simplest way to study these functions is to collect statistics and plot thesefunctions as three dimensional graphs.If the deviation parameter of some stock D < -1 it means the stock may be oversold,because its price is well below the fitting line for some time scale. This is not so clear for usingtrends T.If T < -1 it may not indicate that we have a stock with a very negative trend. The marketmay drop during the time under consideration and most stocks will have a very negative T. Wemust use the difference T - <T>, where <T> is the average value for all stocks. The difference T- <T> should be divided by the standard deviation σT of the distribution of the stock trends forthe day of analysis. So, here and further T means:T ---->
(T - <T>) / σT
To keep things similar, the same idea can be applied to the deviation parameters.D ---->
(D - <D>) / σD
In Chapter 1 we mentioned that the stock may be oversold if its price trend is negativeand its price has sharply declined on some day. One can expect that the stock is oversold insome time frame ifT < -1
and
D < -1
One can also expect that the stock is overbought in some time frame ifT>1
and
D>1
How can we relate the future behavior of stock price with the D and T parameters? Forexample, considering some stock for which we found that T = -0.6 and D = +0.9. Is the stockbullish or bearish?To elaborate this problem we performed a computer statistical analysis. Statistical dataare limited. The stock market is changing and there is no sense in collecting stock histories over20 or 30 years. The period of the last 3 - 5 years is optimal. In this case, we can collect about 1million events to analyze.A straightforward way to analyze the dependence of stock price move ∆P on the D, Tparameters is to find a function∆P = f(D,T)Unfortunately, this is a very complicated way. The function is not linear and availablestatistical data are not sufficient to find the function parameters with good accuracy.We used a different way. The plane D, T was divided into 16 cells as shown in Figure 2.6.
16
Figure 2.6
Definition of the T-D map
Cell #1 corresponds toCell #1T > 1 and D < -1Cell #2 corresponds toCell #2T > 1 and -1 < D < 0and so on. This division allows us to obtain good statistical data (10,000 - 100,000) for everycell. Using these data one can calculate the average stock return depending on the cell number.The T-D map is always related to some time frame for which the T and D parameterswere calculated. The most crucial cells are cells # 4 and #13. One can expect that these cellscorrespond to overbought and oversold stocks. For example, if the trend of some stock is verynegative (T < -1) and the deviation of stock price from the fitting line is also very negative (D <-1) it indicates sharp price drop and the stock may be oversold in the time scale correspondingto the T-D map.To do things more clearly let us show a graph representation of the T-D map.
Figure 2.7
Graphical interpretation of the T-D map
In this figure the slopes of the lines represent trends (T) and the dot positions representdeviations (D).We have developed a general theory of using T-D maps for stock price move prediction.The theory is rather complicated and in these notes we will consider only a few practical
17questions which are related to the simple trading strategies. In the next chapter we will showusing T-D maps for the prediction of the market indexes.
18Chapter 3
Market statistics3.1 Basic definitions3.2 Dow Jones and others3.3 Short term predictions3.4 Average stock and average investor3.1 Basic DefinitionsEvery day after the market closing the trader should start his or her market analysis. Thegoal of this analysis is the list of stocks to buy or sell tomorrow as well as the target prices forselling or buying. Let us call the day of analysis day #0. Tomorrow will be day #1 and so on.DAY #0CLO0
DAY #1OPE1 CLO1
DAY #2OPE2 CLO2
DAY #3OPE3CLO3
DAY #4 ...OPE4 CLO4
OPE1, CLO1, OPE2, CLO2, ... are the stock prices at market opening and market closing on thecorresponding days. MAX1, MIN1, MAX2, MIN2, ... - are the maximal and minimal daily stockprices. These data you can obtain from many Internet services.Usually, we will be interested in relative price change in %. In tables or in the text youwill see equations like<C3 - C1> = 3.3%this is a short notation of the full equation100 <(CLO3 - CLO1)/CLO1> = 3.3or O4-C1 is the same asO4-C1 = 100 <(OPE4 - CLO1)/CLO1>The angular brackets mean averaging over some group of stocks. What group? This willbe additionally explained. These notations are very convenient to describe different tradingstrategies.3.2 Dow Jones and othersConsider prediction of the price move for an individual stock or for a market index. Wewill analyze the market indexes, but all conclusions can be applied to individual stocks as well.As an example, consider the Dow Jones Industrial Average (DJIA). We analyzed aneleven year history of this index. The first problem: how to define the average value of trends(T) and deviations (D)? The number of indexes is very limited and we cannot apply the methodsdescribed in Chapter 2, where we suggested comparing a selected stock with other stocks.For calculation of the averages and standard deviations of D and T parameters one canuse historical data of the index. We performed averaging over 252 previous days. The calculatedaverages are time dependent. This is not convenient for computer analysis, but it does reflectthe market changes over the years.
