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  • How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

  • An independent variable is something the researcher changes or controls.
  • A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1. ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

  • The relevant variables
  • The specific group being studied
  • The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in  if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

  • H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
  • H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.
Research question Hypothesis Null hypothesis
What are the health benefits of eating an apple a day? Increasing apple consumption in over-60s will result in decreasing frequency of doctor’s visits. Increasing apple consumption in over-60s will have no effect on frequency of doctor’s visits.
Which airlines have the most delays? Low-cost airlines are more likely to have delays than premium airlines. Low-cost and premium airlines are equally likely to have delays.
Can flexible work arrangements improve job satisfaction? Employees who have flexible working hours will report greater job satisfaction than employees who work fixed hours. There is no relationship between working hour flexibility and job satisfaction.
How effective is high school sex education at reducing teen pregnancies? Teenagers who received sex education lessons throughout high school will have lower rates of unplanned pregnancy teenagers who did not receive any sex education. High school sex education has no effect on teen pregnancy rates.
What effect does daily use of social media have on the attention span of under-16s? There is a negative between time spent on social media and attention span in under-16s. There is no relationship between social media use and attention span in under-16s.

If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.

  • Sampling methods
  • Simple random sampling
  • Stratified sampling
  • Cluster sampling
  • Likert scales
  • Reproducibility

 Statistics

  • Null hypothesis
  • Statistical power
  • Probability distribution
  • Effect size
  • Poisson distribution

Research bias

  • Optimism bias
  • Cognitive bias
  • Implicit bias
  • Hawthorne effect
  • Anchoring bias
  • Explicit bias

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A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

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Strong Form vs. Weak Form Efficient Market Hypothesis (EMH)

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The Efficient Market Hypothesis (EMH) is a cornerstone of modern finance, but it’s often misunderstood.

It doesn’t claim that markets are perfect or always rational.

Instead, it posits that market prices reflect all available information. This means stock prices aren’t predictable – they adjust instantly to new news or data.

Each piece of information – company earnings, economic forecasts, even whispers of insider trading – slots into place, forming a complete picture of a stock’s worth.

With all the pieces in place, the EMH posits that the price you see is the “true” value, making it difficult to consistently find “undervalued” stocks or other information that allows you to beat a representative benchmark.

Key Takeaways – EMH

The EMH has three flavors: Weak Semi-Strong Strong Weak EMH says past prices can’t predict future movements, so technical analysis is futile. Semi-Strong EMH extends this, claiming all public information is already baked into prices – i.e., fundamental analysis would therefore be inconsequential. Strong EMH takes the most extreme stance, asserting that even insider information is reflected, making it impossible for anyone to consistently beat the market. This doesn’t mean markets are infallible, bubbles can’t occur, some traders/investors can benefit from variance. But the EMH provides a framework for understanding how markets function and what traders/investors can realistically expect. Our take on the matter? If you don’t have an informational or analytical edge on the markets, then the EMH is a reasonable starting point. It’s not easy to spot a mispricing or beat the markets. If you do happen to work up to a point where you do have an edge in whatever form, you may try to carefully take some type of tactical approach to the markets.

Efficient Market Hypothesis isn’t a one-size-fits-all concept.

It comes in different forms, each with distinct implications for traders.

Strong Form Efficiency

This is the EMH in its most extreme form.

It argues that stock prices instantly reflect all information, even insider knowledge.

This means that even those with access to confidential company data or market-moving secrets can’t gain a consistent advantage. If this holds true, it’s essentially a “level playing field” where nobody has an edge.

The Semi-Strong version allows that an informational edge can give some an advantage, but analysis as a whole is generally futile.

Weak Form Efficiency

This is a more moderate version of the EMH.

It suggests that prices already incorporate all past market data, like historical price movements and trading volumes.

This implies that strategies based on charting or technical analysis are futile because past patterns don’t predict future trends.

While it doesn’t dismiss other forms of analysis, it suggests that trying to “ time the market ” based on past data is a losing game.

These are theoretical constructs.

Whether markets align with strong or weak form efficiency or neither is a subject of ongoing debate and research.

Implications on Trading Strategies

The implications of EMH for your strategy or approach to markets depend on which version you believe.

If markets are truly strong form efficient, then it suggests against all active management.

Since all information, public or private, is already factored into prices under this hypothesis, there’s no way to gain an edge through research or analysis.

Fundamental analysis , which involves studying a company’s financial health and growth prospects, becomes irrelevant. Even insider tips are useless.

In 1971, Fischer Black famously wrote in “ Implications of the random walk hypothesis for portfolio management ” that:

Insiders are wrong so often that it hardly seems worth the risk involved.

So, if even people with the most information about a security are wrong so often, then it seems wasteful of your time and risk-bearing capacity to try to beat the market.

The best strategy under this approach?

Have a diversified portfolio of low-cost index funds and ride with market returns.

This version of EMH has a different impact.

It implies that technical analysis, which relies on historical price and volume data to predict future trends, is ineffective.

The market’s past performance won’t give you a crystal ball.

However, fundamental analysis could still hold value.

By understanding a company’s underlying business and its competitive landscape, you might be able to uncover information that hasn’t been fully priced in.

Criticisms & Limitations

Strong form emh.

Strong Form EMH has taken the most heat.

Real-world examples of insider trading leading to substantial profits directly contradict its premise.

There are cases like Raj Rajaratnam or Mathew Martoma, the hedge fund managers convicted of insider trading, who made millions from illegally obtained information.

These cases suggest that private information can indeed be exploited for market gains, casting doubt on the notion that markets are perfectly efficient.

Company executives also do more than the general public about their company.

This is especially the case in extreme scenarios, such as cases of accounting fraud and other forms of dishonesty and illicit behavior.

Weak Form EMH

Weak Form EMH also faces challenges.

Market anomalies like the “January Effect,” where stocks tend to outperform in January, and the success of momentum strategies , where recent winners continue to win, seem to defy the idea that past prices are irrelevant.

These anomalies suggest that predictable patterns might exist, opening the door for potentially profitable strategies based on historical data.

These criticisms don’t completely invalidate the EMH.

They suggest that markets may not be perfectly efficient in all situations.

Anomalies can exist, and those with access to privileged information might gain temporary advantages.

However, the EMH still provides a framework for understanding market behavior and setting realistic expectations for the vast majority of traders.

It reminds us that consistent outperformance is difficult, and successful trading/investing requires more than just following trends or relying on insider tips.

Practical Application & Real-World Relevance

The EMH goes beyond academic theory and has a real impact on how the financial world operates.

Trading & Investment Strategies

Beliefs about EMH have shaped how professionals approach trading and investing.

Those who lean toward strong form efficiency favor passive strategies , like index funds, since they believe no amount of analysis can consistently beat the market.

Or they may simply believe they don’t have the ability to, the resources to do so, or the desire to outperform the market.

Others, more aligned with weak form efficiency, might use fundamental analysis to uncover undervalued stocks, while acknowledging that technical analysis won’t provide an edge (at least not for them).

The debate isn’t just theoretical, it drives literally trillions of dollars in capital allocation decisions in markets.

Policy and Regulation

The EMH also influences financial regulation.

If strong form efficiency holds, regulators might prioritize preventing insider trading, since it’s the only way to gain an unfair advantage.

They might also focus on market transparency, so everyone has access to the same information simultaneously.

Nonetheless, if markets are only weak form efficient, regulators might be less concerned about insider trading, as it wouldn’t necessarily guarantee superior returns.

Instead, they might emphasize educating the public about the limitations of market timing and the importance of diversification .

Not Uniform

Different markets might exhibit varying degrees of efficiency.

For example, large-cap stocks might be more efficient than small-cap stocks due to higher analyst coverage and trading volumes.

This nuance is why understanding the different forms of EMH is important for both traders/investors and regulators.

It provides a framework for making informed decisions and designing effective policies.

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Weak, Semi-strong, and Strong Forms Market Efficiency

Weak, Semi-strong, and Strong Forms Market Efficiency

Eugene Fama developed a framework of market efficiency that laid out three forms of efficiency: weak, semi-strong, and strong. Each form is defined with respect to the available information that is reflected in prices. Investors trading on available information that is not priced into the market would earn abnormal returns, defined as excess risk-adjusted returns.

In the weak-form efficient market hypothesis, all historical prices of securities have already been reflected in the market prices of securities. In other words, technicians – those trading on analysis of historical trading information – should earn no abnormal returns. Research has shown that this is likely the case in developed markets, but less developed markets may still offer the opportunity to profit from technical analysis.

Semi-strong Form

In a semi-strong-form efficient market, prices reflect all publicly known and available information, including all historical price information. Under this assumption, analyzing any public financial disclosures made by a company to determine a stock’s intrinsic value would be futile since every detail would be taken into account in the stock’s market price. Similarly, an investor could not earn consistent abnormal returns by acting on surprise announcements since the market would quickly react to the new information.

Strong Form

In a strong-form efficient market, security prices fully reflect both public and private information. Therefore, insiders could not generate abnormal returns by trading on private information because it would already figure into market prices. However, researchers find that markets are generally not strong-form efficient as abnormal profits can be earned when nonpublic information is used.

In the following graph, we can clearly see that the weak form of market efficiency reflects only past market data. In contrast, the strong form reflects all past data, public market information, and insider information.

Market Prices Reflect

$$ \begin{array}{cccc} \textbf{Forms of market efficiency} & \textbf{Past market data} & \textbf{Public information} & \textbf{Private information} \\ \hline \text{Weak form} & \checkmark & & \\ \text{Semi-strong form} & \checkmark & \checkmark & \\ \text{Strong form} & \checkmark & \checkmark & \checkmark \\ \end{array} $$

Question If a skilled fundamental financial analyst and an insider trader all earn the same long-run risk-adjusted returns, what form of market efficiency is likely to apply? Weak form. Strong form. Semi-strong form. Solution The correct answer is B . Since the insider trader can’t even earn higher risk-adjusted returns than the skilled fundamental financial analyst, the market must be strong-form efficient.

