Revising the Reward-Risk Ratio

This article was first published in the April edition of the Market Technicians Association's newsletter.

Reward-Risk is a term for the ratio of the potential profit to the potential loss of a trade. In using such analysis, the entry price and the prices at which profits or losses will be taken are predetermined. Measuring the units of reward per risk in advance aids in deciding whether to enter a position. However, since the outcome of a trade is uncertain, this widely known and used measurement must be revised in order to account for the probability of the trade’s success or failure, which can be done through expected value.

In expected value, a set of future values, or payouts, are adjusted to reflect the probability that each will materialize. For a stock, given a $10 entry with a profit target of $16 and a stop-loss at $8, the reward-risk is $6 to $2, a 3:1 relationship; these are the set of future values. Additionally, say the probability of prices reaching the target before the stop-loss is 40%. The odds of being stopped out are thus 60% [=1-0.4].To obtain the expected value, one multiplies the chances of a profit by the potential profit, .4*$6 = $2.4, and the chances of loss by the potential loss, .6*$2 = $1.2. Thus, the expected reward-risk (ERR) is $2.4 to $1.2, or 2:1. The expected value is the gain minus the loss, or $1.2 [=$2.4-$1.2]. The unadjusted ratio of $6:$2, or 3:1 will from here on be referred to as the simple reward-risk (SRR). Note how in this example, the SRR is 3:1 but the ERR is 2:1. With a probability of success of .25, instead of .4, the expected reward is $1.5 [=.25*$6], the expected risk is $1.5 [=.75*$2], and the expected value is 0, or breakeven. Calculating an ERR of 1:1 reveals the odds needed to break even on a trade.

To use a non-market and non-monetary example, say a football player makes two-thirds, or roughly 67%, of his field goals. A field goal is worth 3 points if obtained, or 0 points if missed. For this player, his expected value is 2 points [=.67*3 + .33*0]. If in the last play of the game, his team is down by 3 points and he is up to kick a field goal, a strictly rational gambler will bet against the team. If the team is down by 1 point, the gambler will bet for the team. Although non-intuitive, a better description of reality is that this player scores 2 points per field goal rather than 3 points per field goal. Our gambler, by the way, will stay in business.

An SRR accounts for one observation, whereas an ERR accounts for all possible observations. Over the long term, the values of the ERR will materialize, similar to how the football player only scores 2 points per field goal. And like the gambler, a rational trader will base his decisions on ERR profiles that have a positive expected value. A positive expected value, however small, will result in long term success, and vice-versa.

Let us return to the example of the $10 stock with the SRR of 3:1. Given the present market conditions, the trader has assessed that either $16 or $8 will be reached first; whichever target is reached first will close the trade. If the analysis ends there, the trader unwittingly assumes that there is a 50/50 chance of a profit (of $6) or a loss (of $2). The expected return is thus $3 [=.50*$6] and the expected risk is $1 [=.50* $2]. Observe that the $3 profit to $1 loss remains a 3:1 relationship; the SRR equals the ERR. Any and every reward-risk setup that does not define probabilities assumes a 50/50 chance that its respective targets will be met. Therefore, the classical concept of reward-risk does—and has always— incorporated expected value, but as a passive assumption! Determining an expected reward-risk based on trade specific probabilities is not a supplement to the simple reward-risk construction, but rather, a revision of it.

The passive assumption of a 50/50 chance for a profit or loss has exerted a silent influence on the subject of reward-risk. Literature in Technical Analysis often prescribes a minimum reward-risk of 3:1 for one to remain profitable over time. As discussed above, “over time” is when expected values pave over individual observations. If a risk-reward lower than 3:1 is considered to ultimately result in a trader’s ruin, one can extract the assumed probabilities. The breakeven odds for an SRR of 3:1 are 25/75. Therefore, one assumes that successful traders are profitable slightly over 25% of the time, because anything less than 3:1 will result in a negative expected value. Interestingly, this success rate matches the figure of 30%, which is the percentage of time that the market is estimated to be trending.