19
Figure 3.1
The averages (<D>, <T>) and standard deviations (σD, σT) of D8 and T8parameters for the Dow Jones Industrial Average.
Figure 3.1 presents the time dependencies of the averages and standard deviations ofthe D8 and T8 parameters. You can see that these values fluctuate, but the amplitudes of thesefluctuation are not large. The deviation parameters D are more stable than the trend parametersT.To use the idea of T-D mapping to analyze the index price dependence one shouldconsider the variables(T - <T>) / σT(D - <D>) / σDand depending on the values of these variables determine the number of cells of the T-D mapfor every trading day. The cell number is different for different time scales. So, every day wecan determine the T-D cell numbers of the index for 4, 8, 16, ... day frames. We performed thestatistical analysis to calculated the growth probabilities depending on the cell numbers.To eliminate the influence of large time scale market trends we calculated the averagesof the index changes and calculated the probabilities of the index moves, which are larger thanthe average move. As an example, Figure 3.2 shows the probabilities of these moves of the DJIAdepending on the cell number for a 32 day frame.
Figure 3.2
Growth probabilities versus D-T map (32 days)cell number for the DJIA
You can see that the lowest growth probability is observed when the index is in cell #4.This corresponds to the highest values of D and T parameters, i.e. overbought condition. Thesame idea can be used to calculate the growth probabilities for any index.
20Attention! We want to repeat once again: prediction of one stock or index price move isnot very reliable. It is based on the repetitive patterns. Statistical data for one index or stock(even for an 11 year history) is not large enough to make a sure conclusion. Using longerhistorical files is dangerous because of market changing. Consider these calculations only as anillustration of using T-D maps for prediction of stock or index price performance.What can we do? Is it possible to predict the index performance and calculate the error ofestimation? Yes, but you should always consider a group of stocks. The same calculations can bedone for all 30 stocks in the Dow Jones Industrial Average. For every stock you can calculate thegrowth probability depending on the T-D map cell number. Using methods of statistical analysisthe errors can be easily calculated.
Figure 3.3
Two day growth probabilities versus D-T map (16 days)cell number for 30 companies from the DJIA.
Figure 3.3 presents these data. For the calculations, an eleven-year period of historicalstock prices (1988 - 1998) has been used. You can see from this Figure that oversold andoverbought stocks (cells #13 and #4) can be easily identified.Using this approach for prediction of the DJIA performance will be discussed in the next section.3.3 Short-Term PredictionsThe idea of market index prediction is very simple. Let us explain it step-by-step. TheDow Jones Industrial Average will be considered as an example.1. Take the long-term history files for each stock from the DJIA. Calculate the average values ofD and T parameters for different time frames N = 4, 8, 16, 32, ...2. Calculate the average 2 day returns of all stocks for every cell of the T-D map. The return canbe calculated as (CLO2 - CLO0)/CLO0.3. For every day for which you need to predict the market determine the T-D cell number for allstocks from the index. The cell number will indicate the corresponding two day return ofindividual stock.4. Calculate the sum of the returns multiplied by the stock price. This sum is the predicted indexreturn.5. The predicted index return depends on the T-D map time frame. This is why you should usemany time frames (different N) for prediction. The smaller N, the more precisely the indexreturn will be estimated for the period of 2 days.Maybe this description is a bit complicated. Let us explain the main idea using "plainEnglish".What are these "mystic" T-D maps for? They simply indicate certain price patterns. Thereturns depend on these patterns. The computer analyzes the patterns in the past and usesthem to predict the future.The predicted index return we call growth parameter GP. Depending on the number ofdays which were used for patterns (T-D maps) we will use notations GP-4, GP-8 and so on.
21
Figure 3.4
The Growth Parameters (GP-4 and GP-8) for 30 stocks of the DJIA. A period of 128trading days has been considered.
