Misplaced Pages

#577422

127-472: The efficient-market hypothesis ( EMH ) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted basis since market prices should only react to new information. Because the EMH is formulated in terms of risk adjustment, it only makes testable predictions when coupled with

254-416: A martingale , the EMH does not always assume that stocks follow a martingale. Research by Alfred Cowles in the 1930s and 1940s suggested that professional investors were in general unable to outperform the market. During the 1930s-1950s empirical studies focused on time-series properties, and found that US stock prices and related financial series followed a random walk model in the short-term. While there

381-402: A "chronic underestimation of the dangers of asset bubbles breaking". Financial journalist Roger Lowenstein said "The upside of the current Great Recession is that it could drive a stake through the heart of the academic nostrum known as the efficient-market hypothesis." Former Federal Reserve chairman Paul Volcker said "It should be clear that among the causes of the recent financial crisis

508-440: A benchmark for evaluating the effects of factors outside the model that do affect value. The mechanism for determining (corporate) value is provided by John Burr Williams ' The Theory of Investment Value , which proposes that the value of an asset should be calculated using "evaluation by the rule of present worth". Thus, for a common stock, the "intrinsic" , long-term worth is the present value of its future net cashflows, in

635-514: A broad range of goals. Copulas have lately been applied here ; recently this is the case also for genetic algorithms and Machine learning, more generally . (Tail) risk parity focuses on allocation of risk, rather than allocation of capital. See Portfolio optimization § Improving portfolio optimization for other techniques and objectives, and Financial risk management § Investment management for discussion. Interpretation: Analogous to Black-Scholes, arbitrage arguments describe

762-409: A correlation between security and market returns, without (numerous) other economic assumptions. It is useful in that it simplifies the estimation of correlation between securities, significantly reducing the inputs for building the correlation matrix required for portfolio optimization. The arbitrage pricing theory (APT) similarly differs as regards its assumptions. APT "gives up the notion that there

889-400: A formal study of the financial markets themselves, especially market microstructure and market regulation . It is built on the foundations of microeconomics and decision theory . Financial econometrics is the branch of financial economics that uses econometric techniques to parameterise the relationships identified. Mathematical finance is related in that it will derive and extend

1016-454: A large number of researchers have used options to extract state-prices for a variety of other applications in financial economics. For path dependent derivatives , Monte Carlo methods for option pricing are employed; here the modelling is in continuous time, but similarly uses risk neutral expected value. Various other numeric techniques have also been developed. The theoretical framework too has been extended such that martingale pricing

1143-473: A long history of outperforming a benchmark, has written that the core arguments of the EMH are "more true than not" and he accepts a "sloppy" version of the theory allowing for a margin of error. But he also contends the EMH is not completely accurate or accurate in all cases, given the recurrent existence of economic bubbles (when some assets are dramatically overpriced) and the fact that value investors (who focus on underpriced assets) have tended to outperform

1270-429: A market for every time period and forward prices for every commodity at all time periods. A direct extension, then, is the concept of a state price security, also called an Arrow–Debreu security, a contract that agrees to pay one unit of a numeraire (a currency or a commodity) if a particular state occurs ("up" and "down" in the simplified example above) at a particular time in the future and pays zero numeraire in all

1397-565: A number of tests and studies that reportedly support the view that there are trends in the stock market and that the stock market is somewhat predictable. One element of their evidence is the simple volatility-based specification test, which has a null hypothesis that states: where To refute the hypothesis, they compare the variance of ( X t − X t + τ ) {\displaystyle (X_{t}-X_{t+\tau })} for different τ {\displaystyle \tau } and compare

SECTION 10

#1732854757578

1524-455: A particular model of risk. As a result, research in financial economics since at least the 1990s has focused on market anomalies , that is, deviations from specific models of risk. The idea that financial market returns are difficult to predict goes back to Bachelier , Mandelbrot , and Samuelson , but is closely associated with Eugene Fama , in part due to his influential 1970 review of the theoretical and empirical research. The EMH provides

1651-420: A piece of information about the value of a stock (say, about a future merger) is widely available to investors. If the price of the stock does not already reflect that information, then investors can trade on it, thereby moving the price until the information is no longer useful for trading. Note that this thought experiment does not necessarily imply that stock prices are unpredictable. For example, suppose that

1778-399: A prominent theory in the mid-1960s. Paul Samuelson had begun to circulate Bachelier's work among economists. In 1964 Bachelier's dissertation along with the empirical studies mentioned above were published in an anthology edited by Paul Cootner. In 1965, Eugene Fama published his dissertation arguing for the random walk hypothesis . Also, Samuelson published a proof showing that if the market

1905-472: A random walk, some methods or approaches have been proposed, for example, the variance ratio (VR) tests, the Hurst exponent and surrogate data testing . Burton G. Malkiel , an economics professor at Princeton University and author of A Random Walk Down Wall Street , performed a test where his students were given a hypothetical stock that was initially worth fifty dollars. The closing stock price for each day

2032-565: A set of prices exists that will result in an overall equilibrium. (This is in contrast to partial equilibrium, which only analyzes single markets.) The two concepts are linked as follows: where market prices do not allow profitable arbitrage, i.e. they comprise an arbitrage-free market, then these prices are also said to constitute an "arbitrage equilibrium". Intuitively, this may be seen by considering that where an arbitrage opportunity does exist, then prices can be expected to change, and they are therefore not in equilibrium. An arbitrage equilibrium

2159-399: A simplified example see Rational pricing § Risk neutral valuation , where the economy has only two possible states – up and down – and where q u p {\displaystyle q_{up}} and q d o w n {\displaystyle q_{down}} ( = 1 − q u p {\displaystyle 1-q_{up}} ) are

