same logic as previously discussed. Velocity and acceleration are increasingly more sensitive directional indicators: the slightest variation in price movement will cause the acceleration to reverse. It is an indicator of great value when it is used selectively.

OTHER RATE-OF-CHANGE INDICATORS Projected Crossovers

If moving averages can successfully be used to identifj the trend direction, it follows that a projection of the moving average will be valuable in anticipating when the trends will change, if a moving average trading strategj used a single trend, the price at which the standard N-dsy moving average line would cross the price CPl is

sum of last A - I prices

(/V-l)

To calculate the price a.t which two moving averes would cross requires the following: iVx(sum of last iV- \ prices) - At x (sum of last At - I prices)

where iV and M are the lengths of the two moving averages "

The projected crossover price is most useful when it is likely that a trend change wiU occur within a few days, that is, when the two moving averages begin converging and becotne close in value. Acting on the expected price would give the trader a reat advantage in order execution. A plot of this, however, may not be much difiFerent than a simple reLztWe strength measurement. The difference between the price and the moving average line constitutes the relative strength.

The change in the projected crossover is considered a more valuable tool by Lambert. He creates a Market Direction Indicator (MDI) with the following formula:

1 lOO X (crossover price ,,0 crossover price.oj„) ~ average of past 2 days prices

The point at which the MDI crosses the zero line moving hiier is a buy signal, and the point at which it crosses moving lower is a sell signal.

Combining aTrend and Oscillator Directional Parabolic Syxtem

The LHrectionai ParaboUc Syrfem* is a combination of two of Wilders weU-known tech-nlques. Directional Movement and the Parabolic TimeyPrice System. Directional Movement is covered fully in Chapter 23- It gained popularity as a method of selecting the commodi-

" Donald R. Lambert, "The Market Directional indicator," lbnical Analysis of Stocks G Commodtttes (November/December 1983). This article also contains a BASIC computer prcram to calculate the MDI " J. Welles WUder, Jr.. Chart li-atitng Workshop 19 (TreiKl Research. Greensboro, NC. 1980)

ties that were most likely candidates for trend-following sjstems. The Parabolic Time/Price System is covered in Chapter 17 (Additive Techniques"). Although a full reading of both techniques are necessarj, the essence of the combined sjstems can be understood with the following definitions:

+DI14 The 14-dsy upward Directional Index

-DI 14 The 14-dsy downward Directional Index

ADX The average Directional Movement Index

DPS The Directional Parabolic stop

Although shown as -D114, the downward Directional Index is a positive number based on the sum of those

dajs that closed lower. The ADX is a ratio of those days that closed higher with those that closed lower over the past 14 dajs. The ADX is an oscillator based on the scaled ratio of +DI/-DI. The two sjstems combine according to the following rules:

1. If the ADX is up (the +DM14 is greater than the -DM14), take only long Parabolic Sjstem trades; if the ADX is down, take only short trades.

2. if the two sjstems conflict, no trade is entered. A trade may be entered at the time they agree.

3- If a position is held, the Parabolic stop is used. (The stop is now called the DPS instead of the SAR, because il no longer requires a reversal of position.)

4. If no position is held, the Directional Movement equilibrium point is used (the high or low of the day on which the +DM 14 crosses the -DM 14).

Directional Parabolic Revision

In 1980, the entry rules were revised to include an added use of the ADX when it is greater than the +DI14 or the -DI 14. Because the ADX serves as an oscillator and indicates turning points in the trend, when the ADX exceeds the magnitude of the current +DI14 or -DI14 and reverses, the current position should be closed out. If the ADX remains above both the +DI 14 and -DI 14, the maitet is extremely strong and liquidation should stop. The ADX is intended to be a leading indicator for liquidation only. Reversal of the current position only occurs when the Parabolic stop has been penetrated, and the new trade agrees with the direction of the Parabolic Sjstem.

The addition of an oscillator to a trend-following sjstem allows trades to be closed out at more favorable positions than the usual trend exits. If the new direction carries through and the position is reversed, the added feature has worked perfectly; however, if prices turn bad; in the original direction, a reentrj may not be possible. The revised rules are unclear conceming reentry into a position if prices fail to penetrate the DPS and signal a reversal. A reentry might occur if the ADX falls below both the +DI14 and -DI14, indicating that prices are no longer extreme, then turns back in the trend direction. Once reestablished, the DPS can be used and additional exits using the revised rules would apply.

