USDCHF 79% -33% -36% -58% -72% -88% -90% 90% -98% 18% -91% 98% 88% -80% -16% 88% 89% -18% USDJPY 89% -19% -18% -48% -52% -89% -88% 95% -92% 42% -85% 96% 95% -74% -11% 93% 94% -24% 97% AUDJPY AUDUSD AUDNZD AUDCAD CHFJPY EURAUD EURCAD EURCHF EURUSD EURJPY EURGBP GBPCHF GBPJPY GBPUSD NZDUSD NZDJPY CADJPY USDCAD USDCHF USDJPY AUDJPY AUDUSD 51% AUDNZD 28% 8% AUDCAD 31% 82% 45% CHFJPY 71% 54% 71% 62% EURAUD 1% 14% 83% 49% 67% EURCAD 20% 57% 74% 87% 75% 85% EURCHF 88% 27% 32% 13% 51% 0% 8% EURUSD 40% 84% 51% 89% 78% 65% 90% 21% EURJPY 86% 51% 66% 52% 95% 51% 60% 75% 68% EURGBP 33% 44% 86% 67% 82% 88% 90% 27% 81% 73% GBPCHF 8% -32% -72% -62% -60% -90% -88% 20% -73% -38% -89% GBPJPY 88% 25% -1% 0% 45% -24% -14% 79% 6% 63% -7% 44% GBPUSD 23% 83% -34% 58% 17% -14% 26% -2% 56% 12% -3% 1% 21% NZDUSD 16% 65% -70% 24% -15% -52% -15% -5% 22% -13% -34% 32% 19% 86% NZDJPY 66% 38% -53% -8% 7% -64% -40% 53% -5% 25% -38% 64% 79% 46% 68% CADJPY 80% 0% 0% -31% 33% -29% -34% 80% -15% 54% -9% 47% 89% -13% 1% 72% USDCAD -48% -68% 43% -14% -15% 37% 13% -30% -32% -23% 9% -24% -44% -69% -81% -76% -40% USDCHF -7% -75% -39% -85% -59% -65% -87% 17% -92% -39% -71% 81% 24% -57% -24% 25% 46% 21% USDJPY 62% -35% 23% -40% 28% -12% -30% 71% -33% 47% -4% 38% 73% -51% -42% 38% 88% 9% 61% 9
LHS = Intraday The Information Screen in GBP/CHF RHS = Daily Data 10
Indicators Two trend indicators use used in tandem One is a modified moving average crossover rule adjusted for noise (i.e. you need more than just a crossover to generate a trend signal). One is related to the Average True Range indicator based on research by Wells-Wilder. Both must indicate trending markets to generate a signal. On average this only occurs about 15% of the time in both up and down directions. 11
The Information Screen RHS = Daily Data Daily Data Indicator #1 defines trend as +1 for up trend and -1 for downtrend, and zero for trend unclear Indicator #2 defines trend as +1 for up trend and -1 for downtrend, and zero for trend unclear. 12
LHS = Intraday The Information Screen Intraday Data Indicator #1 defines trend as +1 for up trend and -1 for downtrend, and zero for trend unclear Indicator #2 defines trend as +1 for up trend and -1 for downtrend, and zero for trend unclear 13
Process Strengths Well defined option entry and exit points VAR is always limited by the long optionality. Large daily losses are unlikely due to positive gamma Very scalable Opportunity to diversify risk in less correlated exchange rates and other futures contracts. 14
