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Our result of this paper aims to indicate that the beta pricing formula could be applied in a long-term model setting as well.

In this paper, we show that the capital asset pricing model can be derived from a three-period general equilibrium model.

We show that our extended model yields a Pareto efficient outcome.

The capital asset pricing model (CAPM) model can be used for pricing long-lived assets.

Long-term modelling and sustainability can be modelled in our setting.

Our results were only known for two periods. The extension to 3 periods opens up a large scope of applicational possibilities in asset pricing, behavioural analysis and long-term efficiency.

A stylized fact in finance literature is the belief in positive relationship between ex ante return and risk. Hence, a rational investor, by utility preference axiom can only consider committing fund in asset which promises commensurate higher return for higher risk. Questions have been asked as to whether this holds true across securities, sectors and markets. Empirical evidence appears less convincing, especially in developing markets. Accordingly, the author investigates the nature of reward for taking risk in the Nigerian Capital Market within the context of individual assets and markets.

The author employed ex post design to collect weekly stock prices of firms listed on the Premium Board of Nigerian Stock Exchange for period 2014–2022 to attempt to answer research questions. Data were analyzed using a unique M Vec TGarch-in-Mean model considered to be robust in handling many assets, and hence portfolio management.

The study found that idea of risk-expected return trade-off is perhaps more general than as depicted by traditional finance literature. The regression revealed that conditional variance and covariance risks reveal minimal or no differences in sign and sizes of coefficients. However, standard errors were also found to be large suggesting somewhat inconclusive evidence of existence of defined incentive structure for taking additional risk in the market.

In terms of choice of methodology and outcomes, this research adds substantial value to body of knowledge. The adapted multivariate model used in this paper is a rare approach especially for management of portfolios in developing markets. Remarkably, the research found empirical evidence that positive risk-expected return trade-off, as known in mainstream literature, is not supported especially using a typical developing country data.

This study analyzes the static and dynamic risk spillover between US/Chinese stock markets, cryptocurrencies and gold using daily data from August 24, 2018, to January 29, 2021. This study provides practical policy implications for investors and portfolio managers.

The authors use the Diebold and Yilmaz (2012) spillover indices based on the forecast error variance decomposition from vector autoregression framework. This approach allows the authors to examine both return and volatility spillover before and after the COVID-19 pandemic crisis. First, the authors used a static analysis to calculate the return and volatility spillover indices. Second, the authors make a dynamic analysis based on the 30-day moving window spillover index estimation.

Generally, results show evidence of significant spillovers between markets, particularly during the COVID-19 pandemic. In addition, cryptocurrencies and gold markets are net receivers of risk. This study provides also practical policy implications for investors and portfolio managers. The reached findings suggest that the mix of Bitcoin (or Ethereum), gold and equities could offer diversification opportunities for US and Chinese investors. Gold, Bitcoin and Ethereum can be considered as safe havens or as hedging instruments during the COVID-19 crisis. In contrast, Stablecoins (Tether and TrueUSD) do not offer hedging opportunities for US and Chinese investors.

The paper's empirical contribution lies in examining both return and volatility spillover between the US and Chinese stock market indices, gold and cryptocurrencies before and after the COVID-19 pandemic crisis. This contribution goes a long way in helping investors to identify optimal diversification and hedging strategies during a crisis.

In this study, we investigate what drives the MAX effect in the South Korean stock market. We find that the MAX effect is significant only for overpriced stocks categorized by the composite mispricing index. Our results suggest that investors' demand for the lottery and the arbitrage risk effect of MAX may overlap and negate each other. Furthermore, MAX itself has independent information apart from idiosyncratic volatility (IVOL), which assures that the high positive correlation between IVOL and MAX does not directly cause our empirical findings. Finally, by analyzing the direct trading behavior of investors, our results suggest that investors' buying pressure for lottery-like stocks is concentrated among overpriced stocks.

This study seeks to examine the relationship between macroeconomic shock indicators, namely geopolitical risk (GPR), global economic policy uncertainty (GEPU) and financial stress (FS), and returns as well as volatilities on seven carefully selected stock markets in Africa. Specifically, the study intends to unravel the co-movement and interdependence between the respective macroeconomic shock indicators and each of the stock markets under consideration across time and frequency.

This study employed wavelet coherence approach to examine the strength and stability of the relationships across different time scales and frequency components, thereby providing valuable insights into specific periods and frequency ranges where the relationships are particularly pronounced.

The study found that GEPU, Financial Stress (FS) and GPR failed to induce significant influence on African stock market returns in the short term (0–4 months band), but tend to intensify in the long-term band (after 6th month). On the contrary, stock market volatilities exhibited strong coherence and interdependence with GEPU, FSI and GPR in the short-term band.

