What is the Arbitrage Pricing Theory?

Arbitrage pricing theory APT (Arbitrage Pricing Theory) is an extension of CAPM. The pricing model given by APT is the same as CAPM, which is a model under equilibrium. The difference is that APT is based on factor models.

Arbitrage pricing theory

Arbitrage Pricing Theory (APT)

Arbitrage pricing theory leads to a similar model to the capital asset pricing model

The starting point of the arbitrage pricing theory is to assume that the security's return is linked to an unknown quantity of unknown factors.

The factor model is a statistical model. Arbitrage pricing theory is described using a factor model

American Scholar, 1976

The basic mechanism of arbitrage pricing theory is:

Suppose there are three securities, all of which obey

APT and CAPM

1. Arbitrage Pricing Model (APT)

Keynes Beauty Contest

Pageantism is a theory about financial market investment founded by the famous British economist John Maynard Keynes. Keynes used the "beauty pageant theory" to explain the mechanism of stock price fluctuations. He believed that financial investment is like a beauty pageant. It is not essential for investors to buy the stocks that they think are the most valuable. Zhongwen wins the game, and uses a game similar to drums and flowers to describe the risks in stock market investment.

Random Walk Theory

In 1959, Osborne (M.F.M. Osborne) put forward the theory of random walk, thinking that buyers and sellers are as clever and resourceful in stock transactions, and today's stock prices have basically reflected the relationship between supply and demand; The molecular "Brownian motion" has the characteristics of random walk, and its movement path does not follow any rules. Therefore, stock price volatility is unpredictable. According to technical charts, it is actually nonsense to predict the future stock price trend.

Modern Portfolio Theory (MPT)

In 1952, American economist Harry M. Markowit applied the two mathematical concepts of the mean and variance of portfolio returns for the first time in his academic paper "Asset Selection: Effective Diversification" to make it mathematically clear. It defines investor preferences and explains the principle of investment decentralization in a mathematical way. It systematically illustrates the problem of asset portfolio and selection, marking the beginning of Modern Portfolio Theory (MPT). The theory holds that an investment portfolio can reduce non-systematic risks. An investment portfolio is determined by the securities and their weights. The selection of unrelated securities should be the goal of constructing an investment portfolio. It put forward the concept of risk for the first time on the basis of traditional investment returns. It believes that risk rather than return is the focus of the entire investment process. It also proposed an optimization method for investment portfolios. As a result, Markowitz obtained the 1990 Nobel Economy Scholarship.

Efficient Market Hypothesis (EMH)

In 1965, Eugene Fama, a professor of finance at the University of Chicago, published a paper entitled "Price Behavior in the Stock Market", deepened the theory in 1970, and proposed the efficient market hypothesis ( Efficient Markets Hypothesis (EMH). The efficient market hypothesis has a questioned premise that investors participating in the market are rational and able to respond quickly and reasonably to all market information. The theory holds that in a stock market with sound laws, good functions, high transparency, and sufficient competition, all valuable information has been timely, accurately, and fully reflected in the stock price trend, including the current and future value of the enterprise, unless there is a market Manipulation, otherwise it is impossible for investors to obtain excess profits higher than the market average by analyzing past prices.

After the effective market hypothesis was proposed, it became a hot topic of empirical research in the securities market. There is a lot of evidence for and against it, and it is one of the most controversial investment theories. Nevertheless, in the basic framework of the mainstream theory of modern financial markets, this hypothesis still occupies an important position.

On October 14, 2013, the Royal Swedish Academy of Sciences announced that it has awarded American economists Eugene Fama, Lars Pitt Hanson, and Robert J. Schiller the Nobel Prize in Economics for that year in recognition of their research The development trend of the asset market has adopted a new approach.

The Royal Swedish Academy of Sciences states that the three economists "lay the foundation for the perception of asset value." There are few ways to accurately predict the direction of the stock market bond market in the next few days or weeks, but research can predict prices for more than three years.

"These seemingly surprising and contradictory findings are precisely the work of this year's Nobel Laureate analysis," said the Royal Swedish Academy of Sciences.

It is worth mentioning that Eugene Fama and Robert Schiller hold completely different academic views. The former believes that the market is effective, while the latter firmly believes that the market is flawed. This also proves from another aspect that so far human beings The understanding of the logic of asset price fluctuations is still quite superficial, and the distance from us to truly grasp its internal laws is still very far away!

Behavioral Finance (BF)

In 1979, Daniel Kahneman, a professor of psychology at Princeton University, and others published an article entitled "Expectation Theory: Decision Analysis in a State of Risk", establishing a psychological theory of the human risk decision process. Become a milestone in the history of behavioral finance.

Behavioral Finance (BF) is a comprehensive theory that organically combines finance, psychology, and anthropology, and tries to reveal the irrational behavior and decision rules of financial markets. The theory holds that stock prices are not only determined by the intrinsic value of the enterprise, but are also largely affected by the behavior of investors, that is, investor psychology and behavior have a significant impact on the price decision and changes in the securities market. It is a theory corresponding to the efficient market hypothesis, and its main content can be divided into two parts: arbitrage limitation and psychology.

As Kanaman et al. Pioneered the analytical paradigm of "Prospect Theory" and became early pioneers of behavioral finance after the 1980s, the Royal Swedish Academy of Sciences announced in October 2002 that it was awarded to Daniel Kana Man and others this year's Nobel Prize in Economics, in recognition of their outstanding contributions to the comprehensive use of economics and psychological theory to explore investment decision-making behavior.

There are not many behavioral financial models in shape today, and the focus of research is still on qualitative descriptions and historical observations of market anomalies and cognitive biases, as well as identifying behavioral decision attributes that may have a systematic impact on financial market behavior.

It can be roughly considered that by 1980, the building of the classic investment theory had been basically completed. After that, scholars from all over the world have only done some repairs and improvements. For example, further research on the factors that affect the rate of return on securities, empirical and theoretical analysis of "different phases" in various markets, modification of assumptions about option pricing, and so on.