feature, a change of velocity (or momentum) can be detected,or the strength of a current price move can be confirmed.
Quick Calculation of Velocity and Acceleration
‘A less precise but very convenient way of determining velocity and acceleration is the cal-culation of first and second differences. The purpose of these values is to find more sensi-tive indicators of price change, and most traders will find this quick calculation satisfactoryThe results can be used in exactly the same way as the formal mathematical results. Con-sider the following examples:
1. A price series 10, 20, 30, 40, . .. is moving higher by a constant value each day. The
  
first differences are 10, 10, 10, . .. , showing a consistent velocity of 10. ‘The second
” differences, formed by subtracting sequential values in the first-difference series,
a are 0, 0, 0,..., showing that there is no change in speed; therefore, the accelera-- tion is 0.
and weighted moving averages, and exponential smoothing all have constant velocities. 2. Another price series is shown with its first and second differences a
Only those equations with second-order smoothing will work.
‘yihee the process of differentiation is reapplied to the equation for velocity, it results i
 
in the rate of change of the speed with respect to time, or acceleration. This type of accel- cof 2 3 4S é 78 eieration tells whether the velocity is increasing or decreasing at any point in time. The accel- 5 10 15 20 30 45 5045 352~C«‘H SAOeration, also called the second derivative, adds another dimension to momentum and may v 45 8 HHO IS 5 SH 1 SHH HHSimprove the timing of trades. ~ A 0 +5 45-10-10 -5 o +5 +O +10
Let’s assume that the velocity and acceleration have_been calculated blfollowing are the possible combinations that can occur: ~ Cable 6-2). Thewhere S is the price series- Vis the velocity (first differences)
——
 
“ fee ws Price Movément . ‘Ais the acceleration (second differences)
+ ri i -+ ° Price i moving up x consent rte se ‘The original series $ bas two turns in trend clearly shown by the velocity and accelera-+ - Price is moving up at a decreasing rate tion, The velocity V continues to be positive through the sixth value as the underlying0 0 Price is static price moves from 10 to 50. Whenever prices change direction, the velocity changes- + Price is moving down at a decreasing rate sign. The basic upward trend can be associated with a positive velocity and a down-- ° Price is moving down at a constant rate ward trend with a negative one. ~
 
The acceleration, or second difference, shows the change in speed. At the sixth
Price is moving down at an increasing rateitem, the acceleration becomes negative, even though the velocity was positive,
  
152MOMENTUM AND OSCILLATORS
becmse Prlees moved higher ata slower rate, They had been gaining by 5, 10, and 15fay, but on day 6, the gain was only 5 points. Thi in acceltwas a leading indicator ofa trend change Asimila stenstion oneaed on day chand ge. A similar situation occurred on daacceleration slowed and reversed on day 10, one day ahead of the actual wee wee
The relatios ‘tween velocity and acceleration using first and second differe:lationship between veloci ce in using ncescan be interpreted using the same logic as previously di locity cceleration,liscussed. Vel: and aare increasingly more sensitive directional indicators; the slightest variation in price move-
ment will cause the acceleration to reve: it is an indi great value whenn to reverse. Itis icator of ¢ when it is used.
OTHER RATE-OF-CHANGE INDICATORSProjected Crossovers
If movi{Emoving averages can successfully be used to identify the trend direction, i fllows th(¢ moving average will be valuable in anticipating when the trends will
change. If a moving ave irage trading strategy used a single tw i icstandard N-day moving average line would cross the ree cern the price at which the
_ sumotisen prices (5,74)
N-1 W-1
CPL
7 ; ,‘0 calculate the price at which two moving averages would cross requires the following:
cpz = WX (sum of last N- 1 prices) ~ M x (sum of last M ~ 1 prices)@t—-N)where Nand M are the lengths of the two moving averages.*cca projected crossover price is most useful when it is likely that a trend change willoccur within a few days that is, when the two moving averages begin converging andin value. Acting on the expected price would give the trader a great advan-
tawe i d <‘age in order execution. A plot of this, however, may not be much different than a simple
relative strength measurement. The differe! etween the price and the mor erasle th The difference b n the price and the moving average'¢ change in the proje SSOVE ons a more valuable tool by Lambert.The ch the projected crossover is considered valuabl | by Lamb:He creates a Market Direction Indicator (MDI) with the following formula:
Mpy = 100. (crossover pricepreviou — CFOSSOVEF Price edn)average of past 2 day’s prices
The point at which the MDI: : crosses the zero lin ing hi i iPaint at which it crosses moving lower is a sell signa, Baber isa buy signal, and the
Combining a Trend and Oscillator - ~
Directional Parabolic System
The Directional Paraboli tiic Systern®® is a combinati f
The Direction ination of two of Wilder's well-known tech-niques, Directional Movement and the Parabolic Time/Price System Directional Movensent
ly in Chapter 23. It gained popularity as a method of selecting the commodi°° Donald R, Lambert, “The Com :
3 a Market Directional ‘Tndicator,” Technical Ana:wn December 1983). This article also contains a BASIC computer Foren nen won es WovenJ. Welles Wilder, Js., Chart Trading Workshop 1980 (Trend Research, Greensboro, NC, 1980) .
 