2286-518: Is a drift constant σ {\displaystyle \sigma } is the standard deviation of the returns Δ t {\displaystyle \Delta {t}} is the change in time Y i {\displaystyle Y_{i}} is an i.i.d. random variable satisfying Y i ∼ N ( 0 , 1 ) {\displaystyle Y_{i}\sim N(0,1)} . There are other economists, professors, and investors who believe that

2413-405: Is a very close link between EMH and the random walk hypothesis . Early theories posited that predicting stock prices is unfeasible, as they depend on fresh information or news rather than existing or historical prices. Therefore, stock prices are thought to fluctuate randomly, and their predictability is believed to be no better than a 50% accuracy rate. The efficient-market hypothesis emerged as

2540-683: Is consistent with the above , but with the expectation based on "the market" (i.e. arbitrage-free, and, per the theorem, therefore in equilibrium) as opposed to individual preferences. Continuing the example, in pricing a derivative instrument , its forecasted cashflows in the above-mentioned up- and down-states X u p {\displaystyle X_{up}} and X d o w n {\displaystyle X_{down}} , are multiplied through by q u p {\displaystyle q_{up}} and q d o w n {\displaystyle q_{down}} , and are then discounted at

2667-399: Is contradictory to the efficient market hypothesis -- though both concepts are widely taught in business schools without seeming awareness of a contradiction. If asset prices are rational and based on all available data as the efficient market hypothesis proposes, then fluctuations in asset price are not random. But if the random walk hypothesis is valid then asset prices are not rational as

SECTION 20

#1732854757578

2794-426: Is distributed more or less instantly to all market participants. Information may be distributed more or less instantly, but Schwager proposes information may not be interpreted or applied in the same way by different people and skill may play a factor in how information is used. Schwager argues markets are difficult to beat because of the unpredictable and sometimes irrational behavior of humans who buy and sell assets in

2921-435: Is efficient, prices will exhibit random-walk behavior. This is often cited in support of the efficient-market theory, by the method of affirming the consequent, however in that same paper, Samuelson warns against such backward reasoning, saying "From a nonempirical base of axioms you never get empirical results." In 1970, Fama published a review of both the theory and the evidence for the hypothesis. The paper extended and refined

3048-492: Is expressed as the Black–Scholes equation, a partial differential equation describing the changing price of the option over time; it is derived assuming log-normal, geometric Brownian motion (see Brownian model of financial markets ). The key financial insight behind the model is that one can perfectly hedge the option by buying and selling the underlying asset in just the right way and consequently "eliminate risk", absenting

3175-403: Is inefficient, but one has no way of knowing which is the case. The performance of stock markets is correlated with the amount of sunshine in the city where the main exchange is located. While event studies of stock splits are consistent with the EMH (Fama, Fisher, Jensen, and Roll, 1969), other empirical analyses have found problems with the efficient-market hypothesis. Early examples include

3302-461: Is much better suited for individual stocks than it is for the aggregate stock market as a whole. Research based on regression and scatter diagrams, published in 2005, has strongly supported Samuelson's dictum. Peter Lynch , a mutual fund manager at Fidelity Investments who consistently more than doubled market averages while managing the Magellan Fund , has argued that the EMH is contradictory to

3429-682: Is now the standard approach. Random walk hypothesis The random walk hypothesis is a financial theory stating that stock market prices evolve according to a random walk (so price changes are random ) and thus cannot be predicted. The concept can be traced to French broker Jules Regnault who published a book in 1863, and then to French mathematician Louis Bachelier whose Ph.D. dissertation titled "The Theory of Speculation" (1900) included some remarkable insights and commentary. The same ideas were later developed by MIT Sloan School of Management professor Paul Cootner in his 1964 book The Random Character of Stock Market Prices . The term

3556-452: Is one right portfolio for everyone in the world, and ...replaces it with an explanatory model of what drives asset returns." It returns the required (expected) return of a financial asset as a linear function of various macro-economic factors, and assumes that arbitrage should bring incorrectly priced assets back into line. The linear factor model structure of the APT is used as the basis for many of

3683-554: Is some predictability over the long-term, the extent to which this is due to rational time-varying risk premia as opposed to behavioral reasons is a subject of debate. In their seminal paper, Fama, Fisher, Jensen, and Roll (1969) propose the event study methodology and show that stock prices on average react before a stock split, but have no movement afterwards. In Fama's influential 1970 review paper, he categorized empirical tests of efficiency into "weak-form", "semi-strong-form", and "strong-form" tests. These categories of tests refer to

3810-406: Is the stochastic discount factor , and D t + 1 {\displaystyle D_{t+1}} is the dividend the stock pays next period. Note that this equation does not generally imply a random walk . However, if we assume the stochastic discount factor is constant and the time interval is short enough so that no dividend is being paid, we have Taking logs and assuming that

3937-476: Is the focus of "asset pricing models" as follows. Fisher's formulation of the theory here - developing an intertemporal equilibrium model - underpins also the below applications to uncertainty; see for the development. For "choice under uncertainty" the twin assumptions of rationality and market efficiency , as more closely defined, lead to modern portfolio theory (MPT) with its capital asset pricing model (CAPM) – an equilibrium-based result – and to

Efficient-market hypothesis - Misplaced Pages Continue

4064-491: Is the risk-free rate plus the market premium multiplied by beta ( ρ i , m σ i σ m {\displaystyle \rho _{i,m}{\frac {\sigma _{i}}{\sigma _{m}}}} ), the asset's correlated volatility relative to the overall market m {\displaystyle m} . Applying the above economic concepts, we may then derive various economic- and financial models and principles. As above,

4191-559: Is therefore consistent with the equilibrium based capital asset pricing. Both models, in turn, are ultimately consistent with the Arrow–Debreu theory, and can be derived via state-pricing – essentially, by expanding the fundamental result above – further explaining, and if required demonstrating, this consistency. Here, the CAPM is derived by linking Y {\displaystyle Y} , risk aversion, to overall market return, and setting

