Buy when the high of the day penetrates the upper band, and close out longs when the low of the day penetrates the moving average.

Sell when the low of the day penetrates the lower band, and cover shorts when the high penetrates the moving

average.

With both the first and second set of rules, risk is limited to half of the full band width. In the second case, the chances of exiting one trade and remaining neutral are greater than the first.

Timing the Order

The tjpe of execution order placed when following a sjstem will have a long-term effect on its results. The use of a band with a single moving average identifies change of trends when a breakout occurs. Buying during an upside break or selling during a downside break often results in poor entrj prices, and has been known to place the trader in a new trend at the point where prices are readj for a technical adjustment The most frequent complaint of frend followers is that their new positions usually show losses and that it takes a long time before the technical adjustment ends and the new frend retums to its entry price level. This reasoning has caused many variations from the original rules:

Buy (or sell) on the close after an entry signal has been mdicated. Buy (or sell) on the next market open following a signal. Buy (or selO with a delay of 1, 2, or 3 dajs after the signal.

Buy (or sell) after a price retracement of 50°o (or some other value) following a signal. Buy (or sell) when prices move to within a specified rid; relative to a stop-loss point.

These modifications are for the purpose of entering a new position with an immediate profit or preventing excessive risk. Some can be categorized as timing and others as rid; management. If intraday prices are used to signal new enfries and exits, a rule may be added that states:

Only one order can be executed in one day-either the liquidation of a current position or an entry into a new position.

The goal of improving exit and entry points is weft worth spending time and effort. With limited capital, the conservation of the investment is important when the greater number

of trades are expected to lose money. Better entry points will reduce the risk on a laier part of the frades and allow longer drings of poor performance.

Waiting for the right time to enter a trade may have more disadvantages than is apparent. In tests on frend-following sjdems conducted over many years, it can be shown that positions entered at the market opening on the day following the sjstem signal improved fill prices about 75>o of the time but resulted in smaller overall profits for the year. Whj"? Fast breakouts never adjusted back to allow the trader to enter at a better price. The three out of four better fills were more than offset by the one breakout that kept going.

APPLICATIONS OF SINGLE TRENDS

The selection of the frend speed (calculation period) is as important as any of the sjdems rules. The speed determines the activity of trading and the nature of the frend to be isolated. To help this decision, some of the preceding sections have shown comparisons of the different speeds as well as approaches, based on minimizing the magnitude of the forecast errors. Without a computer, extensive examination of alternatives is impossible. Chapter 21 concenfrates on the use of the computer for selection of frend speed and risk parameters for sinele- and multiple-frend sjstems, as well as breakout sjstems. It also includes an analjsis of results

Prior to being able to optimize, the frend period was based on multiples of calendar periods, expressed as frading dajs. In doing this, there is an opportunity to be in phase with behavioral pattems of fraders and brokerage houses, who may work within weekly or monthly spans. The most popular intervals for selection have been 3 dajs, the expected duration of a short price move; 5 dajs, a frading week; 20 to 23 dajs, a trading month, and so on. Included in the next sections are well-known sjdems using single frends, followed by examples of muItipIe-frend sjdems.

MPTDl (A 81 -Weighted Moving Average)

In 1972, Robert Joel Taylor published a sjstem called the "Major Price Trend Directional Indicator" (MPTDI), which was reprinted in summary form in the September 1973 issue of Commodities Magazine. The sjstem was promoted and implemented through Enterex Commodities in Dallas and was tested in 1972 on historical data byDurin and Haiitt Financial Services in West Lafayette, Indiana. It was one of the few well-defined published sjstems, and it served as the basis for much experimentation for current technicians and aspiring analjsis.

MPTDI is based on a stqa-weighted moving average of varjing lengths, with a band of changing widths relative to volatility. It is unique in its complete dependence on incremental values for all aspects of the sjstem: the moving average, entry, and stop-loss points. For example. Table 5-1 shows what conditions might be assigned to gold.