OTHER RATE-OF-CHANGE INDICATORS 153
ties that were most likely candidates for trend-following systems. The Parabolic Time/Pricesystem is covered in Chapter 17 (“Adaptive Techniques”). ‘Although a full reading of bothtechniques are necessary, the essence of the combined systems can be understood with thefollowing definitions:
4DI14_ The 14-day upward Directional Index-DI14 The 14-day downward Directional Index‘ADX The average Directional Movement IndexDPS _ The Directional Parabolic stop
Although shown as -DI14, the downward Directional Index is a positive number based onthe sum of those days that closed lower. The ADX is a ratio of those days that closed highersuith those that closed lower over the past 14 days. The ADX is an oscillator based on thesealed ratio of +DI/-DI. The two systems combine according to the following rules:
1. If the ADX is up (the +DM14 is greater than the -DM14), take only long ParabolicSystem trades; if the ADX is down, take only short trades.
2. Ie the two systems conflict, no trade is entered. A trade may be entered at the timethey agree.
3, Ifa position is held, the Parabolic stop is used. (The stop is now called the DPS in-stead of the SAR, because it no longer requires a reversal of position.)
4. Ifno position is held, the Directional Movement equilibrium point is used (the highor low of the day on which the +DM14 crosses the -DM14).
Directional Parabolic RevisionIn 1980, the entry rules were revised to include an added use of the ADX when it is greaterthan the +DI14 or the ~DI14. Because the ADX serves as an oscillator and indicates turningpoints in the trend, when the ADX exceeds the magnitude of the current +DI14 or -DI14end reverses, the current position should be closed out. If the ADX remains above both theD114 and —DI114, the market is extremely strong and liquidation should stop. T! ‘the ADX isintended to be a leading indicator for liquidation only. Reversal of the current positiononly occurs when the Parabolic stop has been penetrated, and the new trade agrees withthe direction of the Parabolic System. -
‘The addition of an oscillator to a trend-following system allows trades to be closed outat more favorable positions than the usual trend exits, If the new direction carries throughand the position is reversed, the added feature has worked perfectly; however, if pricesturn back in the original direction, a reentry may not be possible. The revised rules areUnclear concerning reentry into a position if prices fail to penetrate the DPS and signal areversal, A reentry might occur if the ADX falls below both the +D114 and —D114, indicat-ing that prices are no longer extreme, then turns back in the trend direction. Once reestab-lished, 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 byone commodity trading advisor.” It is intended to identify an early reversal of the currenttrend by combining the following indicators (applied to an existing uptrend):
1. An outside reversal day (a higher high followed by a lower close)__ 2, Wilder's RSI must exceed 60% (moderately overbought)3. Volume and open interest must be increasing .
1” Blias Crim, “Are You Watching the ‘Right’ Signals?” Futures Qune 1985) 
154MOMENTUM AND OSCILLATORS.
The result is a high likelihood of a downward trend reversal (the opposite applies toigh (the op i
upward trend reversals). Protectiupward trend reversals) ctive stops are placed above the high of the hook on the day
MOMENTUM DIVERGENCE
Divergence is a concey ilipt familiar to mostDivergence a traders. It is frequenth iindustria 5 versus the Dow Jones Utilities, when the Utilities inclicaee a dows fun in theeconomy in adva ce of any sign in the DJIA price pattern. The prices of the S&P 5 00 weealso watched <l osely in conjunction with the 30-year U.S. Treasury bonds. whe a bondprices fl the S ? can nt be ar behind. The underlying relationship of two marke chatt remal ‘te rergence imporsant can also be ¢ presented technically by the slope of trendlinesunsmoothed momentum chart has i rmaics ! : as many irregular ups andPre and vis often Subjected to the same analysis. ‘Trendlines ore deen “serose thep sections and can be inte i ilar to theirprice counterparts (as shown in Figure 6-0), with ew significant diferencess nTces:
1. The trend of a momentuim chart shows thethe rar v speed of the trend, bthe rate of change of price, For example, an unchanged momenumvaee wieof 102-20, 102. 5 onto to of +.10 is inet relative price level; that is, a price sequence20, 102.30, 102.40, .. . would show a mom: aas a he i entum of +. 1!the porizontal line on a chart. In this example, the change (Guomenton i to, butthe rate of change (acceleration or deceleration) is 0. When the Tmomencura inn‘reases, the rate of change is positive; a d 2 entum in-the ; a downtrend in theSe ee een eens that price
 
