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The capital asset pricing model (CAPM) is the most widely used asset pricing model that measures risk–return relationship. The CAPM is based on Markowitz’s mean variance analysis. The advancement of Islamic finance leads to the question whether or not the practice of modern investment theories and analyses such as the Markowitz’s mean variance analysis and CAPM are in accordance to shariah and could be used in pricing Islamic financial assets. Therefore, this paper aims to present a review of the CAPM and to discourse the set of assumptions underlying the model in terms of shariah compliance.

Although most of the assumptions are not contradictory to shariah principles, there are Islamic variables such as prohibition of short selling, purification and zakat that should be taken into consideration when pricing Islamic financial assets. We then develop a mathematical model which is a modification of the traditional CAPM that incorporates principles of Islamic finance and integrating zakat, purification of return and exclusion of short sales.

As a proof-of-concept, this paper presents the results of an empirical study on the proposed shariah-compliant CAPM in comparison to the traditional CAPM. The results show that the proposed Islamic CAPM is appropriate and applicable in examining the relationship between risk and return in the Islamic stock market.

This study contributes to existing body of knowledge by presenting an algorithm and mathematical derivation of the shariah-compliant CAPM which has been lacking in the literature of Islamic finance. The paper offers a novel approach in pricing Islamic financial assets in accordance to shariah, advocated by modern investment theories of Markowitz’s mean variance analysis and CAPM.

Daniel and Titman (1997) contend that the Fama‐French three‐factor model’s ability to explain cross‐sectional variation in expected returns is a result of characteristics that firms have in common rather than any risk‐based explanation. The primary aim of the current paper is to provide out‐of‐sample tests of the characteristics versus risk factor argument. The main focus of our tests is to examine the intercept terms in Fama‐French regressions, wherein test portfolios are formed by a three‐way sorting procedure on book‐to‐market, size and factor loadings. Our main test focuses on ‘characteristic‐balanced’ portfolio returns of high minus low factor loading portfolios, for different size and book‐to‐market groups. The Fama‐French model predicts that these regression intercepts should be zero while the characteristics model predicts that they should be negative. Generally, despite the short sample period employed, our findings support a risk‐factor interpretation as opposed to a characteristics interpretation. This is particularly so for the HML loading‐based test portfolios. More specifically, we find that: the majority of test portfolios tend to reveal higher returns for higher loadings (while controlling for book‐to‐market and size characteristics); the majority of the Fama‐French regression intercepts are statistically insignificant; for the characteristic‐balanced portfolios, very few of the Fama‐French regression intercepts are significant.

The main aspect of security analysis is its valuation through a relationship between the security return and the associated risk. The purpose of this paper is to review the traditional capital asset pricing model (CAPM) and its variants adopted in empirical investigations of asset pricing.

Pricing models are discussed under five categories: the single‐factor model, multifactor models, CAPM with higher order systematic co‐moments, CAPM conditional on market movements and time‐varying volatility models.

The paper finds that the last half‐century has witnessed the proliferation of empirical studies testing on the validity of the CAPM. A growing number of studies find that the cross‐asset variation in expected returns cannot be explained by the systematic risk alone. Therefore a variety of models have been developed to predict asset returns.

There is no consensus in the literature as to what a suitable measure of risk is, and consequently, as to what is a suitable measure for evaluating risk‐adjusted performance. So the quest for robust asset pricing models continues.

From its beginning to its possible demise the paper reviews the history of the CAPM assuring that we are all up to speed with what has been done.

The underlying principle of the Capital Asset Pricing Model (CAPM) is that there is a linear relationship between systematic risk, as measured by beta, and expected share returns. The CAPM attempts to describe this relationship by using beta to explain the differences between the expected returns on various shares and share portfolios. The CAPM has been the subject of considerable theoretical investigation and empirical research. The aim of this article is to establish the current knowledge of the usefulness of the CAPM, i.e. whether it provides a reasonable description of reality and whether it is a useful tool for investment decision‐making. The main conclusion drawn from the study is that the CAPM is useful and that it does describe and explain the risk/return relationship. However, other risk factors (i.e. other than beta) may also be useful for explaining share returns. Investors should therefore be cautious when using the model to evaluate investment performance.

The purpose of this paper is to investigate changes in the commercial real estate market dynamics as a function of and conditional to the shifts in market state-space environment that can influence agent responses.

