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Which GRS Statistic Is Appropriate for Cross-Sectional Tests of Linear Multi-Factor Pricing Models?
No full textFama and French (2015, 2017) introduce the five-factor asset pricing model in the former paper and test their model on data from international financial markets in the latter paper. Each paper tests whether the five-factor model represents returns by way of the Gibbons, Ross and Shanken (1989) (hereafter GRS) statistic. That statistic's null hypothesis jointly sets all cross-section intercepts (alpha) to zero. The GRS statistic developed and presented in equation (4) on page 1124 of GRS (1989) is a cross-section test of the one-factor capital asset pricing model. Using the same data as Fama and French (2015, 2017), we show that the latter authors did not use the GRS (1989) statistic given in equation (4) on page 1124. In fact, they used a version of that statistic appropriate for the five-factor model. To provide clarity on this issue, this paper provides a detailed mathematical derivation of the cross-sectional variance of the OLS estimators of the intercepts when N versions of the K-factor model are estimated. This variance is then used to construct the enhanced version of the GRS statistic. Its finite sample distribution is then rigorously established. To obtain that distribution, restrictions are made on cross-sectional variances and covariances of the errors of pricing models that are inconsistent with times series data. We derive the variance–covariance of the estimated intercepts of the K-factor model without making these restrictions. An almost sure approximation to that estimator is constructed here which is then used to obtain the asymptotic distribution of the GRS statistic. We call it the robust GRS statistic. Using data of Fama and French (2015, 2017), we use the robust GRS statistic to reconstruct their tables 5 and 4, respectively. As the distribution of the robust GRS does not change with the number of factors, in contrast to the finite sample version of this statistic, it allows for a more nuanced comparison of three-, four- and five-factor models. The power functions of the GRS (1989) statistic are compared with the enhanced version of the GRS appropriate for K factors
The Middle Neolithic in south-east England:social landscapes, chronology and interpretation
No full textWhich GRS Statistic Is Appropriate for Cross-Sectional Tests of Linear Multi-Factor Pricing Models?
No full textFama and French (2015, 2017) introduce the five-factor asset pricing model in the former paper and test their model on data from international financial markets in the latter paper. Each paper tests whether the five-factor model represents returns by way of the Gibbons, Ross and Shanken (1989) (hereafter GRS) statistic. That statistic's null hypothesis jointly sets all cross-section intercepts (alpha) to zero. The GRS statistic developed and presented in equation (4) on page 1124 of GRS (1989) is a cross-section test of the one-factor capital asset pricing model. Using the same data as Fama and French (2015, 2017), we show that the latter authors did not use the GRS (1989) statistic given in equation (4) on page 1124. In fact, they used a version of that statistic appropriate for the five-factor model. To provide clarity on this issue, this paper provides a detailed mathematical derivation of the cross-sectional variance of the OLS estimators of the intercepts when N versions of the K-factor model are estimated. This variance is then used to construct the enhanced version of the GRS statistic. Its finite sample distribution is then rigorously established. To obtain that distribution, restrictions are made on cross-sectional variances and covariances of the errors of pricing models that are inconsistent with times series data. We derive the variance–covariance of the estimated intercepts of the K-factor model without making these restrictions. An almost sure approximation to that estimator is constructed here which is then used to obtain the asymptotic distribution of the GRS statistic. We call it the robust GRS statistic. Using data of Fama and French (2015, 2017), we use the robust GRS statistic to reconstruct their tables 5 and 4, respectively. As the distribution of the robust GRS does not change with the number of factors, in contrast to the finite sample version of this statistic, it allows for a more nuanced comparison of three-, four- and five-factor models. The power functions of the GRS (1989) statistic are compared with the enhanced version of the GRS appropriate for K factors
Corruption erodes people's beliefs in morality and justice
No full textIn this research, we argue that corruption adversely affects individuals' perceived morality of politicians and their sense of justice, eroding some key values by which societies are guided. We further analyzed how the erosion of these key values might be negatively associated with people's well-being. We found support for our contentions through multiple studies, including a cross-national study comprising 82 countries surveyed over 32 years (Study 1, n = 210,207). This large-scale study was further supported by two experimental studies (Studies 2 and 3, n = 449) elucidating the mechanisms and causality involved in these processes. Our findings showed that corruption leads individuals to ascribe lower morality to politicians, which in turn is associated with lower perceptions of justice. Our data show that this process is negatively associated with well-being, contributing to a broader understanding of how corruption impacts individuals and societies
Consumer Behaviour in Growth Hacking:Developing and Validating the Shareability Construct
No full textStemming from the explosion of companies’ social data and digital transformation, growth hacking has emerged as a process of rapid experimentation to achieve sustainable business growth. This paper takes a consumer behaviour approach to explore the organic virality of growth hacking. We examine growth hacking through the lens of Social Identity and Self-Expansion theories, exploring how consumers’ drives are determined by social belonging and self-expansion desires. Through a mixed-methods approach, we identify essential dimensions of organic virality resulting from growth hacking tactics, including Shareability, attitude towards the brand, fear of missing out, need for affiliation and willingness to buy/use. It zooms into developing the Shareability construct, uncovering dimensions such as word-of-mouth, referrals, recommendations, sharing attitudes and disinformation. We contribute to growth hacking research by developing and validating the shareability scale as a reliable tool to measure consumers’ propensity towards disseminating growth hacking content, providing actionable implications for growth hackers
The multifunctional organic phase change materials for battery thermal safety in electric transportation systems:A critical review
No full textElectric transportation systems are great alternatives to conventional fossil-fuel-powered transportation systems. The thermal safety of high-energy-density lithium-ion batteries (LIBs), which are the main energy source in electric transportation systems, is one of the most major challenges facing the applications of these systems. Phase change material (PCM)-based battery thermal management systems are an effective solution for battery thermal safety, and they have a great application potential. However, the thermal safety of LIBs involves thermal management and thermal runaway protection, which require composite PCMs (CPCMs) with excellent thermal management cooling effect and stable thermal runaway protection capability. Thus, the optimizing strategies used for enhancing the structural stability, thermal conductivity, and flame retardancy of CPCMs were compared and analyzed. Moreover, the design of PCMs with thermal management and thermal-runaway-flame-retardant suppression capabilities was discussed. Finally, future research directions for using multifunctional PCMs in battery thermal safety systems were proposed based on critical thinking. This review will provide new insights and attract considerable attention to the reliability of thermal safety systems based on multifunctional PCMs in future designs, especially in the field of battery thermal safety
Design of a test bench for 1.5kV solid state circuit breaker for transport electrification
No full textThis paper deals with the detailed design and laboratory testing methodology for a 1.5kV/70A Solid State Circuit Breaker (SSCB) for Medium Voltage Direct Current (MVDC) applications. The paper reviews the parameters and characteristics of wide bandgap semiconductors suitable for the protection of MVDC circuits. This consisting of detailed design process for the selection of the main MOSFET, transient voltage suppressors (TVS) to achieve the allowable voltage transient, current sensor, gate driver, and current limiting inductor for the selected di/dt limit. The laboratory testing methodology uses fast-acting IGBTs which allows for the application of short circuit faults in a controlled environment. The stiff DC grid is created by using an appropriately sized capacitor that holds energy of which only 1% is used for testing. The whole test bench has to be kept in an enclosure that is only opened once the capacitor voltage reaches a safe level. This is first of kind effort to achieve the short circuit fault clearing time of less than 2μs for an MVDC application
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