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strong vs weak hypothesis

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Efficient Market Hypothesis (EMH)

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Written by True Tamplin, BSc, CEPF®

Reviewed by subject matter experts.

Updated on July 12, 2023

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Table of contents, efficient market hypothesis (emh) overview.

The Efficient Market Hypothesis (EMH) is a theory that suggests financial markets are efficient and incorporate all available information into asset prices.

According to the EMH, it is impossible to consistently outperform the market by employing strategies such as technical analysis or fundamental analysis.

The hypothesis argues that since all relevant information is already reflected in stock prices, it is not possible to gain an advantage and generate abnormal returns through stock picking or market timing.

The EMH comes in three forms: weak, semi-strong, and strong, each representing different levels of market efficiency.

While the EMH has faced criticisms and challenges, it remains a prominent theory in finance that has significant implications for investors and market participants.

Types of Efficient Market Hypothesis

The Efficient Market Hypothesis can be categorized into the following:

Weak Form EMH

The weak form of EMH posits that all past market prices and data are fully reflected in current stock prices.

Therefore, technical analysis methods, which rely on historical data, are deemed useless as they cannot provide investors with a competitive edge. However, this form doesn't deny the potential value of fundamental analysis.

Semi-strong Form EMH

The semi-strong form of EMH extends beyond historical prices and suggests that all publicly available information is instantly priced into the market.

This includes financial statements, news releases, economic indicators, and other public disclosures. Therefore, neither technical analysis nor fundamental analysis can yield superior returns consistently.

Strong Form EMH

The most extreme version of EMH, the strong form, asserts that all information, both public and private, is fully reflected in stock prices.

Even insiders with privileged information cannot consistently achieve higher-than-average market returns. This form, however, is widely criticized as it conflicts with securities regulations that prohibit insider trading .

Types of Efficient Market Hypothesis

Assumptions of the Efficient Market Hypothesis

Three fundamental assumptions underpin the Efficient Market Hypothesis.

All Investors Have Access to All Publicly Available Information

This assumption holds that the dissemination of information is perfect and instantaneous. All market participants receive all relevant news and data about a security or market simultaneously, and no investor has privileged access to information.

All Investors Have a Rational Expectation

In EMH, it is assumed that investors collectively have a rational expectation about future market movements. This means that they will act in a way that maximizes their profits based on available information, and their collective actions will cause securities' prices to adjust appropriately.

Investors React Instantly to New Information

In an efficient market, investors instantaneously incorporate new information into their investment decisions. This immediate response to news and data leads to swift adjustments in securities' prices, rendering it impossible to "beat the market."

Implications of the Efficient Market Hypothesis

The EMH has several implications across different areas of finance.

Implications for Individual Investors

For individual investors, EMH suggests that "beating the market" consistently is virtually impossible. Instead, investors are advised to invest in a well-diversified portfolio that mirrors the market, such as index funds.

Implications for Portfolio Managers

For portfolio managers , EMH implies that active management strategies are unlikely to outperform passive strategies consistently. It discourages the pursuit of " undervalued " stocks or timing the market.

Implications for Corporate Finance

In corporate finance, EMH implies that a company's stock is always fairly priced, meaning it should be indifferent between issuing debt and equity . It also suggests that stock splits , dividends , and other financial decisions have no impact on a company's value.

Implications for Government Regulation

For regulators , EMH supports policies that promote transparency and information dissemination. It also justifies the prohibition of insider trading.

Implications of the Efficient Market Hypothesis

Criticisms and Controversies Surrounding the Efficient Market Hypothesis

Despite its widespread acceptance, the EMH has attracted significant criticism and controversy.

Behavioral Finance and the Challenge to EMH

Behavioral finance argues against the notion of investor rationality assumed by EMH. It suggests that cognitive biases often lead to irrational decisions, resulting in mispriced securities.

Examples include overconfidence, anchoring, loss aversion, and herd mentality, all of which can lead to market anomalies.

Market Anomalies and Inefficiencies

EMH struggles to explain various market anomalies and inefficiencies. For instance, the "January effect," where stocks tend to perform better in January, contradicts the EMH.

Similarly, the "momentum effect" suggests that stocks that have performed well recently tend to continue performing well, which also challenges EMH.

Financial Crises and the Question of Market Efficiency

The Global Financial Crisis of 2008 raised serious questions about market efficiency. The catastrophic market failure suggested that markets might not always price securities accurately, casting doubt on the validity of EMH.

Empirical Evidence of the Efficient Market Hypothesis

Empirical evidence on the EMH is mixed, with some studies supporting the hypothesis and others refuting it.

Evidence Supporting EMH

Several studies have found that professional fund managers, on average, do not outperform the market after accounting for fees and expenses.

This finding supports the semi-strong form of EMH. Similarly, numerous studies have shown that stock prices tend to follow a random walk, supporting the weak form of EMH.

Evidence Against EMH

Conversely, other studies have documented persistent market anomalies that contradict EMH.

The previously mentioned January and momentum effects are examples of such anomalies. Moreover, the occurrence of financial bubbles and crashes provides strong evidence against the strong form of EMH.

Efficient Market Hypothesis in Modern Finance

Despite criticisms, the EMH continues to shape modern finance in profound ways.

EMH and the Rise of Passive Investing

The EMH has been a driving force behind the rise of passive investing. If markets are efficient and all information is already priced into securities, then active management cannot consistently outperform the market.

As a result, many investors have turned to passive strategies, such as index funds and ETFs .

Impact of Technology on Market Efficiency

Advances in technology have significantly improved the speed and efficiency of information dissemination, arguably making markets more efficient. High-frequency trading and algorithmic trading are now commonplace, further reducing the possibility of beating the market.

Future of EMH in Light of Evolving Financial Markets

While the debate over market efficiency continues, the growing influence of machine learning and artificial intelligence in finance could further challenge the EMH.

These technologies have the potential to identify and exploit subtle patterns and relationships that human investors might miss, potentially leading to market inefficiencies.

The Efficient Market Hypothesis is a crucial financial theory positing that all available information is reflected in market prices, making it impossible to consistently outperform the market. It manifests in three forms, each with distinct implications.

The weak form asserts that all historical market information is accounted for in current prices, suggesting technical analysis is futile.

The semi-strong form extends this to all publicly available information, rendering both technical and fundamental analysis ineffective.

The strongest form includes even insider information, making all efforts to beat the market futile. EMH's implications are profound, affecting individual investors, portfolio managers, corporate finance decisions, and government regulations.

Despite criticisms and evidence of market inefficiencies, EMH remains a cornerstone of modern finance, shaping investment strategies and financial policies.

Efficient Market Hypothesis (EMH) FAQs

What is the efficient market hypothesis (emh), and why is it important.

The Efficient Market Hypothesis (EMH) is a theory suggesting that financial markets are perfectly efficient, meaning that all securities are fairly priced as their prices reflect all available public information. It's important because it forms the basis for many investment strategies and regulatory policies.

What are the three forms of the Efficient Market Hypothesis (EMH)?

The three forms of the EMH are the weak form, semi-strong form, and strong form. The weak form suggests that all past market prices are reflected in current prices. The semi-strong form posits that all publicly available information is instantly priced into the market. The strong form asserts that all information, both public and private, is fully reflected in stock prices.

How does the Efficient Market Hypothesis (EMH) impact individual investors and portfolio managers?

According to the EMH, consistently outperforming the market is virtually impossible because all available information is already factored into the prices of securities. Therefore, it suggests that individual investors and portfolio managers should focus on creating well-diversified portfolios that mirror the market rather than trying to beat the market.

What are some criticisms of the Efficient Market Hypothesis (EMH)?

Criticisms of the EMH often come from behavioral finance, which argues that cognitive biases can lead investors to make irrational decisions, resulting in mispriced securities. Additionally, the EMH has difficulty explaining certain market anomalies, such as the "January effect" or the "momentum effect." The occurrence of financial crises also raises questions about the validity of EMH.

How does the Efficient Market Hypothesis (EMH) influence modern finance and its future?

Despite criticisms, the EMH has profoundly shaped modern finance. It has driven the rise of passive investing and influenced the development of many financial regulations. With advances in technology, the speed and efficiency of information dissemination have increased, arguably making markets more efficient. Looking forward, the growing influence of artificial intelligence and machine learning could further challenge the EMH.

About the Author

True Tamplin, BSc, CEPF®

True Tamplin is a published author, public speaker, CEO of UpDigital, and founder of Finance Strategists.

True is a Certified Educator in Personal Finance (CEPF®), author of The Handy Financial Ratios Guide , a member of the Society for Advancing Business Editing and Writing, contributes to his financial education site, Finance Strategists, and has spoken to various financial communities such as the CFA Institute, as well as university students like his Alma mater, Biola University , where he received a bachelor of science in business and data analytics.

To learn more about True, visit his personal website or view his author profiles on Amazon , Nasdaq and Forbes .

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Strong, Semi-Strong, and Weak Efficient Market Hypothesis

strong vs weak hypothesis

When it comes to evaluating companies and creating investment strategies, the efficient market hypothesis serves as one of the most important concepts that any sophisticated professional should understand. This theory postulates that markets are efficient and thus do not offer any possibilities of obtaining above-average returns (on a risk-adjusted basis).

Having said that, there are three different definitions of efficiency, each one less strict than the previous one. In this article, we will go through each one of them and discuss them in detail.

