The No Competitive Edge Theorem (NCET) is an intuitive theorem for pricing assets in the financial markets. The theorem applies a robust model of dynamically competing participants who maximize utility through expectations of price. In the model, an improved fair value definition is established that incorporates the competitive interactions between market participants. Through the improved fair value, the NCET cumulates into the argument that efficient market applications are justified without requiring rational participants. Overall, the NCET advances and unifies several key areas including participant behavior, fair value pricing, arbitrage, random walks, and efficient markets.
A. People create and participate in markets because they want satisfaction
B. Participants are satisfied when they fulfill their desires
C. Participants fulfill desires by setting goals and trying to achieve those goals
D. Participants have tangible goals
E. Therefore, satisfaction is a function of all the participants’ goals and results
F. Participants are concerned about future satisfaction
G. Participants seek to maximize their future satisfaction
H. Participants seek the optimal future results that maximize their future satisfaction
I. Participants seek the optimal prices that optimize the expected future results
J. Participants seek to exchange assets at the optimal prices
K. Participants exchange assets at the perceived fair value
K.1 MFV Propositions:
1) PT = MFV | PCET = Ø → PT = NPVB = NPVS
2) PT = MFV | PCET = Ø → μB = dB = rn = μS = dS
3) PT = MFV | PCET = Ø → pB( PT+x ) = pS( PT+x ) for all x ≥ 0
4) PT = MFV | PCET = Ø → LB( PT+x ) = LS( PT+x ) for all x ≥ 0
L. Once assets are exchanged the expected results become actual results
A. Competitive Edges
A competitive edge is having private information about the price distribution and liquidity. More specifically, a competitive edge is having information that the competition does not have about the price process and liquidity. Competitive edges are categorized into three groups; absolute competitive edges, conditional competitive edges, and liquidity competitive edges.
B. Perceived Competitive Edges
With competitive edges defined, a perceived competitive edge is a competitive edge that has been identified by the competition. Only when there are no perceived competitive edges between the exchanging entities can an exchange occur at the MFV.
PCET,Buyer = Ø ∩ PCET,Seller = Ø → PCET = Ø → PT = MFV
Arbitrage under the NCET is defined as knowing that a price other than the MFV price is available or will be available, such that a portfolio including the asset has a positive payoff with no possibility of a return below the risk-neutral return rate of the portfolio. Let arbitrage be defined as the following,
ERPF > rn ∩ p( RPF < rn ) = 0 | PF
In short, arbitrage, under the NCET, is the ability to get risk-free expected returns above the risk-neutral return rate. The NCET definition of arbitrage could be further relaxed by maintaining the current definition, but allowing returns to fall as low as one; ERPF > rn ∩ p( RPF < 1 ) = 0 | PF. This would account for real world speculative arbitrage.
A. The NCET Hypothesis – Do real asset exchanges occur at the Market Fair Value?
The question could be asked, “Do real asset exchanges occur at the market fair value?”. With this question in mind, the NCET hypothesis is that real asset exchanges occur at the market fair value. This logic can be tested by examining equation 1.38 in two parts.
Part One: IE.T,Buyer = Ø ∩ IE.T,Seller = Ø → ΔIT,Buyer = 0 ∩ ΔIT,Seller = 0
Part Two: ΔOPT,Buyer = 0 ∩ ΔOPT,Seller = 0 → PCET,Buyer = Ø ∩ PCET,Seller = Ø
B. The Evidence
B.1 Part One - Do participants appear neutral near asset exchanges?
Of the millions of financial asset exchanges that occur each day, less than a handful have information exchanged. Given the evidence, 99.999% is a reasonable estimate for asset exchanges occurring without information being exchanged.
B.2 Part Two - Do participants take optimal actions to establish their optimal prices?
For this, the NCET turns to the aid of the Efficient Market Hypothesis tests. The EMH tests clearly show that participants eliminate competitive edges because the tests have not identified many, if any, significant perceived competitive edges. Since participants are eliminating competitive edges, they are therefore optimizing their results, which implies they are optimizing their prices.