Figure 3.4 shows the GP-4 and GP-8 parameters for 2-3 day index prediction of the DJIA.The period of 128 trading days ending May 19, 1999 has been considered. The higher the valueof the GP parameters, the more bullish is the DJIA. The prediction is not bad and can be usedfor practical purposes: if you expect a bullish market then you can buy a greater number ofshares. If you see a bearish signal, buy fewer shares or stay away. Wait for a while to havemore profitable opportunities.3.4 Average Stock and Average InvestorWe do not like weighted market indexes - the sum of selected stock prices multiplied bythe number of shares outstanding. Such indexes are good to estimate where the money goes,but for investors or traders it is much more important to know the average stock price change.You do not care about the number of shares outstanding when you reap the profit or take theloss.The Dow Jones Industrial Average is calculated as the sum of the individual stock pricesmultiplied by some coefficient, and it well reflects the happiness of an average trader orinvestor. Nevertheless, market indexes such as the S&P 500 are extremely popular forestimating mutual fund performances and we should compare the performance of our tradingstrategies with this index as well.We have performed a statistical analysis for all NYSE and NASDAQ stocks over the periodfrom 1995 to 1999. Here, some important market statistics will be presented. We need thesenumbers to compare the performance of various trading strategies with the market averages.When thinking about short-term trading we will consider only active stocks. Let us clarify howwe define active stocks.Active StocksWe consider only actively trading stocks. Trading volume on the day of analysis should bemore than 200 000 shares. These stocks have enough liquidity, smaller bid-ask spread andafford the possibility to buy and sell stocks between bid and ask prices. The second condition:closing prices of selected stocks should be more than 10 dollars. Smaller stocks are extremelyvolatile and trading these stocks is very dangerous. The stocks should exist at least 32 previousdays, so as to be able to calculate the deviations, trends and volatilities D, T and V for differenttime frames: N = 4, 8, 16, 32 days.
22Computer analysis shows that every day one can find 1003 +/- 170 active stocks. It isimportant to note that the average daily return of these stocks is larger than daily return of theS&P 500 index. The daily returns have been calculated by comparing closing stock prices.Average Daily Return
S&P 5000.089 %
Active Stocks0.128% +/- 1.21 %
The daily returns of active stocks are high but these returns are not enough to makeprofits from short-term trading. The standard deviation (risk) of active stocks is very high, andwe should develop stock selection systems to increase return and minimize risk.More statistics for active stocksIt is interesting to note that active stock daily returns are not stable! Denote as usualCLO0 as a closing price on the day of analysis, CLO1 as the closing price on the next day, etc.We have calculated the average 1, 2, 3, 4 and 5 day returns of active stocks:<CLO1 - CLO0> = 0.128% +/- 1.21 %<CLO2 - CLO0> = 0.201% +/- 1.79 %<CLO3 - CLO0> = 0.271% +/- 2.20 %<CLO4 - CLO0> = 0.342% +/- 2.58 %<CLO5 - CLO0> = 0.412% +/- 2.93 %The values of <CLOm - CLO0> are very important because we have to develop methodsof trading that beat these numbers. You can see that the average two day return <CLO2 CLO0> for active stocks is less than 2 * <CLO1 - CLO0>. The daily return is decreasing withtime! The next table is a good illustration of this statement.<CLO1 - CLO0> = 0.128%<CLO2 - CLO1> = 0.073%<CLO3 - CLO2> = 0.070%<CLO4 - CLO3> = 0.070%<CLO5 - CLO4> = 0.070%One can see that during the first day after analysis the price change is greater thannormal (S&P 500 change) and for other days the price change is less. This is probably related toour active stock selection method. We have chosen stocks with a minimum trading volume as200,000 shares on the day of analysis. This is abnormal activity for many stocks, and the largechange of price on the first day after analysis is a reaction to this activity.Conclusion: If you select an active stock for trading and if its activity is not normal, do not holdthe stock for a long time. There is a good chance that the stock will behave like a regular stockwith an average market return. Take your profit early, while stock is still active.
