Application of the Theory of Financial States to Extant Market Phenomena

"The grand aim of all science [is] to cover the greatest number of empirical facts by logical deduction from the smallest possible number of hypotheses or axioms."

-Albert Einstein

Source: Lincoln Barnett,?The Universe and Dr Einstein?(1950 ed.)

The Theory of Financial States:

1.???? Any sufficiently large population of stocks will exhibit characteristics mirroring either the macroscopic stock market environment or the population from which they are selected.

2.???? As the number of transactions of a stock increases, the range of its price movement increases, too.

3.???? As the temporal window over which the pricing of a stock or group of stocks is observed narrows, their respective volatilities increase. This also applies to the price movement of a group of stocks as well. That is to say that the volatility observed on a daily scale will be greater than the volatility observed on a monthly scale.

4.???? Past price movements and future price movements are not statistically independent events; information about financial states can be used to identify probability intervals for the future movement of stock prices.

5.???? Information is incrementally integrated into the market beginning the moment it is released, though no piece of information can ever be fully integrated; it is impossible for every single investor to hold every single piece of accurate information about every single stock.

6.???? There will exist stocks with financial states which are projected to perform better than randomly selected stocks. There will also exist stocks with financial states which are projected to perform less favorably than randomly selected stocks. The probability that a population of stocks will increase or decrease in price can be ascribed via the observation of a stock’s financial state.

7.???? The integration of new information into the market, such as financial instruments and fundamentals, constantly alters the expected value for the returns of a population with a specified characteristic or set thereof. Information is never incorporated fully and never incorporated instantaneously.

With that we can apply FAST to extant market phenomena, such as Momentum and Earnings.

Momentum:

Momentum investing is a phenomenon that has been present in the market for centuries. It is predicated upon the precept that past performance possesses the capacity to predict future performance. FAST states that given a set of financial characteristics, such as momentum, that an individual would be able to construct a confidence interval for the change in a stock’s price or group thereof over a defined temporal interval based upon conditional probability. In addition to this, one might construct a confidence interval for the proportion of stocks bearing a set of characteristics which will increase in price at a defined point in the future.

We might also construct a confidence interval for the proportion of stocks bearing characteristic A in time t which will bear characteristic A in time t+n.

The Efficient Markets Hypothesis claims that the price of a stock reflects all available information instantaneously. Various market phenomena, however, contradict this claim. The most salient example would be the post-earnings-announcement drift, wherein the prices of stocks respond to new information for up to two years following favorable earnings announcements. Alterations to the EMH were subsequently put forth in the forth in the form of the weak, medium, and strong versions.

If information were integrated into the market instantly and the strong version of the EMH were true, then prior six-month returns would not display the statistical power to project returns for up to two years for these populations; this phenomena would have gradually become unprofitable when or sometime after it was identified in market literature, yet such is not the case.

Modifications to the efficient markets hypothesis state that information might be integrated slowly, but these alterations do not explain why some information might never be fully integrated before being supplanted by new information. According to FAST however, the proportion of the market that is aware of a piece of information, such as momentum, is itself a phenomenon governed by probability.

One can imagine a trader, for example, who holds 50 shares of stock ABC. Let us suppose that this imaginary investor manages their own stocks with the intention of holding them for long periods of time. If this investor only pays attention to three out of four quarterly earnings announcements, then a critical piece of financial information will never have been integrated into the market. Where the EMH fails to account for the failure of information to be incorporated fully without amendment, this situation arises naturally as a function of the seventh rule of FAST.

This concept would hold true for momentum; if an investor who buys a momentum stock based on its price performance in the previous six months only checks its performance semiannually, then critical pieces of data are never fully integrated into the market.

Because it is impossible for all investors to hold all information at all points in time, it is more accurate to describe the integration of information into the market as being on a spectrum. The same piece of information may reach a different proportion of investors in a given quarter, and would likely exhibit variance if measured over multiple quarters.

The combination of rules number one and seven of FAST tells us that randomly selecting from a population of stocks exhibiting the integration of favorable information will in fact produce greater returns than a collection of randomly selected stocks, which tend to mimic the market. Where the efficient markets fail to explain the predictability of stock prices according the post-earnings announcement drift, short interest, or price momentum, this predictability arises naturally from the FAST’s first rule. If the performance of these stocks ceased to outperform the market, then it would symbolize that fundamentals have ceased to have bearing on the pricing of stocks, which seems to be a highly unlikely scenario to persist over decades or centuries.

In addition to this, rule four allows us to estimate the probability that a proportion of randomly selected stocks will increase in price based upon rule five, which allows us to observe the probabilities of market phenomena in the past and, with rule seven in mind, estimate the probability that a proportion of randomly selected stocks from this group will increase in price with the understanding that this probability may alter over time with the integration of new information into the market. Rule seven might be integrated to estimate the profitability of an investment strategy after publication or proliferation decrease the utility of the strategy.

Certainly, it is the case that momentum investors have been using these rules for decades, and while the strong version of the EMH tells us that this phenomenon should be invalidated by its integration into the market consciousness, momentum investing continues to produce superior returns. FAST, on the other hand, tells us that the capacity of momentum investing to “beat the market” on a risk-adjusted basis is an expected outcome that arises from its first and fourth rules, respectively.

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References

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Earnings

With the consideration that earnings are probably the most widely utilized metric for both the professional and lay investor for the valuation and purchase of securities, any theories of pricing of markets must address them with an explanation. Earnings per share is arguably the most widely known phrase in the markets. Analysts and investors use earnings surprise to evaluate stocks and thereby decide whether or not to purchase them, and a mountain of literature has been compiled over the decades supporting the view that earnings are an indicator of value and future price movements in stocks.

In addition to earnings surprise, quarterly changes and performance relative to analyst forecasts are used by both institutional and individual investors to determine the value of stocks. I introduce earnings continuity, which is the number of consecutive quarters of positive earnings per share reported.

The efficient market hypothesis, in its purest form, argues that prices reflect all publicly available information and do so instantaneously. The framework of this argument centers around investors possessing an awareness of the fundamentals being reported and constantly keeping themselves up-to-date on this information.

The seventh rule of FAST, however, says that the integration of information is neither instantaneous nor complete. It is a gradual phenomenon which takes place over time and may occur faster for some pieces of information and slower for others. Further still, the same information for different stocks may be absorbed by the market at different rates. According to a FAST interpretation, it would be the case that the exact same magnitude of earnings surprise across a sufficiently large distribution of stocks would display a predictable variance, itself being a financial state.

In conjunction with rule number six of FAST, stocks exhibiting earnings surprise, earnings growth, or other favorable earnings information will be of a financial state such that the expected value for their price movement will be greater than that of stocks with unfavorable earnings information. We can then observe qualities such as the post-earnings-announcement drift and further investigate duration of the drift over long periods of time. It may be the case that advances in communications technology and the greater abilities of individual investors to access information has shortened the duration of the drift as a result of information being integrated into markets more quickly.

Where the efficient market hypothesis requires modifications or extensions to explain phenomena such as the post-earnings-announcement drift, or its ability to outperform the market, such events arise naturally from FAST rules one, four, and six, respectively. Where rule six tells us that stocks with favorable financial states will perform better than stocks with unfavorable financial states, rule one tells us that a randomly selected sample from the population of such stocks will be expected to perform better than a randomly selected sample from the market as a whole.

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