The efficient market hypothesis allows for three different definitions of efficiency:

Strong Efficiency

  • Semi-Stong Efficiency
  • Weak Efficiency

Without any further ado, let’s describe each one of them!

Table of Contents

Which are the three forms of the Efficient Market Hypothesis?

The Efficient Market Hypothesis (EMH) is a theory that was written in the year 1970 by Eugene Fama. It postulates a market is efficient when the price of financial assets is correctly based on all existing information. Thus, it is not possible to use this data in order to obtain above-average returns.

Another consequence of this postulate is the theoretical impossibility of arbitraging the price of an asset and obtaining an extraordinary profit based on an analysis of it.

This is because the asset price would change so quickly (whatever the factor affecting its price) that it would be impossible to buy or sell any of them at undervalued or overvalued prices.

In simple terms, the theory of the efficient market hypothesis maintains that at all times and places, the price of an asset is at equilibrium and that agents duly incorporate all available information when valuing it.

Having said that, the degree of efficiency of a given market is also determined by the number of participants (the more they are, the higher the market efficiency will be) and the transaction and information costs (the higher they are, the lower the market efficiency will be).

This theory contemplates three types of efficiency: strong efficiency, semi-strong efficiency, and weak efficiency. Each of these variants is distinguished by having stronger or looser assumptions regarding the definition of efficiency.

Next, we will go on to describe each type of efficiency in more detail.

A strong efficiency market is one where asset prices are reflected by any type of existing information, whether it is public, private, or historical information. In this type of market, no matter what happens, the price will always be adjusted in such a way that no extraordinary profit can be made.

The strong efficiency assumption does not even contemplate the possibility of obtaining an income from the private information that investors possess, nor does it contemplate the existence of privileged information.

The strong efficiency version of the efficient market hypothesis does not contemplate the existence of asymmetrical information of any shape or form. Thus, since investors do not have useful or exclusive information that would allow them to trade at an advantage, they are unable to obtain consistent above-average returns.

Semi-Strong Efficiency

If the market has semi-strong form efficiency, it is assumed that asset prices already contain all public and historical data. In this scenario, it is not useful to use fundamental analysis to infer whether the asset is undervalued or overvalued since this analysis uses public information which is already reflected in the price of the assets.

In other words, in the face of any news or event, the value of the assets would be adjusted in such a way that the investor could not use this type of information in his favor. The only way for the investor to obtain benefits would be through private or privileged information, which in turn has an acquisition cost for the investor (the costs of said information should not exceed the benefits generated by the investments). Likewise, the use of privileged information is illegal and duly controlled in most developed financial markets.

Weak efficiency

Weak efficiency holds that the historical prices of an asset are properly incorporated into its current price. In a market with weak efficiency, past and future prices have no relation to each other. In other words, prices are not autocorrelated.

Therefore, the only way for the investor to obtain any extraordinary profit is through the use of public and private information since this would allow him, at least in theory, to infer the future price based on fundamental analysis, news sources, or other alternative information.

The weak efficiency hypothesis is the most widely accepted in the empirical literature.

Relationship between Efficient Market Hypothesis and Random Walk Theory

In mathematical terms, a Random Walk is a process that consists of a sequence of random steps. In other words, tomorrow’s price will equal today’s price plus a random and unpredictable component.

Likewise, the price in 2 days will be tomorrow’s price plus another random component, or the price of today plus 2 random components. In finance, this random component usually has a mean of 0 and follows a normal distribution.

As a consequence of this, our best forecast for tomorrow’s price will be to say that it will be the same as today’s price. This is because the random component can be both negative and positive, and so we cannot even determine the direction of the following change in price. But we know (or at least assume) that the randomness has a mean of 0, which leads us to predict that the next price will be equal to the current price.

The supposed randomness of the series lies in the different forms of efficiency that we mentioned previously. Even assuming weak efficiency, the validity of the random walk model stands.

As previously said, the EMH also tells us that prices move randomly. New information, such as news, is, by definition, also not predictable, so the moment it becomes known and the effect it will have will also be random.

As we can see, both models are compatible in that they both state that it is impossible to predict future asset prices.

It is because of this that the theory of efficient markets is frequently modeled mathematically through a stochastic process of this type. The Ornstein-Uhlenbeck process is the most used in financial mathematics in these cases.

Frequently Asked Questions

Is technical analysis compatible with the efficient market hypothesis.

Technical analysis is a technique used to study the price of assets based solely on past price and volume data. Adherents to this trading methodology maintain that price series contain patterns that repeat themselves over time and can therefore be used to forecast future variations.

Now, following the concepts of the EHM, is technical analysis useful to us? The answer, in principle, is quite simple: no.

Why is there no value in using technical analysis according to Eugene Fama’s theory? Even in a market with weak form efficiency, future and past prices do not correlate with each other. Therefore, we can conclude that technical analysis and EHM are mutually exclusive.

Are Mean-Reverting and Momentum Strategies compatible with the Efficient Market Hypothesis?

Mean reversion is a trading strategy that is based on mathematical and statistical tools. It tells us that the price of an asset that is trending in one direction will return to its average value in the long term. In other words, this type of strategy maintains that a change in the price of an asset may be due to transactional reasons and temporary inefficiencies, after which the price is expected to converge to its average.

It is common practice to use technical indicators such as the Moving Average Crossover Divergence (MACD) or the Relative Strength Index (RSI) to design mean reversion strategies. The most sophisticated investors, in quantitative terms, use econometric techniques to determine if an asset has (or does not) tend to mean revert. The statistical test used par excellence for these cases is the Hurst Exponent.

strong vs weak hypothesis

Now, are mean reversion strategies compatible with the efficient market hypothesis?

Mean reversion strategies are not compatible, at least in theoretical terms, with the efficient market hypothesis. These strategies are in contradiction with even the laxest version of efficiency: the weak market efficiency. This is because, at least in theory, no information can be extracted based on past prices. The same happens with momentum strategies, which expect price increases (decreases) to be followed by subsequent price increases (decreases).

Is the Efficient Market Hypothesis compatible with Behavioral Finance?

Behavioral Finance is a discipline that studies the way in which human beings make decisions and how these decisions are not always rational or efficient. These mistakes, which are called “cognitive biases,” have been extensively studied empirically and contradict the old paradigm of the rational agent (homo-economicus).

The various and interesting biases studied are several and are beyond the scope of this article, but the reader can refer to the following article .

A clear example of the irrationality of agents when making their investment decisions was presented by Richard Thaler (2016 Nobel Prize). In it, he names the case of the investment company Herzfeld Caribbean Basin Fund, better known as CUBA. Despite the name, this fund does not have hold any assets from the country of the same name. Despite this, the fund has always traded at a discount of 10%-15% compared to a portfolio replicating the same holdings (same net asset value or NAV). The difference, Thaler argues, is only explainable by the name of the fund, thus being a clear example of irrationality.

strong vs weak hypothesis

In the graph, we can see CUBA’s share price and its net asset value from May 2014 to March 2015. While in the early months, the share price tended to be discounted by 10% to 15% with respect to the NAV (as said before), it can be seen that said trend reversed as of December 18, 2014.

But why did this abrupt change occur? The sudden rise in the value coincided with the announcement by Barack Obama (President of the USA at the time) of trying to “relax” diplomatic relations with Cuba. This led markets being optimistic regarding the Cuban economy, and due to irrationality, this optimism also affected the CUBA fund. This event and its consequences on the price of the fund are additional arguments that show a clear example of a strong inefficiency in the market.

What is the relationship between High-Frequency Trading and the Efficient Market Hypothesis?

High-frequency Trading commonly refers to trading algorithms that specialize in exploiting some kind of inefficiency with the least possible latency. Thus, companies specializing in this type of trading develop tailor-made hardware and place and colocate it in the same building as the exchange’s servers. They do the latter to minimize the cable distance between their algorithm’s processor and the Exchange’s processor, which reduces the time required for sending an order and processing it.

These algorithms are used to exploit small inefficiencies, which, if exploited frequently, can lead to considerable profits. If you want to learn more about HFT, you can read this article I wrote .

According to the hypothesis, the inefficiencies of the markets disappear immediately thanks to the efficient agents that arbitrate them. At first glance, the existence of high-frequency trading does not seem to contradict the EMH.

However, we must bear in mind that the EMH maintains that these arbitrations are carried out by various agents and cannot be exploited in a consistent manner by the same agent. But, due to the nature of high-frequency trading, these algorithms are of a winner-takes-all type. Taking into account that each type of possible arbitrage is commonly exploited by its respective fastest algorithm, extraordinary rents can be extracted consistently. This implies a contradiction with the efficient market hypothesis.

Can the Efficient Market Hypothesis explain Market Bubbles?

According to the efficient market hypothesis, financial bubbles should not be able to form. This is because bubbles, by definition, imply that asset prices are strongly above the equilibrium price. Likewise, during the formation of a bubble, extraordinary profits are also obtained through momentum strategies. Momentum is the expectation that a rise (fall) in a price will be followed by another rise (fall) in that price.

As with mean reversion, momentum should also not exist under either version of market efficiency. However, both phenomena have been extensively studied and tested in the academic literature.

Who defined the Efficient Market Hypothesis?

The Efficient Market Hypothesis was formulated for the first time by Eugene F. Fama in 1970. It is based on three characteristics that investors usually possess: rationality, independent deviations of rationality, and arbitration.

  • Rationality means that investors will price assets consistently. That is, according to the expected cash flows discounted at the corresponding discount rate and the available information of that asset.
  • Independent deviations from rationality contemplate the possibility that some individuals erroneously value an asset.
  • Arbitrage neutralizes individual deviations since rational agents will buy cheap assets and sell expensive assets, thus converging the respective prices to their equilibrium values.

