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The purpose of this paper is to analyze the mean-variance capital asset pricing model (CAPM) and downside risk-based CAPM (DR-CAPM) developed by Bawa and Lindenberg (1977), Harlow and Rao (1989), and Estrada (2002) to assess which downside beta better explains expected stock returns. The paper also explores whether investors respond differently to stocks that co-vary with declining market than to those of co-vary with rising market.

The paper uses monthly data of closing prices of stocks listed at the Karachi Stock Exchange (KSE). The data cover the period from January 2000 to December 2012. The standard, downside, and upside betas are estimated for different sub-periods,and then,their validity to quantify the risk premium is tested for subsequent sub-periods in a cross sectional regression framework. Though our empirical methodology is similar to that of Fama and MacBeth (1973) for testing the CAPM and the DR-CAPM, our approach to estimate the downside beta is different from earlier studies. In particular, we follow Estrada ' s (2002) suggestions and obtain the correct and unbiased estimation of the downside beta by running the time series regression through origin. The authors carry out the two-pass regression analysis using the generalized method of moment (GMM) in the first pass and the generalized least squares (GLS) estimation method in the second pass.

The results indicate that the mean-variance CAPM shows a negative risk premium for monthly returns of selected stocks. However, the results for the DR-CAPM of Bawa and Lindenberg (1977) and Harlow and Rao (1989) provide evidence of a positive risk premium for the downside beta. In contrast, the DR-CAPM of Estrada (2002) shows a negative risk premium in some sub-periods while the positive premium in the others. By comparing the risk premium for both downside and upside risks in a single-equation framework, the authors show that the stocks that co-vary with a declining market are compensated with a positive premium for bearing the downside risk. Yet, the risk premium for stocks that are negatively correlated with declining market returns is negative for all the three-downside betas in all the examined sub-periods.

The empirical findings of the paper are of great significance for investors for designing effective investment strategies. Specifically, the results help investors to identify an appropriate measure of risk and to construct well-diversified portfolio. The results are also useful for firm managers in capital budgeting decision-making process as they enable them to cost equities appropriately. The results also suggest that the risk-return relationship implied by mean-variance CAPM is negative and therefore this model is not suitable for gauging the risk associated with stocks traded in KSE. Yet, the authors show that DR-CAPM out performs in quantifying the risk premium.

Unlike prior empirical studies, the authors follow Estrada’s (2002) suggestions where downside beta is calculated using regression through origin to find correct and unbiased beta. Departing from the existing literature the authors estimate three different versions of DR-CAPM along with the standard CAPM for comparison purpose. Finally, the authors apply sophisticated econometrics methods that help in lessening the problem of non-synchronous trading and the issue of non-normality of returns distribution.

The beta coefficient used for the cost of equity calculation is at the heart of the valuation process. This study conducts comparative analyses of the classical capital asset pricing model (CAPM) and downside CAPM risk parameters to gain further insight into which risk parameter leads to better performing risk measures at explaining stock returns.

The study conducts a comparative analysis of 16 risk measures at explaining the stock returns of 4531 companies of 20 developed and 25 emerging market index for 2000–2018. The analyses are conducted using both the global and local indices and both USD and local currency returns. Calculated risk measures are analyzed in a panel data setup using a univariate model. Results are investigated in country-specific and model-specific subsets.

The results show that (1) downside betas are better than CAPM betas at explaining the stock returns, (2) both risk measure groups perform better for emerging markets, (3) global downside beta model performs better than global beta model, implying the existence of the contagion effect, (4) high significance levels of total risk and unsystematic risk measures further support the shortfall of CAPM betas and (5) higher correlation of markets after negative shocks such as pandemics puts global CAPM based downside beta to a more reliable position.

The data are limited to the index securities as beta could be time varying.

Results overall provide insight into the cost of equity calculation and emerging market assets valuation.

The framework and methodology enable us to compare and contrast CAPM and downside-CAPM risk measures at the firm level, at the global/local level and in terms of the level of market development.

This study aims to comparatively analyze the systematic, idiosyncratic and downside risk exposure of both Islamic and conventional funds in Pakistan to see which of the funds has higher risk exposure.

The study analyzes different types of risks involved in both Islamic and conventional funds for the period from 2009 to 2016 by using different risk measures. For systematic and idiosyncratic risk single factor CAPM and multifactor models such as Fama French three factors model and Carhart four factors model are used. For downside risk analysis different measures such as downside beta, relative beta, value at risk and expected short fall are used.

The study finds that Islamic funds have lower risk exposure (including total, systematic, idiosyncratic and downside risk) compared with their conventional counterparts in most of the sample years, and hence, making them appear more attractive for investment especially for Sharīʿah-compliant investors preferring low risk preferences.

As this study shows, Islamic mutual funds exhibit lower risk exposure than their conventional counterparts so investors with lower risk preferences can invest in these kinds of funds. In this way, this research provides the input to the individual investors (especially Sharīʿah-compliant investors who want to avoid interest based investment) to help them with their investment decisions as they can make a more diversified portfolio by considering Islamic funds as a mean for reducing the risk exposure.

