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# Projecting Drawdowns

A key money-management goal is to protect the downside using rigid risk control. We would therefore like to make reasonable projections about potential drawdowns. We have to rely on past analyses to forecast the future, so we should try to err on the side of caution, and bias our forecasts toward the high side. It is better to plan for a larger drawdown than a smaller one.

The previous section suggested that the standard deviation of monthly equity changes for a system is a reasonable tool to project the magnitude of future losses. We first developed the daily equity curve, then converted it into a monthly equity curve, and then calculated the monthly changes in equity. Using spreadsheet software, we can also calculate the standard deviation of monthly equity changes. Let us call this quantity <7i for convenience. A conservative forecast for future drawdowns is 4oi for any system. However, this is only an estimate, and you could consider other nearby values ??such as 5oi or even 3ai.

To test this forecasting technique, we used continuous contracts from January 1, 1985, through December 31, 1990, for these seven arbitrarily selected markets: cotton, Eurodollar, gold, heating oil, Japanese yen, Swiss franc, and U.S. bond. We tested three arbitrary, nonop-timized systems: the 65sma-3cc, a 20-bar breakout on close (CHBOC) with a 10-tick barrier, and a volatility-based system (VOL). The rules for this last system are described in detail in chapter 8 on data scrambling. We used a $ 2,500 initial stop and an exit on trailing 10-day high or low, and allowed $ 100 for slippage and commissions. These choices were all made arbitrarily, without any idea of ??how the systems will perform and without looking at the data.

The logic for entering the markets is quite different for each system, although they have the same exit strategy. Hence, being trend-following in nature, they should all be profitable in trending markets. It is their response to sideways markets that will differentiate system performance. The 65sma-3cc system will probably show smaller losses,

Projecting Drawdowns**219**

**Table 7.10** Simulated profits and drawdowns for the 1985-1990 period (Max P = net profit, MIDD = maximum intraday drawdown)

Market | CHBOC MaxP (S) | CHBOC MIDD ($) | VOL. MaxP (S) | VOL. MIDD (S) | 65sma-3cc MaxP ($) | 65sma-3cc MIDD (S) |

Cotton | 5,245 | -16,005 | 27,165 | -7,330 | 20,675 | -5,815 |

Eurodollar | 13,950 | -1,750 | 9,475 | -8,725 | 9,675 | -4,275 |

Gold | -10,330 | -16,200 | -1,170 | -12,790 | -4,280 | -10,280 |

Heating oil | 15,382 | -20,751 | -32,825 | -50,571 | 21,761 | -13,380 |

Japanese | 38,663 | -11,513 | 59,913 | -8,938 | 13,475 | -11,113 |

yen | ||||||

Swiss franc | 1,450 | -18,663 | 35,075 | -18,750 | 12,350 | -11,400 |

U.S. bond | 17,513 | -10,400 | 49,413 | -9,125 | -17,025 | -28,438 |

56,631 |

-84,701 |

Totals

81,873 |

-95,282 147,046 -116,229

since it tends to be self-correcting during trading ranges. The CHBOC 20-bar breakout will stay out of narrow trading ranges, but will suffer false breakouts during broad trading range markets. The volatility system will be vulnerable to sharp moves within the trading range.

By examining overall system profits and maximum intraday losses, you can better appreciate the analysis of monthly equity changes. Tables 7.10 and 7.11 show that there were wide differences in overall profitability and drawdowns for the three systems over the seven markets.

**Table 7.11** Simulated profits and draw downs for the 1991-95 period (Max P = net profit, MIDD = maximum intraday draw down)

Market | CHBOC MaxP ($) | CHBOC MIDD ($) | VOL. MaxP ($) | VOL. MIDD ($) | 65sma-3cc MaxP ($) | 65sma-3cc MIDD ($) |