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Efficient Market Hypothesis: Strong, Semi-Strong, and Weak

If I were to choose one thing from the academic world of finance that I think more individual investors need to know about, it would be the efficient market hypothesis.

The name “efficient market hypothesis” sounds terribly arcane. But its significance is huge for investors, and (at a basic level) it’s not very hard to understand.

So what is the efficient market hypothesis (EMH)?

As professor Eugene Fama (the man most often credited as the father of EMH) explains*, in an efficient market, “the current price [of an investment] should reflect all available information…so prices should change only based on unexpected new information.”

It’s important to note that, as Fama himself has said, the efficient market hypothesis is a model, not a rule. It describes how markets tend to work. It does not dictate how they must work.

EMH is typically broken down into three forms (weak, semi-strong, and strong) each with their own implications and varying levels of data to back them up.

Weak Efficient Market Hypothesis

The weak form of EMH says that you cannot predict future stock prices on the basis of past stock prices. Weak-form EMH is a shot aimed directly at technical analysis. If past stock prices don’t help to predict future prices, there’s no point in looking at them — no point in trying to discern patterns in stock charts.

From what I’ve seen, most academic studies seem to show that weak-form EMH holds up pretty well. (Take, for example, the recent study which tested over 5,000 technical analysis rules and showed them to be unsuccessful at generating abnormally high returns.)

Semi-Strong Efficient Market Hypothesis

The semi-strong form of EMH says that you cannot use any published information to predict future prices. Semi-strong EMH is a shot aimed at fundamental analysis. If all published information is already reflected in a stock’s price, then there’s nothing to be gained from looking at financial statements or from paying somebody (i.e., a fund manager) to do that for you.

Semi-strong EMH has also held up reasonably well. For example, the number of active fund managers who outperform the market has historically been no more than can be easily attributed to pure randomness .

Semi-strong EMH does not appear to be ironclad, however, as there have been a small handful of investors (e.g., Peter Lynch, Warren Buffet) whose outperformance is of a sufficient degree that it’s extremely difficult to explain as just luck.

The trick, of course, is that it’s nearly impossible to identify such an investor in time to profit from it. You must either:

  • Invest with a fund manager after only a few years of outperformance (at which point his/her performance could easily be due to luck), or
  • Wait until the manager has provided enough data so that you can be sure that his performance is due to skill (at which point his fund will be sufficiently large that he’ll have trouble outperforming in the future).

Strong Efficient Market Hypothesis

The strong form of EMH says that everything that is knowable — even unpublished information — has already been reflected in present prices. The implication here would be that even if you have some inside information and could legally trade based upon it, you would gain nothing by doing so.

The way I see it, strong-form EMH isn’t terribly relevant to most individual investors, as it’s not too often that we have information not available to the institutional investors.

Why You Should Care About EMH

Given the degree to which they’ve held up, the implications of weak and semi-strong EMH cannot be overstated. In short, the takeaway is that there’s very little evidence indicating that individual investors can do anything better than simply buy & hold a low-cost, diversified portfolio .

*Update: The video from which this quote came has since been taken offline.

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A good point to keep in mind is that even if the EMH models aren’t a perfect model of the stock market- if it is close enough that technical analysis or fundamental analysis won’t give you a real advantage then it doesn’t make sense to try them. A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing presents that case very well.

-Rick Francis

Wonderfully concise summary, Mike.

Just for completeness, re: the Semi-Strong EMH, there’s a third option – you could try to invest in stocks and beat the market yourself.

I know, I know – but before I get my hat I’d argue that there’s benefits to this approach over picking one or more active fund managers, in that your dealing charges *may* be lower than the fund’s charges (and at least they’re transparent and under your control) and also you don’t have to try to predict two potentially understandable things – a manager’s performance AND the performance of the sort of stocks he invests in (or even a third – whether he or she is going to stick around).

Of course, a tracker fund sidesteps all of this for most people to deliver better than average results compared to funds, and only slightly worse results compared to the market. 🙂

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What Is the Efficient Market Hypothesis?

Rebecca Baldridge

Updated: May 11, 2022, 1:05pm

What Is the Efficient Market Hypothesis?

The efficient market hypothesis argues that current stock prices reflect all existing available information, making them fairly valued as they are presently. Given these assumptions, outperforming the market by stock picking or market timing is highly unlikely, unless you are an outlier who is either very lucky or very unlucky.

Understanding the Efficient Market Hypothesis

The most important assumption underlying the efficient market hypothesis is that all information relevant to stock prices is freely available and shared with all market participants.

Given the vast numbers of buyers and sellers in the market, information and data is incorporated quickly, and price movements reflect this. As a result, the theory argues that stocks always trade at their fair market value.

Followers of the efficient market hypothesis believe that if stocks always trade at their fair market value, then no level of analysis or market timing strategy will yield opportunities for outperformance.

In other words, an investor following the efficient market hypothesis shouldn’t buy undervalued stocks at bargain basement prices expecting to see large gains in the future, nor would they benefit from selling overvalued stocks.

The efficient market hypothesis begins with Eugene Fama, a University of Chicago professor and Nobel Prize winner who is regarded as the father of modern finance. In 1970, Fama published “Efficient Capital Markets: A Review of Theory and Empirical Work,” which outlined his vision of the theory.

Three Variations Of the Efficient Market Hypothesis

Investors who strongly believe in the efficient market hypothesis choose passive investment strategies that mirror benchmark performance, but they may do so to varying degrees. There are three main variations on the theory:

1. The Weak Form of the Efficient Market Hypothesis

Although investors abiding by the efficient market hypothesis believe that security prices reflect all available public market information, those following the weak form of the hypothesis assume that prices might not reflect new information that hasn’t yet been made available to the public.

It also assumes that past prices do not influence future prices, which will instead be informed by new information. If this is the case, then technical analysis is a fruitless endeavor.

The weak form of the efficient market hypothesis leaves room for a talented fundamental analyst to pick stocks that outperform in the short-term, based on their ability to predict what new information might influence prices.

2. The Semi-Strong Form of the Efficient Market Hypothesis

This form takes the same assertions of weak form, and includes the assumption that all new public information is instantly priced into the market. In this way, neither fundamental nor technical analysis can be used to generate excess returns.

3. The Strong Form of the Efficient Market Hypothesis

Strong form efficient market hypothesis followers believe that all information, both public and private, is incorporated into a security’s current price. In this way, not even insider information can give investors an opportunity for excess returns.

Arguments For and Against the Efficient Market Hypothesis

Investors who follow the efficient market hypothesis tend to stick with passive investing options, like index funds and exchange-traded funds ( ETFs ) that track benchmark indexes, for the reasons listed above.

Given the variety of investing strategies people deploy, it’s clear that not everyone believes the efficient market hypothesis to be a solid blueprint for smart investing. In fact, the investment market is teeming with mutual funds and other funds that employ active management with the goal of outperforming a benchmark index.

The Case for Active Investing

Active portfolio managers believe that they can leverage their individual skill and experience—often augmented by a team of skilled equity analysts—to exploit market inefficiencies and to generate a return that exceeds the benchmark return.

There is evidence to support both sides of the argument. The Morningstar Active vs Passive Barometer is a twice-yearly report that measures the performance of active managers against their passive peers. Nearly 3,500 funds were included in the 2020 analysis, which found that only 49% of actively managed funds outperformed their passive counterparts for the year.

On the other hand, looking at the 10-year period ending December 31, 2020 shows a different picture, since the percentage of active managers who outperformed comparable passive strategies dropped to 23%.

Are Some Markets Less Efficient than Others?

A deeper look into the Morningstar report shows that the success of active or passive management varies considerably according to the type of fund.

For example, active managers of U.S. real estate funds outperformed passively managed vehicles 62.5% of the time, but the figure drops to 25% when fees are considered.

Other areas where active management tends to outperform passive—before fees—include high yield bond funds at 59.5% and diversified emerging market funds at 58.3%. The addition of fees for portfolios that are actively managed tends to drag on their overall performance in most cases.

In other asset classes, passive managers significantly outperformed active managers. U.S. large-cap blend saw active managers outperform passive only 17.2% of the time, with the percentage dropping to 4.1% after fees.

These results seem to suggest that some markets are less efficient than others. Liquidity in emerging markets can be limited, for example, as can transparency. Political and economic uncertainty are more prevalent, and legal complexities and lack of investor protections can also cause problems.

These factors combine to create considerable inefficiencies, which a knowledgeable portfolio manager can exploit.

On the other hand, U.S. markets for large-cap or mid-cap stocks are heavily traded, and information is rapidly incorporated into stock prices. Efficiency is high and, as demonstrated by the Morningstar results, active managers have much less of an edge.

How Star Managers Handle Their Portfolios

Popular investment manager Warren Buffet is one successful example of an active investor. Buffet is a disciple of Benjamin Graham, the father of fundamental analysis, and has been a value investor throughout his career. Berkshire Hathaway, the conglomerate that holds his investments, has earned an annual return of 20% over the past 52 years, often outperforming the S&P 500 .

Another successful public investor, Peter Lynch, managed Fidelity’s Magellan Fund from 1977 to 1990. With his active investment ideology at the helm, the fund returned an average 29% annually and, over the 13-year period, Lynch outperformed the S&P 500 eleven times.

By contrast, another legendary name that stands out in the investment world is Vanguard’s Jack Bogle, the father of indexing. He believed that over the long term, investment managers could not outperform the broad market average, and high fees make such an objective even more difficult to achieve. This belief led him to create the first passively managed index fund for Vanguard in 1976.

The Efficient Market Hypothesis and Other Investment Strategies

Strong belief in the efficient market hypothesis calls into question the strategies pursued by active investors. If markets are truly efficient, investment companies are spending foolishly by richly compensating top fund managers.