A positive expected return can result from various reward-risk proportions and their respective probabilities of success and failure. For example, assume an SRR of 1:2.5, that is, for every potential profit of 1, there is a potential loss of 2.5. With a probability of success of .8, the ERR is 0.8:0.5, or 1.6:1, and the expected value is .30. Over the long term, this reward-risk profile makes .30 per trade—not per every winning trade, but per trade. That’s success. Now, examine a trade with a large profit potential and a “tight” stop-loss, a temptation particular to futures traders. Even with an SRR of 7:1, a 90% chance of being stopped out yields an ERR of 0.7/0.9, or .77:1, and a negative expected value, -.40. Trading only these 7:1 setups ensures a quick bankruptcy. As you can see, even if the SRR is less than 1, any trade with a positive expected value—adjusting for commissions and other frictions—should be undertaken. In this light, the prescription of trading only 3:1 or higher setups is crude, and most likely a result of an implicitly assumed success rate of around 25-30%, which may be related to the fact that markets trend 30% of the time.

Estimating the Probability

Trading is inherently probabilistic. The preceding arguments strongly suggest that if one is to use a reward-risk ratio in assessing trades, an expected value must be calculated and serve as a deciding factor.—Well, that’s the easy part. The real challenge to this model is in determining an accurate measure for the probability that will be used to arrive at expected values. Due to the complex nature of trading in the financial markets, probabilities can only be estimated, not determined. In the examples throughout this article, the probabilities used were assumed to be accurate for the sake of illustration. This section sketches four methods that can be used to estimate the probability of success for a given trade. Note that only one value needs to be calculated, because 1 minus the probability of success equals the probability of failure.

Historical Success Rate

For an individual trader with a consistent style, his historical success rate can be used as a proxy for the probably of success. For example, if he finds that 55% of his trades are winners, .55 and .45 will be the probability of success and of failure, respectively. With these probabilities, an SRR of .82:1 yields an ERR of 1:1, or breakeven.

You will see later on in this article, the probability of success can be inversely related with the reward to risk ratio. As higher price targets are attempted, there are fewer successes and vice-versa. The trader can balance the success rate and reward-risk proportion to see what combination yields the highest expected value. In the example above, the SRR must be greater than .82:1 for profitability. Based on the inverse relationship established above, to maintain a 55% success rate the reward may not extend too far beyond .82:1. Note, however, that if these measures of probability are consistent and accurate all one needs is a positive expected value for a trade to be worthwhile; in this example, even an SRR as “low” as 1.05:1 will have an expected value of 0.1275 per trade.

The historical success rate approach has the following advantages and disadvantages:

Advantages
• Based on empirical data
• Quick and simple to calculate
• Requires no estimates
• A long enough track record has some reliability

Disadvantages
• Past performance is not indicative of future results; the conditions that have allowed that style obtain a given success rate may change
• Not a scientifically rigorous approach

Technical Analysis Statistics

Technical traders use various methods to determine buy and sell signals. These include trendlines, support and resistance, continuation and reversal patterns, indicators, and many more. The statistical success rates of these methods of technical analysis can be used for calculating probabilities.

In Charles Kirkpatrick and Julie Dahlquist’s Technical Analysis, the authors summarize the results from Thomas Bulkowski’s Trading Classic Chart Patterns. In his book, Bulkowski documented the success rate of various technical continuation and reversal patterns from a sample of 700 stocks during a span of ten years. I will use his figures for illustrative purposes.

For a rectangle pattern, also known as a trading range, if there is a viable upward breakout, established after the fact in Bulkowski’s research, 80% of the time there will be a gain of 10%. (Technical Analysis, p. 315) That yields an expected reward of 8%. A stop-loss at -4% [.2*-4% = -8%] is thus the breakeven point. A stop-loss of less than 4% below the entry price is necessary to obtain a positive expected value. Continuing with this example, 75% of rectangle breakouts are false signals, making the ex ante success rate 20% [=.8*(1-.75)]. The expected reward is not 8%, but 2%. A stop-loss at 2.5% yields an expected value of 0. The breakeven SRR is thus 5:1, a 10% gain to a 2.5% loss. Pretty grim. These numbers also assume that the odds already discount the possibility of being stopped-out prior to the 10% gain.

Using technical analysis statistics to determine probabilities has the following advantages and disadvantages:

Advantages
• If technical analysis is used to determine the reward and risk targets, this method is the most consistent with the analysis
• Expected values are simple to calculate
• Requires no estimates

Disadvantages
• The body of research on the success rate of technical patterns and indicators is limited, an enormous hindrance to this approach
• Based on historical data
• Both the success rates of valid signals and the likely percentage gain prior to a reversal of the signal must be known to properly calculate the probability

Volatility of Returns

All else equal, of two price targets in opposing directions, the target closer to the entry price has greater odds of being reached first. To a trader, a stop-loss being reached prior to an upside target is not an inconsequential occurrence. The standard deviation of returns, specified for the expected holding period, aids in assessing the chances of being stopped out of a trade due to the proximity of the profit and loss targets to the entry price.

