trend.
A similar example occurs in the way prices react to economic reports or governmentaction. The first time the Federal Reserve acts to raise rates after a prolonged decline themarket is not prepared and bond prices react sharply lower. Before the next meeting of theFed the market may be more apprehensive, but is likely to be neutral with regard to expec-tation of policy. However, once there is a pattern of increasing rates following signs of infla-tion, the market begins to anticipate the action of the Fed. The sharp move occurs whenthe government fails to take action.
Testing Your Skill
Recognizing.a pattern is both an art and a science. Not everyone has ah eye for patterns;others will see formations where no one else would. The first decision may be the mostimportant: How much of the chart do you use? It is perfectly normal for different timeintervals to show different trends. In some cases, arbitrarily cutting the chart at some pre-vious date might cause a clear trend to disappear. The price scale (the vertical axis) of thechart is another variable not considered by some chartists. When applying methods requir-
Jesse H. Thompson, “What Textbooks Never Tell You,” Technical Analysis of Stocks & Commodities (November/December 1983). 
236 CHARTINGing specific angles, the chart paper is expected to have square boxes. Regardless of theshape of the box, the formations will appear very different from one piece of chart paper,or computerized page, to another. ,
The timeliness of the pattern identification is the most serious problem. Can the for-mation be interpreted in time to act on a breakout, or is the pattern only seen afterward?At different stages of development, the lines may appear to form different patterns. Before
using your charting skills to trade, practice simulating the day-to-day development ofprices as follows:
1. Hold a piece of the paper over the right side of the chart, covering the most recentmonths, or better still, have someone else give you the partial chart.
2. Look at the chart and analyze the formations.
3. Determine what action will be based on your interpretation. Be specific.
4. Move the paper 1 day to the right, or have someone else give you the next day'sprice.
5. Record any orders that would have been filled based on the prior day's analysis.Don’t cheat.
6. Determine whether the new day’s price would have altered your formations andplans.
7. Return to step 3 until finished.
This simple exercise might save a lot of money but may be discouraging. With practiceyou will become better at finding and using formations and will learn to select the onesthat work best. Very few traders base their trading decisions entirely on bar charts. Manyrefer to charts for confirmation of separate technical or fundamental analysis; others willonly use the most obvious major trendlines, looking for points at which multiple indica-
tors converge. The general acceptance of bar charting analysis and the need for visualiza-tion makes it a lasting tool.
10
Volume, Open Interest,and Breadth
 
futures markets. It is a valuable piece of information that is not often used, and one
of the few items, other than price, that is traditionally considered valid data for thetechnician. Nevertheless, there has been little research published that relates this factor tofutures markets; its popular use has adopted the same conclusions as in stock marketanalysis.
The stock and futures markets have two other measures of participation that arerelated, yet not the same. In equities, the large number of shares being traded allow formeasurements of breadth. In the same way that the stock index has become a popularmeasure of overall market trend, the breadth of the market is the total number of stocksthat have risen or fallen during a specific period. When you have the ability to view the big-ger picture of market movement, breadth seems to be the natural adjunct to the index.
In futures, open interest is the measurement of those participants with outstanding,trades; it is the netting out of all open positions in any one market or contract, and it givesan understanding of the depth of volume that is possible. A market that trades only 10,000contracts per day, but has an open interest of 250,000, is telling the trader that there aremany participants who will enter the market when the price is right. These are most likelyto be commercial traders, using the futures markets for hedging.
Vee pattern has always been tied closely to chart analysis in both the stock and
CONTRACT VOLUME VERSUS TOTAL, VOLUME
In futures markets, in which individual contracts specify standard delivery months, the vol-ume of each contract is available, along with the total volume of the market; that is, thetotal volume of all individual contracts. Spread transactions are not included in volume.This information is officially posted one day late, but estimates are available for many mar-kets during the day. Total volume of crude oil is estimated every hour and released to on-line news services. .
Individual contract volume is important to determine the delivery month that is mostactive. Traders find that the best execution fills are most likely where there is greatest liq-idity, Analysts, however, have a difficult time assessing volume trends because there is anatural increase in volume as a contract moves from second month out to the nearby andtraders shift their positions to the closest delivery month; there is a corresponding declinein volume as the delivery date becomes close. Looking only at the volume of one deliverymonth is equivalent to ignoring seasonality in an agricultural market.
Fach futures market has its unique pattern of volume for individual contracts. Some,such as the interest rates, shift abruptly on the last day of the month prior to delivery,because the exchange raises margins dramatically for all traders holding positions in thedelivery month. Currencies are very different and tend to trade actively in the nearestmonth up to one or two days before that contract goes off the board. While volume 
 
