Arbitrage and Diversification in a General Equilibrium Asset Economy

Continuous Equilibrium in Affine and Information-Based Capital Asset Pricing Models

In this chapter we employ SD rules to prove that the CAPM is theoretically intact in a wide range of frameworks corresponding to the assumption about the distribution of returns and the length of the investment horizon. This is a surprising integration of the MV and SD paradigms, as these two paradigms represent two distinct branches of expected utility, each implying a different technique for portfolio investment selection. Each paradigm has its pros and cons. The obvious advantage of the MV approach is that it provides a simple and elegant method for determining the optimal diversification among risky assets which is necessary in establishing the Capital Asset Pricing Model (CAPM) (see Sharpe and Lintner). The main disadvantage of the MV paradigm is that it relies on the assumption of normal distribution of returns (or Elliptic distribution family, where the normal distribution belongs to this family), an assumption not needed for the employment of the SD rules. The normality assumption is obviously inappropriate for most assets traded in the stock market because asset prices cannot drop below zero (−100 % rate of return) whereas the normal distribution is unbounded. As the equilibrium risk-return relationship implied by the CAPM has very important theoretical and practical implications, it has been developed under other frameworks which do not assume normality. Levy has shown that technically the CAPM holds even if all possible mixes of distributions are log-normal (bounded from below by zero). However, this approach has also a drawback as with discrete time models, a new problem emerges: if x and y are log-normally distributed, a portfolio z, where z = α x + (l–α)y, will no longer distribute log-normally. Merton assumes continuous-time portfolio with infinite portfolio revisions and shows that under this assumption, the terminal wealth will be log-normally distributed and the CAPM will hold in each single instantaneous period. By employing the continuous portfolio revision, the nagging problem that the sum of log-normal distributions is not log-normal, which characterizes discrete models disappears. However, the disadvantage of the continuous time model is that the CAPM result breaks down if even minor transaction costs, no matter how small, are incorporated.

Therefore, this research can more deeply reveal the risk factor cognition and evaluation mechanism in the asset pricing theory. Although classic structures such as capital Asset Pricing model (CAPM) and arbitrage pricing theory (APT) have built a solid theoretical foundation, they show limitations in practical verification. These models are usually based on the market efficiency hypothesis, only include a few risk factors, and fail to fully analyze the full dynamics of stock price changes. In view of the increasing complexity and dynamic evolution of financial markets, uncovering more precise risk factors has become a key issue at the academic frontier. At the same time, we also pay attention to the role of some emerging risk factors, such as liquidity risk, credit risk and macroeconomic conditions. This study uses statistical and econometric methods to rigorously identify and quantify these potential risk impacts. By using panel data regression analysis, principal component analysis (PCA), and other machine learning algorithms, we are able to extract the key factors affecting asset prices from a large amount of historical data. Further, through empirical analysis, we evaluate the importance of different factors in different market conditions and their impact on the return on assets. The analysis shows that in addition to the usual market risk considerations, the expected stock returns are also significantly affected by economies of scale, book-to-market value ratio and momentum effects. And core macroeconomic indicators, such as interest rates and inflation, have a significant impact on asset valuations. Especially in the period of financial turbulence, the effect of liquidity risk and credit risk is particularly significant and urgent. The insights from this study can thus promote a deeper understanding of the nature of asset price volatility and further lay the theoretical foundation for a more resilient investment allocation. These insights are also useful for regulators to develop more precise market supervision strategies in order to promote the sound progress of the financial system.

