The SDB Strategy

During the entire testing procedure for the SDB system we only used data up until October 1992. The rest of the data we saved for some out-of-sample testing. Table 15.5 shows the result of trading the entire portfolio on the in-sample data, using the same fixed fractional money management for all markets, and risking no more than 1.5% of total portfolio equity per trade, going into the trade. The starting balance

Days

FIGURE 15.20

The equity curve from trading three different market/system combinations at their optimal f.

Days

FIGURE 15.20

The equity curve from trading three different market/system combinations at their optimal f.

was set to $1,000,000, with $75 deducted for slippage and commission per contract traded.

Just to make sure that it is indeed beneficial to use a fixed fractional trading strategy, even if we keep the/as low as 0.015, you can compare the results in Table

TABLE 15.5

1.5% fixed fractional trading with the SDB strategy (in-sample period).

TABLE 15.5

1.5% fixed fractional trading with the SDB strategy (in-sample period).

Strategy summaries

Profitability

Trade statistics

End Eq ($)

7,462,552

No Trades

424

Total (%)

646

Avg Tr ($)

14,614

Year(%)

17.6

Tr / Mark / Year

2.1

P factor

2.04

Tr / Month

2.8

Risk measurers

Time statistics

Max DD (%)

-17.17

Lng Flat (m)

25.9

Lrg Loss ($)

-148,124

TIM (%)

99.81

Winners (%)

41.75

Avg Days

20.00

15.5 with those in Table 15.6, which shows how much you would have made trading one contract only. The only major drawback with the statistics in Table 15.5 is a little too long flat period. However, research and experimentation show that it is more a result of bad portfolio composition than of the system itself, although at this stage all three variables—the system, the money management, and the portfolio composition—interfere and influence each other, making all three parts equally responsible for results. Nonetheless, in this case the longest flat period remains the same even if /is increased to 2.5% or lowered to 1%. The only thing that happens is that with a higher/comes a higher drawdown and a higher return, and vice versa.

By the way, the optimal / for this portfolio can be found around 14%, which produces a final profit of more than $21.5 billion, corresponding to a yearly rate of return close to 125%, but also a drawdown close to 95%, a largest loss close to $4.5 billion, and a longest flat time of more than 40 months. As should be clear by now, the final return is only a function of how well you would like to sleep at night. In this case we would be making something like $1.75 billion a year, on average—if you believe that is worth sleepless nights, be my guest.

Now that we know the SDB system works fine within a more complete trading strategy incorporating consistent money management on a whole portfolio of market/system combinations, perhaps it is time to look at how the same strategy would have performed on previously unseen data. That we will do, but first we will add another few analysis techniques to our portfolio summary spreadsheet.

We will put together a set of formulae that produce monthly results, resembling those in Figure 15.21, which we will use for further input into a new set of formulae that produce results like those in Tables 15.7 and 15.8.

TABLE 15.6

Single-contract trading with the SDB strategy (in-sample period).

TABLE 15.6

Single-contract trading with the SDB strategy (in-sample period).

Strategy summaries

Profitability

Trade statistics

End Eq ($)

1,329,060

No Trades

424

Total (%)

33

Avg Tr ($)

765

Year (%)

2.32

Tr / Mark / Year

2.1

P factor

1.99

Tr / Month

2.8

Risk measurers

Time statistics

Max DD (%)

-2.53

Lng Flat (m)

20.81

Lrg Loss ($)

-6,726

TIM (%)

99.81

Winners (%)

41.75

Avg Days

20.00

i EZ

fa

m fb

i fc

fd

1 fe

I

23

Dale

Equitj

Top

DD

1

3

30

800602

1.000.000

1.000.000

0.00

31

800630

1002547

1.002.547

0.00

0.25

32

800731

1054785

1.054.785

0.00

5.21

33

800829

1095614

1.035.614

0.00

3.87

3.56

34

800330

1035839

1.095.833

0.00

0.02

3.31

Using Excel to calculate monthly returns.

To start, highlight the cell in the column, one column away from your portfolio calculations and at the same row for where you start the portfolio calculations. In Figure 15.21, that is cell EZ30. In cell EZ30:

=E030

where column EO denotes the daily updated dates. In cell EZ31:

=IF(INT(E031/100)<INT(E032/100),E031,"")

then drag down to fill all the cells in that column. In cell FA30:

=ER30, where column ER the daily updated total equity. In cell FA31:

=IF(INT(E031/100) < INT(E032/100) ,ER31,"")

TABLE 15.7

Cumulative percentage period returns, n months rolling window (in-sample period).