FIGURE 6-14 Divergence of and momentum. The trendline drawnE Be price tur e thacross the price
moves (panel a) and the corresponding momentum (panel b) and MACD (panel c) indicato:1g ) ( :) indicators
   
{ BUNDS6,.TXT-15 min061/98 C=102.38 +18 O=102.48 1102.44 L=102.18
     
(a)
(b)
 
. .CD-PUK 0.0083, “ ——6 PO.wrnggapay lly acl ayo aapNeat ne ae Tas2 "i0R3 horas “ions
 
 
Source: Chart created with TradeStation® by Cmega Research, Inc.
 
MOMENTUM DIVERGENGE 155
 
movement is accelerating at a steady rate (for example, a gain of .10 the first day,the second day, .30 the third, and so on), moving faster and faster, a situation that isnot likely to continue; therefore, these periods are relatively short-lived.
2. The divergence between the price trend and momentum trend creates a verystrong indicator of impending change in the direction of the price trend. A bear-ish divergence occurs when prices continue higher, while momentum moveslower. This is typically seen by drawing a trendline above the rising tops of theprices, as shown in panel @ of Figure 6.14, and above the falling tops of the mo-vrentum indicator, seen in panels b and ¢ of Figure 6-14, The reason for this pat-tern is that prices are actually rising at a slower rate, causing the new price peaksto be farther apart.
Figure 6-14 gives three examples of divergence using two different momentum indica-tors, the difference between prices and a single moving average (Figure 6-14, panel b), andan MACD, the difference between two moving averages (Figure 6-14, panel c). The classicexample is in the center of the chart, where prices make new highs near the close of 10/22,‘chile both of the momentum indicators show lower peaks. In classic divergence the trend-Tines deawn on the price chart must be in absolute contrast © the direction of those drawn.on the momentum-chart. That is, one must be going uP and the other down. The failure ofsromentum to make a corresponding high peak indicates a downturn in prices.
‘On the left side of Figure 6-14 is a bullish divergence, in which prices make new lowswhile the momentum indicators rise. In this case, the MACD is much stronger than thesvandard momentum. On the far right, a bullish divergence appears in the center panel butnot in the MACD indicator. Standard momentum indicates a modest rise in value while theMACD declines quickly. Not all changes in price direction are identified by the divergenceof price and momentum, but it remains a valuable tool.
We can distinguish between a stronger and weaker divergence by measuring the difference in the relative angles of the two trendlines, but mostly by the momentum trend-line. In a bearish divergence situation, the price trend is normally increasing at a slow rate,and becoming slower. When the momentum drops quickly there is a strong divergenceand the price rise is quickly ending.
Slope Divergence
‘To change an interpretive analysis to one that can Pe computerized, there are two tech-niques, one using slopes and the other based on the analysis of peaks. A comparisonelween the rate at which prices and a momentum indicatoy 46 rising or falling will giveenough information to automatically identify a divergence Using a linear regression fea-fure in either a spreadsheet (@51ope) or a strategy testing program (@LinearRegs1ope), theslope of any time interval can be found for both momentum and price over the sameperiod. Because momentum is a detrended sens, the period compared should not be tooTong: otherwise, the slope of the trendline will be zero, a horizontal line, Instead of theteonilines that appear above and below prices and momentum in Figure 6-14, the regression lines will pass through the center of the price movement
Divergence can be any combination of conflicting directions between the slope ofprice and the slope of momentum, including prices rising faster than momentum, momen-fam rising faster than prices, or the opposite. Howeviss ‘classic analysis has focused onvnomentum as a leading indicator of a change in the price trend, which limits the combi-nations to:
1. Prices sising and momentum falling @ bearish divergence)2. Prices falling and momentum rising (@ bullish divergence) 
 