Cambridge Hook

A combined indicator that has received some promotion is the Cambridge Hook, used by one commodity trading advisor. (] ) It is intended to identifj an early reversal of the current trend by combining the following indicators (applied to an existing uptrend):

1. An outside reversal day (a higher high followed by a lower close)

2. Wilders RSI must exceed 60°o (moderately overbought)

3. Volume and open interest must be increasing

17 Elias nm Am You Watchiue tiie T ighf ciauBls?" Futures (lune 1< -))

The result is a high likelihood of a downward trend reversal (the opposite applies to upward trend reversals). Protective stops are placed above the high of the hook on the day that signaled a downward reversal.

MOMENTUM Dn-ERGENCE

Diveience is a concept familiar to most traders. It is frequently seen in the Dow Jones industrials versus the Dow Jones Utilities, when the Utilities indicate a downturn in the economy in advance of any sign in the DEFIANT price pattem. The prices of the S&P 500 are also watched closely in conjunction with the 30-year US. Treasurj bonds. When bond prices fall, the S&P cant be far behind. The underljing relationship of two maitets that make divergence important can also be represented technically by the slope of trendlines and the alignment of relative peak prices.

An unsmoothed momentum chart has as many irregular ups and downs as a normal price chart and is often

subjected to the same analjsis. Trendlines are drawn across the tops and bottoms of chart sections and can be interpreted in a manner similar to their price counte arts (as shown in Figure 6-141, with two significant differences:

1. The trend of a momentum chart shows the speed of the trend, but allows us to see the rate of change of price. For example, an unchanged momentum value of +. 10 is actually a steadj increase of + . 10 in the relative price level; that is, a price sequence of 102.20, 102.30, 102.40.... would show a momentum of +. 10 and would appear as a horizontal line on a chart. In this example, the change (momentum) is. 10, but the rate of change (acceleration or deceleration) is 0. When the momentum increases, the rate of change is positive; a downtrend in the momentum means that the rate of change is negative. A steadj uptrend in the momentum means that price

FIGURE 6-14 Diveience of price and momentum.The trendline drawn aaoss the price moves (panel a) and the corresponding momentum (panel b) and MACD (panel c) indicators shows that the directions diverge.

; rhartcreatedwitiiTra.leibtiouby-liieeaEe -irch.bc

movement is accelerating at a steadj rate (for 1 , a gain of. 10 the first day, 20 the second day, .30 the third, and so on), moving faster and faster, a situation that is not likely to continue; therefore, these periods are relatively short-lived.

2. The diveience between the price trend and momentum trend creates a very strong indicator of impending change in the direction of the price trend. A bearish diveience occurs when prices continue higher, while momentum moves lower. This is tjpically seen by drawing a trendline above the rising tops of the prices, as shown in panel a of Figure 6-14, andabove the falling tops of the momentum indicator, seen in panels b and of Figure 6-14. The reason for this pattem is that prices are actually rising at a slower rate, causing the new price peaks to be farther apart.

Figure 6-14 gives three examples of diveience using two different momentum indicators, the difference between prices and a single moving average (Figure 6-14, panel b). and an MACD, the difference between two moving averages (Figure 6-14, panel c). The classic example is in die center of the chart, where prices make new highs near the close of 10/22, while both of the momentum indicators show lower peaks. In classic diveience the trendlines drawn on the price chart must be in absolute contrast to the direction of those drawn on the momentum chart. That is, one must be going up and the other down. The failure of momentum to make a corresponding high peak indicates a downturn in prices.

On the left side of Figure 6-14 is a bullish diveience, in which prices make new lows while the momentum indicators rise. In this case, the MACD is much stronger than the standard momentum. On the far right, a bullish diveience appears in the center panel but not in the MACD indicator. Standard momentum indicates a modest rise in value while the MACD declines quickly. Not all changes in price direction are identified by the diveience of price and momentum, but it remains a valuable tool.

We can distinguish between a stronger and weaker diveience by measuring the difference in the relative angles of the two trendlines, but mostly by the momentum trendline. In a bearish diveience situation, the price trend is normally increasing at a slow rate, and becoming slower When the momentum drops quickly there is a strong