<s> 1Short-Term Trading Analysis
(Text Level-2)
Vladimir DaraganVersion 1.2Do not distribute.1999 STTA Consulting. All Rights Reserved.
Table of ContentsIntroduction1. Basics of stock trading1.1 How much profit is enough?1.2 Return and risk1.3 Profiting from chaos?1.4 Optimization of the limit and stop orders1.5 Computer analysis and real life1.6 How to buy low and sell high2. Stock price time dependence2.1 Market memory2.2 Trend and volatility2.3 Time scales2.4 Correlations2.5 TD - mapping3. Market statistics3.1 Basic definitions3.2 Dow Jones and others3.3 Short term predictions3.4 Average stock and average investor4. Oversold stocks4.1 Bottom fishing and theory of probabilities4.2 Who is buying oversold stocks?4.3 Stock selection system4.4 Statistics for oversold stocks4.5 Overnight moves5. Basic Trading Strategy5.1 Statistical Analysis of the Basic Trading Strategy5.2 Transaction cost and the Basic Trading Strategy5.3 How dangerous is this game?5.4 Correlation with the market6. Lower Risk Strategies6.1 Stock are oversold - how much?6.2 Low risk strategy6.3 Very low risk strategy7. You bought and ...7.1 Further price drop7.2 Moving up7.3 When to sell8. Limits and Stops8.1 General remarks8.2 Limit orders and average returns8.3 Stop orders and average returns
29. Small stocks9.1 Statistics for small stocks9.2 Risk and return9.3 Small stocks trading strategies10. Selling short10.1 How to define overbought stocks10.2 Statistics for overbought stocks10.3 Selling short strategies11. Other trading strategies11.1 How many days to hold?11.2 How many stocks to buy?11.3 Upgrades and downgrades11.4 Trading tips12. Trading portfolio12.1 Theory of efficient portfolio12.2 Using the theory of efficient portfolioConclusion
IntroductionStock prices go up and down. It would seem that it is simple to make a fast profit fromday trading. You need to buy stocks after a price drop and sell them after some time with aprofit. Unfortunately, this is a minus sum game. Bad stock selection can easily kill you. Thefaster you trade, the faster your losses become large. Every transaction has a cost: bid-askspread and brokerage commissions. Very tiny profits will disappear in a long run when you takeinto account these transaction costs.Nevertheless, day traders still exist and many of them are very rich people. How did theydo that? If you are a professional and trading on the floor of the exchange you can look formicro trends and catch the leaving train right on time. Big capital and zero commissions allowyou to make micro profits constantly.These notes are for nonprofessionals. Can you make profits by short term trading? Yes,you can. You should be very selective when buying stocks for trading and try to anticipate thestock price moves before professionals. Is this possible? The answer is yes. Let us show how todo that and what is the risk of short term trading.We will consider trading stocks. We suppose that you are using on-line discount brokersand you are paying small commissions (10 dollars or less). We also suppose that you are able towatch stock quotes a few times a day and you are able to buy or sell stocks during the tradingday.These notes are not about day trading. Our time frame is 2 - 5 days. Computer analysisand our own experience has shown that this period of stock holding is long enough to makeprofits with reasonable risk level.
3Chapter 1Basics of stock trading1.1 How much profit is enough1.2 Return and risk1.3 Profiting from chaos?1.4 Optimization of the limit and stop orders1.5 Computer analysis and the real life1.6 How to buy low and sell high1.1 How much profit is enoughLet us demonstrate how short-term trading can give you a nice annual return. Suppose,you have developed method which allows to pick the stocks with 2% average move in one day.Suppose also, the transaction cost (bid-ask spread and brokerage commissions) is equal to 1%.Your average profit will be 1 % per trade. If you trade one stock per day your trading capital inone year will be increased as much as1.01252 = 12.2 timesSo, if you find such trading system then your capital will pop up 12 times every year. Butthis is not realistic for a long run. How about 1% per week?1.0152 = 1.68In 5 years every dollar of your trading capital will be transformed to1.685 = 13.3 dollars.We did not consider taxes and possible withdrawing. To make 1% a week you need toearn in average about 0.2% per trade if you are trading one stock per day.It was the demonstration of a miracle of numbers. Very small average daily returns cangive you a large annual return. This is a main idea of the short-term stock trading. Forillustration, let us show the dependence of the annual return on the average daily return.