TABLE 15.7

Cumulative percentage period returns, n months rolling window (in-sample period).

Cumulative

1

3

6

12

24

36

48

60

Most recent

-0.94

3.95

26.37

39.14

54.52

79.46

119.78

159.88

Average

1.43

4.41

8.77

17.65

39.97

69.48

110.03

159.17

Best

13.25

27.13

49.21

62.70

116.21

162.76

228.11

256.53

Worst

-9.09

-12.34

-10.97

-6.54

-11.42

-1.67

8.71

25.23

St. dev.

3.92

7.21

11.26

15.42

29.05

44.40

60.53

69.04

EGM

1.35

4.16

8.19

16.64

36.92

63.56

101.12

149.81

Sharpe ratio

0.36

0.61

0.78

1.14

1.38

1.56

1.82

2.31

Avg. winning

3.57

7.48

12.17

20.80

44.63

70.11

110.03

159.17

Avg. losing

-2.33

-3.52

-3.63

-3.35

-4.26

-1.67

N/A

Annualized percentage period returns, n months rolling window (in-sample period).

TABLE 15.8

Annualized percentage period returns, n months rolling window (in-sample period).

Annualized

1

3

6

12

24

36

48

60

Most recent

-10.71

16.76

59.69

39.14

24.31

21.52

21.76

21.05

Average

18.58

18.84

18.31

17.65

18.31

19.23

20.38

20.98

Best

345.1

161.21

122.64

62.7

47.04

37.99

34.59

28.95

Worst

-68.13

-40.95

-20.74

-6.54

-5.88

-0.56

2.11

4.6

St. dev.

58.63

32.11

23.79

15.42

13.6

13.03

12.56

11.07

Sharpe

0.32

0.59

0.77

1.14

1.35

1.48

1.62

1.9

% winners

63.76

72.11

78.47

86.96

90.48

99.12

100.00

100.00

then drag down to fill all the cells in that column.

You must delete all the blank cells in columns EZ and FA and line up all the other cells containing information underneath each other so that the end result will look like Figure 15.21. This can be done either manually or with the help of a macro. When you are done, continue to calculate the latest equity high and drawdown. In cell FB30:

=FA30

In cell FB31:

then drag down to fill all the cells in that column. In cell FC30:

=(FA30-FB30)*100/FB30

then drag down to fill all the cells in that column.

In columns FD and FE, we calculate the rolling monthly and quarterly returns. In cell FD31:

then drag down to fill all the cells in that column. In cell FE33:

then drag down to fill all the cells in that column.

In columns FF to FK (not shown in Figure 15.21) continue to calculate the rolling 6-, 12-, 24-, 36-, 48-, and 60-month rolling returns. With the above formulae and all other formulae we have used throughout the book, it should be no problem to go on and produce a table like Table 15.7.

To transform the cumulatively compounded values in Table 15.7 to annualized dittos in Table 15.8, simply raise each value by (12/PL), where PL equals the length of the period. For instance, if the most recent monthly return is stored in cell K3, to transfer it into an annualized figure in cell K13, use the following formula in cell K13:

=ROUND(((K3/l 00 +1 )A( 12/K2) -1)* 100,2), where cell K2 denotes the length in months of the original period.

From Tables 15.7 and 15.8 we can, for instance, see that during no 12-month period did we lose any more than 6.54% and never did we produce a losing period lasting longer than 3 years. We also can see that although the percentage of profitable trades was less than 42%, the percentage of profitable months was as high as 64%.

This is such an important finding that it must be explained further for a deeper understanding. Because we have constructed the system to cut our losses short, using such techniques as time-based stops we accomplish two things. First, a single loss won't go on forever, weighting down the results for several months in a row. Second, other trades to come will have an easier time making up for the recently produced loss. In the end, this might mean that a lower percentage of profitable trades will produce a higher percentage of profitable months. Once you have taken your analysis to this point, I think you will agree when I say that it is far more important to have a high percentage of profitable months than it is to have profitable trades. To make sure that the number of winning months will be high, you must have taken that into consideration at step one of your system-building process.

This is the same type of trade-off we must do when we compare the average trade to the standard deviation. The trick is not to have as high as possible an average trade, but only to make sure that it is sufficiently larger than the standard deviation; every change we make to the system that decreases the average trade is all right, as long it decreases the standard deviation even more. (Within reason that is—the mathematical expectancy still must be positive and the average trade large enough to make it worthwhile trading the system.) The positive side effect from all this is that we also are likely to increase the number of trades, which boosts our profits even further according to the fundamental equation of trading.