To the best of the author’s knowledge, this study is the first attempt at world level in looking at the comparative risk analysis of various types of the risks as follows: systematic, idiosyncratic and downside risk, for both Islamic and conventional funds, and thus, provides significant contribution in the literature of mutual funds.

This study seeks to evaluate, in a global context, the impact of Sarbanes Oxley Act on a particular risk measure of importance to investors (risk‐adjusted returns), and two measures of risk due to asymmetry (upside and downside risk). A unique dataset permits a dual evaluation of the law's impact on such measures in leading non‐US economies as well (i.e. “ripple effects”).

Hypotheses are empirically evaluated on a sample (n=712) of the largest US and European firms (control) using daily return data from 1993 through 2009 – one of the most extensive data sets employed in the literature on this topic to date. The reliability of the risk measures is carefully evaluated using multiple approaches, including Fama‐MacBeth regressions. A series of difference‐in‐difference analyses is then employed to empirically assess Sarbanes Oxley's impact on equity risk.

The findings suggest Sarbanes Oxley decreased both risk‐adjusted returns and upside risk, whereas downside risk fails to explain the cross section of returns for the largest US firms. From a global perspective, it is suggested that the enactment of Sarbanes Oxley's in the USA motivated leading non‐US economies to adopt similar regulatory measures, which caused “ripple effects” – e.g. effects similar to those documented in this paper – in leading non‐US economies.

The findings suggest that comprehensive financial regulations, such as Sarbanes Oxley Act, are properly envisaged at the global level, as their impact is not confined to the home country. In an increasingly globalized economy, investor welfare is likely to be influenced – directly as well as indirectly – by economic and financial regulation(s) enacted in foreign economies. Arguably, this suggests the pivotal importance of effective mechanisms of global governance, such that a purely domestic approach to regulation may be short‐sighted. In either case, the findings of this study are entirely relevant if regulators are to consider the broader, global impact of regulation on investor welfare.

This is the first study to empirically analyze, within a global framework, Sarbanes Oxley's risk implications without relying on a series of simple mean variance analyses. Substantive research documents that the methodological approach employed is more precise, reliable as well as “investor relevant”. Furthermore, the authors seek to assess the law's impact on leading non‐US equity markets, a first for the literature. Consequently, this study provides a robust evaluation of the law's (international) impact on firm (equity) risk, making an important contribution to the literature.

The purpose of this paper is to provide the modified measures of risk-adjusted performance evaluation of Malaysian mutual funds using the downside risk concepts, and promote the ability of managers and investors in making logical decisions under the market asymmetry condition.

This study focusses on the performance evaluation of Malaysian mutual funds using eight modified measures of Sharpe, Treynor, M2, Jensen’s α, information ratio (IR), MSR, SPI, and leverage factor. These modified measures use the downside systematic risk and semi-standard deviation instead of systematic risk and conventional standard deviation, respectively, to evaluate the performance of Malaysian mutual funds over the period 2000-2011.

The results indicate that the conventional measures of performance evaluation do not have a crucial influence on the relative evaluation of mutual funds. Three modified measures of Sharpe, Treynor, and M2 have a high correlation with the conventional Sharpe measure and can be used instead of the conventional Sharpe measure. Since, two modified measures of Treynor and M2 display a high rank correlation coefficient with the conventional Treynor measure, they can be replaced with this traditional measure. In addition, two modified IR and MSR measures along with the modified SPI and conventional SPI show very high rank correlation coefficients in relation to each other. The results also document a modified leverage factor less than one for all funds. It can be concluded that the strategy of un-levering the investor’s holding must be followed.

The empirical evidence of this study can be utilized as inputs in the process of decision-making by different types of investors who are interested in participating especially in Malaysian stock market and generally in global stock market under the market asymmetry condition.

The contribution of this study is to modify five measures of M2, IR, MSR, FPI, and leverage factor in the downside risk framework which is a work on a rather under-researched area.

This paper aims to identify and examine the determinants of downside systematic risk in Australian listed property trusts (LPTs).

Capital asset pricing model (CAPM) and lower partial moment‐CAPM (LPM‐CAPM) are employed to compute both systematic risk and downside systematic risk. The methodology of Patel and Olsen and Chaudhry et al. is adopted to examine the determinants of systematic risk and downside systematic risk.

The results confirm that systematic risk and downside systematic risk can be individually identified. There is little evidence to support the existence of linkages between systematic risk in Australian LPTs and financial/management structure determinants. On the other hand, downside systematic risk is directly related to the leverage/management structure of a LPT. The results are also robust after controlling for the LPTs' investment characteristics and varying target rates of return.

Investors and real estate analysts should conscious with the higher returns from high leverage and internally managed LPTs. Although there is no evidence that these higher returns are related to higher systematic risk, there could be the compensation for higher downside systematic risk.