238 VOLUME, OPEN INTEREST, AND BREADTH
 
increases slightly in the next deferred contract, anyone trading sizable positions will needto stay with the nearby contract to the end.
Other than for determining which contract to trade, and perhaps the size order thatthe market can absorb, an analysis of volume as discussed in this chapter must use totalvolume, the aggregate of all contracts, to have a data series that does not suffer the patternsof increasing and decreasing participation based on the coming and going of individualdelivery months. When traders roll from the nearby to the next deferred contract, thetransactions are performed as a spread, and those trades are not included in the volumefigures. Because positions are closed out in one contract and opened in another, there isno change in the open interest.
‘The stock market equivalent to using total volume would be to add the volume for allstocks in a similar group. This would help smooth over those periods when the volume ofone stock is very low. If the group is not highly correlated in price movement, the endresult might be a volume series that has very little to do with the stock you are trading.
Tick Volume
The popularity of quote machines and fast trading requires a measurement of volume thatcan be used immediately to make decisions. Because total volume is not available on atimely basis to day traders, tick volume has become a substitute. Tick volume is the num-ber of changes in price, regardless of volume, that occur during any time interval. Tick vol-ume relates directly to actual volume because, as markets become more active, priceschange back and forth more often. If only two trades occur in a 5-minute period, then themarker is not liquid, regardless of the size of the orders that changed hands. From an ana-lytic view, tick volume gives a reasonable approximation of true volume and can be used asa substieute. From a practical view, it is the only choice. Tick volume patterns are discussedlater in this chapter.
 
VARIATIONS FROM THE NORMAL PATTERNS
One final note of warning when using volume indicators to confirm price direction: mar-kets have patterns in volume that cause the same effect as seasonality. To decide that a buysignal is more important because it came near the end of the trading day, when volume wasmuch higher than midday, is not correct because volume is always higher at the beginningand end of the day. You may conclude, in general, that those two periods produce morereliable trading signals; however, a volume confirmation must be compared against thenormal volume for that time period.
Open interest and market breadth also have seasonal patterns. In agricultural markets,farmers hedge in larger numbers during the growing season than in the winter, raising theopen interest. In stocks, there isa lot of activity associated with the end-of year positioningfor tax purposes, and traditional rallying during holiday seasons. While this predictablemarket activity may be enough to confirm your positions, it does not indicate that some-thing special is occurring. Identifying these variations will be discussed in detail later inthis chapter.
 
Volume Drops and Spikes
Volume spikes are carefully watched because they are seen as a significant positive actionby the traders. For a stock that has been relatively inactive, a volume spike is a warning thatsomething is changing. In futures, a day of very high activity means that the market is sen-sitive to news. In both cases, a sharp increase in volume can be a predictor of change, or atleast of higher volatility. This will be discussed in the section “Volume as a Predictor ofVolatility,” later in this chapter.
STANDARD INTERPRETATION 239
At this time it is worth remembering that a volume spike is a clear indicator of a posi-tive action, while a volume drop can be ambiguous. Volume can decline because there islittle interest in a stock or futures market; buying and selling pressure have been elimi-nated. When a currency, gold, or any traded product reaches a price that is considered fair{also called equilibrium), volume normally declines. Volume may also drop on the daybefore a holiday, or just by chance. While there are seasonal and other predictable patternsassociated with volume drops, they are far less certain than large increases.
STANDARD INTERPRETATION
‘The interpretation of volume has been a part of market lore since charting began. The bestconsolidation of that information was published in the monograph by WL. Jiler, Volumeand Open Interest: A Key to Commodity Price Forecasting, a companion piece to his mostpopular Forecasting Commodity Prices with Vertical Line Charts (see references in Chap-ter 9 (“Charting”).
In both the futures and stock markets, volume has much the same interpretation,when volume increases it is said to confirm the direction of prices. Price changes that occuron very light volume are less dependable for indicating future direction than those changesassociated with relatively heavy volume. An additional uncertainty exists for stocks that arenot actively traded, and for low prices shares where the total dollar volume can be small.In these cases it might be best to look at the accumulated volume of similar companies, orits sector.
Open interest is a concept unique to futures markets, but helps to explain the depthof the market as well as trader expectation. New interest in a market brings new buyers orsellers, which increases the open interest, the net of all outstanding contracts being traded.When the open interest increases while prices rise quickly, it is commonly interpreted asmore traders entering long positions. This may seem strange because for every new buyerof a futures contract there must be a new seller; however, the seller is likely to be someonelooking to hold a position for a few hours or days, looking to profit from the normal upsand downs of price movement. The position trader, who is willing to sit for much moretime holding a long position, is the one who is attributed with the open interest. In reality,no one knows. However, if prices keep rising, the shorts are more likely to be forced out ~while the longs have staying power.
The traditional interpretation of changes in volume and open interest (for futures mar-kets) can be summarized as follows:
 