Another way to illustrate several of the numbers in Tables 15.7 and 15.8 is to create charts like those in Figures 15.22 and 15.23.

Let's take a look at how the SDB strategy would have fared both during the in-sample period from January 1980 to October 1992, and the out-of-sample period from October 1992 to October 1999. As before, the starting equity was set to $1,000,000, and $75 was deducted for slippage and commission per contract traded. Table 15.9 reveals that the ending equity now would have been close to $20,000,000, corresponding to a yearly return of 16.68%. The fact that this is slightly lower than for the in-sample period alone indicates that the strategy has

300.00 250.00 200.00 150.00

0 a5

Time window (months) □ Most recent ■ Average □ Best □ Worst ■ St. dev. B Geo Mean

FIGURE 15.22

A graphical presentation of cumulative monthly returns (in-sample period).

TABLE 15.9

1.5% fixed fractional trading with the SDB strategy (both sample periods).

TABLE 15.9

1.5% fixed fractional trading with the SDB strategy (both sample periods).

Strategy summaries

Profitability

Trade statistics

End Eq ($)

19,949,789

No Trades

730

Total (%)

1,895

Avg Tr ($)

25,184

Year(%)

16.68

Tr/Mark/Year

2.4

P factor

1.52

Tr / Month

3.1

Risk measurers

Time statistics

Max DD (%)

-27.3

Lng Flat (m)

25.9

Lrg Loss ($)

-568,453

TIM (%)

99.88

Winners (%)

39.59

Avg Days

19.00

Time window (months) □ Most recent ■ Average □ Best □ Worst ■ St. dev. B Geo Mean

FIGURE 15.22

A graphical presentation of annualized monthly returns (in-sample period).

not worked as well during recent years. This is further confirmed by a lower profit factor, a larger maximum drawdown, and a lower percentage profitable trades. As you can see, the average trade measured in dollars is much higher in Table 15.9 than in Table 15.5, but, as should be clear by now, this has nothing to do with the strategy's performing any better, but simply because the available equity is so much higher—we can have more money at stake at each individual trade.

From Table 15.10 we also can see that the average trade, measured in percentage terms, has decreased while at the same time the standard deviation has increased. This is not a good sign, because it implies that not only has the strategy turned less profitable, but also it has turned more risky. The percentage of winning months also has decreased somewhat. All in all this is a decrease in performance, but still not too far away from what could be considered tolerable for a professional money manager. In fact, the only thing that most definitely is not tolerable is the longest flat time, although it has stayed intact during the out-of-sample period. Figures 15.24 and 15.25 give you essentially the same type of information as Tables 15.7 and 15.8, and Figures 15.22 and 15.23.

Time window (months) 3 Most recent ■ Average OBest □ Worst BSt. dev.

TABLE 15.10

Monthly returns for the SDB strategy (both sample periods).

Most recent Average Best Worst St. dev. Geo Mean

Sharpe ratio (Annualized) Avg. winning Avg. losing % winners

The Directional Slope Strategy

When we built the Directional Slope System, we used weekly data to filter out some of the daily noise. Unfortunately, to be able to track the system in real time, we now need to transfer it back to a daily strategy by multiplying all the input variables by five. My initial research shows that this inevitably lowers the results somewhat, but so far I have found no proof for ditching this system-building concept altogether, provided that original system logic has been sound and simple and that every effort has been made to keep the system as robust as possible. I must point out however, that my research in this area is still at its initial stages and that only time will prove me right or wrong. Nevertheless, the point here is not to give you the very best systems around, but simply to outline a few tips and tricks on how to go about building one yourself, or—perhaps even more important—to describe the underlying reasoning that you must consider before you sit down in front of the computer.

Table 15.11, and Figures 15.26 and 15.27 show the result of trading the directional slope system on all 16 markets used during the system-building process. As before, we started out with $ 1,000,000 in initial equity, deducting $75 for slippage and commission per contract traded. As you can see, these results aren't too tantalizing, mainly because of a largest drawdown closing in on 60% and a longest flat period of more than 28 months.

However, one major reason for this is that, during the optimization process, I deliberately used markets that I knew from experience would not sit well with a trend-following strategy, such as the S&P 500 index and the CRB index. I did this to pollute the final parameter setting with as many market conditions as possible to increase the likelihood for the model to hold up in the future. Inevitably there will come a day when such trend-following workhorses such as the Japanese yen will stop working and start behaving like the CRB index (which is a notoriously difficult market with any strategy). When that day comes I want to have made sure that I have taken every possible action to keep myself from going broke.