Figure 1.1 Dependence of annual return on the average daily return.You can see that even 0.1% per day produces annual return of 29%. This is about twotimes better then the average annual return of the S&P 500 index.Large returns are always related to higher risk. What is the risk of short-term stocktrading? Is it possible to develop a trading strategy which gives good average returns with lowrisk?This is what these notes are about. We will consider different systems of trading whichallow to achieve maximal average profits with minimal risk.Before getting started let's consider some important definitions associated with stocktrading theory.
41.2 Return and RiskReturn per TradeReturn per trade is the basic term of trading theory. Suppose you bought n shares ofsome stock at the price P0 and sold them at the price P1. Brokerage commissions are equal toCom. When you buy, you pay a cost priceCost = nP0 + ComWhen you sell, you receive a sale priceSale = nP1 - ComYour return in % for one trade is equal toR = Return = (Sale - Cost) / Cost *100%Return can be positive or negative depending on the difference (Sale - Cost). Later, wewill use the letter R for notating return per trade in %.Average ReturnSuppose you have made N trades. Returns per trades were equal to R1, R2, ... RN . Theaverage return for N trades one can define as a simple average<R> = (R1 + R2 + ...+ RN)/NThis definition has some disadvantages. It is a good definition only for small returns. Wewill discuss this problem later when trading strategies will be considered.Risk
You cannot be a winner in every trade you make. Any trading strategy must leave roomfor some losses. Your returns R1, R2, ... can be positive or negative. The Figure 1.2 showsreturns per trade for one of our trading strategies for the 1996 year period.
Figure 1.2. Returns per trade in 1996 for the first stock selected for the Basic TradingStrategy. The dashed line shows the average return per trade (3.64%).You can see from this figure that returns were mostly positive. However, 29% of tradeshad negative returns. This number reflects the risk of trading. To characterize risk more"scientifically" people use the following definition:Risk of returns is the standard deviation of the set of returns for some period of time.You can calculate the standard deviation by using any computer spreadsheet program. Toillustrate the definition of risk let us show the distribution of returns.
5
Figure 1.3
Distribution of returns per trade (1996)
Figure 1.3 presents the distribution (histogram) of returns per trade for data from Figure1.2. These returns are pure returns - no transaction costs have been considered. The standarddeviation σ is a characteristic of the distribution width and is equal to 6.9%.It is clear that the larger the standard deviation, the larger probability of losing money.This is why the standard deviation of the set of returns is considered as risk.1.3 Profiting from chaos?Academicians like chaos. In the simplest stock market theory it is assumed that for shortperiods of time stock prices change randomly. So, probability of growth and decline are equal.In this case it can be shown that there is no chance of making any profit over the long run. Youcan try any strategy with different "stop" and "limit" order levels, but as a result you will be aloser because of brokerage commissions and bid-ask spreads.SL___________________|_________|___________|____________________stopcurrentlimitpriceOn the diagram, S and L are the differences between the current stock price and the stopand limit order levels. The simplest strategy is to buy some stock and wait until the stock pricetouched the stop or limit levels (prices). If the stop level is touched first - you are a loser. If thestock price touches the limit level - you sell the stock with a profit and you are a winner. It canbe shown that this strategy gives you zero average return in case of zero commissions. Thesquared risk for this strategy is equal toσ2 = S * LSo, the larger the deviations of the stop or limit order levels from the stock price, thelarger the risk of this trading strategy.The situation changes when the probability of growth is larger than the probability ofdecline. In this case the probability of touching the limit level is higher than the probability oftouching the stop level and your average return is positive.We will not write long equations to describe the dependence of average returns on thegrowth probability. Later we will consider this dependence using real examples. The importantquestion is the levels of stop and limit orders given different probabilities of stock price growth.We will consider this problem in the next section. For now, we just want just to say, that agrowth probability about 51-52% is not enough to make any profit, because of brokeragecommissions and bid-ask spreads.
