Normativa internacional

By Richard Donchian

Note: If you would like to receive an outline of potential Donchian computer code please send an email to [email protected].

Donchian's 5- and 20-day moving averages In Wall Street there are two conflicting adages:

"You'll never go broke taking a profit." "Cut your losses short and let your profits ride."

Experience has shown that in commodity trading the first of these "old saw" is dangerous and misleading, while the second one may well be regarded as the one most important lesson the inexperienced commodity trader should leam if he wishes to have a better-than-even chance of coming out ahead.

Every well designed trend-following, loss-limiting method for trading in commodities (or stocks) rests on the basic principle that a trend in either direction, once established, has a strong tendency to persist, at least for a time. Among the many trend-following approaches now in use are the Dow Theory, point-and-figure chart techniques, swing methods (other than the Dow Theory), trend-line methods, weekly-rule methods, and moving average methods. This article will confine its scope to moving average methods, and in particular to a comparatively simple 5- and 20-Day Moving Average Method which boasts a 13-1/2 year record in actual operation.

Building a Moving Average

According to Webster, an average is "the quotient of any sum divided by the number of its terms." A 15-day average of copper closing prices, for instance, is the sum of 15 consecutive closes divided by 15.

A moving average is a progressive average in which the divisor (number of items) remains the same, but at regular intervals a new item is added at one end of the series while another item is dropped at the other end of he series.

Table 1 shows a sample computation of a 5-day moving average of the closing prices of December, 1974 New York silver.

To keep a 5-day moving average of the closing price of December silver, you add up the last five closing prices and divide by five. That gives today's 5-day average of closes. When tomorrow's close is available, compare it with the initial close of the nearest 5-day series (the sixth counting back.) If the new close is higher, add the difference to (or if lower, subtract the difference from) the previous total, then divide by five again. This gives tomorrow's 5-day average of closes, and in sequence with today's 5-day average closes is the start of a 5-day moving average of closes.

Continue the process day by day. That's all there is to keeping a moving average.

Moving averages can be calculated for closing prices, for highs and lows, for volume, for open interest, or for any other factor which can be measured and which changes periodically. Various length moving averages may be employed to determine trends. A 10-week average of weekly closing prices, for example, can help measure the direction of major trends. A 10-day moving average of daily highs and daily

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TurtleTrader lows can set up a tolerance band between the high and low averages, within which no action is taken. By buying only when the high average is exceeded on the upside and selling only when the low average is crossed on the downside, rather than by acting on every little crossing of the moving average, fewer whip-saw losses are incurred.

Some students believe that results shown by using moving averages can be improved by (a) employing an

exponential moving average - i.e., in which 1/x of the new figure is added to the previous x unit total and 1/x of the previous total is subtracted; or (b) employing a weighted moving average in which the more recent unit or unites are multiplied by some factor which gives them a greater weight in the total than the earlier units. Other students believe that it is helpful, in plotting the moving averages on line charts, to "push" the moving-average figure forward in to the future by one or more days, weeks, or other unites as the case may be, so that when the next unit of market action takes place, guide points for penetration will already be available.

Not New

The writer was first exposed to the use of moving averages to help increase profits and limit losses back in the 1930s. At that time a story was circulating about Eddie Cantor, who was more successful as an actor than as a speculator. In 1929-1932, when he found himself in a capital-eroding tailspin, he coined the classic definition of a dividend as "salvage from original investment." It seems that two well-dressed gentlemen called on Mr. Canter one day to offer him for $5,000 a method which they claimed would make him money and save him money steadily.

Cantor examined some simulated results, paid the five grand, and received instructions for - you guessed it: keeping a simple 10-week moving average.

The chief value of moving averages as helpful tools in price analysis rests on the following very simple premise: No commodity can ever stage an uptrend without first showing evidence of the preponderance of buying over selling - by the price rising above a moving average. Likewise, no commodity can ever perform a downtrend without first showing evidence of more selling than buying - by the prices'falling below a moving average. Mr. Canter may have felt that he overpaid for the simple method; but, in fact, he got his money's worth. Had he made use of such an average from 1929 to 1932 (or in almost any other period), buying when his stocks crossed the moving average on the upside and selling out and selling short whenever they fell below the moving average, he would have avoided heavy losses and instead made a lot of money on balance throughout his long but apparently erratic market career.