Process Weaknesses Opportunity cost of not buying options on the best ex-post trend signals. Time decay drain of not rebalancing efficiently when there are poor short term trend signals Not enough daily movement in the underlying to make back time decay plus additional gains. 15
Example The Currency Matrix Currency Pair Trend Spot ATR 1m Implied 20 day Actual Vol Test Vol Spread 1m 25d RR Rebalance Points Equalised Base Currency Amount 1 AUDJPY -1 94.85 1.59 17.3% 24.6% Buy? 7.3% -4.3 0.53 1,600,000 2 AUDUSD 0 0.9268 0.0104 12.3% 14.3% 3 AUDNZD -1 1.1674 0.0094 8.3% 7.7% 0.0031 5,700,000 4 AUDCAD 0 0.9392 0.0106 12.3% 10.8% 5 CHFJPY 0 101.08 1.07 7.9% 8.2% 6 EURAUD 1 1.6955 0.0178 11.8% 13.2% Buy? 1.5% 0.9 0.0059 1,400,000 7 EURCAD 1 1.5922 0.0201 12.2% 15.5% Buy? 3.3% -0.1 0.0067 1,000,000 8 EURCHF -1 1.5905 0.0102 6.2% 9.1% Buy? 2.9% -1.3 0.0034 3,900,000 9 EURUSD 1 1.5715 0.0161 10.3% 11.5% Buy? 1.2% -0.6 0.0054 1,500,000 10 EURJPY 0 160.80 1.99 11.9% 13.6% 11 EURGBP 1 0.7980 0.0076 10.0% 12.0% Buy? 1.9% 0.9 0.0025 3,500,000 12 GBPCHF -1 1.9933 0.0251 13.6% 19.3% Buy? 5.7% -1.5 0.0084 640,000 13 GBPJPY -1 201.55 2.96 14.3% 22.2% Buy? 7.9% -3.5 0.99 470,000 14 GBPUSD 0 1.9692 0.0164 9.0% 10.0% 15 NZDUSD 0 0.7938 0.0103 13.8% 13.5% 16 NZDJPY -1 81.23 1.56 20.2% 25.4% Buy? 5.2% -4.6 0.52 1,700,000 17 CADJPY -1 100.99 1.71 19.0% 25.3% Buy? 6.3% -3.8 0.57 1,400,000 18 USDCAD 0 1.0133 0.0107 11.4% 11.6% 19 USDCHF -1 1.0123 0.0137 12.8% 17.5% Buy? 4.8% -1.2 0.0046 2,200,000 20 USDJPY -1 102.35 1.38 13.9% 19.0% Buy? 5.1% -3.1 0.46 2,100,000 The summary of trend signal is on the left. Trend is defined as +1, 0, or -1. There is also a comparison of 1m implied vol to 20 day actual vol as a ready reckoner as to value on the vol curve. A buy is defined as implied below actual vol. A Sell is defined as implied more than 2 vols over actual vol. Risk Reversal skew needs to be a discretionary overlay on strike selection. For example, in AUD/JPY as 40 delta AUD Call is probably better value than a 30 delta AUD Put. Rebalance points is a guide to number of FX pips to target rebalancing. Equalised Base Currency Amount is a guide to relative position sizing. 16
AUD/JPY Trade Purchase Date 12-Mar-08 Price 1.18 JPY pips Premium JPY 295,000 Type AUD Put/JPY Call Expiry Date 11-Apr-08 Strike 90.00 Amount AUD 250,000 Initial Spot 94.90 Initial Delta 28% Initial Greeks are to the right. Sold: 20-Mar-08 Final Spot: 90.70 Price: 1.7 JPY Pips Premium: JPY 425,000 Spot Delta % Theta Delta Amount 97.0-21% 112 -AUD 52,500 96.5-22% -AUD 55,000 96.0-24% -AUD 60,000 95.5-25% -AUD 62,500 95.0-27% 139 -AUD 67,500 94.5-29% -AUD 72,500 94.0-31% -AUD 77,500 93.5-33% -AUD 82,500 93.0-35% 155 -AUD 87,500 92.5-37% -AUD 92,500 92.0-40% -AUD 100,000 91.5-42% -AUD 105,000 91.0-45% 167 -AUD 112,500 90.5-48% -AUD 120,000 90.0-51% -AUD 127,500 89.5-54% -AUD 135,000 89.0-57% 164 -AUD 142,500 88.5-60% -AUD 150,000 88.0-63% -AUD 157,500 87.5-66% -AUD 165,000 87.0-69% 134 -AUD 172,500 86.5-72% -AUD 180,000 86.0-75% -AUD 187,500 85.5-77% -AUD 192,500 85.0-79% 94 -AUD 197,500 17
