Efficiency and Random Walk

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This chapter, which corresponds to the second subdivision of the part, attempts to characterize stock markets. The stock markets are known as efficient and are representative of the perfect competition. They are also known as advanced indicators of the global economic activity. The evolution of stock market indexes show however trajectories whose amplitudes are often considerably higher than those of gross domestic product. The concept and the models of rational expectations (arbitrage and stock price fixing) will give a first argument to try to explain these differences between trajectories. One will consider the efficiency concept, in the sense of Fama, about the stock markets and their instability.

8.1 Market Efficiency and Random Walk: Stock Market Growth and Economic Growth

We will attempt to give the theoretical definition of stock markets given by Economics using different concepts such as the perfect markets and the advanced indicator of the economic activity and through the notion of "value creation" which is transverse to Economics and Finance. Then, we will develop the economic concept of rational expectations and its self-criticism. Lastly, we will analyze the efficiency concept of financial markets.

8.1.1 Stock Exchange: Perfect Competition Market

The abstract definition of a market of perfect competition finds in the stockexchange an archetype satisfying the following criteria:

T. Vialar, Complex and Chaotic Nonlinear Dynamics, © Springer-Verlag Berlin Heidelberg 2009

• The market atomicity is respected. Otherwise, Securities and Exchange Commission1 (CES) identifies the non-respect causes of the atomicity criterion, then they suspend the listings and tradings on the market. This means that the CES makes sure that no investor is price marker, i.e. does not exert power on market.

• The market transparency is respected, the listed-companies have to provide and publish information about their activities. That means that all the potential buyers of equities and shares must be equal in front of the information placed at the disposal by the listed-companies. If it were not the case, i.e. if the CES detected an illegal"insider trading", it must sanction the originator of the offence. Indeed, when one or more investors have access to confidential and internal information of the company (i.e. information which is not publicized) and use the information to obtain abnormally high and illicit profits, then we are, indeed, in the presence of an illegal insider trading. It is said of this kind of investor who carries out such manipulation that it is in an insider position.

• The market homogeneity is respected. This can be summarized in the following way, whatsoever the "number" of an outstanding stock2 on the market, a share having a different number but obviously of the same company (and of an equities group of comparable nature) rigorously satisfied the same needs.

• The market fluidity is respected. This corresponds to the absence of barrier to entry or exit on the market of stocks and shares or equities. Even if the cost of transactions or tradings, nowadays minor, can be regarded as a constraint less and less true, as these costs dropped considerably. The stock market is certainly in vivo very close to the theoretical definition of a perfect market.

8.1.2 Stock Exchange: Advanced Indicator of Economic Activity

Generally the financial system and in particular the stock exchange contribute to the optimization of the resource allowance in the economy. However, they are also places where the information is privileged. The information is the key element of decision-makings for all the actors involved in markets. During a given period, the return or the remuneration of funds and capital (that lets predict the stock exchange market, as well as the interest rates on the bond or monetary markets) leads the investment strategies of companies and also leads the behaviors of individual agents about savings and consumption. The general evolution of the prices of stock, bond, money or currency, is supposed to contain, incorporate and integrate information about future. The future of an economy (i.e. companies, branches of industry and

1 Securities and Exchange Commission (SEC): commonly referred to as the SEC, is the United States governing body which has primary responsibility for overseeing the regulation of the securities industry. It enforces, among other acts, the Securities Act of 1933, the Securities Exchange Act of 1934, the Trust Indenture Act of 1939, the Investment Company Act of 1940 and the Investment Advisors Act. It removed regulatory authority from the Federal Trade Commission.

2 Outstanding stock: The shares of a corporation's stock that have been issued and are in the hands of the public. Also called shares outstanding.

their markets) but also the relation with the foreign economies in terms of exchanges and influence, are represented in stock market prices. Thus, the stock exchange indexes are advanced indicators of economy activity. The supply and demand aggregations of the economic agents is carried out during the fixing of prices and therefore express the expectation of the future by agents. A stock-exchange index as for example the French index synthesizes at a given time all information available and its treatment by agents. Such a treatment can be rational or led by arbitrary choices. Indeed, taking into account the market fluidity (i.e. the absence of barrier to entry) all the types of investors can carry out their choices and anticipations, while including sometimes choices based on a "less rational" treatment of the information. In the stock exchange prices all information and all expectations are thus taken into account, so that it is almost possible to say that "nothing is visible any more". The role of anticipations and expectations in the evolution of the stock-exchange prices leads the economists to consider these prices as advanced indicators of the economic situation in the future. Thus, since the markets incorporate and treat all the data available about the future, the market is a source to use in order to make forecasts. Indeed, the study of stock-exchange indexes can be used to anticipate the gross domestic product (GDP). Accordingly, the study of the French index SBF250 which integrates more companies than the Cac40 (i.e. 250 against 40) can prove to be a considerable source of information to make short-run forecasts. In the United states the S&P500 index, which integrates the first 500 stock-exchange companies, is used officially in the determination of the short-term economic situation forecasts (i.e. conjuncture forecasts) carried out by the "National Office of Economic Research" (NBER).

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