This thesis consists of three empirical studies on what drives stock market dynamics. The first empirical study explores the effect of crude oil price changes on the stock market returns of oil-exporting countries and oil-importing countries as well as those of a number of global stock indices. Using the Ordinary Least Squares (OLS) approach as well as the more robust Quantile Regression (QR) approach to explore the relationship between crude oil and stock market dynamics. The empirical findings suggest that the QR approach provides further insights compared to the OLS approach. For instance, the QR approach is able to identify specific quantiles where a significant relation exists. In particular crude oil price increases tend to have a negative impact on the stock market returns for some oil-exporting countries (such as Mexico, Iraq, Ecuador, and Venezuela) and a positive effect for other oil-exporting countries (such as Brazil and Algeria). However, the OLS approach suggests that these relationships are insignificant at the level of the mean. Overall, the empirical findings confirm that the QR approach can reveal more information about the relationship between crude oil price changes and stock market return across different quantiles of their distribution.The second study explores the extent to which implied volatility extracted from commodity markets and developed stock markets can predict the implied volatility of stock markets in BRICS countries. Using daily data from 2011 to 2016 and employing the newly developed Bayesian Graphical Vector Autoregressive (BGVAR) model of Ahelegbey et al. (2016) which does not suffer from over-parameterization and the identification problems associated with traditional VAR frameworks, this study finds that implied volatilities extracted from global and regional stock markets have a significant predictive power over the implied volatilities in BRICS stock markets. However, the predictive power of implied volatility from commodity markets are significant only in the case of South Africa.The third empirical study analyses the relationship between illiquidity and stock market returns in the G7 and BRICS countries. More specifically, this study explore the extent to which the Amihud (2002) illiquidity measure can improve the explanatory power of three commonly used asset pricing models, namely the Capital Asset Pricing Model (CAPM), the Fama-French three-factor model and the Carhart four-factor model. The empirical analysis is based on 15 years of monthly data on the returns of seven stock portfolios: 100 largest companies (Largest100), small value (S/V), small neutral (S/N), small growth (S/G) stocks, big value (B/V) stocks, big neutral (B/N) stocks, and big growth (B/G) stocks. The findings suggest that incorporating illiquidity as an additional factor results in a significant improvement in the explanatory power of these asset pricing models across several of the sample countries (8 countries in the case of the CAPM and Carhart four-factor model, and 6 countries in the case of the Fama-French three-factor model). For example, in the US adding illiquidity to the CAPM leads to an increase of the goodness of fit by 2.6% in the B/V portfolio, and for the Fama-French three-factor model the goodness of fit increases by up to 3% in all portfolios Moreover, the goodness of fit increases in all portfolios in the US by adding illiquidity to the Carhart four-factor model, with an up to 36% increase in the B/N portfolio.

This paper offers an alternative method for estimating expected returns. The proposed reward beta approach performs well empirically and is based on asset pricing theory. The empirical section compares this approach with the capital asset pricing model (CAPM) and the Fama–French three‐factor model. In out‐of‐sample testing, both the CAPM and the three‐factor model are rejected. In contrast, the reward beta approach easily passes the same test. In robustness checks, the reward beta approach consistently outperforms both the CAPM and the three‐factor model.

This chapter discusses theoretical foundations and empirical evidence for the most prominent asset pricing theory: the Capital Asset Pricing Model (CAPM). It represents a pricing model for risky assets. The CAPM has been extended to the multi– factor model (MFM) and arbitrage pricing theory (APT). The motivation of the latter has been to overcome the problems associated with the market portfolio in the CAPM by introducing a multi–factor approach. The subsequent chapter is kept simple and refers to the CAPM only. In some additional remarks crucial assumptions regarding investors’ preferences and stock return distributions are relaxed. Currently the debate whether exact pricing restrictions in the MFM and APT imply the return to the “good old CAPM” is still going on. By introducing state dependent relationships as well as general nonlinearities in a CAPM model one can try to unify the different views but we will not elaborate on such extensions. A more extensive treatment of static and dynamic portfolio theories is given in Part VI of the book.