Delta Trading History Profit on Option: JPY 130,000 Profit by Improving Average on Delta Hedge JPY 67,000 AUD/JPY Trading History Trade Date Amount Price Traded Value Net Position Average 3/12/2008 23:38 AUD 25,000 94.9 -JPY 2,372,500 AUD 25,000 94.90 -JPY 2,372,500 3/13/2008 0:30 -AUD 25,000 95.3 JPY 2,382,500 AUD 0 JPY 10,000 3/13/2008 3:28 AUD 25,000 94.4 -JPY 2,360,000 AUD 25,000 94.00 -JPY 2,350,000 3/13/2008 4:16 AUD 25,000 94.1 -JPY 2,352,500 AUD 50,000 94.05 -JPY 4,702,500 3/13/2008 5:38 AUD 25,000 93.95 -JPY 2,348,750 AUD 75,000 94.02 -JPY 7,051,250 3/13/2008 10:00 -AUD 25,000 94.14 JPY 2,353,500 AUD 50,000 93.96 -JPY 4,697,750 3/13/2008 10:53 AUD 25,000 94.05 -JPY 2,351,250 AUD 75,000 93.99 -JPY 7,049,000 3/13/2008 12:44 -AUD 25,000 94.45 JPY 2,361,250 AUD 50,000 93.76 -JPY 4,687,750 3/13/2008 16:10 -AUD 25,000 94.9 JPY 2,372,500 AUD 25,000 92.61 -JPY 2,315,250 3/13/2008 18:36 -AUD 25,000 95.46 JPY 2,386,500 AUD 0 JPY 71,250 3/13/2008 22:28 AUD 25,000 95.13 -JPY 2,378,250 AUD 25,000 92.28 -JPY 2,307,000 3/14/2008 4:36 AUD 25,000 94.5 -JPY 2,362,500 AUD 50,000 93.39 -JPY 4,669,500 3/14/2008 8:44 -AUD 25,000 94.75 JPY 2,368,750 AUD 25,000 92.03 -JPY 2,300,750 3/14/2008 11:47 AUD 25,000 94.52 -JPY 2,363,000 AUD 50,000 93.28 -JPY 4,663,750 3/14/2008 12:30 -AUD 25,000 94.7 JPY 2,367,500 AUD 25,000 91.85 -JPY 2,296,250 3/14/2008 13:48 AUD 25,000 94.2 -JPY 2,355,000 AUD 50,000 93.03 -JPY 4,651,250 3/14/2008 15:00 -AUD 25,000 94.13 JPY 2,353,250 AUD 25,000 91.92 -JPY 2,298,000 3/14/2008 15:02 -AUD 25,000 94.03 JPY 2,350,750 AUD 0 JPY 52,750 3/14/2008 17:23 AUD 25,000 93.8 -JPY 2,345,000 AUD 25,000 91.69 -JPY 2,292,250 3/14/2008 18:13 AUD 25,000 93.5 -JPY 2,337,500 AUD 50,000 92.60 -JPY 4,629,750 3/14/2008 18:29 AUD 25,000 93.1 -JPY 2,327,500 AUD 75,000 92.76 -JPY 6,957,250 3/14/2008 19:30 -AUD 25,000 93.6 JPY 2,340,000 AUD 50,000 92.35 -JPY 4,617,250 3/14/2008 19:41 AUD 25,000 93.15 -JPY 2,328,750 AUD 75,000 92.61 -JPY 6,946,000 3/16/2008 22:02 AUD 25,000 92.1 -JPY 2,302,500 AUD 100,000 92.49 -JPY 9,248,500 3/16/2008 22:58 -AUD 25,000 92.9 JPY 2,322,500 AUD 75,000 92.35 -JPY 6,926,000 3/17/2008 14:01 AUD 50,000 89.2 -JPY 4,460,000 AUD 125,000 91.09 -JPY 11,386,000 3/17/2008 17:25 AUD 25,000 88.6 -JPY 2,215,000 AUD 150,000 90.67 -JPY 13,601,000 3/17/2008 17:57 AUD 25,000 88.65 -JPY 2,216,250 AUD 