23Chapter 4
Oversold Stocks4.1 Bottom fishing and theory of probabilities4.2 Stock selection system4.3 Statistics for oversold stocks4.4 Overnight moves4.1 Bottom fishing and theory of probabilityLet us remind you of some old market "axioms". They were taken from the classic book"The Stock Market" by R. Teweles, E. Bradley and T. Teweles.1. Avoid a too frequent switching.2. The stock market has no past.3. No one ever went broke taking profit.4. Never buy a stock after a long decline.More axioms:5. Trend is your friend.6. Never guess the bottom.Our axioms:- All market axioms should be statistically proven.- Do not trust opinions. Trust the theory of probability.Our comments about old market axioms:1. If you choose stocks with high growth probability, a frequent switching between these stockscan give a very good return.2. The growth probability of some specially selected stocks can be very high. These stocks areselected from an analysis of the past. This means that somestocks have a past.3. If you take tiny profits and large losses, you will go broke.4. Buy stocks after a long decline if this decline is abnormally sharp.5. Trend is your friend for a short time. It is better to anticipate the turning point.6. Never guess the bottom. Rather rely on computer methods of bottom prediction. Be anequipped bottom fisher. Your tool is the theory of probability.So, we are breaking six market axioms. This is a serious statement. It should be provenby statistical analysis. Let us show how we can do that. We will startwith a simplest case: oversold stocks.4.2 Stock Selection SystemIn this section we will outline our stock selection approach. Some ideas have been brieflydescribed previously. Here, we will repeat the basics of our stock selection method and considermore important details.The main idea is very simple: the stocks should be oversold. Buy low - sell high. Thisaxiom still works. The only question is: how can we define these "lows" and "highs"?
24Previously, we defined oversold stocks as stocks with a deviation parameter of D < -1.From the results of Chapter 2 you can figure out that in the case when D < -1, the stock priceshould be lower than the support level of the trading range.This contradicts a widely held opinion: breaking down the support level is a bearishsignal. The key point in our method is the analysis of trends T as we described them in Chapter2. For oversold stock the trend should be negative. The more negative the stock price trend, themore oversold this stock.It is mathematically clear how to define oversold stocks by using the deviation parameterD. The trend analysis is more complicated. When we analyze historical data for one stock we cancalculate the average short-term trend Tav and its standard deviation sT. So, for a given stockone can define the oversold condition as:D < -1T < Tav - sTThis approach is good when you analyze one stock. However, we can suggest a muchbetter idea about how to define an oversold stock in the case when we are trying to find suchstock on some particular day among many other stocks. Mathematically, it is more complicatedbut this definition is very effective.First of all, we should take into account the market performance during the few last days.Let us illustrate this idea by a simple example.Suppose that during the last 16 days the market has sharply declined. The standarddeviation of the trend T for the stock XYZ is 3%. During this period the trend of XYZ is lowerthan 3% than its average and its deviation parameter D < -1. Should we consider XYZ asoversold?This stock is oversold if we use the equations shown above. However, you will gethundreds of oversold stocks if you use this definition. Practically, it is not useful. What to do?You should consider the average trends T for all stocks and compare the trend of your stockwith the averages.Considering all stocks is a worthless idea. Some stocks have so little activities that takingthem into account would distort the real situation. We suggest considering only active stocks, aswe did in the previous chapter.1. Trading volume on the day of analysis is more than 200,000.2. The closing price is more than $10.3. Stocks should have at least a 32 day trading history before the day of analysis.Active stocks make the market. Every stock should be compared with other active stocks.We should calculate the average trend for all active stocks and the standard deviation of thedistribution of these trends to compare with given stock trends. In such a manner, we areconsidering the stock together with the market. We can use the equations on this page to defineoversold stocks but remember that the average trend Tav and the standard deviation sT shouldbe calculated for all active stocks. So, to calculate the average trend one can use the equation:Tav = (T1 + T2 + T3 + ... + Tn)/nwhere n is the number of active stocks on the day of analysis; Tk are the trends of stocks. Thestandard deviation sT is the characteristic of distribution of Tk.
25
Figure 4.1
Comparison of the stock trend T with the average value Tav for active stocks.