 
Volume Open Interest Interpretation
Rising ~~ Rising Confirmation of trend
Rising Falling Position liquidation (at extremes)Falling Slow accumulation
 
Falling - Congestion phase
Some of the generally accepted notions for the use of volume and open interest are:
1. Open interest increases during a trending period.
2. Volume may decline but open interest builds during an accumulation phase. Vol-ume occasionally spikes.
3. Rising prices and declining volume/open interest indicate a pending change of di-rection. 
240 VOLUME, OPEN INTEREST, AND BREADTH
 
In the stock market, when confirming the direction of the overall market, the breadthof trading (percentage of rising to total stocks) should be used if it closely approximatesthe stocks in the index. It would be inconsistent, for example, to use the total breadth ofall stocks traded on the New York Stock Exchange, to confirm a move in a portfolio thatcontained only the 30 stocks of the Dow Industrials. In that case, you would need to con-struct an indicator of breadth that used only those 30 stocks.
Exceptions
No method is without exceptions, including volume patterns in the stock market. Thereare days or periods when volume is expected to change, and must be considered in theanalysis. For example, volume is lighter:
On the first day of the weekOn the day before a holidayDuring the summer
It is equally difficult to forget that volume is heavier on triple witching day, when S&P 500futures, options on futures, and options on the cash index all expire at the same time.
In the futures markets, there are similar patterns. Lighter volume will exist during hol-iday periods and summer months, but may be heavier on Fridays and Mondays during atrending market or a weather market for ageicultural products. Liquidation often occursbefore the weekend, and positions are reentered on the first day of the week.
Richard Arms’s Equivolume
Most of the techniques for using volume discussed in this chapter will multiply or accu-mulate volume, creating an index that rises faster as volume increases. Equivolume, acharting method introduced by Richard Arms, takes the unique approach of substitutingvolume for time along the bottom scale of a chart. When volume increases, the price baris elongated to the right, rather than the standard approach of extending the height ofthe bar.
‘There are no systematic methods for using this technique included here, and applica-tions parallel standard chart interpretations; however, analysts can represent this type ofchart by creating a new price series in which the daily closing price is repeated based onthe relative volume. For example, if the normal volume day causes a closing price to berepeated 10 times, then a day with twice the volume will repeat that price 20 times, and aday with half the volume will show 5 prices. This approach may cause a short-term moving,average trend to look strange; however, a linear regression or long-term trend shouldreflect the importance-of varying time.
 
VOLUME INDICATORS
-Both the stock and futures markets are familiar to indicators that use only volume, or thosethat add volume, intending to make other calculations more robust. The following sectiongives the most popular of these indicators, most of which originate in the stock market and
 