4318-515: Is thus a precondition for a general economic equilibrium. "Complete" here means that there is a price for every asset in every possible state of the world, s {\displaystyle s} , and that the complete set of possible bets on future states-of-the-world can therefore be constructed with existing assets (assuming no friction ): essentially solving simultaneously for n (risk-neutral) probabilities, q s {\displaystyle q_{s}} , given n prices. For

4445-464: The Financial Times , dismissed the hypothesis as being a useless way to examine how markets function in reality. Economist Paul McCulley said the hypothesis had not failed, but was "seriously flawed" in its neglect of human nature. The financial crisis led economics scholar Richard Posner to back away from the hypothesis. Posner accused some of his Chicago School colleagues of being "asleep at

4572-545: The Black–Scholes–Merton theory (BSM; often, simply Black–Scholes) for option pricing – an arbitrage-free result. As above, the (intuitive) link between these, is that the latter derivative prices are calculated such that they are arbitrage-free with respect to the more fundamental, equilibrium determined, securities prices; see Asset pricing § Interrelationship . Briefly, and intuitively – and consistent with § Arbitrage-free pricing and equilibrium above –

4699-545: The CAPM (or extensions) as will be seen under § Uncertainty . The difference is explained as follows: By construction, the value of the derivative will (must) grow at the risk free rate, and, by arbitrage arguments, its value must then be discounted correspondingly; in the case of an option, this is achieved by "manufacturing" the instrument as a combination of the underlying and a risk free "bond"; see Rational pricing § Delta hedging (and § Uncertainty below). Where

4826-620: The Ellsberg paradox . The New Palgrave Dictionary of Economics (2008, 2nd ed.) also uses the JEL codes to classify its entries in v. 8, Subject Index, including Financial Economics at pp. 863–64. The below have links to entry abstracts of The New Palgrave Online for each primary or secondary JEL category (10 or fewer per page, similar to Google searches): Tertiary category entries can also be searched. The concepts of arbitrage -free, "rational", pricing and equilibrium are then coupled with

4953-545: The Journal of Econometrics , K. Victor Chow and Karen C. Denning published a statistical tool (known as the Chow–Denning test) for checking whether a market follows the random walk hypothesis. Whether financial data can be considered a random walk is a venerable and challenging question. One of two possible results are obtained, the data does fall under random walk or the data does not. To investigate whether observed data follows

5080-403: The average investor given enough time and so no investor will beat the market average. But Pilkington points out that when proponents of the theory are presented with evidence that a small minority of investors do, in fact, beat the market over the long-run, these proponents then say that these investors were simply 'lucky'. Pilkington argues that introducing the idea that anyone who diverges from

5207-510: The best guess of the future : the assumption of rational expectations . The EMH does allow that when faced with new information, some investors may overreact and some may underreact, but what is required, however, is that investors' reactions follow a normal distribution – so that the net effect on market prices cannot be reliably exploited to make an abnormal profit. In the competitive limit, then, market prices will reflect all available information and prices can only move in response to news:

Efficient-market hypothesis - Misplaced Pages Continue

5334-532: The random walk hypothesis . This news, of course, could be "good" or "bad", minor or, less common, major; and these moves are then, correspondingly, normally distributed; with the price therefore following a log-normal distribution. Under these conditions, investors can then be assumed to act rationally: their investment decision must be calculated or a loss is sure to follow; correspondingly, where an arbitrage opportunity presents itself, then arbitrageurs will exploit it, reinforcing this equilibrium. Here, as under

5461-427: The random walk hypothesis —though both concepts are widely taught in business schools without seeming awareness of a contradiction. If asset prices are rational and based on all available data as the efficient market hypothesis proposes, then fluctuations in asset price are not random. But if the random walk hypothesis is valid, then asset prices are not rational. Joel Tillinghast, also a fund manager at Fidelity with

5588-421: The random walk model of Jules Regnault , but Bachelier did not cite him, and Bachelier's thesis is now considered pioneering in the field of financial mathematics. It is commonly thought that Bachelier's work gained little attention and was forgotten for decades until it was rediscovered in the 1950s by Leonard Savage , and then become more popular after Bachelier's thesis was translated into English in 1964. But

5715-499: The 1980s-2000s saw an explosion of discovered return predictors (e.g. Rosenberg, Reid, and Lanstein 1985; Campbell and Shiller 1988; Jegadeesh and Titman 1993). Since the 2010s, studies have often found that return predictability has become more elusive, as predictability fails to work out-of-sample (Goyal and Welch 2008), or has been weakened by advances in trading technology and investor learning (Chordia, Subrahmanyam, and Tong 2014; McLean and Pontiff 2016; Martineau 2021). Suppose that

5842-587: The CAPM towards risk factor models such as the Fama-French 3 factor model . These risk factor models are not properly founded on economic theory (whereas CAPM is founded on Modern Portfolio Theory ), but rather, constructed with long-short portfolios in response to the observed empirical EMH anomalies. For instance, the "small-minus-big" (SMB) factor in the FF3 factor model is simply a portfolio that holds long positions on small stocks and short positions on large stocks to mimic

5969-631: The CAPM. In general, then, while portfolio theory studies how investors should balance risk and return when investing in many assets or securities, the CAPM is more focused, describing how, in equilibrium, markets set the prices of assets in relation to how risky they are. This result will be independent of the investor's level of risk aversion and assumed utility function , thus providing a readily determined discount rate for corporate finance decision makers as above , and for other investors. The argument proceeds as follows : If one can construct an efficient frontier – i.e. each combination of assets offering

6096-459: The Jensen's inequality term is negligible, we have which implies that the log of stock prices follows a random walk (with a drift). Although the concept of an efficient market is similar to the assumption that stock prices follow: E [ S t + 1 | S t ] = S t {\displaystyle E[S_{t+1}|S_{t}]=S_{t}} which follows