This study happens to be the first of its kind to comprehensively consider how the aforementioned macro-economic shock indicators impact stock markets returns and volatilities over time and frequency. Further, none of the earlier studies has attempted to examine the relationship between macro-economic shocks, stock returns and volatilities in different crisis periods. This study is the first of its kind in to employ data spanning from May 2007 to April 2023, thereby covering notable crisis periods such as global financial crisis (GFC) and the COVID-19 pandemic episodes.

Given the cryptocurrency market boom in recent years, this study aims to identify the factors influencing cryptocurrency pricing and the major gaps for future research.

A systematic literature review was undertaken. Three databases, Scopus, Web of Science and EBSCOhost, were used for this review. The final analysis comprised 88 articles that met the eligibility criteria.

The influential factors were identified and categorized as supply and demand, technology, economics, market volatility, investors’ attributes and social media. This review provides a comprehensive and consolidated view of cryptocurrency pricing and maps the significant influential factors.

This paper is the first to systematically and comprehensively review the relevant literature on cryptocurrency to identify the factors of pricing fluctuation. This research contributes to cryptocurrency research as well as to consumer behaviors and marketing discipline in broad.

We propose a risk factor for idiosyncratic entropy and explore the relationship between this factor and expected stock returns.

We estimate a cross-sectional model of expected entropy that uses several common risk factors to predict idiosyncratic entropy.

We find a negative relationship between expected idiosyncratic entropy and returns. Specifically, the Carhart alpha of a low expected entropy portfolio exceeds the alpha of a high expected entropy portfolio by −2.37% per month. We also find a negative and significant price of expected idiosyncratic entropy risk using the Fama-MacBeth cross-sectional regressions. Interestingly, expected entropy helps us explain the idiosyncratic volatility puzzle that stocks with high idiosyncratic volatility earn low expected returns.

We propose a risk factor of idiosyncratic entropy and explore the relationship between this factor and expected stock returns. Interestingly, expected entropy helps us explain the idiosyncratic volatility puzzle that stocks with high idiosyncratic volatility earn low expected returns.

We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis demonstrates that, under these conditions, the perpetual put option consistently commands a higher price during periods of high volatility compared to those of low volatility. Moreover, we establish that the optimal exercise boundary is lower in high-volatility regimes than in low-volatility regimes. Additionally, we develop an analytical framework to describe American puts with an Erlang-distributed random-time horizon, which allows us to propose a numerical technique for approximating the value of American puts with finite expiry. We also show that a combined approach involving randomization and Richardson extrapolation can be a robust numerical algorithm for estimating American put prices with finite expiry.

This study delves into the nuanced implications of short-sale constraints on stock prices within the context of stock market efficiency. While existing research has explored this relationship, inconsistencies persist in their findings. The purpose of this study is to conduct a comprehensive review of literature to elucidate the reasons behind these disparities.

A systematic review of existing theoretical and empirical studies was conducted following the PRISMA method. The analysis centered on discerning the factors contributing to the divergence in projected stock prices due to these constraints. Key areas explored included assumptions related to expectations homogeneity, revisions, information uncertainty, trading motivations and fluctuations in supply and demand of risky assets.

The review uncovered multifaceted reasons for the disparities in findings regarding the influence of short-sale constraints on stock prices. Variations in assumptions related to market expectations, coupled with fluctuations in perceived information uncertainty and trading motivations, were identified as pivotal factors contributing to differing projections. Empirical evidence disparities stemmed from the use of proxies for short-sale constraints, varied sample periods, market structure nuances, regulatory changes and the presence of option trading.

This study emphasizes the significance of not oversimplifying the impact of short-sale constraints on stock prices. It highlights the need to understand these effects within the broader context of market structure and methodological considerations. By delineating the intricate interplay of factors affecting stock prices under short-sale constraints, this review provides a nuanced perspective, contributing to a more comprehensive understanding in the field.

The purpose of this study is to examine herd behaviour under different market conditions, examine the potential impact of the firm size and stock characteristics on this relationship, and explore how herding affects market prices in the German market.

The authors apply a method that does not rely on theoretical models, thus eliminating the biases inherent in their application. This technique is based on the assumption that macro herding manifests itself in the synchronicity (comovement) of stock returns.

The study’s findings show that herding is more pronounced in down markets and is more pronounced when market returns reach extreme levels. Additionally, the authors have found that there is stronger herding among large companies compared to small companies, and that stock characteristics considered have no effect on the degree of macro herding. Results also suggest that the contemporaneous market-wide information drives macro herding and that macro herding facilitates the incorporation of market-wide information into prices.

The study’s results strongly support the idea of directional asymmetry, which holds that stocks react quickly to negative macroeconomic news while small stocks react slowly to positive macroeconomic news. Additionally, the study’s results suggest that the contemporaneous market-wide information drives macro herding and that macro herding facilitates the rapid incorporation of market-wide information into prices.

To the best of the researchers’ knowledge, this is the first study that examines macro herding for a major financial market using a herding measure based on the co-movement of returns that does not rely on theoretical models.