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Landmarks in the Theory of Financial Markets

Stock Price Changes are unpredictable. The Fair Game hypothesis.

Louis Bachelier (French mathematician) in his doctoral thesis entitled “The Theory of Speculation, was the first to provide a mathematical description of the law that governs the behavior of stock prices over time. One of the implications of Bachelier’s theory is that successive price changes are unpredictable. This result, usually referred to as “the fair-game hypothesis” may be thought of as a first step towards what would later (in the 1960s) be called the random-walk theory.

Distinguishing Risk from Uncertainty

Frank Knight (American economist) introduces a clear distinction between risk and uncertainty. Risk refers to the case in which the probabilities of various outcomes in a game of chance are known to the gambler (or the investor). On the other hand, uncertainty describes the case in which such probabilities are unknown. Obviously, the lack of knowledge/information that characterizes uncertain situations is greater than that associated with cases of risk (known probabilities).

Stock Prices follow a Random Walk: Nobody can beat the Market

Alfred Cowles (founder of Cowles Commission for Economic Research) published an influential article with the provocative title “Can Stock Market Forecasters Forecast?” To answer this question, Cowles analyzed the track records of a large number of professional investment advisors, including financial and insurance services. The answer to the above question was far from reassuring: “It is doubtful”. Specifically, Cowles concludes that the performance results of the professional investors “could have been achieved through a purely random selection of stocks.”

Anticipating the Anticipations of the Market

The famous British economist John Maynard Keynes draws a useful analogy between the stock market and a beauty contest in which the winner is the one who picks the contestant who turns out to be the most popular. In such a case, it is not important to think “which contestant is the most beautiful according to my own taste” but rather “which contestant enjoys the highest probability to be voted as the prettiest one”. In Keynes’ own words: “It is not sensible to pay 25 for an investment of which you believe the prospective yield to justify a value of 30, if you also believe that the market will value it at 20 three months hence.

Diversification is the right way to minimize portfolio risk. Introduction of the risk –exp.return and efficient frontier.

Harry Markowitz (American economist) sets the scene for the future development of modern asset pricing theory, in a short article entitled “Portfolio Selection”. An important element of his theory is the distinction between the variance (risk) of returns of an individual security and that of the returns of the overall portfolio of securities. A rational investor wishes to minimize the risk of the overall portfolio (rather than that of the individual securities) subject to a desired level of expected returns. For each level of risk there is an optimal portfolio that yields the maximum expected return. The set of all these optimal portfolios forms the so-called efficient frontier. It is economically inefficient for an investor to select a portfolio outside the set that defines the efficient frontier.

Introduction of the risk-free asset. In the presence of a risk-free asset, there is only one optimal portfolio of risky assets.

James Tobin (American economist) extends Markowitz’s analysis towards an important direction. He introduces the concept of a risk-free asset (e.g. US Treasury bills or cash) and shows that in the present of such an asset, the problem of portfolio selection simplifies considerably. Specifically, there is a unique optimal portfolio that is superior to all other portfolios on the efficient frontier in terms of risk – expected return characteristics. As a result, all investors should hold the same (super) optimal portfolio regardless of their risk appetite. The level of risk that an investor is willing to assume affects only his decision of how will allocate his capital between the riskless asset and the optimal portfolio of risky assets. Tobin’s theorem is known as the Separation Theorem.

The Probabilities of Extreme Events are higher than those Implied by the Gaussian-bell curve.

Benoit Mandelbrot (French mathematician) provides evidence against the hypothesis that stock returns are distributed in a Normal (Gaussian) fashion. Instead, he puts forward the idea that stock return distributions have much fatter tails than those of the Normal (Gaussian) distribution, meaning that extreme events can happen more often than one believes.

How does Risk affect the Valuation of Stocks? The Birth of Capital Asset Pricing Model (CAPM).

William Sharpe (American economist) decomposes the total risk of a (risky) asset in two components: the systematic component (as measured by asset’s beta) and the idiosyncratic (or residual) one. Any investor should be compensated only for bearing systematic risk; the idiosyn-cratic risk can be diversified away using Markowitz’s methods, which in turn implies that no risk premium should be required for the residual risk. In Sharpe’s own words: “Only the responsiveness of an asset’s rate of return to the level of economic activity is relevant in assessing its risk.” CAPM unifies Samuelson’s and Fama’s theories of efficient markets with Markowitz’s and Tobin’s theories of optimal portfolio selection.

Why stock prices follow random walks

Paul Samuelson (American economist) offers the first theoretical explanation of why stock prices follow random walks. Up to his contribution, the random character of stock prices was treated as a paradox by mainstream economists. Randomness is considered to be the antithesis of Laws (including the economic laws). Does this mean that the determination of stock prices defies economic laws? Samuelson demonstrates that stock price randomness is not at odds with economic theory; quite the contrary, it reflects “the triumph of economic law after competition has done its best”. Here, the object of competition is information. Once new information has been released, it is processed rapidly by the market participants, thus leaving no informational advantage to any single trader. As new information arrives in a non-systematic and unpredictable manner, the stock market prices are also unpredictable.