The explosive growth in assets under management in index and ETF funds suggests that there are many investors who do believe in some form of the theory.

However, legions of day traders depend on technical analysis. Value managers use fundamental analysis to identify undervalued securities and there are hundreds of value funds in the U.S. alone.

These are only two examples of investors who believe that it is possible to outperform the market. With so many professional investors on each side of the efficient market hypothesis, it’s up to individual investors to weigh the evidence on both sides and to reach a conclusion about the efficiency of the financial markets that best matches their investing beliefs.

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Rebecca Baldridge, CFA, is an investment professional and financial writer with over 20 years' experience in the financial services industry. In addition to a decade in banking and brokerage in Moscow, she has worked for Franklin Templeton Asset Management, The Bank of New York, JPMorgan Asset Management and Merrill Lynch Asset Management. She is a founding partner in Quartet Communications, a financial communications and content creation firm.

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Efficient Market Hypothesis (EMH)

Step-by-Step Guide to Understanding the Efficient Market Hypothesis (EMH)

Learn Online Now

What is the Efficient Market Hypothesis?

The Efficient Market Hypothesis (EMH) theory – introduced by economist Eugene Fama – states that the prevailing asset prices in the market fully reflect all available information.

Efficient Market Hypothesis (EMH)

Table of Contents

What is the Definition of Efficient Market Hypothesis?

Eugene fama quote: stock market theory, what are the 3 forms of efficient market hypothesis, emh and passive investing, efficient market hypothesis vs. active management, random walk theory vs. efficient market hypothesis (emh), efficient market hypothesis conclusion.

The efficient market hypothesis (EMH) theorizes about the relationship between the:

  • Information Availability in the Market
  • Current Market Trading Prices (i.e. Share Prices of Public Equities)

Under the efficient market hypothesis, following the release of new information/data to the public markets, the prices will adjust instantaneously to reflect the market-determined, “accurate” price.

EMH claims that all available information is already “priced in” – meaning that the assets are priced at their fair value . Therefore, if we assume EMH is true, the implication is that it is practically impossible to outperform the market consistently.

“The proposition is that prices reflect all available information, which in simple terms means since prices reflect all available information, there’s no way to beat the market.” – Eugene Fama

Weak Form, Semi-Strong, and Strong Form Market Efficiency

Eugene Fama classified market efficiency into three distinct forms:

  • Weak Form EMH: All past information like historical trading prices and volume data is reflected in the market prices.
  • Semi-Strong EMH: All publicly available information is reflected in the current market prices.
  • Strong Form EMH: All public and private information, inclusive of insider information, is reflected in market prices.

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Broadly put, there are two approaches to investing:

  • Active Management: Reliance on the personal judgment, analytical research, and financial models of investment professionals to manage a portfolio of securities (e.g. hedge funds).
  • Passive Investing: “Hands-off,” buy-and-hold portfolio investment strategy with long-term holding periods, with minimal portfolio adjustments.

As EMH has grown in widespread acceptance, passive investing has become more common, especially for retail investors (i.e. non-institutions).

Index investing is perhaps the most common form of passive investing, whereby investors seek to replicate and hold a security that tracks market indices.

In recent times, some of the main beneficiaries of the shift from active management to passive investing have been index funds such as:

  • Mutual Funds
  • Exchange-Traded Funds (ETFs)

The widely held belief among passive investors is that it’s very difficult to beat the market, and attempting to do so would be futile.

Plus, passive investing is more convenient for the everyday investor to participate in the markets – with the added benefit of being able to avoid high fees charged by active managers.

Long story short, hedge fund professionals struggle to “beat the market” despite spending the entirety of their time researching these stocks with more data access than most retail investors.

With that said, it seems like the odds are stacked against retail investors, who invest with fewer resources, information (e.g. reports), and time.

One could make the argument that hedge funds are not actually intended to outperform the market (i.e. generate alpha ), but to generate stable, low returns regardless of market conditions – as implied by the term “hedge” in the name.

However, considering the long-term horizon of passive investing, the urgency of receiving high returns on behalf of limited partners (LPs) is not a relevant factor for passive investors.

Typically, passive investors invest in market indices tracking products with the understanding that the market could crash, but patience pays off over time (or the investor can also purchase more – i.e. a practice known as “dollar-cost averaging”, or DCA ).

1. Random Walk Theory

The “ random walk theory ” arrives at the conclusion that attempting to predict and profit from share price movements is futile.

According to the random walk theory , share price movements are driven by random, unpredictable events – which nobody, regardless of their credentials, can accurately predict.

For the most part, the accuracy of predictions and past successes are more so due to chance as opposed to actual skill.

2. Efficient Market Hypothesis (EMH)

By contrast, EMH theorizes that asset prices, to some extent, accurately reflect all the information available in the market.

Under EMH, a company’s share price can neither be undervalued nor overvalued, as the shares are trading precisely where they should be given the “efficient” market structure (i.e. are priced at their fair value on exchanges).

In particular, if the EMH is strong-form efficient, there is essentially no point in active management, especially considering the mounting fees.

Since EMH contends that the current market prices reflect all information, attempts to outperform the market by finding mispriced securities or accurately timing the performance of a certain asset class come down to “luck” as opposed to skill.

One important distinction is that EMH refers specifically to long-term performance – therefore, if a fund achieves “above-market” returns – that does NOT invalidate the EMH theory.

In fact, most EMH proponents agree that outperforming the market is certainly plausible, but these occurrences are infrequent over the long term and not worth the short-term effort (and active management fees).

Thereby, EMH supports the notion that it is NOT feasible to consistently generate returns in excess of the market over the long term.

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strong vs weak hypothesis

What is the Efficient Markets Hypothesis?

  • Understanding the Efficient Markets Hypothesis
  • Variations of the Efficient Markets Hypothesis

Arguments For and Against the EMH

Impact of the emh, related readings, efficient markets hypothesis.

"It is not possible to outperform the market by skill alone"

The Efficient Markets Hypothesis (EMH) is an investment theory primarily derived from concepts attributed to Eugene Fama’s research as detailed in his 1970 book, “Efficient Capital Markets: A Review of Theory and Empirical Work.” Fama put forth the basic idea that it is virtually impossible to consistently “beat the market” – to make investment returns that outperform the overall market average as reflected by major stock indexes such as the S&P 500 Index .

Efficient Markets Hypothesis

According to Fama’s theory, while an investor might get lucky and buy a stock that brings him huge short-term profits, over the long term he cannot realistically hope to achieve a return on investment that is substantially higher than the market average.

Understanding the Efficient Markets Hypothesis

Fama’s investment theory – which carries essentially the same implication for investors as the Random Walk Theory – is based on a number of assumptions about securities markets and how they function. The assumptions include the one idea critical to the validity of the efficient markets hypothesis: the belief that all information relevant to stock prices is freely and widely available, “universally shared” among all investors.

As there are always a large number of both buyers and sellers in the market, price movements always occur efficiently (i.e., in a timely, up-to-date manner). Thus, stocks are always trading at their current fair market value.

The major conclusion of the theory is that since stocks always trade at their fair market value , then it is virtually impossible to either buy undervalued stocks at a bargain or sell overvalued stocks for extra profits. Neither expert stock analysis nor carefully implemented market timing strategies can hope to average doing any better than the performance of the overall market. If that’s true, then the only way investors can generate superior returns is by taking on much greater risk.

Variations of the Efficient Markets Hypothesis

There are three variations of the hypothesis – the weak , semi-strong , and strong forms – which represent three different assumed levels of market efficiency.

1. Weak Form

The weak form of the EMH assumes that the prices of securities reflect all available public market information but may not reflect new information that is not yet publicly available. It additionally assumes that past information regarding price, volume, and returns is independent of future prices.

The weak form EMH implies that technical trading strategies cannot provide consistent excess returns because past price performance can’t predict future price action that will be based on new information. The weak form, while it discounts technical analysis, leaves open the possibility that superior fundamental analysis may provide a means of outperforming the overall market average return on investment.

2. Semi-strong Form

The semi-strong form of the theory dismisses the usefulness of both technical and fundamental analysis. The semi-strong form of the EMH incorporates the weak form assumptions and expands on this by assuming that prices adjust quickly to any new public information that becomes available, therefore rendering fundamental analysis incapable of having any predictive power about future price movements. For example, when the monthly Non-farm Payroll Report in the U.S. is released each month, you can see prices rapidly adjusting as the market takes in the new information.

3. Strong Form

The strong form of the EMH holds that prices always reflect the entirety of both public and private information. This includes all publicly available information, both historical and new, or current, as well as insider information. Even information not publicly available to investors, such as private information known only to a company’s CEO, is assumed to be always already factored into the company’s current stock price.

So, according to the strong form of the EMH, not even insider knowledge can give investors a predictive edge that will enable them to consistently generate returns that outperform the overall market average.

Supporters and opponents of the efficient markets hypothesis can both make a case to support their views. Supporters of the EMH often argue their case based either on the basic logic of the theory or on a number of studies that have been done that seem to support it.

A long-term study by Morningstar found that, over a 10-year span of time, the only types of actively managed funds that were able to outperform index funds even half of the time were U.S. small growth funds and emerging markets funds. Other studies have revealed that less than one in four of even the best-performing active fund managers prove capable of outperforming index funds on a consistent basis.

Note that such data calls into question the whole investment advisory business model that has investment companies paying out huge amounts of money to top fund managers, based on the belief that those money managers will be able to generate returns well above the average overall market return.

Opponents of the efficient markets hypothesis advance the simple fact that there ARE traders and investors – people such as John Templeton, Peter Lynch, and Paul Tudor Jones – who DO consistently, year in and year out, generate returns on investment that dwarf the performance of the overall market. According to the EMH, that should be impossible other than by blind luck. However, blind luck can’t explain the same people beating the market by a wide margin, over and over again. over a long span of time.