6223-485: The above pricing formulae. DCF valuation formula , where the value of the firm , is its forecasted free cash flows discounted to the present using the weighted average cost of capital , i.e. cost of equity and cost of debt , with the former (often) derived using the below CAPM. For share valuation investors use the related dividend discount model . The expected return used when discounting cashflows on an asset i {\displaystyle i} ,

6350-408: The above to derive various of the "classical" (or "neo-classical" ) financial economics models. Rational pricing is the assumption that asset prices (and hence asset pricing models) will reflect the arbitrage-free price of the asset, as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to

6477-520: The anomaly in neat accordance with modern portfolio theory . Behavioral psychology approaches to stock market trading are among some of the alternatives to EMH (investment strategies such as momentum trading seek to exploit exactly such inefficiencies). However, Nobel Laureate co-founder of the programme Daniel Kahneman —announced his skepticism of investors beating the market: "They're just not going to do it. It's just not going to happen." Indeed, defenders of EMH maintain that behavioral finance strengthens

SECTION 50

#1732854757578

6604-509: The application of decision making under uncertainty to the financial markets . The underlying economic logic yields the fundamental theorem of asset pricing , which gives the conditions for arbitrage -free asset pricing. The various "fundamental" valuation formulae result directly. Underlying all of financial economics are the concepts of present value and expectation . Calculating their present value, X s j / r {\displaystyle X_{sj}/r} in

6731-422: The approach is therefore to "adjust" the weight assigned to the various outcomes, i.e. "states", correspondingly: Y s {\displaystyle Y_{s}} . See indifference price . (Some investors may in fact be risk seeking as opposed to risk averse , but the same logic would apply.) Choice under uncertainty here may then be defined as the maximization of expected utility . More formally,

6858-736: The assumption that 'history tends to repeat itself'." The chartist told Malkiel that they needed to immediately buy the stock. Since the coin flips were random, the fictitious stock had no overall trend. Malkiel argued that this indicates that the market and stocks could be just as random as flipping a coin. Modelling asset prices with a random walk takes the form: S t + 1 = S t + μ Δ t S t + σ Δ t S t Y i {\displaystyle S_{t+1}=S_{t}+\mu \Delta {t}S_{t}+\sigma {\sqrt {\Delta {t}}}S_{t}Y_{i}} where μ {\displaystyle \mu }

6985-449: The basic logic for modern risk-based theories of asset prices, and frameworks such as consumption-based asset pricing and intermediary asset pricing can be thought of as the combination of a model of risk with the EMH. Many decades of empirical research on return predictability has found mixed evidence. Research in the 1950s and 1960s often found a lack of predictability (e.g. Ball and Brown 1968; Fama, Fisher, Jensen, and Roll 1969), yet

7112-703: The beginning of the century in the dissertation submitted by Bachelier (1900) to the Sorbonne for his PhD in mathematics. In his opening paragraph, Bachelier recognizes that "past, present and even discounted future events are reflected in market price, but often show no apparent relation to price changes". The efficient markets theory was not popular until the 1960s when the advent of computers made it possible to compare calculations and prices of hundreds of stocks more quickly and effortlessly. In 1945, F.A. Hayek argued in his article The Use of Knowledge in Society that markets were

7239-471: The best possible expected level of return for its level of risk, see diagram – then mean-variance efficient portfolios can be formed simply as a combination of holdings of the risk-free asset and the " market portfolio " (the Mutual fund separation theorem ), with the combinations here plotting as the capital market line , or CML. Then, given this CML, the required return on a risky security will be independent of

7366-471: The broader market over long periods. Tillinghast also asserts that even staunch EMH proponents will admit weaknesses to the theory when assets are significantly over- or under-priced, such as double or half their value according to fundamental analysis . In a 2012 book, investor Jack Schwager argues the EMH is "right for the wrong reasons". He agrees it is "very difficult" to consistently beat average market returns, but contends it's not due to how information

7493-491: The calculation of damages. In the Supreme Court Case, Halliburton v. Erica P. John Fund, U.S. Supreme Court, No. 13-317 , the use of efficient market theory in supporting securities class action litigation was affirmed. Supreme Court Justice Roberts wrote that "the court's ruling was consistent with the ruling in ' Basic ' because it allows ' direct evidence when such evidence is available' instead of relying exclusively on

7620-403: The case for EMH in that it highlights biases in individuals and committees and not competitive markets. For example, one prominent finding in behavioral finance is that individuals employ hyperbolic discounting . It is demonstrably true that bonds , mortgages , annuities and other similar obligations subject to competitive market forces do not . Any manifestation of hyperbolic discounting in

7747-529: The case of Bitcoin there is no source of value whatsoever" and thus Bitcoin should be priced at zero or worthless. Tshilidzi Marwala surmised that artificial intelligence (AI) influences the applicability of the efficient market hypothesis in that the greater amount of AI-based market participants, the more efficient the markets become. Warren Buffett has also argued against EMH, most notably in his 1984 presentation " The Superinvestors of Graham-and-Doddsville ". He says preponderance of value investors among

SECTION 60

#1732854757578

7874-735: The cash flows, whereas in the valuation formulae, the risk-free rate is applied once these have been "adjusted" for their riskiness; see below.) An immediate extension is to combine probabilities with present value, leading to the expected value criterion which sets asset value as a function of the sizes of the expected payouts and the probabilities of their occurrence, X s {\displaystyle X_{s}} and p s {\displaystyle p_{s}} respectively. This decision method, however, fails to consider risk aversion . In other words, since individuals receive greater utility from an extra dollar when they are poor and less utility when comparatively rich,

8001-550: The certainty-case above, the specific assumption as to pricing is that prices are calculated as the present value of expected future dividends, as based on currently available information. What is required though, is a theory for determining the appropriate discount rate, i.e. "required return", given this uncertainty: this is provided by the MPT and its CAPM. Relatedly, rationality – in the sense of arbitrage-exploitation – gives rise to Black–Scholes; option values here ultimately consistent with