175,000 90.38 -JPY 15,817,250 3/17/2008 18:40 -AUD 25,000 89.2 JPY 2,230,000 AUD 150,000 90.58 -JPY 13,587,250 3/17/2008 19:37 -AUD 25,000 89.9 JPY 2,247,500 AUD 125,000 90.72 -JPY 11,339,750 3/17/2008 19:49 AUD 25,000 89.81 -JPY 2,245,250 AUD 150,000 90.57 -JPY 13,585,000 3/17/2008 20:55 AUD 25,000 89.77 -JPY 2,244,250 AUD 175,000 90.45 -JPY 15,829,250 3/18/2008 5:54 -AUD 25,000 89.48 JPY 2,237,000 AUD 150,000 90.62 -JPY 13,592,250 3/18/2008 8:01 -AUD 25,000 90.3 JPY 2,257,500 AUD 125,000 90.68 -JPY 11,334,750 3/18/2008 10:44 -AUD 25,000 90.21 JPY 2,255,250 AUD 100,000 90.80 -JPY 9,079,500 3/18/2008 12:17 -AUD 25,000 90.58 JPY 2,264,500 AUD 75,000 90.87 -JPY 6,815,000 3/18/2008 18:50 AUD 25,000 91.38 -JPY 2,284,500 AUD 100,000 91.00 -JPY 9,099,500 3/18/2008 19:02 -AUD 25,000 91.73 JPY 2,293,250 AUD 75,000 90.75 -JPY 6,806,250 3/18/2008 23:01 -AUD 25,000 93.11 JPY 2,327,750 AUD 50,000 89.57 -JPY 4,478,500 3/19/2008 0:09 AUD 25,000 92.5 -JPY 2,312,500 AUD 75,000 90.55 -JPY 6,791,000 3/19/2008 1:08 -AUD 25,000 93.1 JPY 2,327,500 AUD 50,000 89.27 -JPY 4,463,500 3/19/2008 4:46 AUD 25,000 92.45 -JPY 2,311,250 AUD 75,000 90.33 -JPY 6,774,750 3/19/2008 5:11 AUD 25,000 92.2 -JPY 2,305,000 AUD 100,000 90.80 -JPY 9,079,750 3/19/2008 6:23 -AUD 25,000 92.33 JPY 2,308,250 AUD 75,000 90.29 -JPY 6,771,500 3/19/2008 8:36 AUD 25,000 91.9 -JPY 2,297,500 AUD 100,000 90.69 -JPY 9,069,000 3/19/2008 8:52 AUD 25,000 91.02 -JPY 2,275,500 AUD 125,000 90.76 -JPY 11,344,500 3/19/2008 9:04 -AUD 25,000 91.6 JPY 2,290,000 AUD 100,000 90.55 -JPY 9,054,500 3/19/2008 9:14 -AUD 25,000 91.23 JPY 2,280,750 AUD 75,000 90.32 -JPY 6,773,750 3/19/2008 11:31 -AUD 25,000 92.3 JPY 2,307,500 AUD 50,000 89.33 -JPY 4,466,250 3/19/2008 12:08 AUD 25,000 92.27 -JPY 2,306,750 AUD 75,000 90.31 -JPY 6,773,000 3/19/2008 14:35 AUD 25,000 91.7 -JPY 2,292,500 AUD 100,000 90.66 -JPY 9,065,500 3/19/2008 14:51 -AUD 25,000 92.3 JPY 2,307,500 AUD 75,000 90.11 -JPY 6,758,000 3/19/2008 16:40 AUD 25,000 90.65 -JPY 2,266,250 AUD 100,000 90.24 -JPY 9,024,250 3/19/2008 19:13 -AUD 25,000 91.01 JPY 2,275,250 AUD 75,000 89.99 -JPY 6,749,000 3/19/2008 19:36 AUD 25,000 90.6 -JPY 2,265,000 AUD 100,000 90.14 -JPY 9,014,000 3/19/2008 23:23 AUD 25,000 90.41 -JPY 2,260,250 AUD 125,000 90.19 -JPY 11,274,250 3/20/2008 4:22 -AUD 25,000 90.85 JPY 2,271,250 AUD 100,000 90.03 -JPY 9,003,000 3/20/2008 6:40 -AUD 25,000 90.7 JPY 2,267,500 AUD 75,000 89.81 -JPY 6,735,500 3/20/2008 6:40 -AUD 25,000 90.7 JPY 2,267,500 AUD 50,000 89.36 -JPY 4,468,000 3/20/2008 6:40 -AUD 25,000 90.7 JPY 2,267,500 AUD 25,000 88.02 -JPY 2,200,500 3/20/2008 6:40 -AUD 25,000 90.7 JPY 2,267,500 AUD 0 JPY 67,000 18