This study provides invaluable insights into the management of real estate risk in Australian LPTs with implications for REITs in other countries. Unlike previous studies of systematic risk in REITs or LPTs, this is the first study to assess downside systematic risk and explore the determinants of downside systematic risk in LPTs.

This paper aims to evaluate the risk‐adjusted performance of the management styles of Malaysian mutual funds using nine modified performance evaluation measures generated by the maximum drawdown risk measure (M‐DRM) based on the modern portfolio theory. The purpose is to report the findings in a manner which is realizable by the average investors and portfolio managers.

This paper evaluates the performance of more than 400 Malaysian mutual funds using risk‐adjusted returns over the two sub‐periods of 2000‐2005 and 2006‐2011. The M‐DRM, as a different measure from downside risk, is applied to improve nine risk‐adjusted performance measures of Sortino, Treynor, M‐squared, Jensen's alpha, information ratio (IR), MSR, upside partial ration (UPR), FPI, and leverage factor. It proposes a new single‐factor model to test the maximum drawdown beta and alpha in the M‐DRM framework.

The evidence clearly indicates that the replacement framework in terms of MDB, the maximum drawdown beta, and the maximum drawdown CAPM can be replaced by the conventional frameworks in terms of MVB, beta, and the CAPM and also MSB, downside beta, and D‐CAPM for modifying nine performance evaluation measures from the management styles of Malaysian mutual funds.

The research evidence reported in this paper can be applied as input in the process of decision making by small and average investors and portfolio managers who are seeking the possibility of participating in the global stock market through mutual funds.

This paper is the first study to estimate a new regression model in the M‐DRM framework to evaluate the performance of Malaysian mutual funds. In addition, it proposes nine modified performance evaluation measures in the M‐DRM framework for the first time.

The purpose of this paper is to propose a new and improved version of arbitrage pricing theory (APT), namely, downside APT (D-APT) using the concepts of factors’ downside beta and semi-variance.

This study includes 163 stocks traded on the Malaysian stock market and uses eight macroeconomic variables as the dependent and independent variables to investigate the relationship between the adjusted returns and the downside factors’ betas over the whole period 1990-2010, and sub-periods 1990-1998 and 1999-2010. It proposes a new version of the APT, namely, the D-APT to replace two deficient measures of factor's beta and variance with more efficient measures of factors’ downside betas and semi-variance to improve and dispel the APT deficiency.

The paper finds that the pricing restrictions of the D-APT, in the context of an unrestricted linear factor model, cannot be rejected over the sample period. This means that all of the identified factors are able to price stock returns in the D-APT model. The robustness control model supports the results reported for the D-APT as well. In addition, all of the empirical tests provide support the D-APT as a new asset pricing model, especially during a crisis.

It may be worthwhile explaining the autocorrelation limitation between variables when applying the D-APT.

The framework can be useful to investors, portfolio managers, and economists in predicting expected stock returns driven by macroeconomic and financial variables. Moreover, the results are important to corporate managers who undertake the cost of capital computations, fund managers who make investment decisions and, investors who assess the performance of managed funds.

This paper is the first study to apply the concepts of semi-variance and downside beta in the conventional APT model to propose a new model, namely, the D-APT.

This study aims to investigate the association between board diversity and systematic risk. The theoretical framework used in this study is based on agency and resource dependency theories.

Using a panel data set of 788 firms listed in the Morgan Stanley Capital International (MSCI) Emerging Markets index from 2015 to 2020, the authors apply Panel-Corrected Standard Error estimation method to test the three proposed hypotheses and the two-stage least squares method is adopted for the endogenous test.

The results suggest that board-specific skills diversity (BSSD) and board independence (BIND) have a negative impact on systematic risk. On the other hand, board gender diversity does not affect systematic risk. The findings reinforce the relevance of board diversity for reducing systematic risk and offer valuable insights for policymakers and investors, suggesting that the presence of directors with specific skills and independent directors could reduce firms’ systematic risk.

The study extends the scope of agency and resource dependency theories by suggesting that the BSSD and BIND reduce agency costs and bring critical resources to the firm’s survival.

The findings support policymakers and managers in reducing systematic risk. In addition, the results demonstrate the importance of policies that encourage board diversity and BIND.

The study demonstrates how companies can reduce systematic risk through board diversity and BIND.

To the best of our knowledge, this is the first study to investigate the association between board diversity and systematic risk only in emerging markets.

The purpose of this paper is to introduce an augmented high-order capital asset pricing model (AH-CAPM) as a new risk-based model to price stocks.

The AH-CAPM is defined as a linear model with high-order marginal moments and co-moments from the joint distributions of the sorted stock portfolio returns and the market return.

The performance of the AH-CAPM is tested in the Chinese and US stock markets. Empirical results show that the high-order marginal moments and co-moments from the joint distributions in AH-CAPM contain the risk and return information implied by the Fama–French factors, indicating it as a better risk measurement. Moreover, the AH-CAPM performs better than the Fama–French three-factor model and the Carhart four-factor model in both the Chinese and US stock markets.

Overall, this study introduces a new asset pricing model with better measurements to incorporate risk information in the stock market.