1. The Power of Moving Averages in Financial Markets By: Michael Viscuso

2. Recall…  A Moving Average is the average of the past n days prices.  A buy point is signaled when today’s price is above its moving average and yesterday’s price is below its moving average.  A sell point is signaled when today’s price is below its moving average and yesterday’s price was above its moving average

3. Recall…. (cont.)  We are looking for the best n – the look-back period of the moving average  Small n’s are more responsive to daily changes  Large n’s are less responsive to daily changes  Pros and cons to both

4. Example of Moving Average for small n. (n=6)

5. Example of Moving Average for medium n. (n=30)

6. Choosing the best n  Choose which n’s you are going to test  Start with the first 12 months and see which n did best over that time period; record it  Calculate best n for month 13 record the pair  Continue for all months in the data set

7. Interpreting results  Chi-squared test  Null Hypothesis: No correlation between best n for past year and best n for next month  Alternative Hypothesis: There is a correlation between best n for past year and best n for next month

8. Observed Results Year 5101520Totals 585301132158 Month1059211214106 1527104 51 20271601457 Totals198772770372

9. Interpretation  Using the Chi-Squared formula we obtain a test statistic of 11.838  Given 9 degrees of freedom this test statistic returns a p-value > alpha =.05 so we do not have enough evidence to reject the Null Hypothesis. Therefore, no correlation.

10. Where to go from here??  Suggestions?  Look back

11. Example of Moving Average for small n. (n=6)

12. Introduction to Stops  Set a price x percent away from the buy/sell price and if at some future date the price exceeds this stop then sell/buy back  Regular Stops  Trailing Stops  Full Stops  Partial Stops

13. Picking your stop  One problem has now become two Pick best n Pick best stops  Also, different method of solving Chi-squared cannot be used because expected counts would be too low

14. Best Attempt  Find best combination since (inception minus a few years) and then test that combination on the years you left out  No worries of expected counts so use as many MAs and %s as you want  List of MAs: 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 25, 30, 40, 50  List of %s (top and bottom): 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0

15. Results of Long Side Trading  Best MA: 3  Bottom Percent: 0.5%  Top Percent: 1.0%  Percent Correct: 50.157%  MA %APR from 1970-1998: 9.26%  DJIA %APR from 1970-1998: 8.48%

16. Results of Short Side Trading  Best MA: 3  Bottom Percent: 0.0%  Top Percent: 0.0%  Percent Correct: 56.326%  MA %APR from 1970-1998: 4.95%  DJIA %APR from 1970-1998: 8.48%  Both Long and Short Side trading together %APR from 1970-1998: 7.66%

17. Now use these parameters…  Long Side MA %APR from 1998- 2003: 5.22%  Short Side MA %APR from 1998- 2003: 6.82%  Long and Short Side MA %APR from 1998-2003: 6.03%  DJIA %APR from 1998-2003: 1.07%

18. Best parameters, Long Side trading  Best MA: 7  Bottom Percent: 1.0%  Top Percent: 1.5%  Percent Correct: 52.99%  MA %APR from 1998-2003: 10.59%

19. Best parameters, Short Side trading  Best MA: 18  Bottom Percent: 1.5%  Top Percent: 2.0%  Percent Correct: 56.92%  MA %APR from 1998-2003: 11.40%  Long and Short Side MA %APR from 1998-2003: 11.00%

20. Leveraging  Using indicators means you are picking and choosing when to be in or out of the market  Therefore, when you are in you have to make it account for all the times you’re out.  Options are one type of leveraging

21. Options  Option pricing is difficult because it is dependent upon six factors, only one of which is price  No source of test data  Approximate the amount of leveraging by buying/selling four times as much as your money allows.

22. The Option Effect  Long Side MA %APR from 1998- 2003: 14.14%  Short Side MA %APR from 1998- 2003: 24.57%  Long and Short Side MA %APR from 1998-2003: 19.81%  DJIA %APR from 1998-2003: 1.07%

23. Greedy Perhaps?  19.81% using the best of the past 28 years vs. 43.06% if you had used the best parameters of the current five years  How do we refine the system to capture more recent advances in other parameters?

24. First Attempt  Use the best parameters of last year for current year  Result: 20.06% vs. 19.81%  Occurred by Chance?....maybe  Also, the percent correct dropped drastically from 50% to 20% … not good

25. Second Attempt  Use the best parameters from the past 3 years, 5 years, and 10 years  Results:  3 years: 13.05%  5 years: 7.90%  10 years: 12.74%  Random … not random?

26. Summary of Results  Back Data: As much as possible: 19.81% 10 years: 12.74% 5 years: 7.90% 3 years: 13.05% 1 year: 20.06% 1 month: 0.49%

27. Interpretation of 1 month result  Using last month’s best parameters for the next month is essentially chasing yesterday’s fad.  Instead, let’s use a sample of past months to create a lower bound on the expected return for the following month and use the parameters that have the highest lower bound.  How many past months should we use?

28. Results  Run test on previous five years to determine best number of past months  Best number of past months = 9  Use this number of past months in choosing which parameters to use for the next month  Result: 0.00% APR  Not any better than 0.49%, however the percent correct, 88.3% (shouldn’t this be around 99%?), was much higher than before

29. Conclusions  Can we conclude anything?  How well was the moving average able to predict buy/sell points? By itself… Using stops  Where was chaotic behavior exhibited? Moving Average predictions? Market? System? All or none of the above?

30. Conclusions (cont.)  What amount of Back Data would you use?... Why?  How much of the results are dependent not upon how much Back Data but the characteristics of that Back Data  How likely is a programming error?

31. Questions??