The Efficient Market Hypothesis is born: Current Prices fully reflect all available information.

Eugene Fama (American Economist) crystallizes the widespread view that stock prices are unpredictable, in the form of the Efficient Market Hypothesis (EMH). The basic tenet of EMH is that market participants are dedicated information hunters. As a result, any new information is pro-cessed rapidly and accurately which in turn implies that this information is incorporated into the current price almost instantaneously. The best processor of information is market itself. As a consequence the optimal portfolio is the market portfolio.

A “Valuable” Formula for Valuing Options: The Black-Scholes-Merton Option Pricing Theory.

Fisher Black, Myron Scholes and Robert Merton (American economists) propose a formula (BSM) for calculating the theoretical (fair) value of European-style options. This was a major breakthrough which produced numerous applications in the financial industry. As Peter Bernstein remarks, “Seldom has the marriage of theory and practice been so productive.”

There are more than one factor affecting stock returns: The Arbitrage Pricing Theory (APT).

Stephen Ross (1976) extends CAPM in several directions, by putting forward the Arbitrage Pricing Model. In the context of APT, stock returns are linearly related to a set of factors (instead of CAPM which assumes the presence of a single factor, namely the returns of market portfolio). Similarly to CAPM, investors holding well-diversified portfolios are interested only in the systematic risk of these portfolios. The systematic risk is captured by the set of factors that are supposed to affect stock returns. Unlike CAPM, APT allows for occasional mispricing of stocks; however these mispricing eventually disappear due to arbitrage.

The volatility of stock returns is not constant over time. Volatility Patterns and Volatility Forecasting: The ARCH/GARCH type of Models.

Robert Engle (American economist) made an important observation (a similar observation was made by Mandelbrot almost twenty years ago but went largely unnoticed). The volatility of stock returns is not constant over time. On the contrary volatility comes in clusters, that is large price changes tend to be followed by large changes and small price changes tend to be followed by small ones. This volatility pattern may be captured by a properly designed model (ARCH/GARCH), which in turn may be used for volatility forecasting.

Concerns over the Efficient Market Hypothesis are mounting

In October 1987, the Dow Jones industrial average lost almost one-third of its value in that single month. Is this type of behavior consistent with EMH? What kind of new information emerged and was instantaneously incorporated in the prices so as to produce such an extreme reaction? As Burton Malkiel remarks, “Too many observers and shocked investors, these events blatantly exposed the failings of the efficient-market theory”.

The Size Premium: low-capitalization stocks over-perform: Eugene Fama and Kenneth French report empirical results suggesting an anomaly in stock prices that is not consistent with efficient markets: The average return of a portfolio consisting of low-capitalization stocks systematically over-performs a portfolio formed by large-capitalization stocks. The difference in performance of the two portfolios is quite significant and cannot be explained by the risk difference in the two portfolios alone.

Book-to-Market (B/M) and Earnings-to Price (E/P) ratios are likely to have predictive abilities with respect to future price movements: Eugene Fama and Kenneth French report another anomaly in the stock market: Stocks with low B/M or E/M (value stocks) tend to outperform stocks with high B/M or E/M (growth stocks). Again these differences cannot be attributed to risk-differential considerations alone.

A Paradigm Shift: “From Efficient Markets to Behavioral Finance”. Since the 1990s a new school of thought emerged whose main views are in sharp contrast with those of the Efficient Market Hypothesis. This new paradigm, usually referred to as Behavioral Finance, acknowledges that psychological factors play a key role in investors’ decision making pro-cess. Instead of assuming that investors are fully rational in the sense of processing information accurately and instantaneously, the advocates of behavioral finance, such as the psychologists Daniel Kahneman and Amos Tversky as well as the economists Werner DeBondt and Richard Thaler, put forward the idea that investors commit several cognitive errors in making investment decisions. These errors are numerous including over-reaction, over-confidence, … All these errors are grouped under the title “investors’ fallacies”. The net effect of these fallacies is that current stock prices may be quite imprecise, meaning that they deviate persistently from the corresponding fair prices.

Implications for Asset Management: If markets are not efficient then prices might not fluctuate randomly. Investors’ fallacies, if properly studied and understood, may reveal predictable elements in market’s behavior which in turn may produce predictable patterns in stock returns. Whoever succeeds in identifying those patterns acquires a significant edge over the rest of the market which in turn is likely to enable him to systematically beat the market. Active portfolio management may prove to be a worthwhile and lucrative endeavour.

Landmarks in the Theory of Financial Markets

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