many of which use the number of advancing and declining stocks. Readers should note the _
way in which the data is used from one technique to another and consider the significanceof these changes. They will be discussed at the end of this section.Volume Momentum and Percentage Change
The most basic of volume indicators are momentum and rate of change. These techniquestreat volume as price. For momentum, this means finding the change in volume over a spe-
VOLUME INDICATORS. 241
cific time interval; percentage change measures the size of the volume change relative tothe starting value.
Volume Momentum = volume today — volume, gays ago
volume today ~ volume nays go
Volume % =VOIUME jys ag0
On-Balance Volume
Made famous by Joseph Granville, On-Balance Volume (OBV)' is now a byword in stockanalyst circles. On days when prices close higher, it is assumed that all volume is repre-sentative of the buyers, on lower days, the volume is controlled by the sellers. Althougheach day yields a new value, these values are added together to form a new series. Theresult is a volume-weighted series. In the following formula, the expression in parenthesessimply uses the closing prices to produce a value of +1, 0, or ~1, which then determineswhether today’s volume will be added or subtracted from the volume series:
close — Close previous
OBVeoday = OBV previous + (
_close ~ closeprevius vot@abs(close — lose presom) ) xvolume
Determining the OBV manually is a simple accumulation process. In Table 10-1, there wasgreater volume on days in which prices rose and lower volume on declining days. This isexpected in a market with a clear uptrend. The advantage of recording the OBV is inobserving when the trend of the prices diverges from the OBV values. The general inter-pretation of OBV is given in Table 10-2.
Because a volume series has many erratic qualities, caused by large variations in vol-ume from day to day, it is most often used by applying a trend from 1 to 100 weeks, thenidentifying a simple volume direction when the OBV value crosses the trend. An upwardtrend in volume is interpreted as a confirmation of the current price direction, while adownturn in volume can be liquidation or uncertainty.
Simple Variation .
An indicator that closely resembles On-Balance Volume is a running total of the days whenvolume increases minus the days when volume delines. That is, add 1 to the cumulativevalue on a day when today’s volume is greater than the previous day, otherwise subtract 1.This volume count indicator (VCI) can be written as:
1 Robert W. Colby and Thomas A. Meyers, The Encyclopedia of Technical Market Indicators (Dow Jones-Irwin,1988) is a comprehensive study of most market indicators, including On-Balance Volume and some other tech-niques included in this section.
 
TABLE 10-1 Calculating On-Balance VolumeClosing Daily Volume On-Balance
Price (in 1,000s) Volume310 25 25315 30 5S318 27 82316 1S 67314 12 55320 28 83
SS 
242 VOLUME, OPEN INTEREST, AND BREADTH
 
eT EEE SEES
TABLE 10-2 Interpreting On-Balance Volume
 
 
Price ByDirection Direction InterpretationUp Up Clear uptrendSideways Moderate uptrend
Down Weak uptrend near reversalSideways Up Accumulation period (bottom)Sideways No determinationDown Distribution period (top)Down Up Weak downtrend near reversalSideways Moderate downtrend
Down Clear downtrendee
volumeaday ~ VOLUME previous
VClipty = VClpresions + Estey = VOT previous __‘ou " @abs (volume gay — VOLUME previous)
Volume Accumulator
A modification to Granville’s OBV system is Mark Chaiken’s Volume Accumulator (VA).Instead of assigning all the volume to either the buyers or the sellers, the Volume Accu-mulator uses a proportional amount of volume corresponding to the relationship of theclosing price to the intraday mean price. If prices close at the high or low of the day, all vol-ume is given to the buyers or sellers as in the OBV calculation.’ If the close is at themidrange, no volume is added.
close — low
———_— - 50 hlost =10%_ 59) 25oloe
VAcoday = VAprevious + (
Other Accumulation Index Techniques
‘The Price and Volume Trend (PVT) applies volume to the percentage price change fromclose to close, which can be positive or negative. The Positive Volume Index (PV1) and Neg-ative Volume Index (NVI) take the approach that a single indicator, which adds and sub-tracts volume based on market direction, is not as informative as two separate series thatcan be viewed at the same time.
close ~ lose previousPVTeatay = PVTprerious + (oe | x volumeCLOSE previous
if close > closeprevious thEN PVIjosay = PVIprevious + Volume
if close < Close previous then” NVIroday = NVIprevious + Volume
‘Separating Advancing from Declining Volume
The most basic of all techniques for determining market breadth is the Advance-DeclineIndex, which creates a new series by adding the net of the number of advancing and declin-ing stocks each day. Unchanged issues are ignored.
2 Both OBV and the Volume Accumulator are characterized as momentum systems. See Chapter 6 for more infor-mation on similar techniques.
VOLUME INDICATORS 243
Advance-Decline Oscillator = Advances — DeclinesAdvance-Decline Indexjuay = Advance-Decline IndeXprevous + advance — decline
In some of the techniques that follow, only the oscillator, or single-period calculation,may be shown. An index can be created by accumulating these values.
Sibbett’s Demand Index
One method that smooths out volume because it uses the total activity of the past 10 daysis James Sibbett's Demand Index. The technique bears a resemblance to the approachused in Wilder's RSI. It can be used as an oscillator with individual daily values or accu-mulated into an index. The individual days are calculated as:
@sum(upside volume, 10)
Demand Index =and index = @sum(downside volume, 10)
where @sum is a function that sums the past 10 days of upside and downside volume,found in the Wall Street Journal under the heading “Trading Activity.” Arthur Merrill,another well-known stock analyst, has suggested applying 5 days to this same technique.
Aspray’s Demand Oscillator
Using direction to separate volume into two series of Buying Pressure and Selling Pressure,Aspray then nets them into his own Demand Oscillator’ Note that during a rising marketthe selling pressure has been divided by a percentage of the volume, which has beenscaled to be greater than 1. The following calculations show the separate steps needed tocreate Aspray’s Demand Oscillator:
For rising prices:Buying Pressure = volumeSelling Pressure = volume‘x SOS, ~ OSC renoClose previous
For declining prices:
. vBuying Pressure olume
(x ye £1O8C oday ~ <Tostast
lose previousand wherek= 3 x close@avg(@highest(high, 2) — @lowest(low, 2), 10)and
Demand Oscillator = BP — SPKis a volatility scaling factor, which is 3 times the closing price divided by the 10-day mov-ing average of the 2-day high-low range, and has a value likely to be well over 100. Forexample, if the S&P is trading at 600 and the average volatility is 10 full basis points (whichis very high for a 10-day average), then K = 1,800/10 = 180. -
3 "Thomas Aspray, “Fine-tuning the Demand Index,” Technical Analysis of Stocks & Commodities June 1986), and“Demand Oscillator Momentum,” Technical Analysis of Stocks & Commodities (September 1989). 
244 VOLUME, OPEN INTEREST, AND BREADTH
 