8128-458: The commercial risk systems employed by asset managers. As regards portfolio optimization , the Black–Litterman model departs from the original Markowitz model – i.e. of constructing portfolios via an efficient frontier . Black–Litterman instead starts with an equilibrium assumption, and is then modified to take into account the 'views' (i.e., the specific opinions about asset returns) of

8255-499: The corporation will be the maximization of its present value, regardless of the preferences of its shareholders. Related is the Modigliani–Miller theorem , which shows that, under certain conditions, the value of a firm is unaffected by how that firm is financed, and depends neither on its dividend policy nor its decision to raise capital by issuing stock or selling debt. The proof here proceeds using arbitrage arguments, and acts as

8382-563: The data to prevent EMH from being conclusively proved. In his book The Reformation in Economics , economist and financial analyst Philip Pilkington has argued that the EMH is actually a tautology masquerading as a theory. He argues that, taken at face value, the theory makes the banal claim that the average investor will not beat the market average—which is a tautology. When pressed on this point, Pinkington argues that EMH proponents will usually say that any actual investor will converge with

8509-499: The decision of one individual) with the effect that the problems are then mathematically tractable. With this measure in place, the expected, i.e. required , return of any security (or portfolio) will then equal the risk-free return, plus an "adjustment for risk", i.e. a security-specific risk premium , compensating for the extent to which its cashflows are unpredictable. All pricing models are then essentially variants of this, given specific assumptions or conditions. This approach

8636-428: The derivative value – true in fact for "every security" – as a linear combination of its state-prices; i.e. back-solve for the state-prices corresponding to observed derivative prices. These recovered state-prices can then be used for valuation of other instruments with exposure to the underlyer, or for other decision making relating to the underlyer itself. Using the related stochastic discount factor - also called

8763-492: The efficient markets theory." Financial economics The subject is concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment". It therefore centers on decision making under uncertainty in the context of the financial markets, and the resultant economic and financial models and principles, and is concerned with deriving testable or policy implications from acceptable assumptions. It thus also includes

8890-404: The efficient-market hypothesis. According to Dreman and Berry, in a 1995 paper, low P/E ( price-to-earnings ) stocks have greater returns. In an earlier paper, Dreman also refuted the assertion by Ray Ball that these higher returns could be attributed to higher beta leading to a failure to correctly risk-adjust returns; Dreman's research had been accepted by efficient market theorists as explaining

9017-429: The first formula, allows the decision maker to aggregate the cashflows (or other returns) to be produced by the asset in the future to a single value at the date in question, and to thus more readily compare two opportunities; this concept is then the starting point for financial decision making. (Note that here, " r {\displaystyle r} " represents a generic (or arbitrary) discount rate applied to

9144-540: The focus on cash flows from securities over time," valuation based on a term structure of interest rates is in fact consistent with arbitrage-free pricing. Indeed, a corollary of the above is that " the law of one price implies the existence of a discount factor"; correspondingly, as formulated, ∑ s π s = 1 / r {\textstyle \sum _{s}\pi _{s}=1/r} . Whereas these "certainty" results are all commonly employed under corporate finance, uncertainty

9271-504: The form of dividends . What remains to be determined is the appropriate discount rate. Later developments show that, "rationally", i.e. in the formal sense, the appropriate discount rate here will (should) depend on the asset's riskiness relative to the overall market, as opposed to its owners' preferences; see below. Net present value (NPV) is the direct extension of these ideas typically applied to Corporate Finance decisioning. For other results, as well as specific models developed here, see

9398-425: The fourth formula (see above regarding the absence of a risk premium here). For a continuous random variable indicating a continuum of possible states, the value is found by integrating over the state price "density". State prices find immediate application as a conceptual tool (" contingent claim analysis "); but can also be applied to valuation problems. Given the pricing mechanism described, one can decompose

9525-514: The human population and are therefore subject to the biases that behavioralists showcase. By contrast, the price signals in markets are far less subject to individual biases highlighted by the Behavioral Finance programme. Richard Thaler has started a fund based on his research on cognitive biases. In a 2008 report he identified complexity and herd behavior as central to the 2007–2008 financial crisis . Further empirical work has highlighted

9652-498: The hypothesis goes against the thinking of Adam Smith and John Maynard Keynes , who both believed irrational behavior had a real impact on the markets. Economist John Quiggin has claimed that " Bitcoin is perhaps the finest example of a pure bubble ", and that it provides a conclusive refutation of EMH. While other assets that have been used as currency (such as gold, tobacco) have value or utility independent of people's willingness to accept them as payment, Quiggin argues that "in

9779-461: The impact transaction costs have on the concept of market efficiency, with much evidence suggesting that any anomalies pertaining to market inefficiencies are the result of a cost benefit analysis made by those willing to incur the cost of acquiring the valuable information in order to trade on it. Additionally, the concept of liquidity is a critical component to capturing "inefficiencies" in tests for abnormal returns. Any test of this proposition faces

9906-649: The information set used in the statement "prices reflect all available information." Weak-form tests study the information contained in historical prices. Semi-strong form tests study information (beyond historical prices) which is publicly available. Strong-form tests regard private information. Benoit Mandelbrot claimed the efficient markets theory was first proposed by the French mathematician Louis Bachelier in 1900 in his PhD thesis "The Theory of Speculation" describing how prices of commodities and stocks varied in markets. It has been speculated that Bachelier drew ideas from

10033-522: The instantaneous change in the bond price P {\displaystyle P} for changes in the (risk-free) short rate r {\displaystyle r} ; the analyst selects the specific short-rate model to be employed. In pricing derivatives, the binomial options pricing model provides a discretized version of Black–Scholes, useful for the valuation of American styled options . Discretized models of this type are built – at least implicitly – using state-prices ( as above ); relatedly,

