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Many studies have shown that from a theoretical and empirical point of view, downside risk-based measures of risk are better than the traditional ones. Despite academic appeal and practical implications, downside risk has not been thoroughly examined in markets outside developed country markets. Using downside beta as a measure of downside risk, this study examines the relationship between downside beta and stock returns in Indian equity market, an emerging market with unique investor, asset and market characteristics.

This is an empirical study done by using ranked portfolio return analysis and regression analysis methodologies.

The study results show that downside risk, as measured by downside beta, is distinctly priced in the Indian equity market. There is a direct positive relationship between downside beta and contemporaneous realized returns, indicating a premium for downside risk. Downside risk carries a higher weightage than upside potential in the aggregate return of the stock portfolios. Downside beta is a better measure of systematic risk than conventional market beta and downside coskewness.

The empirical results support the adoption of downside beta in practice and provide a case for replacing traditional beta with downside beta in asset pricing applications, trading and investment strategies, and capital allocation decision-making.

This is one of the first in-depth studies examining downside beta in Indian equity markets using a broad sample of individual stock returns covering a wide time range of 22 years. To the best of our knowledge, this study is the first one to compare downside beta and downside coskewness using individual stock data from the Indian equity market.

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 paper aims to investigate patterns in UK stock returns related to downside risk, with particular focus on stock returns during financial crises.

First, stocks are sorted into five quintile portfolios based on the relevant beta values (classic beta, downside beta and upside beta, calculated by the moving window approach). Second, patterns of portfolio returns are examined during various sub-periods. Finally, predictive powers of beta and downside beta are examined.

The downside risk is observed to have a significant positive impact on contemporaneous stock returns and a negative impact on future returns in general. In contrast, an inverse relationship between risk and return is observed when stocks are sorted by beta, contrary to the classic literature. UK stock returns exhibit clear time sensitivity, especially during financial crises.

This paper focuses on the impact of the downside risk on UK stock returns, assessed via a comprehensive sub-period analysis. This paper fills the gap in the existing literature, in which very few studies examine the time sensitivity in relation to the downside risk and the risk-return anomaly in the UK stock market using a long sample period.

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.

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 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 risk-return trade-off in the Indian equity market at both the aggregate equity market level and in the cross-sections of stock return using alternative risk measures.

The study uses weekly and monthly data of 3,085 Bombay Stock Exchange-listed stocks spanning over 20 years from January 2000 to December 2019. The study evaluates the risk-return trade-off at the aggregate equity market level using the value-weighted and the equal-weighted broader portfolios. Eight different risk proxies belonging to the conventional, downside and extreme risk categories are considered to analyse the cross-sectional risk-return relationship.

The results show a positive equity premium on the value-weighted portfolio; however, the equal-weighted portfolio of these stocks shows an average return lower than the return on the 91-day Treasury Bills. The inverted size premium mainly causes this anomaly in the Indian equity market as the small stocks have lower returns than big stocks. The study presents a strong negative risk-return relationship across different risk proxies. However, under the subsample of more liquid stocks, the low-risk anomaly regarding other risk proxies becomes moderate except the beta-anomaly. This anomalous relationship seems to be caused by small and less liquid stocks having low institutional ownership and higher short-selling constraints.

The findings have important implications for investors, managers and practitioners. Investors can incorporate the effects of different highlighted anomalies in their investment strategies to fetch higher returns. Managers can also use these findings in their capital budgeting decisions, resource allocations and other diverse range of direct and indirect decisions, particularly in emerging markets such as India. The findings provide insights to practitioners while valuing the firms.

The study is among the earlier attempts to examine the risk-return trade-off in an emerging equity market at both the aggregate equity market level and in the cross-sections of stock returns using alternative measures of risk and expected returns.

Previous studies have shown that stock returns bear a premium for downside risk versus upside potential. We develop a new risk measure which scales the traditional CAPM beta by the ratio of the upside beta to the downside beta, thereby incorporating the effects of both upside potential and downside risk. This “modified” beta has substantial explanatory power in standard asset pricing tests, outperforming existing measures, and it is robust to various alternative modeling and estimation techniques.

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.