Bolton-Tremblay .
Introducing the net advancing stocks compared with the number of stocks that wereunchanged, the Bolton-Tremblay approach also includes a form of geometric weighting ofthe results:
advancing ~ declining
Bolton- iF v=olton-Tremblayodn wanchanged
if Bolton-Tremblay,iay > 0 then ACCUM BTyoday = ACCUM BT peous + VBolton-Tremblayioasyif Bolton-Tremblayiouay < 0 then ACCUM BTyouay = ACCUM BT previous ~ V Bolton-Tremblayioday
SchuttzSchultz chose to look at the advancing stocks only as a percentage of the total stocks:advancinghultz A/Tyoiy = Schultz AT yrewous + agen anchaneed
Schultz A/Toosy = Schultz A/Trrvou + Sa vancing + declining + unchangedMcClellan OscillatorSimilar to the Advance-Decline Index, the McClellan Oscillator does not accumulate thenet change in breadth, but looks at the individual changes as an oscillator:
McClellan Oscillator = advances — declines
Upside/Downside Ratio
A simple upside/downside ratio (UDR) has also been used; however, the ratio value has nosymmetry. When the declining volume is very low, for example, only 20% of the total vol-ume, the UDR will have a value of 4.0. In contrast, if the advancing volume is low, the ratiois limited to the range between 0 and 1.
Advancing volumeDeclining volume -
 
UDR
Tick Volume indicatorIna manner similar to Wilder’s RSI, Blau double smooths the tick volume as a way of con-firming price direction. The Tick Volume Indicator (seen in Figure 10-1) is:vig, 5) = 100% DEMACupticks, 7 §) ~ DEMA(downticks, 7 5)
” *) =" DEMA(upticks, 7, s) + DEMA(downticks, r, s)which ranges from -100 to +100 and where DEMA is the double (EMA) smoothing of thedownticks or upticks over the past s bars, with the initial smoothing over r bars.
Programming Volume Indicators -
Volume indicators are easy programming on both a spreadsheet and Omega’s Easy Lan-guage. The following examples include only some of the indicators discussed in this chap-ter; the others are very similar and can be added using the same form.
Spreadsheet Code
Using Corel's Quattro, the following spreadsheet shows the Eurodollars beginning in April1993. The calculations for On-Balance Volume, Volume Accumulator, and Price-Volume
VOLUME INDICATORS 245
ses
FIGURE 10-1 Blau’s Tick Volume Indicator.
 