10160-490: The investor in question to arrive at a bespoke asset allocation. Where factors additional to volatility are considered (kurtosis, skew...) then multiple-criteria decision analysis can be applied; here deriving a Pareto efficient portfolio. The universal portfolio algorithm applies machine learning to asset selection, learning adaptively from historical data. Behavioral portfolio theory recognizes that investors have varied aims and create an investment portfolio that meets

10287-400: The investor's utility function , and solely determined by its covariance ("beta") with aggregate, i.e. market, risk. This is because investors here can then maximize utility through leverage as opposed to pricing; see Separation property (finance) , Markowitz model § Choosing the best portfolio and CML diagram aside. As can be seen in the formula aside, this result is consistent with

10414-408: The joint hypothesis problem, where it is impossible to ever test for market efficiency, since to do so requires the use of a measuring stick against which abnormal returns are compared —one cannot know if the market is efficient if one does not know if a model correctly stipulates the required rate of return. Consequently, a situation arises where either the asset pricing model is incorrect or the market

10541-878: The list of "Equity valuation" topics under Outline of finance § Discounted cash flow valuation . Bond valuation , in that cashflows ( coupons and return of principal, or " Face value ") are deterministic, may proceed in the same fashion. An immediate extension, Arbitrage-free bond pricing , discounts each cashflow at the market derived rate – i.e. at each coupon's corresponding zero rate , and of equivalent credit worthiness – as opposed to an overall rate. In many treatments bond valuation precedes equity valuation , under which cashflows (dividends) are not "known" per se . Williams and onward allow for forecasting as to these – based on historic ratios or published dividend policy – and cashflows are then treated as essentially deterministic; see below under § Corporate finance theory . For both stocks and bonds, "under certainty, with

10668-444: The lower case is used, as in the above equations.) With the above relationship established, the further specialized Arrow–Debreu model may be derived. This result suggests that, under certain economic conditions, there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy. The Arrow–Debreu model applies to economies with maximally complete markets , in which there exists

10795-486: The market by significant margins". However, Munger also believes "extreme" commitment to the EMH is "bonkers", as the theory's originators were seduced by an "intellectually consistent theory that allowed them to do pretty mathematics [yet] the fundamentals did not properly tie to reality." Burton Malkiel in his A Random Walk Down Wall Street (1973) argues that "the preponderance of statistical evidence" supports EMH, but admits there are enough "gremlins lurking about" in

10922-522: The market is predictable to some degree. These people believe that prices may move in trends and that the study of past prices can be used to forecast future price direction. There have been some economic studies that support this view, and a book has been written by two professors of economics that tries to prove the random walk hypothesis wrong. Martin Weber, a leading researcher in behavioural finance, has performed many tests and studies on finding trends in

11049-452: The mathematical or numerical models suggested by financial economics. Whereas financial economics has a primarily microeconomic focus, monetary economics is primarily macroeconomic in nature. Four equivalent formulations, where: Financial economics studies how rational investors would apply decision theory to investment management . The subject is thus built on the foundations of microeconomics and derives several key results for

11176-399: The model. With intertemporal portfolio choice , the investor now repeatedly optimizes her portfolio; while the inclusion of consumption (in the economic sense) then incorporates all sources of wealth, and not just market-based investments, into the investor's calculation of required return. Whereas the above extend the CAPM, the single-index model is a more simple model. It assumes, only,

11303-455: The most effective way of aggregating the pieces of information dispersed among individuals within a society. Given the ability to profit from private information, self-interested traders are motivated to acquire and act on their private information. In doing so, traders contribute to more and more efficient market prices. In the competitive limit, market prices reflect all available information and prices can only move in response to news. Thus there

11430-538: The observation that small neglected stocks and stocks with high book-to-market (low price-to-book) ratios (value stocks) tended to achieve abnormally high returns relative to what could be explained by the CAPM . Further tests of portfolio efficiency by Gibbons, Ross and Shanken (1989) (GJR) led to rejections of the CAPM, although tests of efficiency inevitably run into the joint hypothesis problem (see Roll's critique ). Following GJR's results and mounting empirical evidence of EMH anomalies, academics began to move away from

11557-456: The other states. The price of this security is the state price π s {\displaystyle \pi _{s}} of this particular state of the world; also referred to as a "Risk Neutral Density". In the above example, the state prices, π u p {\displaystyle \pi _{up}} , π d o w n {\displaystyle \pi _{down}} would equate to

11684-487: The piece of information in question says that a financial crisis is likely to come soon. Investors typically do not like to hold stocks during a financial crisis, and thus investors may sell stocks until the price drops enough so that the expected return compensates for this risk. How efficient markets are (and are not) linked to the random walk theory can be described through the fundamental theorem of asset pricing . This theorem provides mathematical predictions regarding

11811-410: The preceding , equaling the riskless return plus an adjustment for risk. A more modern, direct, derivation is as described at the bottom of this section; which can be generalized to derive other equilibrium-pricing models. Black–Scholes provides a mathematical model of a financial market containing derivative instruments, and the resultant formula for the price of European-styled options . The model

11938-755: The present values of $ q u p {\displaystyle \$ q_{up}} and $ q d o w n {\displaystyle \$ q_{down}} : i.e. what one would pay today, respectively, for the up- and down-state securities; the state price vector is the vector of state prices for all states. Applied to derivative valuation, the price today would simply be [ π u p {\displaystyle \pi _{up}} × X u p {\displaystyle X_{up}} + π d o w n {\displaystyle \pi _{down}} × X d o w n {\displaystyle X_{down}} ] :

12065-513: The price of a stock, assuming that there is no arbitrage , that is, assuming that there is no risk-free way to trade profitably. Formally, if arbitrage is impossible, then the theorem predicts that the price of a stock is the discounted value of its future price and dividend: where E t {\displaystyle E_{t}} is the expected value given information at time t {\displaystyle t} , M t + 1 {\displaystyle M_{t+1}}