61.4 Optimization of the limit and stop ordersConsider the situation: an amateur is trading stocks. His choices are terrible and his styleof trading is not getting better. What can we do for this guy? How can we improve his return?Suppose the average growth probability of the stocks selected by this amateur is 40%.He cannot believe that his choice is always bad and he just wants to have some trading strategyto improve his return. He likes the stop-limit strategy described in the previous section and hewants to know what stops and limits are best for him.The equations for calculating the optimal stop and limit levels are rather complicated, andhere we will just give you the answer: L/S ratio should be more than 10 in this case. So, thestop order should be very close to the stock price at the moment of purchase. This is the onlystrategy that can help this guy to survive any longer in the market.The same idea can be applied to a bear market. If you buy stocks when market isdeclining your stop orders should be as close to the purchase price as possible.For experienced professional traders, when stock picks are excellent and the growthprobability of these stocks is high (for example, 60%) the stop order level should be far awayfrom the purchase price. The same rule can be applied to a bull market. Do not place stoporders close to the purchase price if you are sure about your stocks or when the market isrising. For example, if you expect a profit about 30% your stop orders should be about 20% lessthan the purchase price. We will consider this problem in detail later, when some specific tradingstrategies will be analyzed.1.5 Computer analysis and the real lifeIt is so easy to lie using statistical analysis. Probabilities, distributions, standarddeviations, ... - all this stuff is made specially to leave the truth in the dust. Give us any chartand we will develop an excellent trading system with 90% growth probability.
Figure 1.4
Funny curve
You can also draw some funny curve like the one shown in Figure 1.4, and we can"explain" every maximum and minimum of this curve. The analysis will show a 20% return oneach trade, and we can write a nice book about a new revolutionary trading system.When can one believe in the results of computer statistical analysis? Consider anexample.You can start your own analysis. Take the chart of some stock and find the patterns whenthe stock is ready to rise or to fall. Write down these patterns. Take another chart. Check allpreviously selected patterns and see what happened. Take another chart... Take anotherchart... Do it for thousands of stocks. Check your patterns for bull and bear markets. Look forwhat is working and what is not working. And give us the percentage of events when yourpatterns are working. If this number is more than 60%, we will use your patterns for trading. Itcan be profitable.So, you have to analyze a large number of stocks over a long period of time to draw aconclusion. However, even after such analysis you can not give 100% guarantee of future
7results. Your statistical analysis will give you the standard deviation of your expected returns,and you should use these numbers to estimate possible troubles.What patterns do we believe in? We like trading ranges if we can call them as patterns.There is a real crowd psychology behind these patterns. All traders know about trading ranges,and this fact makes trading ranges rather reliable. Our computer analysis has shown: yes, theywork.
Figure 1.5
Trading ranges for stable and growing stocks
How do trading ranges work? What average profit can you obtain using trading ranges asa basic of your trading strategy? What time scale should you consider to obtain maximal profit?How about the trends?These are the questions we are going to answer. We performed a computer analysis forthousands of US stocks for a period of almost 5 years. For some stocks, an 11 year tradinghistory has been considered. Now, let us say a few words about general problems of computeranalysis.Every day you can load down the files from all the US stock exchanges. You can see inthese files the opening price, maximum and minimum prices during the trading day, closingprice and trading volume for thousands of stocks. We will use simple notations for theseparameters:OPE, MAX, MIN, CLO, VOLYou do not know what the bid-ask spreads are. However, this is important for short-termtraders. We would not recommend short-term trading of stocks with spreads of 4% and more.Fortunately, the spreads are not so large. Usually, for active stock they are about 0.5 - 1%. SeeTable 1.1 as an example. So, you need to develop a trading strategy with an average profit of1.5% to have an average 0.5 - 1% return per trade.Table 1.1 Bid-Ask spreads of selected stocks from the list of potentially bullish stocks.March 25, 1999Ticker
Price
Spread %
STK
26.2
0.2
PGNS
10.5
0.6
SWLDY
5.8
1.1
FSII
6.2
1.0
MYLX
6.5
1.9
RDRT
6.5
1.9
SANG
15.2
0.4
CATP
11.7
0.5
SFAM
12.2
1.0
8HTCM
24.2
0.2
OXE
21.2
0.9
FRND
8.7
1.4
SKS
24.5
0.3
Average spread =
0.88%
For other actively trading stocks like Intel, Microsoft, Yahoo!, ... spreads (in %) are muchlower. In our calculations we will assume that transaction cost (bid - ask spread + brokeragecommissions) is equal to 1.5%. Further, we will also analyze dependence of the average annualreturns on the transaction cost.1.6 How to buy low and sell highLet us talk more about trading ranges and the possibility of making profits. The mainproblem is how to define the trading range. Everything is clear when the trading range has beenestablished and you can see a couple of oscillations. Draw the support and resistance lines andyou are ready to start trading. The problem with established ranges is their stability. Theycannot exist forever. When you define support and resistance lines, the trading range is ready todisappear. What to do? Do not use trading ranges for making trading decisions!Hey! a couple of paragraphs above we talked about tricks that work and now werecommend that you not use them? Yes, we repeat - do not use trading ranges! Do not usethem if you want to make a good profit. You have to buy oversold stocks and sell shortoverbought stocks. Your profit will be much higher.
Figure 1.6
Which stock is oversold?
Let us illustrate what we are talking about. First, how do we define oversold andoverbought stocks? Have a look at Figure 1.6. Which panel presents the best possibility to makea fast profit? We like panel C. The stock had a very well-established downtrend. One day, thestock price sharply went through the floor. What happened? Usually, downtrend is related torumors about bad earnings. Do not see the fundamentals of this stock. They may be excellent.Low p/e ratio, small debt, good yield. But something is going on. The market is always right.One day the bad news is released. This stock will be the main theme on CNBC. A specialarticle at the MarketWatch Web site will be published. All major brokerage firms will downgradethe stock. It opens for trading with a downside price gap, and its price continues to fall further.In the middle of the trading day the stock can recover a little, but it can fall further by themarket closing.This is your stock. Buy it! The stock is oversold.Why are the other stocks (panels A and B) not oversold? Ask technicians about that. Theywill tell you about breaking trading range, head and shoulders, etc. Fundamentalists will tell youabout bad prospects for the industry and for this particular stock. There will be a lot of guys who
9do not like this stock. A lot of people will hear these comments and selling pressure canaccelerate.The stock from panel C was a pure candidate for a long time. Everybody who knowsabout downtrends was out of this stock. Most of traders and investors like rising stocks. Ourstock from panel C was out of the game. Nobody cared any longer about it.Who is buying the stock from the panel C after sharp price drop? Why can the stock pricerise in the next couple of days?- Short sellers will close their positions. They have nothing more to expect.- Bottom fishers are ready to buy.- The company will buy some shares back.- The company becomes a target for acquisition.Do not worry about coming bad news. Let us show an example. Look at headline newsabout Osicom Technologies Inc. (FIBR). This news was released just before the stock jumpedfrom 5 1/4 to 7 1/2 during intra-day activity.
--------------------------------------------------------------------------------------------PRN
04/23 13:06 Osicom Technologies Inc. Misled Investors About '$90 Million Contract', Pomerantz Lawsuit Alleges ...
BW04/23 12:22 Stull, Stull & Brody Announces Class Periods for Class Action Complaints ...
PRN04/23 10:02 Notice To Osicom Technologies Inc. Shareholders Who Purchased Securities From July 1, 1998 Through ...
PRN04/23 09:58 Bernstein Liebhard & Lifshitz, LLP Commences Class Action on Behalf of Purchasers of OsicomTechnologies,Inc....
BW04/23 08:38 The Law Firm Of Abbey, Gardy & Squitieri, LLP Filed Class Action Against Osicom Technologies
BW04/23
08:00
Osicom
Technologies
Comments
on
Current
Status
of
Its
Core
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Business
Operations
...
However, it is still a risky game. More bad news can be released and the price willplummet even further. If the market is bad there is a little chance for fast recovery.Nevertheless, the risk of this game is smaller than for other strategies. This important fact willbe discussed in detail later.If you bought stock a after sharp drop - do not hold it for a long time. 3-4 days is enoughto make a fast profit. After this period the stock becomes similar to other stocks. The probabilityof growth is diminishing and it is better to jump to other stocks with higher growth probabilities.This is the main idea of our trading strategies.
10Chapter 2
Stock price time dependence2.1 Market memory2.2 Trend and volatility2.3 Time scales2.4 Correlation2.5 TD - mapping2.1 Market memoryIn the textbooks you can read: the market has no memory and stock price changes arerandom. Generally, this is wrong. However, if you randomly pick some stock, then there is asmall chance of finding a situation when the growth probability is much larger than 50%.Extraordinary events do not occur every day with any given stock. Our friends frequently ask usabout some particular stocks. Usually, we have nothing to say. The computer shows 49 - 51% ofgrowth probability for these stocks. It is really a random walk.The situation is completely different if you analyze the whole market - thousands ofstocks. In this case, you are able to find a group of stocks with high probabilities of strongupside or downside moves. Computer analysis showed that for some stocks the growthprobability can be 66% or higher. The analysis is based on the stock price histories. So we cansay: some stocks at some time have memory. The people who traded these stocks remembertheir actions, and the behavior of these people is predictable.2.2 Trend and VolatilityTrendTrend is a simple intuitive term. If a stock price is increasing one can say the trend of thisstock is positive. If a stock is declining - the trend is negative. You can also say: a stock hasmomentum. This is standard terminology. In many books on technical analysis of the stockmarket you can read about momentum investments: buy stocks with the highest growth rates.Do not do that for short-term trading. You can obtain the highest return if you do theopposite: buy stocks with the most negative trends.We need to define trends mathematically. This is the only way to tell the computer howto find stocks with large negative trends. The simplest method is using the linear fit of stockprice-time dependence.
Figure 2.1
Different trends
Consider N trading days and draw the fitting line L(i) through the points Pi, where Pi isthe closing stock price on the i-th day.1 23...N|___|___|___|___|___|___|___|___|___|___|___|___|___|___|___|___|PNP1 P2 P3 ...
11The N-th day is the day of interest, the day of the analysis.L(i) = A + Bii= 1, 2, ..., NThe coefficient B is the slope of the fitting line. The slope can be considered as the pricetrend of the stock. It characterizes the average daily price change (in $) during N days.However, this value is not perfect when comparing trends of different stocks. The stock of Intel(INTC) can have B = 2 and the stock of Vivus (VVUS) can have B = 0.5 for certain periods oftime. These numbers cannot be used to compare the trends of these stocks. This is becauseVVUS costs $5 and INTC costs $80. Relatively, VVUS has a larger trend than INTC.We will define a trend as the average price change in % during one trading day.Mathematically this can be written asTrend = T = <∆P/P> * 100%This definition has one disadvantage. What price P should be used in this equation? Usingthe current stock price is not a good idea. In this case, trend will be very volatile. It is better touse a more stable price characteristic: the value of the linear fitting line on the day #N - the dayof the analysisP = A + B*NThe final equation for trend looks likeT = B/(A + B*N) * 100%This equation we used in our computer analysis of the stock market. Such a definition oftrend substantially reduces the influence of price fluctuations during the final days. Figure 2.2shows an example of trend calculations for a 16 day time frame.
Figure 2.2
Example of stock trend calculations for a 16 day time frame.
Another way to define the trend is by using logarithmic scaling. This is a good idea if youstudy a stock's long history of price change, for example, from 1 to 100 dollars. For short-termtrading this change is unrealistic and we will keep things as simple as possible. So, we will usesimple linear fits, and trends are related to the slope of the fitting lines.VolatilityConsider another important characteristic of stock time performance - the volatility.There are many different ways to determine this parameter. For our goal we need to relate thischaracteristic to the linear fitting line. One can define the volatility as the standard deviation ofstock prices from the fitting line during some period of time.σ2 = <(Pi - A - Bi)2 >where averaging is performed during N days.
12So, when we talk about volatility we should mention how many days have beenconsidered for averaging.
Figure 2.3
Different volatilities
There is a similar relativity problem in the definition of volatility. One should divide σ bythe current stock price characteristic to be able to compare volatilities of different stocks.Similarly, as we did for trend, we define volatility V as the ratio of σ to the value of the linearfitting line on the day of the analysisV = σ/ Pwhere P = A + B*N.The higher the stock volatility, the higher the trading return and the higher the risk. Youshould always remember this important fact when you select stocks for trading.Deviation (D-parameter)The deviation or D-parameter, which will be defined here, is crucial for short-term stocktrading. Briefly, this is a characteristic of deviation of the current stock price from the fitting line.This characteristic is important for the definition of oversold or overbought stocks.A simplest idea of the definition of overbought and oversold stocks is the location of thestock closing price relative to the trading range. We assume that when the stock price is in thetrading range, the stock performance is normal. If the price is out of this range, the stock maybe oversold or overbought.
Figure 2.4
Illustration for the definition of D-parameter
We define trading range as a channel between support and resistance lines. Usually,these lines are determined intuitively from the stock price charts. This is not a good way if you
13use the computer to analyze stock price performance. The line drawing depends on the trader'sskill and this method can be used only for representation of stock performance in the past.Some traders use minimal and maximal prices to draw the support and resistance lines, otherslike closing prices. There is a problem of what to do with points which are far away from thetrading channel, etc.We suggest using the standard deviation σ (σ2 = <(Pi - A - Bi)2 >) for the definition of thesupport and resistance lines. Mathematically this can be written asSupport line = A + Bi- σResistance line = A + Bi + σwhere A + Bi is the equation of the linear fitting stock price time dependence; i is the daynumber.One should notice that the definition of the support and resistance lines depends on thenumber of trading days being considered. You should always indicate what time frame has beenused. This important question will be analyzed in the next section.To characterize the deviation of the stock closing price from the fitting line we haveintroduced a new stock price characteristic: - deviation, or D-parameter.D = (PN - A - BN)/ σwhere N is the number of days which were used for linear fitting, PN is the closing stock price onthe day #N (the day of the analysis) A and B are the linear fitting parameters, and σ is thestandard deviation of closing prices from the fitting line.Let us explain the meaning of this equation. The difference (PN - A - BN) is the deviationof the current stock price from the fitting line. D-parameter shows the value of this deviation inσ units. One can sayD < -1 the stock may be oversoldD > +1 the stock may be overboughtthe words "oversold" and "overbought" should be used together with the number of trading daysconsidered. So it more precise to say: the stock is oversold in the 30 day time frame.We have now introduced some definitions. What about the practical use of these ideas?Are stocks really oversold or overbought if their prices are out of the trading channel? Thereshould be some "forces" which attract the stock price back to the trading channel. Theseproblems will be considered in the next chapters. Here, we should consider more methods ofdescribing stock price time dependence so that we may be ready to better understand theresults of computer analysis.2.3 Time ScalesSuppose you found some stock which looks oversold on a monthly time scale. However,on a weekly time scale the stock price is close to the resistance line. Would you buy this stockfor short-term trading? If you want to lose your money - buy! A good stock for trading should beoversold in many different time scales.Which time scales (or the number of days in history N) should be considered for shortterm trading? Short-term we define as 1 - 5 days. It is obvious that a period of one year is notinteresting. Trades have already forgotten what happened a year ago. We will use the followingtime scales:N= 4N= 8N= 16N= 32Computer analysis has shown that this is enough. Very little correlation between stockprice moves and deviation D and trends T for longer time scales has been found. We will use thefollowing notations for corresponding D and T
14D4 , T 4D8 , T 8D16, T16D32, T32The volatility V will always be calculated over a 32 day period. This value is rather stableand reflects the last 1.5 month of stock price history.V = σ32/ PThe parameters D and T for different time scales are not independent. If D4 is large thenD8 will be larger than the average value. This is also true for T parameters. Large values of shortperiod trends give larger values for longer trends. Later we will show correlation of differentparameters.The correlation of D and T is the reason why we do not consider parameters forcontinuous time scales like N = 4, 5, 6, and so on. The smaller time scales (N = 2 or N = 3) arenot good for calculating fitting lines. However, the last day price change can be important, andwe will consider this price change in the analysis of different trading strategies.2.4 CorrelationCorrelation is an important concept in statistics. It describes the relationship between tworandom variables. Quantitative description of correlation can be done by using the correlationcoefficient c. For two random variables X and Y the correlation coefficient can be calculated asc = <(X - Xo)(Y - Yo)>/(σX σY)where Xo and Yo are the average values of X and Y ; σX and σY are the standard deviations ofthese variables. The angular brackets denote averaging.The correlation coefficients vary from -1 to +1. For positive c one can say that thevariables X and Y are correlated or positively correlated. For negative c one can say that thevariables X and Y are anticorrelated or negatively correlated. Positive correlation means that achange in the value of X causes a change in the value of Y in the same direction.
Figure 2.5
D8 - D16 and D8 - T8 correlation's
In the previous section we mentioned that trends T and deviations D for different timescales are correlated. Now we can present the values of the corresponding correlationcoefficients. Figure 2.5 shows the correlation between D8 and D16. Data are collected for theperiod 1995 - 1999 for actively traded US stocks with prices > $10. One can see a strongcorrelation between these variables (c = 0.66). Fig. 2.5 shows little correlation between D8 andT8 parameters. The correlation coefficient in this case is equal to -0.03.
15These observations give us the idea of using the two parameters T and D together tostudy the relationship between (T, D) pairs and trading returns.Now we are ready to understand the concept of T-D mapping, which will be considered in thenext section.2.5 T-D MappingWe have shown that trends T and deviations D, even for same time scale, areuncorrelated. So, they can be used as independent variables, and we will study differentfunctions of these variables. For example:Return = f1(T, D)Risk = f2(T, D)Probability of Positive Returns = f3(T, D)and so on. The