DEUTSCHE MARK DM E91-20 min
 
 
hone") 5700
Hon yrital
 
     
0.50f-1.50
 
 
‘Tick Volume Indicator
 
1.00
     
Tick Volume Indicator
0.001.50
 
 
L ERGODIC _TVi(32) Z ERGODIC_TVI OSCILLATORaie 1200 4g 1200 arez_ 200 2312.00
 
eSSource: William Blau, Momentum, Direction, and Divergence (John Wiley & Sons, 1995, p.45).© 1995 WilliamBlau. Reprinted by permission of John Wiley & Sons, Inc.
‘Trend are shown in the rightmost three columns. The spreadsheet code for these calcula-tions are shown after the sample output.
Col Name Start Row
A Date 5
B High 5
c Low 5
D Close 5
E Volume 5
F  OBV 7 @IF(D7-D6>0,F6+F7, @1F(D7-D6<0,F6-E7,F6))
G  vaAcC 7 #G6+{((D7-C7)(B7-C7))-0.5)'2°E7__
H. PVT 7 +H6+E7*(D7-D6)/D6
1 MAP 45 @AVG(D26.045)
J PX 48 (148-146)" 100/145 -K MA 45 @AVG(D6.D45) -Lo MADIFF 948, «+K48-Ka5
M Mav 45 @AVG(F26.F45) [for OBV]
N Vx 48 (M48-M45)"100/M45
O DVG 48 @IF(J48*N48<0,J48-N48,0)
P  OBVVX _ Signal from row 49
 
@IF(L49>0#AND#L48<=0#AND#N49>=S083, "buy",@IF(L49>0#AND#L48<=0,"exitS",@IF(L49<=0#AND#L48>0#AND#N49>=$D83,"sell”,
- @IF(L49<=0#AND#L48>0,"exitL",@IF(L49<SDS3,"exitALL"," *))))Q — OBV VX DVG Signal from row 49
  
246 VOLUME, OPEN INTEREST, AND BREADTH
@IF(L49>0#AND#L48<=0#AND#N49>=$D$3#AND# @ABS(049)<=SES3,"bu@IF(L49>0#AND4L48<=0,"exitS",@IF(L49<=0#AND#L48>0,#AND#N49>=$D$3#AND#@ ABS(049)<=$ES3, "sell",@IF(L49<=0#AND#L48>0,“exitL”,@IF(L49<$D$3#AND# @ ABS(049)>$ES3,"exitALL"," *)))))
 
 
R  MomOsc 25  (@AVG(E22.£25) - @AVG(E25.E6))"100/@ AVG(E22-E25)
S  AvgMom 45 @AVG(R26.R45)
T  StDevMom 45 @STD(R26.R45)
U Mom Signal 45 @IF(L45>0#AND#L44<=0#AND#R45>=S45-$FS3°T45, "buy",@IF(L45>0#AND#L44<=0,"exitS",@IF(L45<=0#AND#L44>0#AND#R45>=S45-SFS3"T45,"sell",@IF(L45<=O# AND#L44>0,"exitL"," "))))
vo ROC 25 — (E25-E6)"100/E6
W AvgROC 45 @AVG(V26-V45)
X  StDevROC 45 @STD(V26.V45)
Y ROC Signal 45 — @IF(L45>0#AND#L44<=0#AND#V45>=W45-SFS3°T45, “buy”,
@IF(L45>0#AND#L44<=0,"exitS",@IF(L45<=0# AND#L44>0#AND#V45>=W45-$F$3°T45, "sell", @IF(L45<=O#AND#L4420, "exit
 
"))Omego’s Easy Language Code
‘The following program code gives an example of a system that uses one of eight volumemeasurements to filter the entry or exit of a trade. When the input ttype is negative the
input values are treated as an entry filter; when ttype is positive the values are used for anexit filter.
(PJK Volume: Create a volume filterCopyright 1995-1998, PUKaufman. All rights reserved.}
inputs: period(20), ttype(1), maxdn(0), maxdvg(0), npsdi.5), ddays(3);vars:  px(0),-vxi0), Kvol(O), map(O), mav(O),sdiff(0), madays(0),macO), dvgCO),ndO), madiff(O), avgv(O), sdv(0), tentry(O), avg2(0), type