A. Modeling MFV
Modeling MFV requires a neutral stance where buyers and sellers can mutually agree on pricing. This is accomplished by establishing models with no perceived competitive edges, which means assuming that both parties have equal abilities and relevant information sets. For this to be true, both parties must know all public information and not have any relevant private information. Hence, MFV models incorporate all public information.
B. Establishing random walks for the MFV
Random Walks under the NCET, called MFV Random Walks, are a type of random walk where all prices are MFV prices. This is critical for assigning fair price probabilities used in derivative pricing and other pricing applications dependent on the price process distribution. MFV Random Walks have two fundamental properties:
This means that MFV price processes are martingales across all possible time frames after discounting at the risk-neutral return rate (Fabozzi, Focardi, Kolm 2006) (note 4.1).
In most cases, the absence of perceived competitive edges means the distribution is not Gaussian and does not have a constant variance; if a finite variance even exists. For most markets, the evidence so greatly outweighs these two possibilities that no sane participant could consider them realistic or fair (Ross 2005, pg 61). Applying either of these possibilities to the price process would create a perceived competitive edge for either the buyer or seller. For some derivatives, options for example, portfolio replication strategies could be used to capture profits from miss priced derivatives.
While the expected future prices cannot have dependencies on price or returns, the other properties of the distribution can have dependencies. Distribution moments greater than one can have any number of dependencies on past information. Thus, price processes incorporating memory effects into the pricing properties are admissible. There is ample evidence of various dependencies found in nearly all markets. These dependencies are well beyond a random chance (Ross 2005, pg 61). In light of this, GARCH, stochastic volatility, ARIMA, and fractal processes, to name a few, are reasonable choices for modeling MFV price processes (Fouque, Papanicolaou, Sircar 2000; Peters 1994; Rebonato 2004 ) (note 4.2).
C. Derivative pricing under the MFV Random Walk
Derivatives are traded assets, meaning they are subject to the NCET. An important by-product of MFV derivative pricing is that the risk-neutral world is natural property of the underlying asset and not an artificial mathematical property of derivative pricing. While Fischer Black (1973) proved, with his brilliant portfolio substitution, that the risk-neutral world must be artificially applied to derivative pricing, it is not a readily intuitive proof. The NCET bridges the gap between Fisher Black’s proof and common sense.
However, the NCET application to MFV Random Walks would be incomplete without Black’s proof. Fisher Black proved the expected return must be the risk-neutral return rate to eliminate arbitrage opportunities. Without arbitrage, the MFV argument that the expected return must be the risk-neutral return rate would be like a city with laws but no police to enforce the laws. Arbitrage is the market’s police, which keeps prices and expected returns in check. It was Fisher Black’s work that proved the arbitrage competitive edge exists and must be eliminated from MFV Random Walks.
The NCET model explains the higher expected returns by working in parallel with game theory and risk aversion concepts. Using the NCET model, risk adverse participants can be modeled as seeking prices that optimize their expected results and goals for given level of risk. For participants with goals aimed at maximizing returns, the model reduces to classical view of risk adverse participants (i.e. participants who seek the best prices that maximize their returns for a given level of risk).
A. Price and Expectations
Prices are mostly the result of the active participants’ taking action based on their expectations of other active participants. Several studies support this logic (Froot, Scharfstein, Stein 1992) and higher order expectation models exists (Allen, Morris, Shin 2004). This ideology does not negate the fact that prices are impacted by supply and demand, market risks, macro economic events, and so forth. .
For most participants, the “value” of the asset is nothing more than what they can sell it for later. People buy and sell based on their expectations about what others will pay in the future. Arbitrage is also nothing more than expectations, which Behavioral Finance has touched upon. The concept of expectations has been around a long time. It was magnificently presented by Keynes (1937) “beauty contest” example. People don’t bet on the “beauty” of the contestants as much as who everyone else thinks is the most “beautiful”.
B. Price and Risk
This relationship between expectations and expected results/goals directly affects the participants’ risk. Risk, identified in italics, is a measure of the chances of not achieving the highest expected satisfaction. Some of these factors have started showing up in published theories and models. Behavioral Finance includes some of them.
