1、1,John Ehlers 805-927-3065 eMiniZ.com IndiceZ.com IS,Colleagues In Trading Seminar 17 Feb 2007,2,ENGINEERS ARE AS,AS ANYONE,3,Fibanacci Ratios,4,Patterns,Thousands of patterns have been catalogued Double Bottom, Head Vars: gamma(0), alpha(0), beta(0), BP(0), Lead(0); beta = Cosine(360 / Period); gam

2、ma = 1 / Cosine(720*delta / Period); alpha = gamma - SquareRoot(gamma*gamma - 1); BP = .5*(1 - alpha)*(Price - Price2) + beta*(1 + alpha)*BP1 - alpha*BP2; Lead = (Period / 6.28318)*(BP - BP 1); Plot1(BP,bp); Plot2(Lead, lead);,36,BandPass Filter,Eliminates both high frequency and low frequency noise

3、,Design is a tradeoff between selectivity and transient response,37,BandPass Response Study,38,Channelized Receiver,Uses a bank of contiguous bandpass filters Spacing and bandwidth are controllable Detect the amplitude at the output of each filter,Can use resolution enhancement transform also,39,How

4、 to Use Measured Cycles,Replace fixed-length parameters with dominant cycle fraction Makes these indicators adaptive to current market conditions Examples RSI: 0.5*dominant cycle Stochastic: 0.5*dominant cycle CCI: dominant cycle MACD: 0.5*dominant cycle & dominant cycle By definition, trends have l

5、ow cycle content Cycle peaks or valleys can be used to pick the best entry in the direction of the trend,40,Adaptive Strategy Improvement,Fixed-Length RSI (and length optimized),DFT-Tuned RSI,41,Trends,Slope is constant across one full cycle period This defines a trend for me,I model the market as a

6、n “instantaneous trendline” plus the dominant cycle,Best to trade the trend if the slope is greater than the cycle peak-to-peak amplitude,Trends can also be defined on the basis of cycle length for mode-switching strategies,42,Strategy Design,KISS Base strategy on some sound principle Establish orth

7、ogonal parameters Use at least 30 trades per parameter in testing Minimizes curve-fitting ALWAYS evaluate using out-of-sample tests Optimize on percent profitable trades (in TradeStation) Better to optimize on (ProfitFactor) * (% Profitable),43,Voting Systems,Systems that have voting components can

8、be effective Example: Elders Triple Screen System System components should be uncorrelated to avoid weighted votes RSI and Stochastic are highly correlated, for example A moving average and oscillator tend to be uncorrelated 5:1 time spread is adequate to use the same indicator in two timeframes to

9、produce a valid vote,44,Trading Your IRA,Cannot sell short or trade Futures in most IRAs Create “synthetic” shorts and longs using options In the money options have a delta = 1 (theoretically, 0.8 practically) In the money option is better than having a built-in stop loss You cannot lose more than y

10、ou paid for the option A worthless option can possibly be revived before expiration Options produce leverage A $4 option on a $130 index gives 0.8*(130/4) = 26:1 leverage Trade ProShares for 2X leverage both long and short www.IS will soon be available to do this QLD Ultra QQQ SSO Ultra S&P500 DDM U

11、ltra DOW30 MVV Ultra MidCap 400 UWM Ultra Russell QID UltraShort QQQ SDS UltraShort S&P500 DXD UltraShort Dow30 MZZ UltraShort MidCap 400 TWM UltraShort Russell,45,How to Optimize Strategies,Start with orthogonal parameters Optimize one parameter at a time View Strategy Optimization Report Display s

12、hould be a gentle “mound” around the optimal parameter value An “erratic” display shows the parameter is not optimizing anything just different performance for different parameter values Iterate optimization through the parameter set to reduce optimization time This is called a “hillclimb” optimizat

13、ion If the parameter values change much your parameters are not orthogonal,46,Portfolio Diversification,All issues within the portfolio should be uncorrelated to reduce risk If so, each doubling of issues reduces variation from mean equity growth by .707 Portfolio reaches a point of diminishing retu

14、rns 4 issues cuts variance in half 16 issues cuts variance in half again 64 issues required to reduce variance by half again Better strategy is to trade indices to get the benefit of their averaging,47,Monte Carlo Analysis,Shows statistics of a large number of trades Enables the use of recent, more

15、relevant trades Enables statistical evaluation of risk and reward/risk ratio,48,Trading System Evaluation,Profit Factor and % Profitable Trades are all you need to know to evaluate trading systems These are analogous to Payout and Probability of Winning in gaming Glossary:,$W = gross winnings #W = n

16、umber of winning trades $L = gross losses (usually normalized to 1) #L = number of winning trades PF = Profit Factor = $W / $L % = Percent Winning Trades (1-%) = Percent Losing Trades .as fractions,49,Some Interesting Relationships,Breakeven occurs when T = 0. In this case:,50,Weighted Average Trade

17、,Optimize by setting that derivative to zero (zero slope at the inflection point). Doing this, we get:,51,Consecutive Losing Trades,Probability of a losing trade is (1-%) Probability of a second losing trade is (1-%)2 Probability of N consecutive losing trades is (1-%)N A good trading system has, sa

18、y, 60% winners Therefore it has 40% losing trades q = 0.4 q = r + 2r2 + 3r3 + 4r4 + 5r5 + . If q = 0.4 then r = 0.2349 Probability of getting 4 losers in a row is 4r4=0.0122 If you trade 50 times per year, the probability of getting 4 losers in a row is 60.9% Thats almost a promise it will happen,N=

19、3,N=4,N=5,52,Fractional Strategy Equity Growth,Idea is to commit a fractional part of current capital to each trade rather than a fixed trade amount,53,Optimal f,Optimize f by setting the derivative of Expectation to zero (zero slope),This is exactly Ralph Vinces Optimal f Kaufman formulation should

20、 use (Gross Wins) / (Gross Losses) = PF,54,Sharpe Ratio, etc,RMS is synonymous with 1 Sigma variation (for a Normal probability distribution),Since Expectation is only slightly greater than unity:,Sharpe Ratio = (E-I) / s 1 / RMS Trading System Simulation,55,Bertrands Ballot Theorem,If candidate A u

21、ltimately gets “a” votes and candidate B ultimately gets “b” votes (ab), then the probability of Candidate A leading throughout the ballot counting process is (a-b) / (a+b) In our case, let a = %*PF and b = (1-%),PF must be greater than 2 (even then % must be certainty) Conclusion: It is almost a promise your account will go underwater some time after you start trading!,56,SVD,Single Value Decomposition (SVD) Must be done in C or BASIC Generate a callable DLL in EasyLanguage Code is available in Numeric Recipes Use only the first EigenValue Orthogonalizes