156 MOMENTUM AND OSCILLATORS.
The strength of a bearish divergence, which can be used to select which situations are bestfor trading, can be determined by the momentum slope provided prices are rising, or thenet 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 momentummovement.
Divergence Using Peak Comparisons
The identification of divergence for a short-term trader is very different from the sl petechnique that applies to the major moves seen in the Dow Jones Industrials and Utilities.In this application, the peaks (or valleys) of any momentum indicator are comparedagainst the corresponding peaks (or valleys) of the price series (upon which the momen-tum was calculated). If the momentum peaks are declining and the price peaks are risingthere is a divergence. In Figure 6-14 the ups and downs between the peaks are ignored,and only the points at which the prices form swing highs and lows are compared with cor.responding momentum values.
It is easier to find divergence by looking at a chart on a quote screen than to programit into a computer. Translating what you see into a systematic analysis of divergence signalsis very difficult. There are a number of steps necessary for signaling a bearish divergence:
 
1. Identify each momentum peak and record its value, MP,. The standard ap-proach to finding a momentum peak is to locate each momentum value that ishigher than the previous values and higher than the next 7 values. In addition, thefirst momentum peak of a sequence must be above a threshold level, for example80, to assure that an overbought situation has occurred. It seems reasonable that allmomentum peak values should be greater than some level, for example 50, to avoidhaving already reached the correction objective before a position can be entered(see Step 4).
2. Identify the price peaks corresponding to each momentum peak, PP,. This isdone in the same way as Step 1 or the corresponding value of the price can be used,
assuming that it produced a peak.
. Compare the last momentum peak, MP,, with the previous momentum peak,MP,_ 1, and their corresponding prices, PP, and PP,_,. A bearish divergence ex-ists if PP, > PP,, and MP, < MP,_,. A stronger divergence exists if MP,_, — MP, islarger.
4, Enter a short position when the divergence is identified, provided prices havenot already reached the correction level or anticipated profit. This fourth steppoints out a problem in this method of finding a divergence. The need to wait anumber 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 lagneeded to recognize the next declining momentum peak gives the price a chance tocorrect before a signal can be generated. -
5. Exit the short position when the current momentum moves above the lastmomentum peak. This new momentum high indicates that the divergence, usedas the entry criteria, has disappeared and there is no basis for this trade. The exactprice at which this occurs cannot be calculated in advance.
6. Exit the short position when the market has corrected or an objective hasbeen reached. Once the momentum has declined to the midpoint level of 50 forthe 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 sup-port levels.
ye
 
7MOMENTUM SMOOTHING 157
Single, Double, and Triple Divergences
In fewer cases, double and triple divergences will occur. A double divergence is one inwhich 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 offindicating that price is soon to follow. Multiple di ergences are expected to be more reli-able than single, and represent a prolonged period in which prices are rising at a slower
and slower rate.
  
