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diveience and the price rise is quickly ending. Slope Diveience

To change an inte retive analjsis to one that can be computerized, there are two techniques, one using slopes and the other based on the analjsis of peaks. A comparison between the rate at which prices and a momentum indicator are rising or falling will give enough information to automatically identifj a diveience. Using a linear regression feature in either a sjreadsheet (otS] ope) or a strategj testing program (taLi nea rRegSI ope), the slope of any time interval can be found for both momentum and price over the same period. Because momentum is a detrended series, the period compared should not be too long; otherwise, the slope of the trendline will be zero, a horizontal line. Instead of the trendlines that appear above and below prices and momentum in Figure 6-14, the regression lines will pass through the center of the price movement.

Diveience can be any combination of conflicting directions between the slope of price and the slope of momentum, including prices rising faster than momentum, momentum rising faster than prices, or the opposite. However, classic analjsis has focused on momentum as a leading indicator of a change in the price trend, whidi limits the combinations to"

1. Prices rising and momentum failing (a bearish divergence)

2. Prices falling and momentum rising (a bullish diveience)

The strength of a bearish diveience, which can be used to select which situations are best for trading, can he determined bv the momentum slope provided prices are rising, or the net of the rising slope of prices and the falling slope of momentum. In the second case, the difference between the slopes must be converted to a common denominator, because the angle of price movement can cover a far wider range than the angle of momentum movement.

Diveience Using Peak Comparisons

The identification of diveience for a short-term trader is very, different fran ihe slope technique ihat applies to the major moves seen in the Dow Jones Industrials and Utilities this application, the peaks (or vallejs) of any momentum indicator are compared aaainst the corresponding peaks (or vallejs) of the price series (upon which the momentum was calculated), if the momentum peaks are declining and the price peaks are rising there is a diveience, In Figure 6-14 the ups and downs befcveen the peaks are ignored, and only the points at which the prices form swing highs and lows are compared with corresponding momentum values.

it is easier to find diveience by looking at a chart on a quote screen than to program it into a computer. Translating what you see into a sjstematic analjsis of diveience signals is very difficult. There are a number of steps necessary for signaling a bearish diveience:

1 . Identifj each momentum peak and record its value, MPi. The standard approach to finding a momentum peak is to locate each momentum value that is higher than the previous n values and higher than the next n values. In addition, the first momentum peak of a sequence must be above a threshold level, for example 80, to assure that an oveibought situation has occurred- It seems reasonable that all momentum peak values should be greater than some level for example 50. to avoid having alreadj reached the correction objective before a position can be entered (see Step 4).

2. Identifj the price peaks corresponding to each momentum peak. PP,. This is done in the same way as Step 1 oi the corresponding value of the price can be used, assuming that it produced a peak.

3. Compare the last momentum peak, MP,, with the previous momentum peak. MPi -, and their corresponding prices, PPi andPPi -, A bearish diveience exists if PPi -PPi -, and MP, =:MPi -, A stronger diveience exists ifMP:~MPiislaier

4. Enter a short position when the diveience is identified, provided prices have not alreadj reached the correction level or anticipated profit. This fourth step points out a problem in this method of finding a diveience. The need to wait a number of days after a momentum high will cause many- of the signals to be too late. Although the price may have been higher at the time of the second peak, the lag needed to recognize the

next declining momentum peak gives the price a chance to correct before a signal can be generated.

5. Exit the short position when the current momentum moves above the last momentum peak. This new momentum high indicates that the diveience. used as the entrj criteria, has disappeared and there is no basis for this trade. The exact price at which this occurs cannot be calculated in advance.

6. Exit the short position when the market has corrected or an objective has been reached. Once the momentum has declined to the midpoint level of 50 for the RSI and stochastic, it should be considered neutral and cannot be expected to continue on to negative values. A price objective can be set using volatility or support levels.

Single, Double, and Triple Diveiences

In fewer cases, double and triple diveiences will occur. A double diveience is one in which three momentum peaks are declining and price is rising in each case. Most often, the second momentum peak is only slightly lower than the first, and the last peak drops off indicating that price is soon to follow. Multiple diveiences are expected to be more reliable than single, and represent a prolonged period in which prices are rising at a slower and slower rate.