The trends T and deviations D depend on the time frame. Stocks can be oversold in a 128day frame and overbought in a 4 day frame. If you want to buy stocks and sell them in 2 - 5days you do not need to consider a one year time period. We have performed the 11 yearhistory analysis of 250 stocks from the S&P 500 index and found a very little correlationbetween short-term returns and deviation D and trend T parameters for 128 and more days.The optimum time frames are 16 - 32 days. Stocks which are oversold in these time frames givethe maximal expected returns if only one time frame is considered.For more detailed analysis one should consider two time frames. In Chapter 2 we haveshown that D and T parameters for different time intervals are correlated. The smaller thedifference between time frames, the smaller the difference between (D, T) prediction potentialof stock performance. So, consideration of 16 and 32 day frames gives very similar results.If we have a 32 day frame as a basic we should consider much smaller periods of time. 4days is the minimal interval for which the deviation D and trend T parameters can becalculated (see Chapter 2 for details). Computer analysis shows that stocks have very goodgrowth potential if they are oversold in both 4 and 32 day frames.In order to sort stocks by their growth potential we introduced the sorting parameter:Sorting parameter = (T/sT)32 + D32 +(T/sT)4 + D4The smaller the value of the sorting parameter, the larger the growth potential of thestock. This is a method of sorting stocks in our daily list of potentially bullish stocks.The most bullish stocks are located in T-D cell #13 (see Chapters 2 and 3) for 32 and 4day time frames. Let us remind you: a stock is in cell #13 when its trend and deviation are verynegative. On a graph you can see an accelerated drop of the stock price. Such stocks are veryoversold.There is a problem related to real trading. If you perform your analysis on day #0 aftermarket closing and find some bullish stocks, then there is a good chance to see an overnightprice gap for these stocks. For short-term trading this means you will have nothing to buy in themorning. Your profit is gone. How can one overcome this problem?You can buy expensive services and before market closing perform a price screening forthe whole market. After calculating the sorting parameters (SP) for all stocks you have tochoose those with minimal SP. These stocks are very bullish.We suggest using a cheaper method. Computer testing and our experience show that thismethod works very well. The idea is simple. You have to be prepared before market closing. Youshould have a list of potentially bullish stocks and before market closing check the prices ofstocks from this list. If you find stocks which are oversold in 32 and 4 day frames - these stocksare potential winners. There is a good chance for these stocks to open with an upside gap andgo up further.
26How can you know that stocks are oversold in both time frames by the end of the tradingday without performing calculations? Here, the theory of probability starts working. You shouldselect stocks which are oversold in 16 - 32 day time frames (using our language, they are in T-Dcell #13 in these frames). The stocks may be not oversold in shorter time frames. This is whywe regard these stocks as potentially bullish stocks.Our goal is to be prepared for the next day. The stocks from the list will or will not bebullish at the end of the next trading day (day #1) depending on price performance during day#1. If the prices of listed stocks fall during the next day the stocks will still be oversold in the 16- 32 day frames.If the price drop is between 5 and 10%, the probability is very high that the stock will beoversold in a 4 day frame. So, it is highly possible that the stock will be oversold in both timeframes and that it is very bullish. You can buy this stock before market closing and you areready to catch the overnight upside price gap.We will call the stocks from the list of potentially bullish stocks as oversold stocks if theirprices drop during the next trading day.You can ask: why don't we consider only stocks which are oversold in 32 and 4 dayframes on the day of the analysis? If they drop further during the next day they will be"superoversold" stocks.It is not a bad idea if you want to be placed in the Guinness Book of World Records to seta record average return per one trade. If your goal to make a good annual return, however youshould think in a different way.The probability of finding "superoversold" stocks is very low. Most of these stocks go upduring the next day and they will not be oversold at the end of day #1. Week after week youwill have nothing to buy. Your annual return will be small if you trade only such "superoversold"stocks. In the next section we will show some statistical data to illustrate this statement.So, we have to balance between the number of stocks in the list and the quality of thesestocks.The last trick involves stock price performance during the day of analysis. The stock pricedrop during the day of analysis increases the growth probability of this stock. The daily numberof stocks which are oversold in a 16-32 day frame is relatively large and we can leave in the listonly stocks which declined during the day of analysis. This additional condition slightly reducesthe list of potentially bullish stocks but increases the average growth probability of the stocksfrom the list.This selection method was obtained from our computer analysis. We will continue ourwork, and if we find a more efficient way of stock selection it will be published. We havepresented the general idea of finding potentially bullish stocks. Even non-professional traderscan use this approach, which seems to be a profitable one.4.3 Statistics for Oversold StocksLet's remind ourselves of some definitions introduced in the previous sections.Active stocks - these are the stocks with trading volumes on the day of analysis of morethan 200,000, with closing prices of more than $10 and with at least a 32 day trading historybefore the day of analysis.Potentially bullish stocks - active stocks which are located in DT cell #13 in the 16 or 32day frame. They are oversold in these frames. In this section we will not consider the conditionthat stocks should decline during the day of analysis.Oversold stocks - these are the stocks from the list of potentially bullish stocks and theirprices dropped during the next trading day, i.e. closing price CLO1 on day #1 is less than theclosing price CLO0 on day #0: CLO1 < CLO0.Now we should consider some statistics to prove our statement that "potentially bullishstocks" really are bullish. First of all, we need to mention that the number of potentially bullishstocks is about 2.3% of active stocks. On average, you can find 23 +/- 11 stocks per day.We calculated the average price change for 1, 2, 3, 4, and 5 days as well as the risk toreturn ratios for active and potentially bullish stocks. The results arepresented in Table 4.1.