In some cases the change in risk leads to portfolio changes, which creates more buying and selling. In the absence of news, the amount of buying and selling must largely be a function of the aggregate change in risk due to price and other factors (this is supported, in part, by Fischer Black’s analysis of Noise (1986)). Often the participants become over or under leveraged with respect to their risk. In this regard, large price swings and “irrational exuberance”, often characterized as irrational prices and noise, are a natural property of price processes.
C. Price, Expectations, and Risks - The Price Process
This paper has shown that price, expectations, and risk are dependent functions of each other. There is never an information, price, expectation, or risk equilibrium. They are all constantly in a state of change. This is what drives prices; it is not just news (this is supported, in part, by Fischer Blacks analysis of Noise (1986)). Information feeds expectations, expectations feed risk, and risk feeds more prices. The interdependence of price and certain risk factors has been partially captured in some asset pricing models (CAPM, APT, etc.). A final key is that prices are a constant feedback system. Reflexivity (Soros 2003), self-learning agent based models, nonlinear dynamic theories, and so on, are all related to the NCET model.
A. Expected Return and Risk
The NCET has shown that for asset exchanges to occur participants must establish MFVs and apply MFV random walks. However, real price processes do not follow MFV random walks because risk alters the expected return where the expected return is a function of the active participant’s expectations (note 6.1).
B. Risk Aversion
A reasonable assumption is that most participants want the optimal prices that maximize their expected return given a certain level of risk. If a participant had to pick between two investments with equal expected returns but unequal risks, the participant would choose the investment with the least risk (this has been proven for risk adverse participants using utility curves in economic game theory (Von Neumann, Morgenstern 1953), which could be modeled using the NCET model). From the perspective of the NCET model, this simply means participants would compete for the optimal prices of the assets with the lowest risk for a given level of expected return.
C. The Participants Fair Value
In real markets, participants form their own fair value, called the Participant Fair Value (PFV), which is different from the MFV.
D. Risks and the Return Distribution
To eliminate risk competitive edges from price processes, all moments of the return distribution must be related to the risks. The expected return and spread of returns are only the first and second moments. The existence of higher moments in asymmetric return distributions is critical because the effect of risks on the return distribution is generally not equally weighted about the expected return. However, for simplicities sake, this paper will limit the discussion to the first and second moments and ignore distributions with more than two inflection points.
p( returns ) = ƒ ( risks ) → h = ƒ ( risks ) (6.1)
μ = r + h → μ = r + ƒ ( risks ) (6.2)
As already argued in this paper, new information affects risks. From equation 6.1, it is clear that new information also affects the expected return because the risk is altered. New information ultimately drives more prices. Changes in the risk premium cause risk adverse participants to alter their portfolios in order to maintain specific risk aversion levels. MFV pricing brings a good question. Even if the MFV is based on the risk-free rate, aren’t call options for stocks undervalued as a whole? The simple answer is yes. While arbitrage keeps the price locked to the risk-free rate, the fact remains that risky assets will generally have greater expected returns than the risk-free rate. This implies the PFV may not equal the MFV for certain options given certain risk-free interest rate levels. However, the expected profits are small and often eliminated by commissions and bid/ask spreads.
A. Why are Efficient Markets Useful
Why do people need efficient market theory? Efficient markets are the foundation for various optimal asset allocation theories, asset pricing models, risk prediction models, etc. All of these models are derived from the fundamental purpose of efficient markets; to establish “fair” random walks in a predominately risk adverse world.
What efficient markets do is create a hypothetical situation where MFV random walks and real price processes can be merged without allowing any perceived competitive edges. The result is an efficient market random walk. Efficient market random walks have all the properties of MFV random walks with the exception that the expected return can be greater than the risk-neutral return rate (this is proven using the NCET model in subsection D). These random walks can be applied in several ways to produce a multitude of invaluable economic and financial models that are useful to everyone. Efficient market theory, research, application, and offshoots are critical to the finance world. Eugene Fama’s (1965) famous “Efficient Market Hypothesis” was a giant leap forward in economics and finance.