D UE to Sharpe (1964), Lintner (1965) and Mossin (1966), the Capital Asset Pricing Model (CAPM) has been employed to estimate systematic and performance measure and to predict the risk-return relationship. The predictive ability of this model has been examined by Friend and Blume (FB) (1973), Black, and Scholes (BJS) (1972) and Blume and Friend (BF) (1970). They have concluded that the empirical results obtained from the CAPM are significantly different from the ex ante expectation of this model. The effects of investment horizon on the estimate of the systematic were first investigated by (1969). Based upon the instantaneous systematic concept, he concluded that the logarithmic linear form of the CAPM can be used to eliminate the effects of time horizon on the estimated systematic risk; in other words, the basic specification for the CAPM is a Cobb-Douglas type functional form. Levy (1972) has shown that the assumption of a holding period that is different from the true investment horizon will lead to systematic bias of the performance measure index. Recently, Cheng and Deets (CD) (1973) have shown that the logarithmic linear form of the CAPM not only implies a linear relationship but produces an instantaneous risk, dependent upon the length of observed horizon.' In addition, they proposed a new instantaneous systematic entitled the Cheng-Deets instantaneous systematic risk to substitute for the Jensen instantaneous Neither nor CD has ever investigated the effects of finite investment horizon when market equilibrium is not instantaneous. The main purposes of this paper are to derive two alternative functional forms for the CAPM, which will explicitly include the investment horizon parameter, to improve the explanatory power of the CAPM, and to reduce the bias of the estimated systematic risk. In the second section the risk-return relationship is reexamined under the assumptions that true investment horizon is either observable or not observable. In the third section both likelihood ratio and constant elasticity of substitution (CES) function methods are proposed to derive a testable generalized CAPM in accordance with the assumption that all investors have identical investment horizons.2 In the fourth section models derived in the third section are related to Merton's (1970, 1973) continuous time models and Fama and Macbeth's (1973, 1974) empirical work, which supports the linearity of CAPM. In the fifth section, a set of sample data from the New York Stock Exchange (NYSE) during 19671972 will be employed to estimate the related parameters of the nonlinear CAPM being derived in this paper. In addition, the results obtained from nonlinear CAPM will be compared with those obtained from the linear CAPM. Finally, in the last section, the results of this paper will be summarized.

Since Sharpe (1964) derived the CAPM, it has been the benchmark of asset pricing models and has been used to calculate the cost of equity capital and other asset pricing determinations for more than four decades. Many researchers have tried to relax the original assumptions and generalize the static CAPM. In addition, Merton (1973) and Black (1976) have generalized the static CAPM in terms of intertemporal CAPM. In this chapter, we survey the important alternative theoretical models of capital asset pricing and provide a complete review of the evolution of both static and intertemporal asset pricing models. We also discuss the interrelationships among these models and suggest several possible directions for future research. In addition, we review the asset pricing tests in terms of individual companies’ data instead of portfolio data. Our results might be used as a guideline for future theoretical and empirical research in capital asset pricing.

In a competitive market, what should the rate of return on insurance companies’ equity be? What premiums should insurance companies charge? Traditionally, the answers to these questions have been based on actuarial and accounting concepts.1 More recently financial models of the insurance firm have been developed. Ferrari (1968) suggested a descriptive model which allowed an algebraic expression for the rate of return on equity as a function of the premiums charged to be derived. Combining this with the capital asset pricing model (CAPM) meant that an equilibrium value for the return on equity and the corresponding level of premiums could be found. This model is known as the insurance CAPM.2 The development of other asset pricing models in finance has also led to insurance counterparts. Thus the Arbitrage Pricing Theory, and option pricing models have been used to derive the return on equity and the level of premiums.3 Although the approaches based on asset pricing models have advantages compared to those based on traditional actuarial and accounting concepts, they are not ideal. One of the most important problems is that they are not well suited for finding premiums when an insurance company has multiple divisions. The difficulty is that it is not clear how earnings on reserves should be allocated among the various divisions of the firm.

The specification of the stochastic process for stock prices is an important assumption underlying most equilibrium and option-pricing models in modern finance. This is particularly true of the continuous-time capital asset pricing models where it is assumed that asset prices follow diffusion processes with continuous sample paths (see Merton 1973a; Breeden 1979; Grossman and Shiller 1982). The extent to which the implications of these models generalize to discontinuous sample paths is an unanswered question in theoretical finance. However, the answer to this question is of more than just theoretical interest since accumulated empirical evidence appears to be inconsistent with the continuous sample path assumption (see Rosenberg 1972; Oldfield, Rogalski, and Jarrow 1977; Rosenfeld 1982). One purpose of this paper is to provide some answers to this question. We do this by extending Merton's (1973a) intertemporal asset pricing model, in the special case of a constant investment opportunity set, to include discontinuous sample paths for asset prices. The constant investment opportunity set assumption is imposed because we are interested in obtaining sufficient conditions under which an instantaneous capital asset pricing model (CAPM) results. The extension of our model to a stochastic opportunity set is discussed briefly in the text. This paper investigates an economy where stock prices follow a jump-diffusion process. The first part of the analysis derives a sufficient condition under which an instantaneous CAPM will characterize equilibrium expected returns. The sufficient condition is that the jump component of a stock's return must be unsystematic and diversifiable in the market portfolio. The second part of the paper is an empirical investigation of the satisfaction of this condition. The evidence is seen to be inconsistent with the satisfaction of this hypothesis, that is, the market portfolio appears to contain a jump component.