The analytical design uses a comparative computational experiment to address the performance of property assets in the current market based on comparison with prior structural patterns. The latent variables developed across market sectors are used to test agent behavior contingent on the perspectives of capital asset pricing conditionals (CAPM) and a behavioral momentum/herd construct. The state-space momentum analysis can assist the comparative analysis of current levels and shifts in property asset performance given the issues that have arisen with the financial crisis of 2007-2009.

An analytic approach is employed framed by a situation-dependent model. This frame considers risk profiles characterizing the perspectives and preferences guiding a delineated market state. This perspective is concerned with the possibility of shifts in market momentum and representativeness conditioning investor expectations. It is observed that the current market (post-crisis) has changed significantly from the prior operations (despite the diversity observed in prior market states). The dynamics of initial findings required an additional test anchored to the performance of the general capital market and the real economy across time. This context supports the use of a modified CAPM model allowing the consideration of opportunity cost in a space-time dynamic anchored with the consideration of equity, debt, riskless asset and liquidity options as they varied for the representative agents operating per market state.

This paper integrates neoclassical and behavioral economic constructs. Combines asset pricing with prospect theory and allows the calculation of endogenous time-preferences, risk attitudes and formulation and testing of hyperbolic discounting functions.

The research shows that market structure and agent behavior since the financial crisis has changed from the investment and valuation perspectives operating as observed and measured from 1970 up to 2007. In contradiction to the long-term findings of Reinhart and Rogoff (2008), but in compliance with common perspectives and decision heuristics often employed by investors, this time things have changed! Discounting and expected rates of return are dynamic and are hyperbolic and not constant. Returns and investment for property assets are situational (market state-space specific) and offer a distinct asset class, not appropriately estimated by many of the traditional financial models.

Assist in supporting insights to measure in errors and equations that result in inefficient resource allocation and beta discounting that supports the financial crisis created by assets subject to long-term decision needs (delta function).

The paper offers a combination and comparison of neoclassic asset pricing using a modified CAPM (two-pass) approach within the structural frame of Kahneman and Tversky’s (1979) prospect theory. This technique allows the consideration of the effects of present bias, beta-delta functions and the operation of the Allais Paradox in market states that are characterized by gains and losses and thus risk aversion and risk seeking behavior. This ability for differentiation allows for the development of endogenous time-preferences and hyperbolic discounting factors characteristic of commercial property investment.

This paper aims to study the cross section of expected returns on Shari’ah-compliant stocks in Pakistan by using single- and multi-factor asset pricing models.

To estimate cross section of expected returns of Shari’ah-compliant stocks, the study uses capital asset pricing model (CAPM), Fama-French three-factor model and Fama-French five-factor model. Data for the period 2001-2015 on 217 companies are used. For the market portfolio, PSX-100 and Dow Jones Islamic Index for Pakistan are used.

The study could not find empirical support for CAPM using Lintner (1965), Black et al. (1972) and Fama and Macbeth (1973) approach. Nonetheless, the relation between beta and returns is positive in up-market and negative in down-market. The results of Fama-French three-factor and five-factor models suggest that size premium is positive and significant for explaining the cross section of stock returns of small size stocks, whereas value premium is positive and significant for explaining the cross section of returns of high value stocks.

The results suggest that fund managers can use Shari’ah-compliant stocks for portfolio diversification and for offering specialized investments given the positive market excess returns and the existence of size and value premium on Shari’ah-compliant stocks.

This is the first study on Fama-French (2015) five-factor model for Islamic capital markets in Pakistan.

The aim of this study is to investigate the role of efficiency in capital asset pricing. The paper explores the impact of a four-factor model that involves an efficiency factor on the returns of Nasdaq technology firms.

The paper relies on data of 147 firms from July 2007 to June 2017 to examine the impact of efficiency on stock returns. The performances of the capital asset pricing model (CAPM), Fama–French three-factor model and the proposed four-factor model are evaluated based on the time series regression method. The parameters such as the GRS F-statistic and adjusted R² are used to compare the relative performances of all models.

The results show that all factors of the models are found to be valid in asset pricing. Also, the paper provides evidence that the explanatory power of the proposed four-factor model outperforms the explanatory power of the CAPM and Fama–French three-factor model.

Unlike most asset pricing studies, this paper presents a new asset pricing model by adding the efficiency factor to the Fama–French three-factor model. It is documented that the efficiency factor increases the predictive ability of stock returns. Evidence implies that investors consider efficiency as one of the main factors in pricing their assets.