Time window (months)

12

24

36

48

60

□ Most recent

7.32

13.01

54.07

43.72

50.81

■ Average

18.96

42.60

72.79

109.65

158.72

□ Best

79.15

132.02

172.18

228.11

266.43

□ Worst

-21.34

-11.42

-1.67

8.71

25.23

■ St. dev.

18.79

31.91

47.55

59.03

65.57

BGeo Mean

17.47

38.98

66.12

101.17

The cumulative monthly returns for the SDB strategy (both sample periods).

To get a feel for how much each market is contributing to the end result you can put together a table like Table 15.12, where I simply divided the total closed-out profit for each market by the total profit for the portfolio as a whole. In this case, we can see that the S&P 500 lowers the result by close to 25%, while the crude

TABLE 15.11

1.5% fixed fractional trading with the directional slope strategy.

TABLE 15.11

1.5% fixed fractional trading with the directional slope strategy.

Strategy summaries

Profitability

Trade statistics

End Eq ($)

17,011,080

No Trades

2,885

Total (%)

1,601

Avg Tr ($)

4,420

Year(%)

15.73

Tr / Mark / Year

9.3

P factor

1.06

Tr / Month

12.4

Risk measurers

Time statistics

Max DD (%)

-57.56

Lng Flat (m)

28.24

Lrg Loss ($)

-2,374,435

TIM (%)

98.06

Winners (%)

29.71

Avg Days

Time window (months)

-40

12

24

36

48

60

B Most recent

7.32

6.31

15.5

9.49

8.56

■ Average

18.96

19.42

20

20.33

20.94

□ Best

79.15

52.32

39.62

34.59

29.66

□ Worst

-21.34

-5.88

-0.56

2.11

4.6

■ St. dev.

18.79

14.85

13.84

12.3

10.61

The annualized monthly returns for the SDB strategy (both sample periods).

FIGURE 15.25

The annualized monthly returns for the SDB strategy (both sample periods).

oil alone is making up for more than 90% of the final profit. When interpreting these numbers, however, one must be very careful not to make any hasty conclusions. For one thing, just because one market happens to have a low or negative contribution factor doesn't mean it is inferior to other markets; it could be that particular market (no matter how profitable it seems to be by itself) simply happens to have all its profitable trades when the portfolio as a whole is in a drawdown, which will result in a lesser number of contracts traded when compared to a market that always happens to work at its best when the portfolio has reached a new equity high. Similarly, it could very well be that a market with a negative expectancy contributes positively to the portfolio as long as its winning trades tend to happen at the most opportune moment. Furthermore, even if it is reasonable to assume that a market will have a negative contribution to the portfolio result, it still might add positively to the very same bottom line by being uncorrelated enough to markets to keep the equity level up when the other markets are in a slump. Also, note that both the winning and losing percentages are surpassing 100%. This is because these numbers are picked from the aggregate portfolio, in which ending equity is not a straight line function of the equity of the individual markets.

Anyway, just for the heck of it, let us take a look at Table 15.13 and Figure 15.28 to see how the directional slope system would have performed, had we only traded only the nine markets that added the most to the bottom line. The nine mar-

45,000,000

40,000,000

35,000,000

30,000,000

15,000,000

10,000,000

5,000,000

800602 820531 840531 860530 880531 900531

Months

FIGURE 15.26

45,000,000

40,000,000

35,000,000

30,000,000

15,000,000

10,000,000

5,000,000

800602 820531 840531 860530 880531 900531

Months

FIGURE 15.26

The equity curve for the directional slope strategy. TABLE 15.12

Individual contribution factors for the directional slope strategy.

Market

Contributing

Corn

-24.98

S&P 500

-24.82

Juice

-59.71

Live cattle

-23.61

Lumber

4.77

Coffee

49.77

Japanese yen

51.33

Copper

12.25

Gold

-3.30

Eurodollar

0.16

Dollar index

-4.49

Cotton

7.40

CRB

-5.52

Crude oil

91.46

Canada dollar

7.34

T-bonds

21.96

Total

100.01

■60.00

800602 820531 840531 860530 880531 900531 920529 940531 960531 980529

Months

FIGURE 15.27

The drawdown curve for the directional slope strategy.

kets were lumber, coffee, Japanese yen, copper, dollar index, cotton, crude oil, Canada dollar, andT-bonds. As you can see, this time the maximum drawdown has decreased to 27.5%, which is considerably better than it was from trading all markets. Unfortunately, this is counterbalanced by a maximum flat period that is much too long. Another interesting observation that can be made from comparing Figures 15.26 and 15.28 is that Figure 15.26 at one point had a maximum total equity of close to $40,000,000, before the result started to turn south in the middle of 1998.