27Table 4.1 Average price change (returns) for active and potentially bullish stocks. Risk to returnratios are shown in parenthesis.Price change
Active stocks
Potentially bullish stocks
<CLO1 - CLO0>
0.13 % (9.3)
0.62% (9.2)
<CLO2 - CLO0>
0.20 % (9.0)
1.14% (6.7)
<CLO3 - CLO0>
0.27 % (8.1)
1.38% (6.6)
<CLO4 - CLO0>
0.34 % (7.6)
1.55% (5.9)
<CLO5 - CLO0>
0.41 % (7.1)
1.73% (6.3)
One can see that average returns for potentially bullish stocks are 4 - 5 times larger thanfor active stocks. Risk to return ratios for potentially bullish stocks are less than the ratios foractive stocks. However, risk of trading is still high and let us show the methods of stockselections which allow us to reduce trading risk.The simplest risk reduction method is trading only oversold stocks. Remember, thesestocks appear only at the end of day #1 (next day after the analysis).You are able to buy these stocks at price CLO1. So, we can consider only the pricechange between day #1 and day #2, #3, ... .Table 4.2 represents some statistical data. We have considered stocks with various levelsof price drops during day #1. Let us repeat again: potentially bullish stocks have no restrictionsfor closing prices CLO1 and CLO0. In this table, for simplicity, we are using C0, C1 , .. notationsinstead of CLO0, CLO1, ... .Table 4.2 Average price change per day in % for all potentially bullish stocks and for oversoldstocks (C0 < C1) with various levels of price drop during trading day #1.Potentially BullishStocks
C1 < C0
C1 < 0.95C0
C1 < 0.9C0
<Nst/day>
23.1
9.71
2.36
0.65
C2 - C1
0.53 (10)
0.56 (10)
1.53 (5.3)
2.63 (3.9)
C3 - C2
0.26 (20)
0.51 (11)
1.24 (5.8)
2.03 (3.8)
C4 - C3
0.19 (26)
0.38 (14)
0.56 (12)
0.27 (27)
C5 - C4
0.21 (23)
0.32 (16)
0.21 (30)
0.44 (14)
Risk to Return ratios are shown in parenthesis. <Nst /day> is the average number ofstocks which were observed per day.You can see that oversold stocks with a price drops of more than 5% and 10% on day #1give excellent returns during the first two days of trading (days #2 and #3). The risk to returnratio for oversold stocks with a price drop more than 10% is remarkably low. During the firsttwo days after the day of purchase (day #1) this ratio is less than a half of that for allpotentially bullish stocks! This is why we called a trading strategy with selection of such stockslow risk strategy.The only disadvantage of applying a low risk strategy is the fact that these stocks arerare. The average number of such stocks per day <Nst /day> = 0.65, i.e. you are able to findsuch a stock only once during two trading days. So, if you choose the strategy to buy and sellonly stocks with C1 < 0.9C0, you’ll have relatively few trading opportunities and your annualreturn can suffer.In the next chapters we will analyze various trading strategies in detail. Here, let's outlinesome problems related to the trading strategy optimizations. Stock selection is one of theseproblems. The second problem is the time of stock holding. You buy stocks at market closing onday #1. When should you sell these stocks to obtain maximum return with minimum risk?A simple idea is to wait until daily price changing become normal, i.e. close to the dailyprice change of all active stocks.