12192-480: The price, is consistent with the equation, as the formula is the solution to the equation.) Since the formula is without reference to the share's expected return, Black–Scholes inheres risk neutrality; intuitively consistent with the "elimination of risk" here, and mathematically consistent with § Arbitrage-free pricing and equilibrium above. Relatedly, therefore, the pricing formula may also be derived directly via risk neutral expectation. Itô's lemma provides

12319-408: The pricing kernel - the asset price is computed by "discounting" the future cash flow by the stochastic factor m ~ {\displaystyle {\tilde {m}}} , and then taking the expectation; the third equation above. Essentially, this factor divides expected utility at the relevant future period - a function of the possible asset values realized under each state - by

12446-407: The pricing of derivative instruments. Economic equilibrium is a state in which economic forces such as supply and demand are balanced, and in the absence of external influences these equilibrium values of economic variables will not change. General equilibrium deals with the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that

12573-446: The pricing of these obligations would invite arbitrage thereby quickly eliminating any vestige of individual biases. Similarly, diversification , derivative securities and other hedging strategies assuage if not eliminate potential mispricings from the severe risk-intolerance ( loss aversion ) of individuals underscored by behavioral finance. On the other hand, economists, behavioral psychologists and mutual fund managers are drawn from

12700-549: The random walk hypothesis, because according to Weber, there are trends and other tips to predicting the stock market. Professors Andrew W. Lo and Archie Craig MacKinlay, professors of Finance at the MIT Sloan School of Management and the University of Pennsylvania, respectively, have also presented evidence that they believe shows the random walk hypothesis to be wrong. Their book A Non-Random Walk Down Wall Street , presents

12827-491: The random walk hypothesis. Another test that Weber ran that contradicts the random walk hypothesis, was finding stocks that have had an upward revision for earnings outperform other stocks in the following six months. With this knowledge, investors can have an edge in predicting what stocks to pull out of the market and which stocks — the stocks with the upward revision — to leave in. Martin Weber’s studies detract from

12954-664: The relationship between rationality and efficiency is as follows. Given the ability to profit from private information , self-interested traders are motivated to acquire and act on their private information. In doing so, traders contribute to more and more "correct", i.e. efficient , prices: the efficient-market hypothesis , or EMH. Thus, if prices of financial assets are (broadly) efficient, then deviations from these (equilibrium) values could not last for long. (See earnings response coefficient .) The EMH (implicitly) assumes that average expectations constitute an "optimal forecast", i.e. prices using all available information are identical to

13081-406: The required models. This derivation begins with the assumption of "no uncertainty" and is then expanded to incorporate the other considerations. (This division sometimes denoted " deterministic " and "random", or " stochastic ".) The starting point here is "Investment under certainty", and usually framed in the context of a corporation. The Fisher separation theorem , asserts that the objective of

13208-455: The resulting expected utility hypothesis states that, if certain axioms are satisfied, the subjective value associated with a gamble by an individual is that individual ' s statistical expectation of the valuations of the outcomes of that gamble. The impetus for these ideas arises from various inconsistencies observed under the expected value framework, such as the St. Petersburg paradox and

13335-399: The results to what would be expected for uncorrelated ϵ t {\displaystyle \epsilon _{t}} . Lo and MacKinlay have authored a paper, the adaptive market hypothesis , which puts forth another way of looking at the predictability of price changes. Peter Lynch , a mutual fund manager at Fidelity Investments , has argued that the random walk hypothesis

13462-415: The return on security j {\displaystyle j} as X j / P r i c e j {\displaystyle X_{j}/Price_{j}} ; see Stochastic discount factor § Properties . The Black-Scholes formula is found, in the limit, by attaching a binomial probability to each of numerous possible spot-prices (i.e. states) and then rearranging for

13589-406: The risk adjustment from the pricing ( V {\displaystyle V} , the value, or price, of the option, grows at r {\displaystyle r} , the risk-free rate). This hedge, in turn, implies that there is only one right price – in an arbitrage-free sense – for the option. And this price is returned by the Black–Scholes option pricing formula. (The formula, and hence

13716-405: The risk-free interest rate; per the second equation above. In pricing a "fundamental", underlying, instrument (in equilibrium), on the other hand, a risk-appropriate premium over risk-free is required in the discounting, essentially employing the first equation with Y {\displaystyle Y} and r {\displaystyle r} combined. This premium may be derived by

13843-464: The risks small stocks face. These risk factors are said to represent some aspect or dimension of undiversifiable systematic risk which should be compensated with higher expected returns. Additional popular risk factors include the "HML" value factor (Fama and French, 1993); "MOM" momentum factor (Carhart, 1997); "ILLIQ" liquidity factors (Amihud et al. 2002). See also Robert Haugen . Economists Matthew Bishop and Michael Green claim that full acceptance of

13970-414: The stock market. In one of his key studies, he observed the stock market for ten years. Throughout that period, he looked at the market prices for noticeable trends and found that stocks with high price increases in the first five years tended to become under-performers in the following five years. Weber and other believers in the non-random walk hypothesis cite this as a key contributor and contradictor to

14097-423: The stock market. Schwager also cites several instances of mispricing that he contends are impossible according to a strict or strong interpretation of the EMH. The 2007–2008 financial crisis led to renewed scrutiny and criticism of the hypothesis. Market strategist Jeremy Grantham said the EMH was responsible for the current financial crisis, claiming that belief in the hypothesis caused financial leaders to have

14224-484: The switch", saying that "the movement to deregulate the financial industry went too far by exaggerating the resilience—the self healing powers—of laissez-faire capitalism." Others, such as economist and Nobel laurete Eugene Fama , said that the hypothesis held up well during the crisis: "Stock prices typically decline prior to a recession and in a state of recession. This was a particularly severe recession. Prices started to decline in advance of when people recognized that it