Honestly now, pretend it is early 1998 and that you just finished building this very same system using these very same markets. Would you then decide to trade it with all the available markets or only the nine markets that, in hindsight, turned out to produce the best result, considering the deep drawdown that started later that same year?

I bet most of you would have gone with the original portfolio, one reason being that common knowledge dictates that, "with a long-term strategy you should trade as many markets as possible, because you never know which one will take off next, producing that huge winner that will make it possible to build a house on the moon." This is very backward reasoning, however, because, for one thing, the more markets you trade the more likely it is that you will be caught on the wrong side when panic strikes any one of them. Additionally, because all our funds are

Months

FIGURE 15.28

The equity curve for the directional slope strategy traded on the nine best markets.

Months

FIGURE 15.28

The equity curve for the directional slope strategy traded on the nine best markets.

limited, margin constraints might keep us from trading as many markets as we wish. Therefore, it makes sense only to trade those that can provide us with the highest likelihood of success. Just because we used markets like the S&P 500 and CRB index to build the system does not mean we have to trade them if there are more viable alternatives.

I am aware that this last statement to some extent contradicts my previous statements that there is no difference between any two time series and that we should place as many trades as possible. But that is in the long run, and is why we use markets like the S&P 500 and CRB index when we build the system, to make sure that when the Japanese yen starts to perform just as "badly" at least I have built in some sort of catastrophe protection. And that is why we are not trading at each market/system combination's historical optimal f.

In the short run, however, I know that there are some differences (indicated by the different optimal /s). It would be foolish to try to squeeze in markets like those mentioned, or markets that are too correlated with each other, as long as I can't justify it for any other reasons, such as the likelihood of minimizing the drawdown or flat time by increasing the number of trades.

In ten years' time, however, the picture might look very different and perhaps then I will be better off substituting all markets completely. The argument against this last sentence is that, I would be leaving a lot of money on the table while wait-

TABLE 15.13

Results for a preferred portfolio with the directional slope strategy.

TABLE 15.13

Results for a preferred portfolio with the directional slope strategy.

Strategy summaries

Profitability

Trade statistics

End Eq ($)

20,709,401

No Trades

1,646

Total (%)

1,971

Avg Tr ($)

10,867

Year (%)

16.91

Tr / Mark / Year

5.3

P factor

1.23

Tr / Month

7.1

Risk measurers

Time statistics

Max DD (%)

-27.54

Lng Flat (m)

26.33

Lrg Loss ($)

-1,509,982

TIM (%)

98.06

Winners (%)

31.83

Avg Days

11.00

ing for the evidence to be strong enough to warrant the switch. True, but my answer to that is the same as for the type I and type II errors: "Better safe than sorry."

Furthermore, you have to decide what it is you are trying to achieve. We are discussing trend-following strategies, consisting of a money management regimen, a portfolio of markets, and a trend-following system, and the same reasoning holds true for the complete strategy as it does for the single system. That is, we are not trying to pick tops and bottoms, but rather to jump on a market in motion once the trend has proved itself and then ride that move until our stops and exit techniques tell us that it is no longer there.

Another practical reason why we shouldn't trade every market is that the more markets we trade the more inefficient the strategy will be, lowering the optimal / for the portfolio as a whole. And because we like to have plenty of room between the/we are using and the true optimal/ we had better not bog down the portfolio too much. My research shows that a portfolio of 12 to 18 different, low-correlated markets, possibly traded with as many as three different systems, seems to work best. But this conclusion is based on my personal preferences, and I urge you to do your own research to come up with a portfolio that makes the most sense to you.

The DBS Strategy

For the DBS system the results are pretty much the same as those for the directional slope strategy, with the same markets producing similar results. This is indicated by Table 15.14, which shows that both the flat time and the drawdown are a little too steep. Rather than once again going through why this is the case, only repeating the discussion regarding the directional slop strategy, let's just move on.

TABLE 15.14

1.5% fixed fractional trading with th DBS strategy.

TABLE 15.14

1.5% fixed fractional trading with th DBS strategy.

Strategy summaries

Profitability

Trade statistics

End Eq ($)

21,787,934

No Trades

1,581

Total (%)

2,079

Avg Tr ($)

11,425

Year(%)

17.21

Tr/Mark/Year

5.1

P factor

1.11

Tr / Month

6.8

Risk measurers

Time statistics

Max DD (%)

-42.37

Lng Flat (m)

30.67

Lrg Loss ($)

-1,123,734

TIM (%)

99.98

Winners (%)

33.9

Avg Days

11.00

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