Assume a trade with an expected four month holding period. The security in question has a historical four month mean return of 1% and a standard deviation (σ) of 3%. The entry price is $10, profits will be taken at $10.70, and a stop-loss is placed at $9.80. Once these reward-risk targets are set, one can determine the distance, in standard deviations, of each from the entry price. In this example, the upside target is 7%, 2σ from the mean of 1% and the stop-loss is at 2%,-1σ from the mean. On a normal distribution, +2σ or higher is reached 2.4% of the time and -1σ or lower is reached 16% of the time. The balance for which neither target is achieved is 81.6%. The image below depicts these zones; red is for the loss target, green is for the profit target, and blue is neither.



Two assumptions needed to simplify the example is that the trader will not readjust the stop-loss or the price target and that after the four month holding period, the trade will be exited at the middle of the blue target range if neither target has been met. Since there are three probabilities involved, there must be a third step in calculating expected value.

Expected reward: .024*7% = .168%
Expected risk: .16*-2% = -.32%
Expected exit if neither target achieved (middle of blue range): .816*2.5% = 2.04%; since the result is positive, must be added to expected reward
Expected reward-risk: 2.208% to .32% = 6.9:1
Expected value = .168% + -.32% + 2.4% = 1.89% profit
The simple reward-risk of 7% to 2%, or 3.5:1, is not a meaningful number

Let’s examine the reverse setup, in which the profit target is 1σ, 4%, and the stop loss is 2σ, -5%:



Expected reward: .16*4% = .64%
Expected risk: .024*-5% = -.12%
Expected exit if neither target achieved (middle of blue range): .816*-0.5% = -.408%; since the result is negative, must be added to expected risk
Expected reward-risk: .64% to .528% = 1.2:1
Expected value: .64% + -.12% + -.408% = .132% profit
The simple reward-risk of 4% to 5%, or .8:1, is not a meaningful number

As you can see, the proximity of profit and loss targets to an entry price, and the resulting probability of which target will be reached first, shapes the reward-risk profile. Also, where the trade is closed if neither target is reached will significantly impact the expected value. If the exit price was assumed to be at breakeven, instead of at the middle of the blue range, the first and second trades would have an expected value of -.152% and .52%, respectively.

Note that such an analysis is direction neutral; it simply relies on volatility to characterize the potential profitability of a trade. Someone seeking only to identify statistical setups may find this direction neutral quality appealing; however, a discretionary trader usually buys with the bias that prices will rise.

The volatility of returns approach has the following advantages and disadvantages*:

Advantages
• Accounts for the randomness of market direction
• Sets more realistic expectations of whether a profit or loss target will be achieved
• Scientifically sound way to extract probabilities

Disadvantages
• Does not incorporate the tools of technical analysis, e.g., trend lines, patterns, indicators
• Statistics are imperfect predictors
• Assumes a normal distribution of returns

*Direction neural is either an advantage or a disadvantage, depending on the trading style

Multi-Factor Model

Another approach is to use a multi-factor model to the determine probabilities. Such a model calculates the statistical relationship of various independent variables, called “factors,” to the dependant variable, resulting in the following equation:

P = α + c1F1 + c2F2 + c3F3 + ……+ cnFn + e

where:
P = dependant variable (in this case, probability of success)
α = intercept term (the of value P if all factors equal zero)
c = factor coefficient
F = factor
e = error term (due to imperfect statistical relationships)

A trader could determine that the following five factors are sufficient to explain a trade’s probability of success: technical strength, fundamental strength, the entry price’s distance, measured in standard deviations, from the profit target, the entry price’s current distance, measured in the inverse of the standard deviation, from the stop-loss, and the trader’s historical success rate. The coefficient is the degree to which each factor influences the dependant variable, holding all other factors equal. The table below lists the five factors, their coefficients, and the factors’ values for a particular trade. (All listed values are simply illustrative.)


*This value indicates that the stop loss is negative 2 standard deviations from the entry price [1/σ = 1/-2 = -.5]. There is an inverse relationship between the price’s distance from the stop-loss and the probability of success.