Cotton | 18,430 | -5,265 | 9,195 | -11,425 | 33,060 | -8,940 |

Eurodollar | 3,850 | -2,200 | -4,675 | 1,525 | -2,225 | |

Gold | -12,630 | -12,630 | -17,750 | -18,660 | -870 | -2,510 |

Heating oil | -7,080 | -15,813 | -24,330 | -25,296 | -5,113 | -10,261 |

Japanese | 19,563 | -11,200 | 27,463 | -1 3,925 | 44,500 | -3,538 |

yen | ||||||

Swiss franc | 17,925 | -9,000 | 18,700 | -10,850 | 5,750 | -12,313 |

U.S. bond | -7,531 | -19,756 | -1,288 | -9,556 | ^ T, 538 | -10,706 |

Totals |

32,527 |

-75,864 |

12,340 |

-94,387 |

74,314 |

-50,493 |

**220** Ideas for Money Management

The 65sma-3cc system produced the smallest total drawdown, followed by the CHBOC system. Note the large drawdowns produced by the volatility system in heating oil from òèñÿ÷³ äåâ'ÿòñîò â³ñ³ìäåñÿò ï'ÿòü to 1990. Gold, heating oil and U.S. bonds were difficult to trade with these systems. Note also the large fluctuations in profits and losses over the test periods. You should focus on relative differences in system performance.

We would like to see if this interval analysis can project future drawdowns. Hence, we exported the daily equity curves, converted them into monthly curves, and used a spreadsheet to develop information on changes in equity over 1, 3, 6, 7, 8, 9, and 12 months.

In most systems tested, the periods of drawdown usually last less than 9 months. Hence, we paid greater attention to the 6 to 9-month range. We calculated the standard deviation of the monthly equity changes, and then determined the worst performance over any of the above intervals, hoping that the ratio of the worst interval performance to the standard deviation of monthly equity changes would be 5 or less.

The equity calculations were repeated for the next block of data, from January 1, 1991, through June 30, 1995, without changing the system. The new test period was an "out of sample" test to check stability. We then did the interval equity change calculations in a bid to see if the forecast for the worst drawdown based on the data from 1 985 to 1990 had held up on the data from 1991 to 1995 Ideally, the standard deviation of monthly equity changes would be roughly comparable in the two periods, to reinforce our confidence in this approach.

Table 7.12 shows the standard deviation of monthly equity changes and maximum drawdown for the three systems over each period. The monthly standard deviation was quite stable. The ratio of the average loss was approximately four times the monthly standard deviation over both time periods. This is encouraging, since we did an "out of sample" test without optimization using arbitrarily selected systems and markets. These data show that it is reasonable to project future drawdowns by using the standard deviation of monthly equity changes, assuming a potential loss of four to five times the monthly standard deviation.

Once you know the projected loss, you can immediately gauge a possible equity level to trade the system or portfolio. Let us say you wanted to keep the drawdowns below 20 percent. To be safe, let us use a target of 15 percent, with a 5-percent cushion for future uncertainties. Hence, if you had a calculated standard deviation of $ 6,000, then a 5x forecast would be a drawdown of- $ 30,000. Since we want to keep projected drawdowns at the 15-percent level, the approximate equity level is $ 200,000 for trading this system or portfolio.

Changing Bet Size after Winning or Losing**221**

**Table 7.12** Comparison of standard deviation and theoretical losses for three systems over two different time periods using monthly changes in equity

Ratio of | ||||||

Worst | Ratio of | |||||

Monthly Standard | Worst | Drawdown to | Monthly Standard | Worst | Worst Drawdown | |

Deviation | Drawdown | Standard | Deviation | Drawdown | to | |

System | (1985-1990) ($) | (1985-1990) (S) | Deviation (1985-1990) | (1991-1995) ($) | (1991-1995) (S) | Standard Deviation (1985-90) |

CHBOC | 6,879 | -21,977 | 3.2x | 5,944 | -28,587 | 4.2x |

VOL | 4,229 | -21,729 | 5.2x | 4,739 | -11,277 | 2.7x |

65sma-3cc | 6,080 | -25,550 | 4.2x | 5,804 | -23,072 | 3.8x |

Average |

**X**

**X**

5,496 |

-20,979 |

**5,729 -23,085**

Remember that our projections are only approximations of what might happen, and no guarantee that losses will remain at or near this level. However, the method discussed in this section does provide an objective tool to plan for reasonable equity losses. You must rigidly enforce the risk control mechanism incorporated into the system tests, otherwise these forecasts are meaningless. Ideally, once we have protected the downside, the design of our system and future market action will take care of performance on the upside.

Summary | Introduction | Channel Breakout on Close with Trailing Stops | Channel Breakout on Close with Volatility Exit | Channel Breakout with 20-Tick Barrier | Channel Breakout System with Inside Volatility Barrier | Statistical Significance of Channel Breakout Variations | Day Exit Reference System | Two ADX Variations | The Pullback System |