The Rationale

The particular method submitted in this article is a simple one using unweighted 5- and 20-day moving averages of closing prices. Signals to buy or sell are not given when the shorter average crosses the longer average, but are dictated by precise rules outlined later in this article.

One unique advantage of the 5- and 20-Day Moving Average Method is that it has a 13-1/2 year record of

continuous monitoring on a day-to-day basis. Since its inception on January 1, 1961, each signal has been sent over wires to readers, signals have been summarized in a weekly Hayden Stone trend-timing market letter, and a record bas been kept of results after commissions based on the worst prices which could have been obtained at the openings or closes when action signals were effected. Actual results are shown in Tables II and III. The results are labeled

"hypothetical" because there is no single actual account which has followed every signal for the full 13-1/2 year period. It is safe to state, however, that one or more actual executions, have taken place in accordance with every signal.

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The 5- and 20-Day Moving Average Method, on a one-contract-per commodity basis, after commissions and not reinvesting profits, has produced a 13-year net hypothetical gain of $183,552, and a net gain so far this year of more than $100,00. The overall margin requirement was less than $20,00 until 1972, but it is almost $60,000 today. Even though it seems to produce profitable results in markets which enjoy good sustained moves, it must not be regarded as any guaranteed or get-rich quick panacea. In fact, the method has several rather apparent disadvantages.

Purchases, for example, are never made at or near bottoms and sales are never made at or near tops. Action is taken only on the way up, after a bottom has been made, or on the way down after a top. To the inexperienced trader it may not make sense to sell on the way down after the top has been passed, when, if he had been a bit smarter, he could have sold at a considerably higher price just a short time before. This natural reluctance to settle for less than once could have obtained often leads the beginner to try to "outsmart the market," to try to do better than the method. Unfortunately, actions based on human emotion or judgements tend to be humanly fallible, so that efforts to improve on a tested method tend, in practice, to make one's results poorer rather than better.

Likewise, purchases are often made at strong spots where demanded by others is great, and sales are often made when other sellers are competing actively for the relatively scarce bids Consequently, orders are not always filled at

"good" prices. To be conservative, results shown in our tabulated summaries should probably be shaded by about five per cent to compensate for the tendency in this type of method to get relatively poor executions.

During periods which are characterized by narrow ranges, all trend-following methods tend to register small to moderate "whip-saw" losses. During protracted narrow fluctuating periods, a series of these small to moderate losses can add up to fairly sizeable cumulative loss. It is at such times that traders tend to stop following the methods often just before a pronounced money-making trend gets underway.

Despite these advantages, the method has some very important advantages which tend to outweigh the drawbacks:

Diversification lowers potential, but, more importantly, lessens loss risks. In commodity trading, loss risks cannot be eliminated; but the writer firmly believes that they can be controlled and limited. Experience has demonstrated that a commodity trading method which pays strict attention to limiting losses can normally produce gratifying net annual gains.

Losses are always limited, because positions must be closed out at definite points when the price fulfills certain requirements with regard to the moving average. In commodity trading, the use of low margins and high leverage magnifies the risk on every transaction. The importance of definite loss-limiting rules cannot be over-emphasized.

Profits are not limited. Whenever there is a lengthy, sustained move - and in most years there are many such important moves in many commodities - the method automatically captures as profit a large slice out of the middle of the move. As long as the move continues without a valid crossing of the moving average in the opposite direction, positions are maintained. In this way, profits are unlimited.

Errors of judgement are greatly reduced. Because the method is almost entirely automatic, it virtually eliminates dependence on human market judgement. It is possible, and perhaps advisable, to us the method as an adjunct to fundamental factors, and seasonal trends. For instance, one way to combine the method with fundamentals would be to take heavier positions when the method indications are sup-

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TurtleTrader ported by one or more of the fundamental factors. Another way would be to confine positions to those commodities in which the method indications are in agreement with one or more of the fundamentals.

Indecision is greatly reduced. If you trade on a definite trend-following, loss-limiting method, you can do it without taking a great deal of time from your regular business. Since action is taken only when certain evidence is registered, you can spend a minute or two per commodity in the evening checking up on whether action-taking evidence is apparent, and then in one telephone call in the morning place or change any orders in accord with what is indicated.

One of the most difficult spots in which a commodity trader may find himself comes when he has a position which shows a loss. He vacillates between fear that the loss will get bigger and wishful thinking that the market will turn.