In addition, those who argue that the EMH theory is not a valid one point out that there are indeed times when excessive optimism or pessimism in the markets drives prices to trade at excessively high or low prices, clearly showing that securities, in fact, do not always trade at their fair market value.

The significant rise in the popularity of index funds that track major market indexes – both mutual funds and ETFs – is due, at least in part, to widespread popular acceptance of the efficient markets hypothesis. Investors who subscribe to the EMH are more inclined to invest in passive index funds that are designed to mirror the market’s overall performance, and less inclined to be willing to pay high fees for expert fund management when they don’t expect even the best of fund managers to significantly outperform average market returns.

On the other hand, because research in support of the EMH has shown just how rare money managers can consistently outperform the market, the few individuals who have developed such a skill are ever more sought after and respected.

Thank you for reading CFI’s guide on Efficient Markets Hypothesis. To keep learning and advancing your career, the following resources will be helpful:

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The Weak, Strong and Semi-Strong Efficient Market Hypotheses

Though the efficient market hypothesis as a whole theorizes that the market is generally efficient, the theory is offered in three different versions: weak, semi-strong and strong.

The basic efficient market hypothesis posits that the market cannot be beaten because it incorporates all important determinative information into current share prices . Therefore, stocks trade at the fairest value, meaning that they can't be purchased undervalued or sold overvalued . The theory determines that the only opportunity investors have to gain higher returns on their investments is through purely speculative investments that pose substantial risk.

The three versions of the efficient market hypothesis are varying degrees of the same basic theory. The weak form suggests that today’s stock prices reflect all the data of past prices and that no form of technical analysis can be effectively utilized to aid investors in making trading decisions. Advocates for the weak form efficiency theory believe that if fundamental analysis is used, undervalued and overvalued stocks can be determined, and investors can research companies' financial statements to increase their chances of making higher-than-market-average profits.

Semi-Strong Form

The semi-strong form efficiency theory follows the belief that because all information that is public is used in the calculation of a stock's current price , investors cannot utilize either technical or fundamental analysis to gain higher returns in the market. Those who subscribe to this version of the theory believe that only information that is not readily available to the public can help investors boost their returns to a performance level above that of the general market.

Strong Form

The strong form version of the efficient market hypothesis states that all information – both the information available to the public and any information not publicly known – is completely accounted for in current stock prices, and there is no type of information that can give an investor an advantage on the market. Advocates for this degree of the theory suggest that investors cannot make returns on investments that exceed normal market returns, regardless of information retrieved or research conducted.

There are anomalies that the efficient market theory cannot explain and that may even flatly contradict the theory. For example, the price/earnings  (P/E) ratio shows that firms trading at lower P/E multiples are often responsible for generating higher returns. The neglected firm effect suggests that companies that are not covered extensively by market analysts are sometimes priced incorrectly in relation to their true value and offer investors the opportunity to pick stocks with hidden potential. The January effect shows historical evidence that stock prices – especially smaller cap stocks – tend to experience an upsurge in January.

Though the efficient market hypothesis is an important pillar of modern financial theories and has a large backing, primarily in the academic community, it also has a large number of critics. The theory remains controversial, and investors continue attempting to outperform market averages with their stock selections.

Related Articles

Has the efficient market hypothesis been proven correct or incorrect, is the stock market efficient, what does the efficient market hypothesis have to say about fundamental analysis, what is the efficient market hypothesis, why does the efficient market hypothesis state that technical analysis is bunk, top 7 market anomalies investors should know.

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Adam Becker

Author and astrophysicist, weak forms and strong forms.

For Cameron Neylon, because he kept asking me for this…

The Sapir-Whorf hypothesis 1 states that language affects thought — how we speak influences how we think. Or, at least, that’s one form of the hypothesis, the weak form. The strong form of Sapir-Whorf says that language determines thought, that how we speak forms a hard boundary on how and what we think. The weak form of Sapir-Whorf says that we drive an ATV across the terrain of thought; language can smooth the path in some areas and create rocks and roadblocks in others, but it doesn’t fundamentally limit where we can go. The strong form, in contrast, says we drive a steam train of thought, and language lays down the rails. There’s an intricate maze of forks and switchbacks spanning the continent, but at the end of the day we can only go where the rails will take us — we can’t lay down new track, no matter how we might try.

Most linguists today accept that some form of the weak Sapir-Whorf hypothesis must be true: the language(s) we speak definitely affect how we think and act. But most linguists also accept that the strong Sapir-Whorf hypothesis can’t be true, just as a matter of empirical fact. New words are developed, new concepts formed, new trails blazed on the terrain of thought. Some tasks may be easier or harder depending on whether your language is particularly suited for them — though even this is in dispute . But it’s simply not the case that we can’t think about things if we don’t have the words for them, nor that language actually determines our thought. In short, while the weak form of Sapir-Whorf is probably correct, the strong form is wrong. And this makes some sense: it certainly seems like language affects our thoughts, but it doesn’t seem like language wholly determines our thoughts.

But the Sapir-Whorf hypothesis isn’t the only theory with strong and weak forms — in fact, there’s a whole pattern of theories like this, and associated rhetorical dangers that go along with them. The pattern looks like this:

  • Start with a general theoretical statement about the world, where…
  • …there are two forms, a weak form and a strong form, and…
  • …the weak form is obviously true — how could it not be? — and…
  • …the strong form is obviously false, or at least much more controversial. Then, the rhetorical danger rears its head, and…
  • …arguments for the (true) weak form are appropriated, unmodified or nearly so, as arguments for the strong form by the proponents of the latter. (You also sometimes see this in reverse: people who are eager to deny the strong form rejecting valid arguments for the weak form.)

I don’t know why (5) happens, but I suspect (with little to no proof) that this confusion stems from rejection of a naive view of the world. Say you start with a cartoonishly simple picture of some phenomenon — for example, say you believe that thought isn’t affected by language in any way at all. Then you hear (good!) arguments for the weak form of the Sapir-Whorf hypothesis, which shows this cartoon picture is too simple to capture reality. With your anchor line to your old idea cut, you veer to the strong form of Sapir-Whorf. Then, later, when arguing for your new view, you use the same arguments that convinced you your old naive idea was false — namely, arguments for the weak form. (This also suggests that when (5) happens in reverse, this is founded in the same basic confusion: people defend themselves from the strong form by attacking the weak form because they would feel unmoored from their (naive) views if the weak form were true.) But why this happens is all speculation on my part. All I know for sure is that it does happen.

Cultural relativism about scientific truth is another good example. The two forms look something like this:

Weak form : Human factors like culture, history, and economics influence the practice of science, and thereby the content of our scientific theories.

Strong form : Human factors like culture, history, and economics wholly determine the content of our scientific theories.

It’s hard to see how the weak form could be wrong. Science is a human activity, and like any human activity, it’s affected by culture, economics, history, and other human factors. But the strong form claims that science is totally disconnected from anything like a “real world,” is simply manufactured by a variety of cultural and social forces, and has no special claim to truth. This is just not true. In her excellent book Brain Storm — itself about how the weak form of this thesis has played out in the spurious science of innate gender differences in the development of the human brain — Rebecca Jordan-Young forcefully rejects the strong form of relativism about science, and addresses both directions of the rhetorical confusion that arises from confounding the weak form with the strong:

The fact that science is not, and can never be, a simple mirror of the world also does not imply that science is simply “made up” and is not constrained by material phenomena that actually exist—the material world “pushes back” and exerts its own effects in science, even if we accept the postmodern premise that we humans have no hope of a direct access to that world that is unmediated by our own practices and culturally determined cognitive and linguistic structures. There is no need to dogmatically insist (against all evidence) that science really is objective in order to believe in science as a good and worthwhile endeavor, and even to believe in science as a particularly useful and trustworthy way of learning about the world. 2

Successful scientific theories, in general, must bear some resemblance to the world at large. Indeed, the success of scientific theories in predicting phenomena in the world would be nothing short of a miracle if there were absolutely no resemblance between the content of those theories and the content of the world. 3 That’s not to say that our theories are perfect representations of the world, nor that they are totally unaffected by cultural and political factors: far from it. I’m writing a book right now that’s (partly) about the cultural and historical factors influencing the debate on the foundations of quantum physics. But the content of our scientific theories is certainly not solely determined by human factors. Science is our best attempt to learn about the nature of the world. It’s not perfect. That’s OK.

There are many people, working largely in Continental philosophy and critical theory of various stripes, who advocate the strong form of relativism about science. 4 Yet most of their arguments which are ostensibly in favor of this strong form are actually arguments for the weak form: that culture plays some role in determining the content of our best scientific theories. 5 And that’s simply not the same thing.

Another, much more popular example of a strong and weak form problem is the set of claims around the “power of positive thinking.” The weak form suggests that being more confident and positive can make you happier, healthier, and more successful. This is usually true, and it’s hard to see how it couldn’t be usually true — though there are many specific counterexamples. For example, positive thinking can’t keep your house from being destroyed by a hurricane. Yet the strong form of positive-thinking claims — known as “the law of attraction,” and popularized by The Secret — suggests exactly that. This states that positive thinking, and positive thinking alone, can literally change the world around you for the better, preventing and reversing all bad luck and hardship. 6 Not only is this manifestly untrue, but the logical implications are morally repugnant: if bad things do happen to you, it must be a result of not thinking positively enough . For example, if you have cancer, and it’s resistant to treatment, that must be your fault . While this kind of neo-Calvinist victim-blaming is bad enough, it becomes truly monstrous — and the flaw in the reasoning particularly apparent — when extended from unfortunate individual circumstances to systematically disadvantaged groups. The ultimate responsibility for slavery, colonialism, genocide, and institutionalized bigotry quite obviously does not lie with the victims’ purported inability to wish hard enough for a better world.