From the values on the third column of the table, note that the stock is in a strong technical position, a neutral fundamental position, and the trader is profitable 60% of the time. Let us assume the trade in question is from the example used in this article’s section on volatility: the trader aims for a 4% return (1σ) with a 5% risk (-2σ). Let us also assume that the intercept and error term equal zero. Using the factor model and the values from the table, the probability of success is as follows:

P = 0 + 1.2(7) + 1(5) + -1.5(1) + 2.2(-.5) + .8(60) = .588

The probability of success for this trade is 58.8%. With a 4% return and a 5% stop loss, the ERR is 2.35%/2.06%, or 1.14:1, with an expected value of 0.292.

The multi-factor model approach has the following advantages and disadvantages:

Advantages
• Various inputs can be used, including inputs from the above stated methods
• Model acknowledges that more than one factor influences probabilities
• Scientifically valid

Disadvantages
• Extremely complex to construct correctly
• Some inputs may require estimates
• Requires a large supply of data
• Model must be properly specified, that is, it must properly account for the factors that influence the dependant variable

Revising the simple reward-risk measure to account for expected value results in a much richer analysis. It may also prove to be more accurate in determining a trader’s long term profitability. As such, research on how to best estimate the probability of success or the probability of failure for a trade with a defined reward and risk would be valuable.

To quickly touch upon two complications not addressed in this article: first, the ERR discussed here was for the onset of a trade; once the trade is executed, the ERR profile will change as a function of price action, changing probabilities, and trader decisions, such as raising a stop-loss. Second, conditional probabilities may be needed to calculate viable expected values.

To summarize the major points of this article:

• Trading is probabilistic by nature
• Expected value should be incorporated into reward-risk analysis
• To determine the expected reward-risk (ERR), first multiply the reward by probability of success and the loss by the probability of loss; the ratio of these two is the ERR
• The expected reward minus the expected risk is the expected value of the trade
• An ERR of 1:1 is a breakeven setup, with an expected value of zero
• The simple reward-risk ratio (SRR) is actually an ERR that passively assumes that the probability of success is .50
• A positive expected return can result from various reward-risk proportions and their respective probabilities of success and failure
• The classical prescription of a 3:1 SRR may have been implicitly based on the fact that the percentage of winning trades was slightly higher than 25%
• The crux of calculating an expected reward-risk ratio is in estimating a viable probability of success or of failure
• I have introduced four possible methods for estimating the probability to be used in calculating the ERR. These are, the trader’s historical success rate, statistics on methods of technical analysis, volatility of returns, and a multifactor model
• Research on methods of obtaining the probability of trade success in the context of reward-risk would greatly contribute to this type of analysis

Lessons in Sentiment

There was a powerful uptrend in the stock market from September 2010 to February 2011, interrupted by one correction in November. I have anecdotally observed that 1344 exceeded the price target that many were expecting before another correction would ensue.

Throughout much of this trend, as early as December when the S&P 500 was in the low 1200s, high levels of bullishness, measured by investor polls and option put/call ratios, were often quoted as a reason to expect a 5% or greater correction. I was also guilty of these forecasts, embarrassingly early.

What have I learned? For anticipating market turning points, extreme bullish or bearishness is only part of the sentiment picture. This sentiment sets the conditions for what I am hypothesizing is a better sentiment-based timing tool—that is, capitulation. Synonymous with surrender, this is the preferred term in finance for two similar behaviors. First, capitulation is when investors who have held on to positions during a bear market with the tenet that “prices always go back up,” finally cannot endure the pain of seeing the value of their accounts drop, and decide to sell. This is an event that defines a primary trend. Smaller trends and turning points can be affected by the second type of capitulation, in which the callers of a bottom in a bear market give up and turn bearish, or the callers of a top in a bull market give up and turn bullish.

It is not extreme sentiment that will cause the market to turn, but rather, capitulation. One would expect capitulation to occur in an environment of extreme sentiment. As long as there is a significant enough group of individuals calling for a top, there may be 1) short sellers and 2) buyers on the sideline, not wanting to enter at a top. A top occurs once there are no buyers left—investors on the sidelines can still buy and shorts must buy to cover positions. These two groups must be converted before the actual top is printed.

A great and sad irony results from these phenomena. If capitulation is a necessary condition for a top or a bottom, then the market will not turn until it occurs. Think about that. As long as a group of individuals hold on to their belief that the markets will turn, the markets won’t turn. The majority’s conviction must be broken because this conversion, ipso facto, caps off the trend.