Alternating Divergence Peaks _‘A common pattern is that there is a lower momentum peak between two declining peaksFor example, the first momentum peak is at 90, the next at 60, and the last at 75 erstudying the chart manually, most analysts will ignore the lower peak in the middle anconsider the 90-75 divergence. This combination can be automated by looking at the mostrecent momentum peak, 4, and the one back 2, i — 2, along with their correspondingPrices.
Converting a Divergence into a Trend Trade a ten
i trades represent a clear chart pattern of slowing price direction. At the sameume wey are countertrend trades and have a higher degree of risk. Before the October1987 stock plunge, there were numerous divergence signals in the S&R, both long-termand short-term, and many traders posted losses trying to sell what might have been the topof the market. Most gave up before the decline. If, in fact, the greatest opportunities comewhen the divergence is strong, that is, the decline in the momentum peaks is large, thenthe best results will come from entering a short position, then holding that short when along trend turns to a short one. By entering the trend trade early (and exiting the old.longposition), a divergence can become a large profit rather than a small one.
MOMENTUM SMOOTHING
When Blau’s work on double smoothing was discussed in the section, “True StrengthIndex,” it was still being compared with other momentum indicators. The most importantpart of his work, however, is in using price change as a substitute, or proxy, for prices rem.selves, then smoothing them to define the trend. A long-term moving average, app ed toprices, produces a lag of one-half the period of the moving average; that is, a 200-day mov-as a lag of 100 days. .‘ss The - aie moving average technique applied to price change, or momentum, sivesvery different results because price changes, also called first differences, remove thunderlying trend and make price movement more sensitive. Applying a Jong.term m nin 8average to momentum is an excellent substitute for price, yet it oscillates arounage value of zero in a manner similar to other momentum indicators.
Double Smoothing of Momentum
moothing of momentum is an extension of normal momentum smoothing, andreulsin value that has less noise than the original momentum series, and retains is low:Jag characteristics, provided that one of the smoothing periods is very lange. Doublsmoothing of momentum can be smooth substitute for price, without a significant lag(see Figure 6-12). The shape of Blau’s True Strength Index (TSI), first smooth ed over a300-day period, then smoothed again over a 5-day period, closely approximates the resultof a 5-day exponential smoothing (EMA). When applied using the same smoothing pertods, this can be very useful for identifying divergence beween two markets. In Figure § 15the trend of the TSI line is still up at the end of February 1994, making a new high in 
158 MOMENTUM AND OSCILLATORS.
 
FIGURE 6-15 Double-smoothed momentum applied to the Dow Jones Average andDow Jones Utilities, showing divergence. t
 
     
  
ere ees
O71 86 C=5729.980 +75.351 O=5670.141 H=S749.191 L=S637.262
Lengthy W/V
    
 
[True Strength index 18.81
        
 
x]xal\olz
 
Cereslo7s01/96 C=220.650 +350 0=220.720 H=221.560 L=218.840Ts : .
at tet
yet nema enen Maggette
HTrue Strength index 7.25
 
 
bu FW
     
 
Source: Chart created with TradeStation® by Omega Research, Inc:
the prices and indicator, while the utilities are steadily heading lower. In December 1994there is a turn up in the TSI for the utilities that will lead the DJIA throughout 1995.
TSI(close,300,5) =
100 x @SmoothedAverage(@Smoothedaverage (close — close{1]),300),5)@SmoothedAverage(@Smoothedaverage (@abs (close ~ close[1]),300),5)
When the 5-day momentum is replaced by a 1-day momentum, or the daily pricechanges, the second smoothing can be any length, and the result is a very effective substi-tute for a moving average of price with the significant added advantages of a detrendedseries, lower noise, and less lag. When plotted, the series fluctuates around the value zerounless there has been a strong trend during the full period, as in the stock index.
 
SOME FINAL COMMENTS ON MOMENTUM _
Momentum and oscillators are not the only tools for determining overbought and oversoldconditions. Because they can be very different from either a charting technique or movingaverages, they have taken their place as timing indicators within other more structured sys-tems. When the time interval for calculation is small, these indicators can be highly unsta-ble, jumping from frequent overbought signals to just as frequent oversold ones. Bothfaster and slower speeds have the problem of risk control. The method implies that a posi-tion be entered contrary to the direction of price movement. Although chart interpreta-tions attempt to remedy this, unusually large losses may result.
It is not likely that an indicator can be found that will identify only the trades that willbe profitable. It is far more likely that an indicator will add more patterns to the already dif-ficult combinations that are seen in price; therefore, it is not clear whether an indicator willsimplify trading or make it more complex. If you need to interpret the indicator becauseeach situation creates new decisions, then you've got the wrong one.
159SOME FINAL COMMENTS ON MOMENTUM
Indicators can be designed to reach extremes when a specific situation occurs. Duringother times it tells us nothing. One practical use of any oscillator is to show when a marketis relatively overbought or oversold. If you are using a trending approach, and each tradeis held about 20 days, an oscillator can be tuned to provide entry timing. For example, iyou are willing to wait up to 2 days to enter a long position based on the daily close, thenconstruct a 10-period oscillator of 5-, 10-, or 15-minute data. Test the oscillator to see if itgenerates 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 buying dips rather than rallies. 
 