He hates to face up to his loss and admit that his original judgement was wrong. "Should I wait for a rally?" When a rally comes, "Is it enough of a rally or should I wait for more?" "At what point in a further move against me should I take my beating and get out?" In such a situation only the most cold-blooded experience-hardened trader can think clearly and objectively. A definite method, which at all times includes precise criteria for closing out one's losing trades promptly, avoids all such emotionally unnerving indecision.

The Method

The rules for the 5- and 20-Day Moving Average Method break down into two categories: general, and supplemental. We'll discuss the general rules first.

For application of the following rules, the extent of penetration of the moving average is broken into units as follows:

1. Commodities priced at lees than 4.00 (none today) - one unit equals 0.1.

2. Commodities selling between 4.00 and 15.00 (potatoes) - 0.3 or nearest fraction.

3. Commodities selling between 15.00 and 40.00 (soybean oil, hogs, and sugar) - .05 or nearest fraction. For instance, a 0.3 penetration or a .07 penetration would count as one unit, an .08 penetration as two units.

4. Commodities selling between 40.00 and 100.00 (cotton, citrus, eggs, bellies, cattle, copper, and

cocoa are now in this group) - .10 or nearest fraction; in this case .15 would could as one unit, .16 as two units.

5. Commodities selling between 100 and 400 (corn, oats, soybean meal, plywood, lumber, platinum are now in this group) - .20 or nearest fraction.

6. Commodities selling over 400 (wheat, soybeans, and recently silver) - .40 or nearest fraction.

7. In all the rules which are listed below, no closing price penetration of the moving averages counts as a penetration at all unless it amounts to at least one full unit. For instance, in cocoa a .09 penetration would be disregarded, but a .10 penetration would count.

Basic Rule A. Act on all closes which cross the 20-day moving average by an amount exceeding by one full unit the maximum penetration in the same direction on any one day on the preceding occasion (no matter how long ago) when the close was on the same side of the moving average. For example, if the last time the closing price of cotton was above the moving average it stayed above for one or more days, and the maximum amount above on any one of the days was 64 points. (The unit cotton is .10). This principle - the requirement that a penetration of the moving average exceed -one of more previous penetrations - is a feature of the 5- and 20-Day Method which distinguishes it from other moving average methods.

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Basic Rule B. Act on all closes which cross the 20-day moving average and close one full unit beyond (above or below, in the direction of the crossing) the previous 25 daily closes.

Basic Rule C. Within the first 20 days after the first day of a crossing which leads to an action signal, reverse on any close which crosses the 20-day moving average and closes one full unit beyond (above or below) the previous 15 daily closes.

Basic Rule D. Sensitive 5-Day moving average rules for closing out positions, and for re-instating positions in the direction of the basic 20-day moving average trend are:

1. Close out positions when the commodity closes below the 5-day moving average for long positions, or above the 5-day moving average for short positions, by at least one full unit more than the greater of (a) the previous penetration on the same side of the 5-day moving average; or (b) the maximum point of any previous penetration within the preceding 25 trading sessions. If the distance between the closing price and the 20 day moving average in the opposite direction to the Rule D close-out signal has been greater within the prior 15 days than the distance from the 20-day moving average in either direction within 60 previous sessions, do not act on Rule D close-out signals unless the penetration of the 5-day average also exceeds by one unit the maximum distance both above and below the 5-day average during the preceding 25 sessions.

2. After positions have been closed out by Rule D, re-instate positions in the direction of the basic trend (a) when the conditions in paragraph 1 above are fulfilled; (b) if a new Rule A basic trend signal is given; or (c) if new Rule B or Rule C signals in the direction of the basic trend are given by closing in new low or new high ground.

3. Penetrations of two units or less do not count as points to be exceeded by Rule D unless at least two consecutive closes were on the side of the penetration when the point to be exceeded was set up.

Supplementary General Rules

1. Action on all signals is deferred for one day except on Thursday and Friday. For example, if a basic buy signal is given for wheat at the close on Tuesday, action is taken at the opening on Thursday morning. The same one-day delay applies to Rule D close-out and re-instate signals.

2. For signals given at the close on Friday, action is taken at the opening on Monday.

3. For signals given at the close on Thursday (or the next to last trading day of the week), action is taken at the Friday (or weekend) close.

4. When there is a holiday in the middle of the week or a long weekend, signals given at the close of the sessions prior to the holiday are treated as follows: (1) for sell signals, use weekend rules; (2) for buy signals, defer action for one day, as is done on regular consecutive trading sessions.