Sometimes, capitulation is identifiable by major spikes in volume coupled with parabolic moves in what are called blow-off tops and panic bottoms. There are no polls set to capture this type of surrender, per se. What one must identify is the conversion of bulls to bear or of bears to bulls, not the absolute level of each. To do so, one must scout for viable anecdotal evidence. Perhaps technical tools can be devised to measure this conversion.

In summary, in an environment of extreme sentiment, one must look and wait for capitulation in order to better time a turning point. For this to happen, I hypothesize that the majority of countertrend forecasters or traders, by necessity, have to convert. Until they do so, an established trend will continue.

Cognitive Behavioral Analysis of Financial Markets

Note: the content of this post was published in the Technically Speaking enewsletter in early March of 2011. A prior draft, which was much cruder conceptually, appeared in this blog in 2010.

In this post, I explore investor psychology and investment themes within a framework borrowed from the branch of psychology known as cognitive-behavioral theory. Studies have found cognitive-behavioral therapy to be one of the most effective forms of therapy. Its concepts and tools are extremely powerful and I believe that they are just as applicable for investing.

In the context of financial markets, cognition refers to the mental representation and attitude towards information, fundamental or otherwise. (The “mental representation of and attitude towards” information can be abbreviated to the “perception of” information.) Stated simply, cognition deals with how an investor interprets new information, namely, whether it is fundamentally positive or negative, and the investor’s attitude towards it, namely, whether the market has overvalued, undervalued, or fully valued its significance. Over/under/fully valued is equivalent to being over/under/fully discounted. These perceptions translate to three possible behaviors, choosing to buy, sell, or hold. A change in price has the unique quality of being a consequence of behavior, a stimulus of behavior, and information. Investors learn buying and selling behavior through these various inputs.

These principles and dynamics can be summarized by the following definition:

• Cognitive-behavioral analysis – asset prices are governed by learned investor behavior, and the mental representation of and attitude towards information

Compare this with the traditional postulates of financial markets:

• Fundamental analysis – asset prices reflect the present value of future cash flows discounted by a required rate of return
• Technical analysis – prices reflect the balance of investor supply and demand for a given asset

There is certainly overlap among these types of analysis. One of them need not prove to be “right” at the expense of the others; rather, they are supplementary approaches to the study of a complex subject. An advantage to multiple approaches is that each provides alternative focuses, interpretations, and at times, novel insights.

Bubbles are a classic example of a market phenomenon that can be concisely explained by the principles of cognitive-behavioral analysis. New era thinking and investor exuberance (cognition), and rising prices (behavior and information) all participate in a self-reinforcing cycle. That explanation satisfies the conditions of the theory. Note that irrationality, in this framework, is not an element of bubbles. (If anything, astute investors who correctly identify a bubble can be categorized as irrational if they chose to short sell such a market.) The new era thinking, even if fundamentally unsound, is in essence a rationalization of price behavior. This is an important point because a bubble does not burst when investors turn from “irrational to rational,” it bursts when their perception changes.

Recall that the “mental representation and attitude towards” information can be abbreviated to the “perception of” information. A popularly shared and enduring perception, like new era thinking, is an investment theme. In recent history, an economic news release falling below expectations has often propelled markets higher because it has signified an extension of the loose monetary policy that is fueling the bull market, a dominant investment theme. In this case, the disappointing unemployment release is mentally represented as fundamentally positive; the attitude towards it is that the market has not fully discounted the extension of quantitative easing; the end result is a bidding up of prices. In analyzing such information, fundamentals are too ambiguous and too focused on a longer time frame. Technicals do recognize the relationship between news releases and price action, but they fail to give due prevalence to the investment theme.

If in market phases as different as the dot.com bubble and a bull market driven by monetary policy investors are operating by the same cognitive-behavioral principles, then one can induce that investor psychology is a prevalent force throughout all market cycles! As technicians have always stated, human behavior is an essential element of financial markets.

Now that I have broadly defined cognitive-behavioral analysis, I want to provide an application that aptly that falls under its conceptual framework.

Paradigm Shifts

A paradigm shift, also referred to as a gestalt shift, is a sudden, revolutionary change in a dominant perception. Both of these interchangeable terms are also taken from psychology. Paradigm comes from Greek for “pattern”, and gestalt is a German word meaning “shape” or “form.” Studies in gestalt psychology were precursors of cognitive theory. A commonly used analogy for a paradigm shift is that of the perception of a three-dimensional drawing:



In the rectangular prism above, rectangle ABCD can appear to be anterior if one’s vision focuses on it; however, a focus on rectangle EFGH can suddenly shift the viewer’s perception, making it anterior and rectangle ABCD posterior.