The purpose of this paper is to compare traditional methods of estimating the cost‐of‐equity (capital asset pricing model and Fama and French three‐factor model) with a new approach, implied cost‐of‐equity method, to provide lodging analysts, investors, executives and researchers with a more reliable way to estimate cost‐of‐equity.

The study uses data from publicly traded lodging firms in the USA that provide all necessary financial data for cost‐of‐equity estimation. The data range from 1976 to 2005.

The study finds that the price‐to‐forward earnings (PFE), using the implied cost‐of‐equity (ICE), approach, estimates cost‐of‐equity of publicly‐traded lodging firms more reliably, compared with CAPM.

The study recommends that lodging industry analysts, investors, executives and researchers adopt the ICE approach, especially using the PFE model, to estimate cost‐of‐equity of publicly‐traded lodging firms.

The study attempts to provide a more reliable approach to estimate cost‐of‐equity for publicly‐traded lodging firms, specifically compared with the traditional approach, the CAPM.

The purpose of this paper is to consider the attainment of the corporate objective of the UK Companies Act of 2006 Section 172(1) from the perspective of financial valuations that are reliant on the cost of capital. The cost of capital plays an important role in many of the models and propositions that are routinely used for financial valuation and decision making.

From the perspective of financial valuations that are used to guide decision making that is in accordance with the corporate objective of the UK Companies Act of 2006 Section 172(1), managers and directors require a valid, reliable, and interpretable cost of capital. The theory, models, and propositions of financial management, whether they be investment, financing, or distributions (Sections 829‐853) decisions, are dependent on the cost of capital. This paper has three main tasks. First, the relevant sections of UK corporate statute with regard to the corporate objective need to be identified and presented. Second, a brief review of the function and role of the cost of capital for the valuations upon which investment, financing, and dividend decisions are based, is undertaken to ensure that the role and function of this key financial metric is clearly recognized. Third, since the capital asset pricing model (CAPM) is so widely and exclusively used, often without recourse to other approaches to calculation of the cost of capital, an update of CAPM empirical evidence is undertaken to affirm the 2004 findings and subsequent recommendations by Fama and French that the CAPM is not an acceptable way of calculating the cost of capital.

It is doubtful whether directors, who use an empirically invalid and unreliable valuation model such as the CAPM to calculate the cost of capital, will be able to meaningfully and purposefully make decisions consistent with the “enlightened shareholder value”. Managers and directors need to use approaches to the cost of capital that are valid and can be empirically verified.

This paper recommends that directors of public companies who make decisions using financial valuations that embody the cost of capital should ensure that models other than the CAPM are used; otherwise, they may find it difficult unable to defend challenges to their statutory duty of attaining the corporate objective.

An update of CAPM empirical evidence is undertaken to affirm the findings and subsequent recommendations by Fama and French (2004) that the CAPM is not an acceptable way of calculating the cost of capital.

