Generalized Capital Asset Pricing Model Research Articles

Testing for herding behaviour among energy sectors in Chinese stock exchange

Herding behaviour in stock markets leads a group of investors to imitate others and make the same economic decisions as other market participants, causing excess market volatility and price instability. This paper aims to test for the herding behaviour in different energy sectors of Chinese Stock Exchange. Firstly, Generalized Capital Asset Pricing Model (GCAPM) is employed to observe the stocks in energy sectors during financial crisis, which can test for the nonlinear relationship between return of particular portfolio and the average return of market. The empirical results indicate the presence of herding behaviour in energy sectors. Secondly, artificial neural networks are used to predict the herding behaviour in Chinese stock markets. It is advisable that during the periods when the stock market is unstable, investors should keep awake to avoid herding behaviour.

Calibrating Risk Preferences with Generalized CAPM Based on Mixed CVaR Deviation

The generalized Capital Asset Pricing Model based on mixed CVaR deviation is used for calibrating risk preferences of investors protecting investments in S&P500 by means of options. The corresponding new generalized beta is designed to capture tail performance of S&P500 returns. Calibration is done by extracting information about risk preferences from option prices on S&P500. Actual market option prices are matched with the estimated prices from the pricing equation based on the generalized beta. In addition to the risk preferences, an optimal allocation to a portfolio of options for the considered group of investors is calculated. I Introduction The Capital Asset Pricing Model (CAPM, see Sharpe (1964), Linther (1965), Mossin (1966), Treynor (1961, 1962)) after its foundation in the 1960’s became one of the most popular methodologies for estimation of returns of securities and explanation of their combined behavior. This model assumes that all investors want to minimize risk of their investments, and all investors measure risk by the standard deviation of return. The model implies that all optimal portfolios are mixtures of the Market Fund and risk free instrument. The Market Fund is commonly approximated by some stock market index, such as S&P500. An important practical application of the CAPM model is the possibility to calculate hedged portfolios uncorrelated with the market. To reduce the risk of a portfolio, an investor can include additional securities and hedge market risk. The risk of the portfolio in terms of CAPM model is measured by “beta”. The value of beta for every security or portfolio is proportional to the correlation between its return and market return. This follows from the assumption that investors have risk attitudes expressed with the standard deviation (volatility). The hedging is designed to reduce portfolio beta with the idea to protect the portfolio in case of a market downturn. However, beta is just a scaled correlation with the market and there is no guarantee that hedges will cover

The CAPM and Beta in an Imperfect Market

The General Capital Asset Pricing Model (GCAPM) incorporates certain market imperfections (see Levy, 1978 and 1980). Levy concludes that in GCAPM equilibrium, all investors do not necessarily hold the market portfolio and that a security's own variance is priced. We show that financial intermediaries, responding to potential abnormal profits, relax an important GCAPM constraint. The introduction of intermediaries into the GCAPM leads to results not unlike those of the CAPM itself. If an asset's own variance affects its price, we conclude that this feature provides a major reason for the existence of financial intermediaries.

GCAPM (I): A Microeconomic Theory of Investments

Based on the invisible hand of the market, this paper proposes a general microeconomic theory of investments under the framework of neoclassical microeconomics. theory requires minimum assumptions and allows investors to have time-variant and heterogeneous investment utilities and expectations. It prescribes a set of static and dynamic Capital Asset Pricing (Theorems and) Models - collectively labeled as GCAPM. GCAPM unifies currently seemingly-conflicting modern finance theories and connects them more closely to real-world finance. GCAPM independently derives a set of new paradigms under its heterogeneous world and shows that Sharpe's paradigms are alive and well but were overzealously misinterpreted for decades. most noticeable misinterpretation is the widely accepted beta risk premium hypothesis, which wrongfully asserts that holding higher-beta-risk assets should generate higher ex-post returns. GCAPM shows that, as far as beta risk is concerned, it is prudent beta risk management rather than reckless beta risk taking that produces higher ex-post returns. GCAPM's general equilibrium also supports Ross and Roll's APT, which has been criticized as an arbitrage-free hypothesis without supporting equilibrium theories. GCAPM shows that the quality of a capital market equilibrium is only as good as the quality of its member investors. It agrees with the nascent behavioral finance theory that investors' psychological weaknesses and cognitive biases can influence capital asset pricing. However, GCAPM shows that competitive capital markets share a common evolutionary force that will eliminate known irrational investment behavior over time and mature capital markets should mainly reflect investors' normative financial needs, investment objectives, risk tolerances, and best forecasts of future economic states. Release Note: I had made substantial structural changes to the previous edition of GCAPM (I) paper. static and dynamic cases of GCAPM are now thoroughly discussed in two separate Sections. A new Section, titled The Quality of Capital Market and Behavioral Finance, is added to address the flaws of human investment behavior and capital markets' evolution forces. old Section regarding canonical asset pricing is removed from the paper and will be published in a separate paper tilted Canonical Asset pricing and Asset Allocation Theorems. Except for the misinterpreted beta risk premium hypothesis, whose empirical tests prematurely declared the death of CAPM, materials regarding other misinterpretations are removed and will be discussed in a separate paper titled CAPM Paradoxes and their GCAPM Interpretations. A 1997 version of this paper was titled: General Capital Asset Pricing Model (GCAPM): A Complete Mathematical Appendix A 2001 version of this paper was titled: General Capital Asset Pricing Models (GCAPM) - Part I: A Microeconomic Theory of Investments (Mathematical Edition)

Multi-Moments Method for Portfolio Management: Generalized Capital Asset Pricing Model in Homogeneous and Heterogeneous Markets