In financial markets, the sudden, revolutionary change in a dominant perception can result in a change in a price trend. The cousin of this concept is the catalyst. The catalyst, however, is a fundamental event, and may or may not result in a new trend. The difference subtly captured by cognitive-behavioral analysis is that the trend reversal is primarily a psychological event caused by a change (shift) in investor perception (paradigm).

In Inside the House of Money, a series of interviews with global macro investors, an anonymous currency trader elaborates on the subject:

"What signals a great macro trade?

I’m looking for signs of a gestalt shift in the markets, where all of a sudden, the market’s view on something instantly changes…

A gestalt shift usually comes after volatility gets pumped up because everyone is out there buying insurance. When people are buying options to protect positions, it means they have an underlying position they’re nervous about.

The big trades in macro are when the market is going to reprice a view or shift to a whole different concept. I spend a lot of time looking at where market sentiment is in hopes of finding the next shift."

Bernard Baruch also makes note of a paradigm shift, referring to it as a break in the “continuity of thought,” in his autobiographical, Baruch: My Own Story, published in 1957.

"A bull market, for example, will be sweeping along and then something will happen—trivial or important—and first one man will sell and then others will sell and the continuity of thought toward higher prices is broken.
'Continuity of thought'— what a wonderful expression that is."

Baruch continues, proving an example:

"The first time I heard [the expression] was while I was operating in steel stock which J.P. Morgan was trying to accumulate. The general market was on the rise. Then, while these operations were going on, the stock of Rock Island broke. At the time I happened to be with Middleton Burrill, who remarked, "That collapse is going to break the continuity of bullish thought." I had never heard the expression before, but I saw at once that Burrill was right and even though Steel was being supported by the Morgans, I sold and took my profits."

Arguably, a paradigm shift abruptly ended the bear market of 2007-2009. This shift was: the financial system will not utterly collapse. On March 10th, 2009, the day after the closing low of the bear market, Citigroup CEO Vikram Pandit delivered a letter to employees stating that he expected the bank to have its first profitable quarter since 2007. This release caused the paradigm shift. The S&P 500 closed 6.4% higher that day and ended up 10.7% for the week.

The 2009-present bull market commenced three months after the Central Bank first established a target federal funds rate of between 0 and .25%. This policy has been a major fundamental driver for the bull market. Note, however, that the Fed action did not serve as a catalyst! Prior to March 2009, investors took advantage of rallies caused by loosening monetary policy and related programs to unload on stocks. It was the comment by Citi’s CEO that restored investor confidence. The day of the announcement, I remember my father ominously stating, “Investor psychology has changed.”

The first leg of the bull market, spanning from March to May of 2009 can be framed by four events related to the financial system. In fact, the major and minor inflection points of the first leg occurred on these four news releases. Below is a chart in which the events are marked. These pivot points were clear signs that the health of the financial system and quantitative easing was an investment theme dominating market activity.



Cognitive-behavioral analysis implicitly suggests that investors place a thorough research focus on identifying investment themes, which can greatly influence market behavior over an intermediate term. Moreover, the early detection of a paradigm shift can prove valuable. One way to identify themes is to detect which material events or news releases frame market pivot points, as in the example above.

Given the current predominance of Federal Reserve policy over populous thought, a paradigm shift in this theme would probably be significant, to say the least. The chart below is from Google Trends. The y-axis in the upper chart represents the search volume on Google, worldwide, for the keywords “quantitative easing.” The lower chart is of news reference volume. (Please ignore the flags with letters; they represent specific news articles not shown in the figure below.) One can see the degree to which this term has become prevalent.



Conclusion

Cognitive-behavioral analysis is a conceptual framework intended to improve the understanding and predictability of financial markets. This method considers investor perception and behavior paramount in determining price trends. Paradigm shifts, discussed in this article, is one applied concept, but the richness of the field of psychology, established through decades of research, provides various other applications (a topic for future articles).

Just as behavioral finance, which has also inherited conclusive studies and principles from psychology, is now a mature subset of finance, a theory such as cognitive-behavioral analysis can broaden the current theories of finance that are professionally and academically regarded. Such broadening can loosen the strongholds of fundamental analysis, the efficient market hypothesis, and modern portfolio theory in the investment community.