Seasonality
hapter 3 introduced prices as a time series and identified its four components as thetrend, the seasonal pattern, the cycle, and the chance movement; it included variousways of finding the trend using statistical analysis and forecasting techniques. Chap-ter 4 then showed various ways to calculate trends. Of all techniques, the trend is over-whelmingly the most popular foundation for trading systems. In this and Chapter 8 we willturn our attention to two other principal components, the seasonal and cyclic movements.Seasonality is a cycle that occurs yearly. It is most often associated with the planting andharvesting of crops, which can directly affect the feeding and marketing of livestock. Nor-mally, prices are higher when a product is not as readily available, or when there is a greaterdemand relative to the supply, as often occurs with food during the winter months. For grain,the season is dominated by planting, harvesting, and weather-related events that occur inbetween. Most crops have been produced in the Northern Hemisphere, but South Americansoybeans and orange juice have become significant factors since the early 1980s, as have Aus-tralian and New Zealand beef and lamb, resulting in a structural change in seasonal patterns.Globalization has not only affected financial markets, but nearly everything we purchase. ;Consumer habits can cause a seasonal pattern in metals and stocks as weather does foragricultural products. Passenger airline traffic is much heavier in the summer than in thewinter, and profits of that industry, especially companies not diversified, reflect seasonal-ity, Eastman Kodak once had a classic pattern caused by much more active picture takingduring the summer months, when most workers take vacations. This seasonal activity alsoincreased demand on silver, a major ingredient of film coating, which developed a co-dependent pattern before a substitute was found. -
A CONSISTENT FACTOR
Even when the impact of seasonality on agricultural products is not clear from the pricepatterns, it is still there. Consider the following factors that do not change:
1. More corn, wheat, and soybeans are sold during harvest than at any other time of year
“because there is not enough available storage to hold all of the new crop. Rental stor-age, when available, requires a minimum three-month charge. Lack of storage and theneed for immediate income result in greater sales and cause prices to decline.
2. Because feedgrains are’harvested only once each year, forward contracts include astorage cost as part of the total carrying charge. Therefore, each forward deliveryprice should be higher within the same crop year.” -
Sometimes the price pattern of forward months does not seem to reflect the addedCosts of carry. Occasionally these markets will even invert and the nearest delivery will tradeata price higher than the deferred months, a situation familiar to crude oil and copper. TheCost of carry, however, still exists in an inverted or backwardation market. Extreme short-term demand pushes the nearest delivery much higher, while the events causing price dis-ruption are expected to be temporary. The normal carry is still there, it is just overwhelmedby temporary demand.
 
POPULAR METHODS FOR CALCULATING SEASONALITY 161
It is important to be able to identify seasonal patterns. The methods for finding themare simple, and made more so by the use of a spreadsheet and a computer. These will bediscussed in this chapter along with some practical applications.
THE SEASONAL PATTERN
Seasonal patterns are easier to find than the longer-term cycles or economic trends,because they must repeat each calendar year. Although any 12-month period can be usedto find the seasonal pattern, academic studies usually begin with the new crop year forgrains, just following harvest, when prices tend to be lowest. This approach will make thecarrying charges, which increase steadily throughout the new crop year, more apparent.For uniformity, the examples in this chapter will always begin with a calendar year, whichassumes no knowledge of where the season starts, and can be equally applied to stocks. Itwill always include carrying charges as an integral part of the market price.
United States agricultural production is considered to be the standard for seasonal,even though a wheat crop is harvested continuously throughout the year in different partsof the world. Prices are expected to be lower during the U.S. harvest and highest duringthe middle of the growing season. The influence of world stocks and anticipated harvestfrom other major producers in South America or Russia will cause an overall dampeningor inflating of prices, rather than change the seasonal pattern. While the costs of trans-porting grain to the United States is not practical, except for special products, each pur-chaser in the world market will select a supplier at the best price. This fungibility has adirect impact on the U.S. market, which must alter its local price based on export demand.
Industrial commodities have seasonal price variation based on demand. Silver, althoughincreasingly used in electronics as a conductor,