We use a new set of consistent measures of risks, in terms of the semi-invariants of pdf's, such that the centered moments and the cumulants of the portfolio distribution of returns that put more emphasis on the tail the distributions. We derive generalized efficient frontiers, based on these novel measures of risks and present the generalized CAPM, both in the cases of homogeneous and heterogeneous markets. Then, using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their natural multivariate generalizations, we offer exact formulas for the moments and cumulants of the distribution of returns of a portfolio made of an arbitrary composition of these assets. Using combinatorial and hypergeometric functions, we are in particular able to extend previous results to the case where the exponents of the Weibull distributions are different from asset to asset and in the presence of dependence between assets. In this parameterization, we treat in details the problem of risk minimization using the cumulants as measures of risks for a portfolio made of two assets and compare the theoretical predictions with direct empirical data. Our extended formulas enable us to determine analytically the conditions under which it is possible to have your cake and eat it too, i.e., to construct a portfolio with both return and smaller larger risks.

General Capital Asset Pricing Model (GCAPM) - A Microeconomic Theory of Investments

The traditional CAPM can not explain empirically flat beta risk premiums and pronounced equity style effects. This paper proposes a new capital asset pricing model - GCAPM, which restores the invisible hand of markets as the sole mechanism for any competitive capital market equilibriums. GCAPM firmly links capital asset pricing with investors' time-variant and heterogeneous investment objectives, risk concerns, and asset valuations. It bestows modern finance paradigms with broader definitions and richer economic contents. It shows that, under the new light, CAPM paradigms are alive and well, independent of its framework and assumptions. It also shows that modern finance paradigms have been seriously mis-interpreted, mis-modeled, mis-tested, and mis-applied in many occasions, including those causing recent CAPM controversies. In its Mathematical Appendix, GCAPM provides first-hand, closed-form derivations of modern finance paradigms, a new set of asset pricing theorems, and various forms of capital asset pricing models from the perspective of competitive capital market equilibrium. It reveals the competitive equilibrium model behind Ross and Roll's APT (1976) for the first time since 1976. It also proposes a new Canonical Capital Asset Pricing Model, which supports for Sharpe's (1988-95) return-based style analyses and enhances CAPM's two asset-pricing portfolios into a set of market-driven canonical asset-pricing portfolios. GCAPM resolves CAPM controversies, unifies positive and normative thoughts of finance, establishes missing links between modern finance paradigms and real-world financial practices, and provides a new framework for financial studies.

Possible explanations of no-synergy mergers and small firm effect by the Generalized Capital Asset Pricing Model

The Sharpe-Lintner Capital Asset Pricing Model (CAPM) and the General Capital Asset Pricing Model (GCAPM) suggested by Levy (1978), Merton (1987), and Markowitz (1989) are compared and analyzed.

The CAPM and beta in an imperfect market

The General Capital Asset Pricing Model (GCAPM) incorporates certain market imperfections. Levy concludes that in GCAPM equilibrium, all investors do not necessarily hold the market portfolio and that a security's own variance is priced. We show that financial intermediaries, responding to potential abnormal profits, relax an important GCAPM constraint. The introduction of intermediaries into the GCAPM leads to results not unlike those of the CAPM itself. If an asset's own variance affects its price, we conclude that this feature provides a major reason for the existence of financial intermediaries.

Asset Pricing Models When the Number of Securities Held Is Constrained: A Comparison and Reconciliation of the Mao and Levy Models

ln a paper published in 1978, Levy [5] proposed a general capital asset pricing model (GCAPM), which he obtained by maximizing investors1 utility when the number of securities held in each investor's portfolio is con? strained. Although Levy's resultant asset pricing model is somewhat dif? ferent in appearance than the asset pricing model proposed by Mao [81 in 1971, it can be shown that both models are not only quite comparable in content but that both result in some very promising theoretical and empirical implications. Thus, the purpose of this paper is twofold. First, these two important contributions to the literature on asset pricing in imperfect markets will be compared and contrasted. Second, it will be shown that both models can yield a clinical form of the traditional CAPM, which appears to be more desirable for empirical testing purposes. This paper is organized into four sections. In Section I, the paper by Mao [81 is reviewed. The similarities and differences of the asset pric? ing models proposed by Mao [8] and Levy [5] are discussed in Section II. In Section III, the implications of the clinical forms of the traditional CAPM proposed by Mao and Levy are examined with particular reference to Roll's [93 recent criticisms of the validity of past empirical tests of the traditional CAPM. In the fourth and final section, some concluding remarks are presented._

Abstract--Investment Horizon and the Functional Form of the Capital Asset Pricing Model: An Empirical Investigation

This paper derives a generalized Capital Asset Pricing Model (CAPM) to allow the investment horizon to be explicitly introduced into the risk-return relationship of capital asset pricing. It is shown that the systematic risk estimated from this generalized CAPM includes finite systematic risk, Jensen systematic risk, and Cheng–Deets (CD) systematic risk as a special case. From the relationship among the finite horizon type CAPM, the Jensen instantaneous type CAPM, and the generalized CAPM, it is found that the investment horizon problem can be treated as a functional form problem which is similar to determining whether a Cobb-Douglas type or a CES type production function is appropriate in estimating a production relationship. As the rates of return on security and market rates of return are log normally distributed, it is shown that Jensen instantaneous systematic risk is identical to CD instantaneous systematic risk. Under this circumstance, it also is shown that the finite systematic risk is approximately equal to the instantaneous systematic risk times an adjustment factor.