This study aims to detect herding behavior during the COVID-19 pandemic, compare investor trading behavior pre (2015 to 2019) and post (2020 to 2022) pandemic, and examine how investors react in panic and uncertainty. Current asset pricing theory states that cross-sectional returns should reflect systematic risks like stock prices, where Capital Asset Pricing Model (CAPM) betas are often viewed as return volatility, but they do not account for price volatility. To reflect the uncertainty, CAPM and Asset pricing theory are not sufficient so the gap is filled by behavioral finance that examines investors’ personalities and trading behaviors to explain market swings. It examines which stock price data influences investors’ decisions that is depicted by herding behavior. People “herd” when they do not make individual decisions. Unpredictability, worry, and panic often cause such behavior and COVID-19 epidemic worsened such factors that hurt global economy and stock markets. Financial data cannot reveal herding behavior for which two models, Cross-sectional standard deviation (CSSD) and Cross-sectional absolute deviation (CSAD), acknowledged by Christie and Huang (1995), are used to identify herding behavior in Bangladesh’s capital market during the COVID-19 pandemic. CSSD uses standard deviation to understand investor herd behavior, while CSAD uses absolute deviation. As mentioned in the literature review from the journal of Christie and Huang (1995) that the CSSD model and CSAD model will provide a conflicting result, the above finding shows the same because in CSSD model, no herding behavior is found but in the CSAD model, the herding behavior is found in the bullish markets for the year 2020 and in the bearish markets from 2015 to 2022.

Failure of Asset Pricing Models: Transaction Cost, Irrationality, or Missing Factors

Arbitrage Theory has turned out to be a fundamental tool in analysing financial markets and financial decisions. Financial decision making benefits from Arbitrage Theory by the concept of valuation by arbitrage. Loosely speaking, valuation by arbitrage enables us to reveal existing riskless arbitrage opportunities in cases a choice has to be made among two or more financial decision alternatives. The underlying concept will be explained at a later stage. Arbitrage Theory itself is concerned with the analysis of financial markets and theories thereof. It can be seen as a theoretical basis of any reasonable theory of financial asset prices. The following introduction is to show that all the capital asset pricing models advanced in the literature — we will, of course, consider a sample only — share a common structural property. At a later stage we will see that this common property can be deduced from a very simple model of those financial markets which do not provide risk-free arbitrage opportunities.KeywordsAsset PriceRisky AssetFinancial AssetCapital Asset Price ModelCommon MarketThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Asset pricing theories provide an understanding of the risk factors that determine the price of assets. The identification of risk factors assists investors in seeking out profitable investment opportunities. The difficulty in observing how investors identify such opportunities and how they react to it has largely restricted the literature from determining the factors that matter to an investor. There is a paucity of empirical studies that give insight into the investment decision-making process of an investor. Some of the recent studies that seek to fill this gap have used mutual fund flows to infer which asset pricing model investors use. The fund flows are used as a measure of investors’ response for the identification of a positive net present value investment opportunity. These studies suggest that the Capital Asset Pricing Model (CAPM) is closest to the asset pricing model used by investors in the US market. Taking this literature forward, we enquire whether investors from Indian markets exhibit a similar pattern when making investment decisions. Using the fund flows to actively managed equity schemes, we have investigated the risk factors that matter for mutual fund investors in India for the period from April 2006 to December 2019. We use alternative performance measure and then evaluate the sensitivity of fund flows to each of the performance measures. Our results suggest that investors assess the performance of competing investment opportunities based on naïve measures. Further, though uncertainty has a negative impact on fund flow, the flow–performance relation is not sensitive to the level of uncertainty.

Estimating the cost of equity for the regulated energy and infrastructure sectors in India