B. Classical Efficient Markets
Classical efficient market theory is founded on the relationship between the price and risk described in Section V. The idea is that rational participants know all the information and correctly factor the information into the price. The current price is the fair price, and the expected return is the risk-free rate plus a risk premium. The only way to increase the expected return is to invest in riskier assets with higher risk premiums. This issue is theoretically resolved by applying the Rational Expectations Theory. Roughly speaking, it says the actual result is the expected result plus a random error term. Therefore, the participants expected risk premiums tend to be the actual risk premiums.
C. Introduction to NCET Efficient Markets
The NCET’s view on efficient markets is completely indifferent to this problem. The NCET efficient market model is not designed with the intention of justifying efficient market applications. Instead, the model is designed to be valid for any level of market efficiency. The independence of the model from market efficiency allows market efficiency tests to be independent of the model.
D. NCET Model of Efficient Markets
To model this hypothetical market of predominately risk adverse participants using the NCET model, the known risks (note 7.2) are included into the public information set. The participants are still competing for price, but now they are competing for the optimal prices that maximize the expected returns given the known risks. In an efficient market the expected return, μR, is based on the known risks. This implies the EMFV is perceived as the net present value of the asset in a risk-adverse world where the exchanging participants know the price distribution and liquidity.
E. MVF versus EMFV
“Hypothetical” efficient markets are sometimes confused with the “real” markets. MFV hits the bank account while the EMFV does not. The second major distinction between efficient markets and the real world is that the real world is uncertain, while efficient markets are hypothetically certain (risks and probabilities can be assigned).
F. Participant Behavior
The NCET efficient markets do not require rational expectations or rational participants. The NCET qualifies participants as being quasi-rational. Quasi-rationality is the minimum sanity required by participants to maintain a market. In other words, quasi-rationality is the minimum rational behavior required to establish the NCET’s fair value.
The application of quasi-rationality maintains the core link between the classical rationality and the NCET’s rationality. In the classical sense of rationality, humans seek the highest well-being. This concept is mirrored by the NCET’s view that participants seek the highest possible satisfaction. Participants act quasi-rational with respect to their individual personalized satisfaction. All things considered, rationality has to do with the participants’ position, abilities, information, capital constraints, risk aversion, emotional resilience, and so on.
The NCET does not specifically argue against rational participants or rational expectations. This is because rational participants are a subset of quasi-rational participants. However, the NCET model does argue for quasi-rational participants because participants are more accurately represented by quasi-rationality than by classical rationality. Several studies support the idea that participants are not rational. Researchers have shown that participants do not always follow Neumann-Morgenstern rationality. Participants often demonstrate significant levels of loss aversion, violate Bayes rule for predicting uncertain outcomes, and are swayed by how problems are presented to them (Shleifer 2000).
G. NCET Efficiency versus Classical Efficiency
The NCET model’s flexibility with regards to market efficiency shares similar ties with the EMH’s strong, semi-strong, and weak forms. The strongest form of the NCET’s market efficiency does not allow any competitive edges for any participant. The semi-strong form allows for limited competitive edges, but not systematic competitive edges or other reasonably easily identifiable competitive edges (such as correlation analysis, simple technical analysis techniques, etc). The weakest form allows for unlimited competitive edges for all participants. While the NCET has borrowed the famous EMH terminology, the difference between the forms is not an “apples to apples” comparison. For example, the NCET’s strongest form leads to identical results as the EMH’s strong from (i.e. in both cases no one has any competitive edges). However, the NCET’s semi-strong form does not lead to the same results as the EMH semi-strong form, but instead leads to results closer to the EMH’s weak form.
A. NCET and the Efficient Market Hypothesis
For decades the EMH has stood as the corner stone of efficient market theory. However, in recent years new theories and studies have strongly challenged the EMH. The NCET is not a new challenge to the EMH, but instead an evolution of efficient market theory.
The core of EMH is that most participants are rational and that the impacts of irrational participants are self-neutralizing or eliminated by arbitrage. If most investors are rational, then the EMH propositions should exist, which implies models and theories based on the propositions are correct. The test of the propositions provides reasonably strong evidence supporting the propositions. Therefore, models and theories based on the propositions and EMH logic are justified. This is the major purpose of the EMH; to justify applying its propositions and logic to models and theories.
The NCET is a different approach to justifying the application of models and theories based on efficient market concepts. Under the NCET, participants do not need to be mostly rational to justify efficient market applications. Participants merely need to be quasi-rational
A.1 Justifying Quasi-Rational Participants
The logic behind participants being quasi-rational and subject to the NCET is strongly supported by thorough research and sound practical common sense.
A.2 Justifying the NCET’s Semi-Strong Form Efficiency
The strong evidence and logic that participants are quasi-rational and subject to the NCET provides a robust realistic picture of participants. Applying quasi-rational participants subject to the NCET yields a close approximation of the EMH propositions.
The end result is that the market’s forecast roughly approximates the true forecast. This result is similar to applying the Rational Expectations Theory, but there is a major difference. Nothing about the NCET says that prices are rational or that the true forecast is rational. Rational Expectations Theory makes excellent sense in certain economic areas, but it is not required for financial markets.
A.3 Justifying Efficient Market Theory Applications
B. NCET’s Efficient Market Advantages
C. NCET Quasi-Rationality
The NCET’s notion of quasi-rational participants is a very broad generalization of participant behavior. Satisfaction also has emotional, psychological, physiological, and other elements.
D. Key Take Away
E. NCET and Behavioral Finance
Behavioral Finance (BF) is a type of quasi-rational approach. It shares many similar features with the NCET. As BF research has shown, “noisy” traders can, in fact, reinforce themselves, which creates definite impacts on other participants, including arbitragers.
The No Competitive Edge Theorem (NCET) has three major contributions to finance and economics. First, it advances the definition of fair value by incorporating the direct and indirect effects of competing participants. Second, it eliminates the need for the Efficient Market Hypothesis’s rational participants by showing that the propositions are the by-product of quasi-rational participants subject to the NCET. Third, it unifies several key areas of finance and economics such as participant behavior, fair value pricing, arbitrage, random walks, risk aversion, and efficient markets. Along with these achievements are several other benefits, starting with the NCET model.
The NCET model applied a generic utility function to show that participants seek satisfaction by fulfilling desires. The level of fulfillment is determined by how well the participants meet or exceed their goals. Regardless of their desires, all participants are competing for price. This creates a fiercely competitive environment where participants can affect each other both directly and indirectly. In this selfish non-cooperative competition, any honest information provided near asset exchanges could be used against the participant providing the information. The risks associated with these effects cause participants to appear completely neutral near and during asset exchanges. To appear neutral, participants avoid giving away any competitive edges, which means no information can be exchanged. The result is an enhanced fair value, called the market fair value (MFV).
The MFV advances existing fair value definitions by incorporating the dynamic interrelationships between participants. The MFV represents the exchange price where neither exchanging participant knows that the other participant has any competitive edges. The absence of perceived competitive edges implies the exchange price is perceived as the net present value of the asset in a risk-neutral world where the exchanging participants know the future price distribution and liquidity.
Since the MFV requires a risk-neutral-world, risk-neutrality is a natural property of MFV pricing; risk-neutrality is not the result of eliminating arbitrage. Also, arbitrage identified by the competition is a perceived competitive edge, which means arbitrage is a violation of MFV. This is completely opposite to the current ideology that fair value is the absence of arbitrage. In this regard, risk-neutrality, No Arbitrage theory, and arbitrage-free pricing are not independent stand-alone theories, but rather subcomponents of the NCET.
The argument that real exchanges occur at the MFV was tested using the NCET hypothesis and EMH tests. The evidence strongly supported the hypothesis. The amount of refuting evidence was small and mostly circumstantial. Due to the minimal refuting evidence, the vast majority of asset exchanges must be occurring at the MFV.
The application of MFV pricing extends into random walks. MFV random walks are price processes based on MFV prices. These random walks are required for pricing derivatives and other assets dependent on price processes. Since MFV random walks are absent of any perceived competitive edges, all prices are martingales once the prices are appropriately discounted. The absence of perceived competitive edges also implies that all dependencies affecting the price process must be priced into derivative assets. This offers precedence to using advanced modeling techniques that are not Gaussian based.
While MFV random walks are critical to establishing the MFV, real price processes do not follow MFV random walks. This is due to many factors, one factor being that the expected return is related to risk. Risk was shown as a function of expectations. New information causes a change in expectations, which creates a chain reaction leading to changes in risk. Since every new price is new information, there is a continuous flow of information that causes continuous changes in risk, which ultimately leads to more prices. This process never stops. The result is an unbalanced market composed of multiple dynamic feedback systems. The unbalanced relationship between information and risk implies that there is never a price, risk, expectation, or information equilibrium. This eliminates the existence of a universal “fundamental value”.
Efficient markets are a special application of the NCET. In an efficient market, the NCET shows that participants are still competing for the best price, but they do so in the presence of a known relationship between risks and the return distribution. By incorporating the known risks into the NCET model, an efficient market fair value (EMFV) is established. EMFVs have the same properties as MFVs, with the exception that the expected return can be greater than the risk-neutral return rate.
The NCET’s version of efficient markets is related to the Efficient Market Hypothesis (EMH). The EMH’s propositions are the result of quasi-rational participants subject to the NCET. The propositions remain critical to efficient market theory, but some of them may need updated to reflect the NCET’s logic and rationale for efficient markets. Under the NCET, efficient market applications remain justified because the evidence supports the NCET’s semi-strong form efficiency. However, participants are not assumed to be rational, prices are not assumed to be rational, and rational expectations is not required.
The NCET frees financial theories and models from the EMH’s dependency on rational participants. Participants are motivated to take actions, gather information, and make exchanges. Markets are not assumed to be perfectly efficient; meaning participants are not necessarily wasting time by performing technical analysis, fundamental analysis, or any other analysis.
The NCET’s greatest contribution is that it unifies the areas of participant behavior, fair value pricing, arbitrage, random walks, risk aversion, and efficient markets by applying one simple concept – competitive edges. All of these areas seamlessly fall together under the umbrella of the NCET.
Allen, Franklin, Stephan Morris, and Hyun Song Shin, 2004, Beauty Contest and Iterated Expectations in
Asset Markets, Cowles Foundation Discussion Paper No 1406.
Baker, Malcolm, and Jeffery Wurgler, 2006, Investor Sentiment and the Cross-Section of Stock Returns,
Journal of Finance 61, 1645–1680.
Beechey, Meredith, David Gruen, and James Vickery, 2000, The Efficient Market Hypothesis: A Survey,
Research Discussion papers 2000-2001, Reserve Bank of Australia, Sydney.
Bernoulli, Daniel, 1954, Exposition of a New Theory on the Measurement of Risk, Econometrica 22, 23-
Black, Fischer, and Myron Scholes, 1973, The pricing of options and corporate liabilities, Journal of
Political Economy 81, 637–654.
Black, Fischer, 1986, Noise, Journal of Finance 41, 529-543.
Brennan, Michael J., Ashley W. Wang, and Yihong Xia, 2004, Estimation and Test of a Simple Model of
Intertemporal Capital Asset Pricing. Journal of Finance 59, 1743-1776.
Brown, Gregory W., and Michael T. Cliff, 2005, Investor Sentiment and Asset Valuation, Journal of
Business 78, 405-440.
Busse, Jeffrey A. and T. Clifton Green, 2002, Market efficiency in real time, Journal of Financial
Economics 65, 415–437.
Camerer, Colin, 2003, Behavioral Game Theory (Princeton University Press, New Jersey).
Camerer, Colin, George Loewenstein, and Matthew Rabin, 2004, Advances in Behavioral Economics,
(Princeton University Press, New Jersey).
Conlisk, John, 1996, Why Bounded Rationality? Journal of Economic Literature 34, 669-700.
Cox, John C., Jonathan E. Ingersoll, Jr., and Stephen A. Ross, 1985, An Intertemporal General Equilibrium
Model of Asset Prices, Econometrica 53, 363-384.
De Long, J. Bradford, Andrei Shleifer, Lawrence H. Summers, and Robert J. Waldmann, 1990, Noise
Trader Risk in Financial Markets, Journal of Political Economy 98, 703-738.
Duffie, Darrell, 1996, Dynamic Asset Pricing Theory (Princeton University Press, New Jersey).
Duffie, Darrell, and Rui Kan, 2002, Universal State Prices and Asymmetric Information, Journal of
Mathematical Economics 38, 191-196.
Fabozzi, Frank, Sergio M. Focardi, and Petter N. Kolm, 2006, Financial Modeling of the Equity Market
(John Wiley & Sons, Inc., New Jersey).
Fama, Eugene F., 1965, The Behavior of Stock-Market Prices, Journal of Business 38, 34–104.
Fama, Eugene F., 1970, Efficient Capital Markets: a Review of Theory and Empirical Work, Journal of
Finance 25, 383–417.
Fama, Eugene F., 1991, Efficient Capital Markets: II, Journal of Finance 46, 1575–1617.
Fama, Eugene F., 1998, Market Efficiency, Long-term Returns, and Behavioral Finance, Journal of
Financial Economics 49, 283–306.
Froot, Kenneth A., David S. Scharfstein, and Jeremy C. Stein, 1992, Herd on the Street: Informational
Inefficiencies in a Market with Short-Term Speculation, Journal of Finance 47, 1461-1484.
Fouque, Jean-Pierre, George C. Papanicolaou, and K. Ronnie Sircar, 2000, Derivatives in Financial
Markets with Stochastic Volatility (Cambridge University Press, United Kingdom).
Gibbons, Robert, 1992, Game Theory for Applied Economists (Princeton University Press, New Jersey).
Harris, Larry, 2002, Trading and Exchanges: Market Microstructure for Practitioners (Oxford University
Press, United Kingdom)
Harrison, J. Michael, and David M. Kreps, 1979, Martingales and Arbitrage in Multiperiod Securities
Markets, Journal of Economic Theory 20, 381-408.
Hicks, John, 1946, Value and Capital 2nd edition (Clarendon Press, Oxford).
Hirshleifer, David, 2001, Investor Psychology and Asset Pricing, The Journal of Finance 56, 1533–1597.
Hull, John C., 2005, Options, Futures, and Other Derivatives ( Prentice Hall, New York).
Keynes, John Maynard, 1936, The General Theory of Employment, Interest, and Money (Macmillan,
Knight, Frank H., 1921, Risk, Uncertainty and Profit (University of Chicago Press, Chicago).
Kogan, Leonid, Stephen A. Ross, Jiang Wang, and Mark M. Westerfield, 2006, The Price Impact and
Survival of Irrational Traders, Journal of Finance 61, 195-229.
LeBaron, Blake, 1992, Some Relations Between Volatility and Serial Correlations in Stock Market
Returns, Journal of Business 65, 199-219.
Liang, Bing, 1999, Price Pressure: Evidence from the "Dartboard" Column, Journal of Business 72, 119-
Madhavan, Ananth, 2000, Market microstructure: A survey, Journal of Financial Markets 3, 205-258.
Markowitz, Harry, 1952, Portfolio selection, Journal of Finance 7, 77-91.
Merton, Robert C., 1973, An Intertemporal Capital Asset Pricing Model, Econometrica 41, 867-887.
Mishkin, Frederic S., 1983, A Rational Expectations Approach to Macroeconomics (The University of
Chicago Press, Chicago).
Muth, John F., 1961, Rational Expectations and the Theory of Price Movements, Econometrica 29, 315-
Myagkov, Mikhail, and Charles R. Plott, 1997, Exchange Economies and Loss Exposure: Experiments
Exploring Prospect Theory and Competitive Equilibria in Market Environments, The American
Economic Review 87, 801-828.
Nash, John, 1951, Non-Cooperative Games, The Annals of Mathematics 54, 286-295.
Nerlove M., and I. Fornari, 1998, Quasi-rational expectations, an alternative to fully rational expectations:
An application to US beef cattle supply, Journal of Econometrics 83, 129-161.
O'Hara, Maureen, 1998, Market Microstructure Theory (Blackwell Publishers).
Penman, Steven H., and Theordore Sougiannis, 1998, A Comparison of Dividend, Cash Flow, and Earnings
Approaches to Equity Valuation, Contemporary Accounting Research 15, 343–383.
Peters, Edgar E., 1994, Fractal Market Anal