Alternating Diveience Pecks

A common pattem is that there is a lower momentum peak between two declining peaks. For example, the first momentum peak is at 90, the next at 60, and the last at -5. When studjing the chart manually, most analjsts will ignore the lower peak in the middle and consider the 90-75 diveience. This combination can be automated by looking at the most recent momentum peak, i, and the one back 2, i - 2, along with their corresponding prices.

Converting aDiveience into a Trend Trade

Diveience trades represent a clear chart pattem of slowing price direction. At the same time they are countertrend trades and have a higher degree of rid;. Before the October 1987 stock plunge, there were numerous diveience signals in the S&P, both long-term and short-term, and many traders posted losses trying to sell what might have been the top of the martlet. Most gave up before the decline. If, in fact, the greatest opportunities come when the diveience is strong, that is, the decline in the momentum peaks is laie. then the best results will come from entering a short position, then holding that short when a long frend turns to a short one. By entering the trend frade early (and exiting the old long position), a diveience can become a laie profit rather than a small one


When Blaus work on double smoothing was discussed in the section "True Sfrength Index," it was still being compared with other momentum indicators. The most important part of his woric however, is in using price change as a substitute., or proxj, for prices themselves, then smoothing them to define the trend. A long-term moving average, applied to prices, produces a lag of one-half the period of the moving average, that is, a 200day moving average has a lag of 100 dajs.

The same moving average technique applied to price change, or momentum, gives very different results because price changes, also called first differences, remove the underljing trend and make price movement more sensitive. Appljing a long-term moving average to momentum is an excellent substitute for price, yet it oscillates around the average value of zero in a manner similar to other momentum indicators

Double Smoothing of Momentum

Double smoothing of momentum is an extension of normal momentum smoothing, and results in a value that has less noise than the original momentum series, and retains its lowlag characteristics, provided that one of the smoothing periods is very laie. Double smoothing of momentum can he a smooth substitute for price, without a significant lag (see Figure 6-12). The shape of Blaus True Strength Index (TSI), first smoothed over a 300day period then smoothed again over a 5-day period, closely approximates the result of a 5-day exponential smoothing (EMA). When applied using the same smoothing periods, this can be very useful for identifjing diveience between two martlets. In Figure 6-15 the trend of the TSI line is still up at the end of Februarj 1994, making anew high in both

FIGURE 6-15 Double-smoothed momentum applied to the Dow Jones Average and Dow Jones Utilities, showing divergence.

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the prices and indicator, while the utilities are steadily heading lower. In December 1994 there is a turn up in the TSI for the utilities that will lead the D A throughout 1995.

TSI (close, 300,5) =

100 X (gSmoothedAverage((gSmoothedAverage(close - close[l])3Q0),5) @Smoo(hedAverage(@Smoo(hedAverage((aabs(close - close(ll),300),5)

When the 5-day momentum is replaced by a 1-day momentum, or the daily price changes, the second smoothing can be any length, and the result is a very effective substitute for a moving average of price with the significant added advantages of a detrended series, lower noise, and less lag. When plotted, the series fluctuates around the value zero unless there has been a strong trend during the full period, as in the stock index


Momentum and oscillators are not the only tools for determining oveibought and oversold conditions. Because they can be very different from either a charting technique or moving averages, they have taken their place as timing indicators within other more structured sjstems. When the time interval for calculation is small, these indicators can be highly unstable, jumping from frequent oveibought signals to just as frequent oversold ones. Both faster and slower speeds have the problem of rid; confrol. The method implies that a position be entered contrarj to the direction of price movement. Although chart interpretations attempt to remedj this, unusually laie losses may result.

It is not likely that an indicator can be found that will identifj only the trades that Will be profitable. It is far more likely that an indicator will add more pattems to the alreadj difficult combinations that are seen in price: therefore, it is not clear whether an indicator will simplify trading or make it more complex, if you need to interpret the indicator because each situation creates new decisions, then youve got the wrong one.

indicators can be designed to reach extremes when a specific situation occurs. During other times it tells us nothing. One practical use of any oscillator is to show when a market is relatively oveibought or oversold, if you are using a trending approach, and each frade is held about 20 dajs, an oscillator can be tuned to provide entry timing. For example, if you are willing to wait up to 2 dajs to enter a long position based on the daily close, then construct a 10-period oscillator of 5-, 10-, or 15-minute data. Test the oscillator to see if it generates at least one, but preferably two, oversold signals during each 2-day period. If so, use it to time your entry and you are likely to be bujing dips rather than rallies.

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