14351-573: The terms corresponding to N ( d 1 ) {\displaystyle N(d_{1})} and N ( d 2 ) {\displaystyle N(d_{2})} , per the boxed description; see Binomial options pricing model § Relationship with Black–Scholes . More recent work further generalizes and extends these models. As regards asset pricing , developments in equilibrium-based pricing are discussed under "Portfolio theory" below, while "Derivative pricing" relates to risk-neutral, i.e. arbitrage-free, pricing. As regards

14478-403: The theory is simply 'lucky' insulates the theory from falsification and so, drawing on the philosopher of science and critic of neoclassical economics Hans Albert , Pilkington argues that the theory falls back into being a tautology or a pseudoscientific construct. Nobel Prize-winning economist Paul Samuelson argued that the stock market is "micro efficient" but not "macro efficient": the EMH

14605-794: The theory, included the definitions for three forms of financial market efficiency : weak, semi-strong and strong (see above). Investors, including the likes of Warren Buffett , George Soros , and researchers have disputed the efficient-market hypothesis both empirically and theoretically. Behavioral economists attribute the imperfections in financial markets to a combination of cognitive biases such as overconfidence , overreaction, representative bias, information bias , and various other predictable human errors in reasoning and information processing. These have been researched by psychologists such as Daniel Kahneman , Amos Tversky and Paul Slovic and economist Richard Thaler . Empirical evidence has been mixed, but has generally not supported strong forms of

14732-402: The two corresponding probabilities, and in turn, the derived distribution, or "measure" . The formal derivation will proceed by arbitrage arguments. The analysis here is often undertaken assuming a representative agent , essentially treating all market participants, " agents ", as identical (or, at least, assuming that they act in such a way that the sum of their choices is equivalent to

14859-409: The two usual areas of focus are Asset Pricing and Corporate Finance, the first being the perspective of providers of capital, the second of users of capital. Here, and for (almost) all other financial economics models, the questions addressed are typically framed in terms of "time, uncertainty, options, and information", as will be seen below. Applying this framework, with the above concepts, leads to

14986-520: The underlying is itself being priced, such "manufacturing" is of course not possible – the instrument being "fundamental", i.e. as opposed to "derivative" – and a premium is then required for risk. (Correspondingly, mathematical finance separates into two analytic regimes : risk and portfolio management (generally) use physical (or actual or actuarial) probability, denoted by "P"; while derivatives pricing uses risk-neutral probability (or arbitrage-pricing probability), denoted by "Q". In specific applications

15113-567: The underlying mathematics , and, with Itô calculus more generally, remains fundamental in quantitative finance. As implied by the Fundamental Theorem, the two major results are consistent . Here, the Black Scholes equation can alternatively be derived from the CAPM, and the price obtained from the Black–Scholes model is thus consistent with the assumptions of the CAPM. The Black–Scholes theory, although built on Arbitrage-free pricing,

15240-542: The use of capital, "Corporate finance theory" relates, mainly, to the application of these models. The majority of developments here relate to required return, i.e. pricing, extending the basic CAPM. Multi-factor models such as the Fama–French three-factor model and the Carhart four-factor model , propose factors other than market return as relevant in pricing. The intertemporal CAPM and consumption-based CAPM similarly extend

15367-399: The utility due to today's wealth, and is then also referred to as "the intertemporal marginal rate of substitution ". Bond valuation formula where Coupons and Face value are discounted at the appropriate rate, "i": typically a spread over the (per period) risk free rate as a function of credit risk ; often quoted as a " yield to maturity ". See body for discussion re the relationship with

15494-463: The work was never forgotten in the mathematical community, as Bachelier published a book in 1912 detailing his ideas, which was cited by mathematicians including Joseph L. Doob , William Feller and Andrey Kolmogorov . The book continued to be cited, but then starting in the 1960s the original thesis by Bachelier began to be cited more than his book when economists started citing Bachelier's work. The concept of market efficiency had been anticipated at

15621-511: The world's money managers with the highest rates of performance rebuts the claim of EMH proponents that luck is the reason some investors appear more successful than others. Nonetheless, Buffett has recommended index funds that aim to track average market returns for most investors. Buffett's business partner Charlie Munger has stated the EMH is "obviously roughly correct", in that a hypothetical average investor will tend towards average results "and it's quite hard for anybody to [consistently] beat

15748-643: Was a recession and then continued to decline. That was exactly what you would expect if markets are efficient." Despite this, Fama said that "poorly informed investors could theoretically lead the market astray" and that stock prices could become "somewhat irrational" as a result. The theory of efficient markets has been practically applied in the field of Securities Class Action Litigation. Efficient market theory, in conjunction with " fraud-on-the-market theory ", has been used in Securities Class Action Litigation to both justify and as mechanism for

15875-569: Was an unjustified faith in rational expectations, market efficiencies, and the techniques of modern finance." One financial analyst said "By 2007–2009, you had to be a fanatic to believe in the literal truth of the EMH." At the International Organization of Securities Commissions annual conference, held in June 2009, the hypothesis took center stage. Martin Wolf , the chief economics commentator for

16002-474: Was determined by a coin flip. If the result was heads, the price would close a half point higher, but if the result was tails, it would close a half point lower. Thus, each time, the price had a fifty-fifty chance of closing higher or lower than the previous day. Cycles or trends were determined from the tests. Malkiel then took the results in chart and graph form to a chartist , a person who "seeks to predict future movements by seeking to interpret past patterns on

16129-515: Was popularized by the 1973 book A Random Walk Down Wall Street by Burton Malkiel , a professor of economics at Princeton University , and was used earlier in Eugene Fama 's 1965 article "Random Walks In Stock Market Prices", which was a less technical version of his Ph.D. thesis. The theory that stock prices move randomly was earlier proposed by Maurice Kendall in his 1953 paper, The Analysis of Economic Time Series, Part 1: Prices . In 1993 in

#577422