If gold were trading in an average range of 250 to 350 points each day, the weighting factor for the moving average would be TYPE C, indicating medium volatility (TYPE A is lowest). Using TYPE with a 15-day moving average, the most recent 5 dajs are given the weight 3, the next 5 dajs 2, and the last 5 dajs are weighted by I. The buy and sell signals use the corresponding entry-signal pendration of 250 points above the moving average as a buy signal and 250 below as a sell entrj The highs or lows of intraday trading are used to activate the entrj based on values calculated after the close of trading on the prior day. A stop-loss point is fixed at the time of entry equal to the value on the same line as the proper volatility. The penetration of the stop-loss will cause the liquidation of the current trade. A new signal in the reverse direction will serve as both a stop-loss and reentry point.

There is a lot to say in favor of the principles of MPTDI. It is individualized with respect to markets and self-adjusting with changing volatility. The stop-loss serves to limit the initial risk of the trade and allow the coordination of a money management approach. The fixed risk differs from moving averages using standard bands, because a moving average and its band can back away from sjstementrj points on a gradual reversal of the price trend But there are some rough etes to the sjstem. The incremental ranges for volatility, entry points, and stops seem a crude measure. Even if they are accurate in the center of the range, they must get doubtful at the exfremes at the point of change fran one range to another. Analjsis will find that they may need to study price movement at discrete levels, such as those shown in MPTDI, to be able to generalize a price or volatility pattem.

The Volatility Sjstem

Another method that includes volatility and is computationally simple is the Volatility Sjstem. Signals are generated when a price change is accompanied by an unusually large move relative to average volatility. If the average volatility measured over N dajs is

where Z> is the maximum of (a)

(b) \ .-1

(c) .1

and Hi is the hi on day / C, is the close on day i I,is the low on day i

TVading rules are en as

Sell if the dose drops more than x V(/V) firom the previous dose.

Buy if the dose rises by more than : x V(N ) firom the previous dose. The value of : is generally about 3.0.

* (Scott, Foresmin, Glenvlew, IL, 1<>84, p. 231).

Note that the average volatility should not include the current day t. A comparison of todays volatility using an average containing that value might cause inconsistent signals.

The 1 O-Day Moving Average Rule

The most basic application of a moving average sjstem was proposed by Keltner in his 1960 publication. How to Make Money in Commodities (The Keltner Statistical Service, Kansas City, 1960). Of three mechanical sjstems presented by Keltner, his choice of a moving average was based on performance and experience. The sjstem itself is quite simple: a 10-day moving average based on the average of the daily high, low, and closing prices, with a band on each side formed from the lOday moving average of the high-low range. A buy signal occurs on peneU-ation of the upper band and a sell signal when the lower band is broken; positions are always reversed.

The 10-Day Moving Average Rule is basic, but it does account for the fundamental volatility principle and serves as an example of the actual use of moving averages. Keltner expresses his preference for this particular technique because of its identification of minor rather than medium- or long-term trends, and there are some performance figures that substantiate his conclusion. As an experienced trader, he prefers the speed of the 10-dajf moving average, which follows the market prices with more reasonable rid; than slower methods. A side benefit to the selection is that the usual division required by a moving average calculation can be substituted by a simple shift of the decimal place; in an era before the pocket calculator, who knows how much impact that convenience had on Keltners choice?

Triple Exponential Smoothing

A triple exponential smoothing technique was described by Hutson as another approach to trend following. Substituting the log of the price for the price itself he applied an exponential smoothing three times using the same smoothing constant. A buy signal was generated when the triplesmoothed series rose for 2 consecutive dajs; a sell signal followed a 2-day decline.

The smoothing constant selected would normally be faster (less than a 20-day equivalent, when 2/(n + 1) is used to convert the n dajs to a smoothing constant) for a triple smoothing than for a single smoothed line. It is interesting to see what actually happens when a series is smoothed three times. For exanple, a triple smoothing of a straight 3-day moving average gives the following: