“The risk-reducing formulas behind portfolio theory rely on a number of demanding and ultimately unfounded premises. First, they suggest that price changes are statistically independent from one another…The second assumption is that price changes are distributed in a pattern that conforms to a standard bell curve. Does financial data neatly conform to such assumptions? Of course, they never do.”
Benoit B. Mandelbrot
Suppose you have two traders each following the same trading system. The system produces a signal to buy Microsoft stock. The first trader initiates right when he must, based on the system, but for some reason, the second trader misses the signal. The market now goes up in the desired direction boosting the value of Microsoft stock. The second trader finally initiates and buys Microsoft stock, but obviously later than the first trader. Two questions: Should the second trader make the trade since he missed the signal the first time around? And if the second trader does, isn’t he still missing out on potential profit since he got in later than the first trader?
Now let’s say that, instead of just the same system, the two traders have the same amount of money. Two more questions: Doesn’t this scenario imply that the first trader who got in at the right time is risking more money since the second trader still got in the trade but did not have to do so as early as the first trader? Doesn’t the second trader have an advantage since he is risking less?
The answer to each of these questions is the same. Both traders are in the same position. Both have the same advantage. Great traders avoid personalizing their trading as it blinds them to the reality of what is actually happening in the market. The market is the market whether you participate or not, so personal circumstances don’t matter. Both traders are in the same situation, in the same market with the same position, with the same money and the same attitude. Why must these two traders act differently just because one has a slightly different past in terms of when he entered the trade?
This article has caused some confusion among readers. Reader feedback:
“But, timing is crucial.”
“Stops are money management.”
Timing of entry is not the critical issue in overall trading success (it is maybe 10% of your overall success). Additionally, money management (which is widely misunderstood) is much more than stop placement. Placing a stop does not tell you how much to buy or sell.
So how much thought have you given to money management recently? Or are you still too preoccupied by all kinds of indicators or fundamental buy, sell and holds to focus on the subject? Eventually, however, you’ve got to ask yourself the most important question of all, “How much?” right?
Getting a straight answer to that one may be tough. There’s still a lot of confusion about risk or money management from so-called gurus. I recently saw the following comment regarding money management from a “guru”:
[We] use very simple money management: Trade one contract per trading signal in the markets with no pyramiding.
This is NOT money management. When you hear someone describe money management like this trading guru, run don’t walk the other direction as you are about to be conned.
So if money management isn’t some set amount of shares or contracts picked out of thin air, what is it? Money management answers the question of “how much?” At all times, given the risk you are taking, the money you have, and the volatility of the market — you must know the optimal number of shares or contracts to be long or short.
In my opinion money management or position sizing or bet sizing just doesn’t get the attention it deserves. Gibbons Burke of MarketHistory.com observes:
Money management is like sex. Everyone does it one way or another, but not many like to talk about it and some do it better than others. But there’s a big difference: Sex sites on the Web proliferate, while sites devoted to the art and science of money management are somewhat difficult to find.
Money management is ultimately a defensive concept. It keeps you in the game. For example, money management tells you whether you have enough new money to trade additional positions. Trend followers all realize that you need to make small bets initially to simply stay alive and play another day. So, if you start at $100,000, and you’re going to risk 2 percent, that will be $2,000. You say to yourself, “Why am I only risking $2,000. That’s nothing compared to what I’ve got to bet.” But that’s not the point. First things first. You can’t predict where the trend is going to go, so you can’t afford to risk all of your capital out of the gate. Trend follower Craig Pauley points out:
There are traders who are unwilling to risk more than 1% but I would find it surprising to hear of any trader who risks more than 5% of assets per trace. Bear in mind that risking too little doesn’t give the market the opportunity to allow your profitable trade to occur.
Think about money management as you would about getting into physical shape. You can’t lift weights six times a day for hours each day for 30 straight days without hurting yourself. There’s an optimum amount of lifting you can do per day that gets you ahead without setting you back. You want to be at that optimal point just as you want to get to an optimal point with money management. Trend follower, Ed Seykota, author of The Trading Tribe book, describes this optimal point with his concept of “heat”.
Placing a trade with a predetermined stop-loss point can be compared to placing a bet. The more money risked, the larger the bet. Conservative betting produces conservative performance, while bold betting leads to spectacular ruin. A bold trader placing large bets feels pressure – or heat – from the volatility of the portfolio. A hot portfolio keeps more at risk than does a cold one. In portfolio management, we call the distributed bet size the heat of the portfolio.
Trading correctly is 90% money management, a fact that most people want to avoid or don’t understand. However once you have money management down, your personal psychology will be 100% of your trading success. Once you have the rules, you still need to follow them!
Why then do traders have such trouble keeping their trading proportional? Why is it so hard for them to find that optimal point? Fear. Trend follower Tom Basso points out that traders usually begin trading small and then as they get more confident increase their trading size. Once they get to a certain comfort level of say, 1000 contracts, they often stay there, suddenly fearful that turning up the “heat”, to use Seykota’s term, will increase their risk. For trend followers like Basso, the goal is to keep things on constant leverage.
Few traders make the move to a proactive posture in which risks are actively managed for a more efficient use of capital. How do you avoid trading less instead of trading the optimal amount at whatever capital you have? You need to create an abstract money world. Don’t think about what money can buy. Just look at the numbers like you would when playing a board game like monopoly or risk.
And since your capital is always changing, it’s important to continually rebalance your portfolio. Trend follower Paul Mulvaney points out that:
Trend following is implicitly clear about dynamic re-balancing which is why I think successful traders appear to be fearless. Many hedge fund methodologies make risk management a separate endeavor. In Trend following it is part of the internal logic of the investment process.
There it is: the key is a risk understanding. That’s what money management is really all about. Managing risk.
“When any trader makes a decision to buy or sell (short), they must also decide at that time how many shares or contracts to buy or sell — the order form on every brokerage page has a blank spot where the size of the order is specified. The essence of risk management is making a logical decision about how much to buy or sell when you fill in this blank. This decision determines the risk of the trade. Accept too much risk and you increase the odds that you will go bust; take too little risk and you will not be rewarded in sufficient quantity to beat the transaction costs and the overhead of your efforts. Good money management practice is about finding the sweet spot between these undesirable extremes. on a per-trade basis.”
Money management is the crucial concept for all traders and investors. But, mainstream press never writes of its importance. The author below, for example, simply opines a feel good market view. Nothing he says could help you make a dollar.
TurtleTrader editorial comments are bold.
“How to Weather the Tech Stock Storm”, by SCOTT HERHOLD at Mercury News:
With an avalanche of earnings reports, the stock market last week demonstrated almost perfect schizophrenia. The semiconductor equipment people confessed to woes. But Intel exceeded expectations. EBay thrived. Microsoft stumbled. Sun bounced [TurtleTrader® comment: His point? The market always changes, he states the obvious. Volatility is nothing new. Prepare for it]. The market climbed. The market fell. But mostly, the market shuffled sideways. Was it all sound and fury signifying nothing? And where does an investor go from here? Is this the time to jump in ahead of a potential rally later this year? Or is it a time for caution? [TurtleTrader® comment: You need a plan ahead of time]
Some of the people I trust have thrown up their hands and decided, at least as long ago as last spring, to take a year off from owning tech stocks. Much like scavengers pawing through the embers of a fire, they plan to revisit the terrain next year to see what remains [TurtleTrader® comment: This is no plan]. This is a tempting point of view. It has definition. But things can change rapidly. So if you’re still paying attention and your wounds from 2000 have more or less cauterized, here are some of the factors you must be thinking about: Remember just who’s playing this game. You may remember the television commercial that shows a short, fat guy who dreams of playing pro basketball and dunking the ball past the NBA stars. In a lot of ways, that guy illustrates the plight of the individual investor in today’s market. The volatility of the market last week was driven largely by hedge funds and other institutional investors, who move quickly in and out of stocks, often covering their positions by taking out options like puts and calls [TurtleTrader® comment: Markets move for a variety of reasons, identifying why is a waste of effort, concentrate on how you react within a strategy].
Friday was the day that options settled. And that caused fierce jockeying to take advantage of earnings news. Everyone in the market is playing the same game, says Harvey Baraban, a San Francisco stock market trader and educator. It’s very nervous, scared money. But it’s also very large and very aggressive. [TurtleTrader® comment: Why is money emotional, people are emotional, money has no feelings]
Memo to investors: If you think you can beat the pros at this short-term game, you can probably outdunk Shaquille O’Neal as well. You’ve got a healthy fantasy life. At the same time, the absence of individual investors makes it harder to restart the market [TurtleTrader® comment: Markets don’t stop or need to be re-started, they move, have a system that takes advantage of moves]. Keep an eye on the longer term [TurtleTrader® comment: Finally, some truth]. Yes, this means paying attention to the overall economy, which is still delivering dismal news. Every other day, the other shoe drops, says David Gold, a venture capitalist with Indosuez Ventures in Menlo Park. I think we have a centipede or millipede crawling across with so many shoes dropping.
The key equation is capital spending, which has been put on virtual hold at many companies. That in turn has caused piles of unused inventory. But capital spending is not uniform across the board — and some sectors do better than others [TurtleTrader® comment: More fundamental data useless to a trader trying to make money in the market]. An interesting study was done recently by Techtel, an Emeryville research firm that tracks the real tech demands of companies. (A real need describes what a company really uses, not what a salesman has persuaded them to commit to. If a company has bought 1,000 Oracle software seats but uses only 500, real demand is the 500). The good news here is that demand, after falling sharply at the end of 2000, shows signs of flattening out or even strengthening, particularly in areas like mid-range servers and storage area networks. The bad news: Soft spots exist with PCs and database software. We don’t see overall demand going up, says Michael Kelly, Techtel’s chairman. We see it as basically flat.
But he adds: Flat is good. [TurtleTrader® comment: Flat is good for no one]
Memo to investors here: It’s worth making distinctions amid tech stocks. The Techtel study would suggest that certain outsourcing companies — including IBM and EDS — are better positioned for revival than, say, a PC maker like Dell or a database software supplier like Oracle. Sun is stronger in higher-end servers than in mid-range machines. Keep watching the charts. We’re not talking about astrology here — though given the market’s performance over the past year, we might just as well. But there are some technical patterns that are worth thinking about. Essentially, the market has been on a downward slide for the past 16 months [TurtleTrader® comment: Yes, we know]. Yes, there was a major bounce after the market hit a low in early April. But the current market is testing those lows once again. The technicians say a strong surge upward will probably reverse that longer-term downward trend.
So when will that happen? [TurtleTrader® comment: No one knows. If you even attempt a prediction you will likely lose money. Trend Following trading, for example, never predicts, it reacts to market movement telling you how much to buy or sell at a given time] One cautiously optimistic view comes from WitSoundview’s technical strategist, Arnold Berman, who has studied the number of confessions — or preannouncements of earnings disappointments — among tech companies. Partly because investors are used to bad news, disappointing results no longer pack the wallop they once did. Berman says the stock of the typical preannouncing company declined only 9 percent in the second quarter — compared with 26 percent last year.
The overall picture on technology remains negative, Berman writes. If we argued differently, we’d be like the TV weatherman who tells his viewers it’s not raining when a glance out the window shows it’s pouring. However, a good weather forecaster doesn’t predict rain for tomorrow just because it’s raining today. Memo to investors: Be cautious, yes. But don’t be blind. Sometime the clouds will part [TurtleTrader® comment: An article that says almost nothing. A great example of the financial press helping no one].
“It is a common notion that after you have profits from your original equity, you can start taking even greater risks because now you are playing with their money. We are sure you have heard this. Once you have profit, you’re playing with their money. It’s a comforting thought. It certainly can’t be as bad to lose their money as yours? Right? Wrong. Why should it matter whom the money used to belong to? What matters is who it belongs to now and what to do about it. And in this case it all belongs to you.”
The gambler’s fallacy and concept of availability error are key for traders. Trend followers have an understanding of these concepts built into their trading style.
The Gambler’s Fallacy
One of the easiest mistakes to make with trading is thinking that past trades influence future ones. This common mistake is sometimes called the gambler’s fallacy, and it often leads people to bet more money and to bet more often than they otherwise would. For example, many people know how to figure that there is only a one in sixteen chance that a fair coin will come up heads four times in a row. But if the coin has already come up heads three times in a row, then the chances that it will do so a fourth time are the same as they would be if it had never been tossed before–one in two. However, it is easy to make the mistake of thinking that this coin has only a one in sixteen chance of coming up heads. It seems that the coin should make the average of past tosses come out right. But in reality, the coin does not remember past tosses and feels no obligation to even out the number of heads and tails that have come up before. As we make more and more coin tosses, the ratio of heads to the total number of tosses will approach one half, but this does not mean that there will be exactly (or even close to) the same number of heads as tails, nor does this mean that in the course of a few tosses things will come up anywhere near even.
Misunderstanding this fact leads many traders to believe they have more information than they really do, and can cause them to be more willing to over-trade than they otherwise would.
The second major mistake people make, and which increases their tendency to over-trade, is called availability error by psychologists. This is the common tendency we all have to focus only on good, unusual, or easily remembered experiences, forgetting the bad, common, or less available ones. For example, hearing that someone has won the lottery sticks in our mind more than hearing that someone has lost the same lottery. We remember winners more than losers, and mistakenly think that the chances match our memory. This explains why people put more money into slot machines that are in large groups, where they can hear and see signs that others are winning, rather than into lone machines, where they have no recent memory of someone’s winning. And people consistently do this, despite the fact that the odds are just as bad for the group as for the lone machine. Memories of winners are simply more available for the large groups than the loners.
We may also think that if we know or have heard of a winner it must not be very hard to trade successfully. Many people have a story about how their Aunt or their brother-in-law’s boss’s friend once won on some great trade. But there are several things that are omitted from such stories. Most important is the fact that someone lost thousands of dollars before and after making that great trade. Many so called great trades are really only small wins that barely cover the cost of trading, and which serve to entice people to continue trading and losing more money. The markets take advantage of our tendency toward availability error and exploit our memory of the one great trade while encouraging us to forget the many losses.
Moreover, when we hear the story of our brother-in-law’s boss’ friend’s great trade, we tend to assume that because we have heard of this person and have some connection to him or her, however remote, and winning must be more likely than we had thought. But we never hear the story of our co-worker’s Uncle who lost fifty thousand dollars in the market gambling on tips with no strategy. And if we wanted to hear all the stories of the times that our relatives’ acquaintances’ friends or our friends’ acquaintance’s relatives lost money while trading, we would have no time for anything else. Indeed, by such a chain of associations you can hear the story of essentially every other person in the entire world.
Many hear the word correlation and they go to sleep. You can’t sleep though — it’s too important to grasp. Definition:
Correlation coefficients gauge how closely an advisor’s performance resembles another advisor. Values exceeding 0.66 may be viewed as having significant positive performance correlation. And consequently, values exceeding -0.66 may be viewed as having significant negative performance correlation.
Some examples of correlation in action taken from CSI Data:
Just what is correlation, and how do we derive the correlation coefficient? Correlation is a statistical term giving the strength of linear relationship between two random variables. More simply defined, it is the historical tendency of one thing to move in tandem with another. The correlation coefficient can be a number from -1 to +1, with -1 being the perfectly opposite behavior of two investments (e.g., up 5% every time the other is down 5%), and +1 reflecting identical investment results (up or down the same amount each period). The further away from +1 you get (and thus closer to -1), the better a diversifier one investment is for the other. Correlation coefficient is found by taking the covariance between two variables and dividing by the square root of the product of each of the two variances (trust us on this part). No wonder the eyes of so many glaze over when discussing the topic of correlation. However, it has some very tangible uses, if they can be explained to the novice. The most simplistic description of correlation is the tendency for one investment to “zig” while others are “zagging”.
A great excerpt from Tom Basso, taken out of Financial Planning Magazine:
Why then would we want to time the market, if all the studies have shown that actual client timing is so poor? The answer is that actual client timing has been driven more by investor psychology than logic. Our simple timing strategy (or more sophisticated ones used by many investment managers) forces the investor to buy when the market is moving up, not question the direction or how long the move will last. It forces the investor to sell out of the market after he’s made large profits, is euphoric with the market, but the market starts to move lower. It helps to provide the discipline that the typical investor lacks. Another psychological aspect that drives me to use timing techniques on my portfolio is understanding myself well enough to know that I could never sit in a buy and hold strategy for two years during 1973 and 1974, watch my portfolio go down 48% and do nothing, hoping it would come back someday. Timing strategies give me the psychological lift that allows me to react to market risks and modify my exposure to those risks over time. It’s empowering to be able to know that I can cut losses short and let gains run. It keeps my investing mind concentrated on doing the right thing each day, rather than succumbing to all emotional swings that most investors go through in up and down markets. If an investor’s mental process is not sharp and disciplined, the market has ways of teaching that investor what risk really is.
Another Thought from Tom Basso:
Investors who time the stock market are constantly faced with the prospect of becoming impatient when, over a shorter time frame, there doesn’t seem to be value added by a timing strategy. Frequently, their excuse for abandoning a timing strategy is it doesn’t work anymore or I could have made more money with a buy and hold strategy. Investor psychology is heavily at work here. The investor, at that point, does not remember why they developed or started using their timing strategy in the first place. Many times I have seen investors forget what to expect in the best case, worst case, and expected case scenarios. I maintain that if the investor can understand exactly what to expect from a strategy, they will be less surprised when the timing strategy does exactly as expected. I constructed this study to help investors learn more about the action of the stock market and what timing programs generally should provide the investor.
More thoughts from an excerpt of, A Perspective on Risk by Jim Little, and Sol Waksman:
Sound investment policy is really about intelligent risk management. There is no such thing as a risk free investment. Even an investment in cash exposes the investor to the risk that his buying power will erode through inflation. The real issue is not whether you want to take risk, but which risks and how many of them you are willing to accept. To make intelligent decisions as to how much of a particular risk is right for you, and how to blend risks properly to lower overall portfolio risk, you must have accurate measurements about how much risk each sector of your portfolio is exposing you to. Some investors rely on conventional wisdom (or lack thereof) to dictate their asset allocation. Others rely upon outdated statistics. The wise investor continues to study the facts.
And another excerpt from, We Have Met the Enemy by Jack D. Schwager:
We have met the enemy, and it is us. This famous quote from Walt Kelly’s cartoon strip Pogo would serve as a fitting universal motto for investors. In my experience, investors are truly their own worst enemies. The natural instincts of most investors lead them to do exactly the wrong thing with uncanny persistence. In a nutshell, the heart of the investor blunder is the tendency to commit to an investment right after it has done very well and to liquidate an investment right after it has done poorly. Although these types of investment decisions may sound perfectly natural, even instinctive, they are also generally wrong…I would like to relate two personal experiences that made me appreciate this general principle in very real terms. The first occurred about a decade ago, when I worked for a firm where part of my job responsibilities included evaluating commodity trading advisors (CTAs). I made the striking discovery that the majority of closed accounts showed a net loss for virtually all the CTAs I reviewed–even those which had no losing years! The obvious implication was that investors were so bad in timing their investment entries and exits that most of them lost money even when they chose consistently winning CTAs. It goes against human nature to invest in what has been going down instead of what has been going up.
Fundamental analysis, buy and hold, value investing, CNBC, stock pickers, day trading–stop. Enough. Those typical investing approaches, popularized by media for decades, are not the way to build true wealth. Explore trend following and learn something different.
Some mistakenly believe that trend following will cease to work if too many people trade as trend followers. We have addressed this question over the years, but decided to approach the issue from a different angle: human nature and the lottery.
Take this CBSNews.com excert for example:
The odds of winning the Powerball lottery are more than 80 million to one, a fact that seems lost on most lottery players. A survey taken last year by the consumer group Consumer Federation of America shows over a quarter of Americans believe the lottery is their best chance at gaining wealth in their lifetime. “Many don’t fully appreciate the odds against their winning the lottery,” said Stephen Brobeck, executive director of the Consumer Federation of America. “Some are not aware of the opportunities for even moderate-income families to save and build wealth.” Opponents of state-sanctioned lotteries believe the problem is much deeper. The deputy director of the Council on Compulsive Gambling of New Jersey calls the lottery a national addiction. “It’s culturally OK and socially acceptable to play the lottery,” said Kevin O’Neill, adding that near-wins are “instant reinforcement” to continue playing.
Look at how many people play a losing game like the lottery and still continue to play, day after day, year after year. The outcome of the purchase of a Lotto ticket is based on objective probabilities, but people still play. What are the odds?
- The odds of winning the California Super Lotto Jackpot are 1 in 18 million.
- If one person purchases 50 Lotto tickets each week, they will win the jackpot about once every 5,000 years.
- If a car gets 25 miles per gallon, and a gallon of gas is bought for every Lotto ticket bought, there will be enough gas for about 750 round trips to the moon before the jackpot is won.