In short, easily-confused strong and weak forms of a theory abound. I’m not claiming that this is anything like an original idea. All I’m saying is that some theories come in strong and weak forms, that sometimes the weak forms are obviously true and the strong obviously false, and that in those cases, it’s easy to take rhetorical advantage (deliberately or not) of this confusion. You could argue that the weak form directly implies the strong form in some cases, and maybe it does. But that’s not generally true, and you have to do a lot of work to make that argument — work that often isn’t done.

Again, I strongly suspect other people have come up with this idea. When I’ve talked with people about this, they’ve generally picked it up very quickly and come up with examples I didn’t think of. This seems to be floating around. If someone has a good citation for it, I’d be immensely grateful.

Image credit: Zink Dawg at English Wikipedia , CC-BY 3.0. I was strongly tempted to use this image instead.

  • This is apparently a historical misnomer, but we’ll ignore that for now. [ ↩ ]
  • Rebecca M. Jordan-Young, in Brain Storm: The Flaws in the Science of Sex Differences, Harvard University Press, 2011, pp. 299-300. Emphasis in the original. [ ↩ ]
  • See J.J.C. Smart,  Philosophy and Scientific Realism , and Hilary Putnam,  Mathematics, Matter, and Method . [ ↩ ]
  • Bruno Latour is the first name that comes to mind. [ ↩ ]
  • See, for example, Kuhn, who even seems to have confused himself about whether he was advocating the strong or the weak version. [ ↩ ]
  • The “arguments” in favor of this kind of nonsense take advantage of more than just the confusion between the strong and weak forms of the thesis about positive thinking. They also rely on profound misunderstandings about quantum physics and other perversions of science. But let’s put that aside for now. [ ↩ ]

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One thought on “ weak forms and strong forms ”.

There’s Occam’s Rusty Razor at work. Weak versions of theories necessitate lots of conditionals. Simpler just to eschew all conditionals. But simplicity itself is a virtue only with lots of subtlety and conditionality. Rusty razors butcher. Eschew Occam’s Rusty Razor.

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How to understand the difference between "Strong" & "Weak" Hypotheses in the case of Bolinger/Lieberman's views of Intonation?

1. non-whorfian contexts and missing czech equivalents.

To begin with, I am not sure if this is the right place to ask a question that may just as well pertain to scientific terminology in general. Nevertheless, it was only when I was reading a paper on Cross-language comparison of intonation by R. D. Ladd that I encountered the use of weak vs. strong in a context other than the Sapir-Whorfian linguistic relativity , where two versions of a S-W hypothesis are offered:

"The strong version says that language determines thought, and that linguistic categories limit and determine cognitive categories[.]"
"[T]he weak version says only that linguistic categories and usage influence thought and certain kinds of non-linguistic behavior."

In addition, I have never encountered the terms strong / weak hypothesis (or its translation silná / slabá hypotéza ) in Czech linguistic literature . I might be wrong, but we either do no use these terms in Czech at all, or we do have some analogical terms that simply do not translate as silná / slabá and that I have only been failing to encounter. In the very few texts I have been able to find on the internet using silná / slabá among my search criteria the authors seem to be using them, rather idiosyncratically, as direct translations from English, i.e. anglicisms of a sort.

2. Close encounters in Ladd's paper

I think I should first explain the particular context I encountered the terms in. In the opening section of the above-mentioned paper, Ladd criticizes the various unversalist opinions on intonation as hardly tenable. He chooses Bolinger and Lieberman to exemplify this, and describing the latter's views her says:

Lieberman (1967), for example, put forth a strong hypothesis relating intonational phrasing to the control o f breath and subglottal pressure in speech production, in connection with which he made broadly similar claims about universal functions of intonation to those made by Bolinger. Specifically, he suggested that all linguis­tically significant uses of intonation in all languages could be reduced to a distinction between 'marked breath group' and 'unmarked breath group' (corresponding roughly to phrasefinal rise and fall respectively), plus local prominence for accent on individually informative words; lexical tone was seen as overlaid on the two breath group types.

3. Glimpses of what the distinction might be about

So far, I have been able to put some pieces together from various online sources, most of which where non-linguistic and none actually discussed the essence of the difference. My current understanding, then, is very roughly as follows:

Strong hypotheses are simply strong claims, perhaps too strong, as they include a lot of details and particular assumptions, making the hypotheses as wholes difficult, if not impossible, to test and defend.

Weak hypotheses are more careful and focused more narrowly on a single aspect of a phenomenon - one that is easier to test, before one ever moves on to the other aspects.

4. Interpretation of the text by Ladd

Now, it seems that Lieberman's position is to be seen as strong , because he makes a lot of untestable (?) assumptions at once. If that is the case, what would a weak version of his hypothesis look like?

I will be extremely grateful for a fully-fledged answer, but I will also appreciate any comments, references, examples anyone can offer. And if someone can even come up with appropriate Czech equivalents, it will be just perfect! On the other hand, I won't object to migrating this question to another, more appropriate forum, if necessary.

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strong vs weak hypothesis

Preference Hypothesis and Strong Ordering (Explained With Diagram)

strong vs weak hypothesis

Samuelson’s revealed preference theory has preference hypothesis as a basis of his theory of demand.

According to this hypothesis, when a consumer is observed to choose a combination A out of various alternative combinations open to him, then he ‘reveals’, his preference for A over all other alternative combinations which he could have purchased.

In other words, when a consumer chooses a combination A, it means he considers all other alternative combinations which he could have purchased to be inferior to A. That is, he rejects all other alternative combinations open to him in favour of the chosen combination A. Thus, according to Samuelson, choice reveals preference. Choice of the combination A reveals his definite preference for A over all other rejected combinations.

From the hypothesis of ‘choice reveals preference’ we can obtain definite information about the preferences of a consumer from the observations of his behaviour in the market. By comparing preferences of a consumer revealed in different price-income situations we can obtain certain information about his preference scale.

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Let us graphically explain the preference hypothesis. Given the prices of two commodities X and Y and the income of the consumer, price line PL is drawn in Fig. 12.1. The price line PL represents a given price-income situation. Given the price-income situation as represented by PL, the consumer can buy or choose any combination lying within or on the triangle OPL.

In other words, all combinations lying on the line PL such as A, B, C and lying below the line PL such as D, E, F and G are alternative combinations open to him, from among which he has to choose any combination. If our consumer chooses combination A out of all those open to him in the given price-income situation, it means he reveals his preference for A over all other combinations such as B, C, D, E and F which are rejected by him. As is evident from Fig. 12.1, in his observed chosen combination A, the consumer is buying OM quantity of commodity X and ON quantity of commodity Y.

Choice Reveals Preference

Besides, we can infer more from consumer’s observed choice. As it is assumed that a rational consumer prefers more of both the goods to less of them or prefers more of at least one good, the amount of the other good remaining the same, we can infer that all combinations lying in the rectangular shaded area drawn above and to the right of chosen combination A are superior to A.

Since in the rectangular shaded area there lie those combinations (baskets) of two goods which contain either more of both the goods or at least more of one good, the amount of the other remaining the same, this means that the consumer would prefer all combinations in the rectangular shaded area to the chosen combination A. In other words, all combinations in the shaded area MAN are superior to the chosen combination A.

As seen above, all other combinations lying in the budget-space OPL are attainable or affordable but are rejected in favour of A and are therefore revealed to be inferior to it. It should be carefully noted that Samuelson’s revealed preference theory is based upon the strong form of preference hypothesis.

In other words, in revealed preference theory, strong- ordering preference hypothesis has been applied. Strong ordering implies that there is definite ordering of various combinations in consumer’s scale of preferences and therefore the choice of a combination by a consumer reveals his definite preference for that over all other alternatives open to him.

Thus, under strong ordering, relation of indifference between various alternative combinations is ruled out. When in Fig. 12.1a consumer chooses a combination A out of various alternative combinations open to him, it means he has a definite preference for A over all others; the possibility of the chosen combination A being indifferent to any other possible combination is ruled out by strong ordering hypothesis.

J. R. Hicks in his “A Revision of Demand Theory’ does not consider the assumption of strong ordering as satisfactory and instead employs weak ordering hypothesis. Under weak ordering hypothesis (with an additional assumption that the consumer will always prefer a larger amount of a good to a smaller amount of it), the chosen combination A is preferred over all positions that lie within the triangle OPL and further that the chosen position A will be either preferred to or indifferent to the other positions on the price-income line PL.

“The difference between the consequences of strong and weak ordering, so interpreted amounts to no more than this that under strong ordering the chosen position is shown to be preferred to all other positions in and on the triangle, while under weak ordering it is preferred to all positions within the triangle, but may be indifferent to other positions on the same boundary as itself.”

The revealed preference theory rests upon a basic assumption which has been called the ‘consistency postulate’. In fact, the consistency postulate is implied in the strong ordering hypothesis. The consistency postulate can be stated thus: ‘no two observations of choice behaviour are made which provide conflicting evidence to the individual’s preference.”

In other words, consistency postulate asserts that if an individual chooses A rather than B in one particular instance, then he cannot choose B rather than A in any other instance when both are available to the consumer. If he chooses A rather than B in one instance and chooses B rather than A in another when A and B are present in both the instances, then he is not behaving consistently.

Thus, consistency postulate requires that if once A is revealed to be preferred to B by an individual, then B cannot be revealed to be preferred to A by him at any other time when A and B are present in both the cases. Since comparison here is between the two situations consistency involved in this has been called ‘ two term consistency by J.R. Hicks.

Weak Axiom of Revealed Preference (WARP):

If a person chooses combination A rather than combination B which he could purchase with the given budget constraint, then it cannot happen that he would choose (i.e. prefer) B over A in some other situation in which he could have bought A if he so wished. This means his choices or preferences must be consistent.

This is called revealed preference axiom. We illustrate, revealed preference axiom in Figure 12.2. Suppose with the given prices of two goods X and Y and given his money income to spend on the two goods, PL is the budget line facing a consumer. In this budgetary situation PL, the consumer chooses A when he could have purchased B (note that combination B would have even cost him less than A). Thus, his choice of A over B means he prefers the combination A to the combination B of the two goods.

Now suppose that price of good X falls, and with some income and price adjustments, budget line changes to P’L’. Budget line P’L’ is flatter than PL reflecting relatively lower price of X as compared to the budget line PL. With this new budget line P ‘U, if the consumer chooses combination B when he can purchase the combination A (as A lies below the budget line P’L’ in Fig. 12.2), then the consumer will be inconsistent in his preferences, that is, he will be violating the axiom of revealed preference.

Such inconsistent consumer’s behaviour is ruled out in revealed preference theory based on strong ordering. This axiom of revealed preference according to which consumer’s choices are consistent is also called ‘ Weak Axiom of Revealed Preference or simply WARP. To sum up, according to the weak axiom of revealed preference.

“If combination A is directly revealed preferred to another combination B, then in any other situation, the combination B cannot be revealed preferred to combination A by the consumer when combination A is also affordable”.

Now consider Figure 12.3 where to start with a consumer is facing budget line PL where he chooses combination A of two goods X and Y. Thus, consumer prefers combination A to all other combinations within and on the triangle OPL. Now suppose that budget constraint changes to P ‘L’ and consumer purchases combination B on it.

As combination B lies outside the budget line PL it was not affordable when combination A was chosen. Therefore, choice of combination B with the budget line P ‘L’ is consistent with his earlier choice A with the budget constraint PL and is in accordance with the weak axiom of revealed preference.

Consumer's Preferences are Inconsistent

Transitivity Assumption of Revealed Preference :

The axiom of revealed preference described above provides us a consistency condition that must be satisfied by a rational consumer who makes an optimum choice. Apart from the axiom of revealed preference, revealed preference theory also assumes that revealed preferences are transitive.

According to this, if an optimising consumer prefers combination A to combination B of the goods and combination B to combination C of the goods, then he will also prefer combination A to combination C of the goods. To put it briefly, assumption of transitivity of preferences requires that if A> B and B> C, then A > C.

In this way we say that combination A is indirectly revealed to be preferred to combination C. Thus, if a combination A is either directly or indirectly revealed preferred to another combination we say that combination A is revealed to be preferred to the other combination. Consider Figure 12.4 where with budget constraint PL, the consumer chooses A and therefore reveals his preference for A over combination B which he could have purchased as combination B is affordable in budget constraint PL.

Now suppose budget constraint facing the consumer changes to P’L’, he chooses B when he could have purchased C. Thus, the consumer prefers B to C. From the transitivity assumption it follows that the consumer will prefer combination A to combination C. Thus, combination A is indirectly revealed to be preferred to combination C. We therefore conclude that the consumer prefers A either directly or indirectly to all those combinations of the two goods lying in the shaded regions in Figure 12.4.

Revealed Preferences are Transitive

It is thus evident from above that concept of revealed preference is a very significant and powerful tool which provides a lot of information about consumer’s preferences who behave in an optimising and consistent manner. By merely looking at the consumer’s choices in different price-income situations we can get a lot of information about consumer’s preferences.

It may be noted that the consistency postulate of revealed preference theory is the counterpart of the utility maximisation assumption in both Marshallian utility theory and Hicks- Allen indifference curve theory. The assumption that the consumer maximises utility or satisfaction is known as rationality assumption. It has been said that a rational consumer will try to maximise utility or satisfaction.

Recently, some economists have challenged this assumption. They assert that consumers in actual practice do not maximise utility. The revealed theory has the advantage that its rationality assumption can be easily realised in actual practice. The rationality on the part of the consumer in revealed preference theory only requires that he should behave in a ‘consistent’ manner.

Consistency of choice is a less restrictive assumption than the utility maximisation assumption. This is one of the improvements of Samuelson’s theory over the Marshallian cardinal utility and Hicks-Allen indifference curve theories of demand.

It is important to note that Samuelson’s revealed preference is not a statistical concept. If it were a statistical concept, then the preference of an individual for a combination A would have been inferred from giving him opportunity to exercise his choice several times in the same circumstances.

If the individual from among the various alternative combinations open to him chooses a particular combination more frequently than any other, only then the individual’s preference for A would have been statistically revealed. But in Samuelson’s revealed preference theory preference is said to be revealed from a single act of choice.

It is obvious that no single act of choice on the part of the consumer can prove his indifference between the two situations. Unless the individual is given the chance to exercise his choice several times in the given circumstances, he has no way of revealing his indifference between various combinations.

Thus, because Samuelson infers preference from a single act of choice the relation of indifference is inadmissible to his theory. Therefore, the rejection of indifference relation by Samuelson follows from his methodology. “The rejection of indifference in Samuelson theory is, therefore, not a matter of convenience but dictated by the requirements of his methodology.”

Related Articles:

  • Choice of Revealed Preference (With Diagram)
  • Hick’s Logical Theory of Demand: Preference Hypothesis and Logic of Ordering
  • The Revealed Preference Hypothesis (With Diagram)
  • Consumption Theory on Revealed Preference Approach

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What's the difference between simple induction and strong induction?

I just started to learn induction in my first year course. I'm having a difficult time grasping the concept. I believe I understand the basics but could someone summarize simple induction and strong induction and explain what the differences are? The video I'm watching explains that if $P(k)$ is true then $P(k+1)$ is true for simple induction, and for strong induction if $P(i)$ is true for all $i$ less than equal to $k$ then $P(k+1)$ is true. I don't really know what that means.

Mike Pierce's user avatar

  • $\begingroup$ For further reading regarding mathematical induction read this . $\endgroup$ –  user170039 Commented Aug 12, 2016 at 4:37

2 Answers 2

With simple induction you use "if $p(k)$ is true then $p(k+1)$ is true" while in strong induction you use "if $p(i)$ is true for all $i$ less than or equal to $k$ then $p(k+1)$ is true", where $p(k)$ is some statement depending on the positive integer $k$ .

They are NOT "identical" but they are equivalent.

It is easy to see that if strong induction is true then simple induction is true: if you know that statement $p(i)$ is true for all $i$ less than or equal to $k$ , then you know that it is true, in particular, for $i=k$ and can use simple induction.

It is harder to prove, but still true, that if simple induction is true, then strong induction is true. That is what we mean by "equivalent".

Here we have a question. It is not why we still have "weak" induction - it's why we still have "strong" induction when this is not actually any stronger.

My opinion is that the reason this distinction remains is that it serves a pedagogical purpose. The first proofs by induction that we teach are usually things like $\forall n\left[\sum_{i=0}^n i= \frac{n(n+1)}{2}\right]$ . The proofs of these naturally suggest "weak" induction, which students learn as a pattern to mimic.

Later, we teach more difficult proofs where that pattern no longer works. To give a name to the difference, we call the new pattern "strong induction" so that we can distinguish between the methods when presenting a proof in lecture. Then we can tell a student "try using strong induction", which is more helpful than just "try using induction".

Wouter's user avatar

  • 7 $\begingroup$ Another important reason for the distinction is that when working in other well-ordered sets, they need no longer be equivalent (strong induction always works, simple induction might require more base cases to still work). $\endgroup$ –  Tobias Kildetoft Commented Oct 7, 2013 at 8:01
  • 6 $\begingroup$ I dislike the isolation of weak induction. I’d rather see induction taught first in terms of (non-existence) of a least counterexample. Strong induction comes naturally that way, and weak induction is obviously just a special case; moreover, since least ultimately generalizes to well-founded relations in general, you also get structural induction. $\endgroup$ –  Brian M. Scott Commented Oct 7, 2013 at 8:09
  • 5 $\begingroup$ I don't get how it is "harder to prove" that strong induction implies weak. That direction is completely straightforward, since the base case and induction step for a "weak" induction proof directly imply the induction step of strong induction. $\endgroup$ –  hmakholm left over Monica Commented Oct 7, 2013 at 9:34
  • 1 $\begingroup$ @Tobias: Yes, so if you have done the step for weak induction, you have proved $P(n)$ with strictly fewer assumptions that long induction allows you to use, and you can reuse your induction step unchanged. In contrast, if you want to go in the other direction you have, in general, to change what the property you prove is. $\endgroup$ –  hmakholm left over Monica Commented Oct 7, 2013 at 9:43
  • 6 $\begingroup$ Don't you mean it's easier to see that strong induction implies simple induction, and it's harder to prove that simple induction implies strong induction? If you assume $(\forall i \le k): p(i) \implies p(k+1)$ is true, then it's straightforward to show that $p(k)\implies p(k+1)$ is true, like you said, taking the case $i=k$. The harder proof is showing the reverse direction (simple to strong). $\endgroup$ –  chharvey Commented Oct 1, 2016 at 3:28

One example of the use of strong induction is in the inductive proof that any prime $p\not \equiv 3 \pmod 4$ is the sum of squares of two integers. We have $2=1^2+1^2.$ For prime $p\equiv 1 \pmod 4,$ at some point in the proof we need to employ the inductive hypothesis that every prime $q$ such that $p>q\not \equiv 3 \pmod 4$ is the sum of two squares, because (after a fair bit of other work) such a $q$ appears in the algebra but we don't know which one it is.

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strong vs weak hypothesis

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