The nature and extent of our knowledge of stock market efficiency are examined. The development of “efficiency”, as a way of thinking about stock markets, is traced from Roberts (1959) and Fama (1965) onward. The early work successfully introduced competitive economic theory to the study of stock markets and paved the way for a flood of empirical research on the relation between information and stock prices. This literature irreversibly altered our views on stock market behavior. The theory and evidence of seemingly‐rational use of information lay in sharp contrast to prior beliefs. It was associated with a widespread increase in respect for stock markets, financial markets, and markets in general, at the time. Researchers began developing and using a variety of formal models of security prices. Nevertheless, “efficiency” has its limitations, both theoretically (as a way of characterizing markets) and empirically (by stretching the quality of the data, the estimation techniques used, and our knowledge of price behavior in competitive markets). Extensive evidence of anomalies suggests either that the market systematically misprices securities or that the theoretical or empirical limitations are binding, or both. The less interesting research question now is whether markets are efficient, and the more interesting question is how we can learn more about price and transactions behavior in competitive stock markets. The concept of an “efficient stock market” has stimulated both insight and controversy since Fama (1965) introduced it to the financial economics literature. As a construct, “efficiency” models the stock market in terms of the reaction of prices to the flow of information. Like all theory choices, modelling the market in this fashion involved tradeoffs. The benefits included opening the literature to an abundance of high‐quality researchable data, covering a variety of information, and the resulting insights obtained on the role of information in setting prices. The opportunity costs included temporarily closing the literature to alternative ways of viewing stock markets, for example by modelling public information as a homogenous good and thus ignoring factors such as differences in beliefs among investors, differences in information processing costs, and the “animal spirits” that might drive group behavior. The costs also included reliance on particular asset‐pricing models of how an “efficient” market would set prices. Not surprisingly, the ensuing deluge of research has produced some startling evidence, for and against the proposition that financial markets are “efficient”. Strongly‐conflicting views and puzzling anomalies remain. The early evidence seemed unexpectedly consistent with the theory. The theory, and its implications, also seemed clear at the time. After a period that seems short in retrospect, the growing body of evidence in favor of the efficient market hypothesis emerged as one of the most influential empirical areas of economics. Fama's (1970) review described a flourishing, coherent and confident literature. This research had an irreversible effect on our knowledge of and attitude toward stock markets, and financial markets generally. It coincided with an emergence of interest in, and respect for, all markets among economists and politicians, and influenced the worldwide trend toward “liberalizing” financial and other markets. The research consistently appeared to show an unbiased reaction of stock prices to public information. The property of “unbiased reaction” to public information, which formed the basis of the early definitions of “efficiency”, was seen to be an implication of rational, maximizing investor behavior in competitive securities markets (Fama 1965, p.4). Reduced to a basic level, the reasoning was that any systematicallybiased reaction to public information is costlessly publicly observable, and thus provides pure profit opportunities to be competed away. Characterizing the market in terms of its reaction to information is only one of many feasible ways of modelling stock price behavior, but it introduced economic theoryto the empirical studyof stock prices, which had received little serious attention from economists prior to that point. Despite the subsequent spate of anomalies, the early efficiency literature not only adapted standard economic theoryto provide the first formal economic insights into how stock prices behave, but it helped pave the way for an outporing of theoretical and empirical work on stock markets and capital markets in general. Subsequent empirical research was not as consistent with the theory. Evidence of “anomalous” return behavior now is widespread and well‐known. It generallytakes the form of variables (for example, size, day‐of‐the‐week, P/E ratio, market/book value ratio, rank of scaled earnings change, dividend yield) that are significantly but inexplicablyrelated to subsequent abnormal stock returns. Much of this evidence has defied rational economic explanation to date and appears to have caused many researchers to strongly qualify their views on market efficiency. Disagreement has not been not confined to the evidence. The literature has produced a variety of research designs, ranging from the “market model” of Fama, Fisher, Jensen and Roll (FFJR, 1969) to Shiller's (1981a,b) variance‐bounds tests. The very term “efficiency” has engendered controversy: there is a modest literature on precisely what efficiency means, on the role of transaction costs, and on whether efficient markets are logically feasible. Making sense of this literature requires careful definition of “efficiency” in this context and careful analysis of the type of evidence that has been offered in relation to it. This involves an assessment of the strengths and weaknesses of both the theory of efficient markets, as a way of characterizing stock markets, and of the data and research designs used in testing it. Not surprisingly, a mixed conclusion emerges. While the concept of efficient markets was an audacious departure from the comparative ignorance and suspicion among economists of stock markets that preceded it, and provides valuable insights into their behavior, the concept has its limitations, in terms of both its internal logical coherence and its fit with the data. Section 1 ofthis survey sketches the development of the efficient market theory, reviewing the principal contributions in terms of their usefulness in guiding and evaluating empirical research. Section 2 addresses the limitations inherent in what is knowable about stock market efficiency, given the present state of theory about how security prices might behave in an “efficient” market. It argues that there are binding limitations in the theoryof asset pricing, some of which are known and others of which are unknown or even unknowable. These limitations must be borne in mind when choosing whether to interpret the data as evidence of: (1) market efficiency, under the maintained hypothesis that a specific research design, including a specific model of asset pricing used to benchmark price behavior, correctly describes pricing in an efficient market; or (2) the ability of our models and research designs to encapsulate how prices behave in an efficient market, under the maintained hypothesis of efficiency. Against this background, section 3 then provides an assessment of the accomplishments of the theory of stock market efficiency, including an interpretation of the evidence. It focuses on the nature and influence of the evidence and does not attempt to provide a comprehensive literature taxonomy. The final section offers conclusions. The principal conclusion is that the theory of efficient markets has irreversibly enhanced our knowledge of and respect for stock markets (and perhaps for all financial market or even for markets in general) but that, like all theories, it is fundamentally flawed.