- It is three times more likely for a person driving ten miles to buy a Lotto ticket to be killed in a car accident than to win the jackpot.
You have better chance for the following events to happen long before you ever win the lottery:
- Dealt a royal flush on the opening hand in a poker game (1 in 649,739).
- Killed by terrorists while traveling abroad (1 in 650,000).
- Die from flesh-eating bacteria (1 in 1 million).
- Heart disease caused by eating a steak a week (1 in 48,000).
- Killed by a lightning strike (1 in 30,000).
Trend following trading is different. It requires you to accept an understanding of odds. As long the majority consistently play losing games (like the lottery), the same lack of odds understanding will enable trend followers to keep winning.
One reader posted this:
For example, the Canadian 6/49 Lottery has 6 numbers drawn from a total of 49 balls with the numbers 1 through 49 on them. The probability here is 1 in 13,983,816. Before the first ball with a number on it is drawn, or randomly selected, there are 49 balls in the hopper. The first ball is drawn and put aside. After this first ball is drawn, there is 48 balls in the hopper. After the first two balls are drawn, there is 47 balls, or numbers, remaining. This continues until there are 44 balls remaining in the hopper when the sixth winning number is drawn. The Canadian 6/49 draws a bonus ball, which is drawn from the remaining balls after the sixth number is drawn. This last, or Bonus, number is used to select a second tier winner, and has amounted to more than $693,000.00. The Irish Lotto 6/42 has 6 numbers drawn from a total of 42 balls. This brings the odds down to 1 in 5,245,786. The US PowerBall draws 5 numbers from a total of 45 balls. Then, 1 number is drawn from a separate set of balls numbered from 1 to 42. This little detail makes the odds here 1 in 80,089,128.
Have you thought about your trading with this level of precision? Trend followers do every day.
One of the best books covering the history of risk in society is Against the Gods: The Remarkable Story of Risk, by Peter L. Bernstein. Bernstein delves into the trading psychology (otherwise known as behavioral finance) all trend followers live and die by:
Imagine that you are on your way to see a Broadway play for which you have bought a ticket that cost $40. When you arrive at the theater, you discover you have lost your ticket. Would you lay out $40 for another one? Now suppose instead that you plan to buy the ticket when you arrive at the theater. As you step up to the box office, you find that you have $40 less in your pocket than you thought you had when you left home. Would you still buy the ticket? In both cases, whether you lost the ticket or lost the $40, you would be out a total of $80 if you decided to see the show. You would be out only $40 if you abandoned the show and went home. Kahneman and Tversky found that most people would be reluctant to spend $40 to replace the lost ticket, while about the same number would be perfectly willing to lay out a second $40 to buy the ticket even though they had lost the original $40. This is a clear case of the failure of invariance. If $80 is more than you want to spend on the theater, you should neither replace the ticket in the first instance nor buy the ticket in the second. If, on the other hand, you are willing to spend $80 on going to the theater, you should be just as willing to replace the lost ticket as you are to spend $40 on the ticket despite the disappearance of the original $40. There is no difference other than in accounting conventions between a cost and a loss.
Prospect Theory suggests that the inconsistent responses to these choices result from two separate mental accounts, one for going to the theater, and one for putting the $40 to other uses–next month’s lunch money, for example. The theater account was charged $40 when the ticket was purchased, depleting that account. The lost $40 was charged to next month’s lunch money, which has nothing to do with the theater account and is off in the future anyway. Consequently, the theater account is still awaiting its $40 charge.
Trend followers do not allow themselves to create these artificial accounts. They always work to eliminate discretion by relying on the pure numbers. Great traders know the secret to great trading is their own objectivity.
On Ed Seykota’s web site (The Trading Tribe) he was once asked about using index cards with charts. The reader wanted to know how that worked. Ed responded: You can use index cards with charts; use a card to cover up the right side of the graph, and reveal it to yourself one day at a time, …
On Ed Seykota’s web site he was once asked about using index cards with charts. The reader wanted to know how that worked. Ed responded:
You can use index cards with charts; use a card to cover up the right side of the graph, and reveal it to yourself one day at a time, to simulate trading.
Ed’s response inspired us to create a visual example of his wisdom:
This is a key. As a chart slowly reveals itself think about what the best way to trade it might be. You only get one bar per day. That bar must tell you what to do long before you know what the end of the chart (or trend) will look like.
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