A number of authors have found that firm size and book-to-market-value capture the cross-sectional variation in average stock returns. More importantly, these variables have been shown to out-perform the CAPM's β coefficient in explaining the cross-section of US stock returns. However, these studies all employ variants of the two-step estimator due to Fama and MacBeth (Fama, E.F., MacBeth, J.D., 1973. Risk, return and equilibrium: Empirical tests. Journal of Political Economy 71, 607–636), which impose implicitly the restriction that idiosyncratic returns are uncorrelated. In this paper we use a one-step estimator due to McElroy et al. (McElroy, M.B., Burmeister, E., Wall, K.D., 1985. Two estimators for the APT model when factors are measured. Economics Letters 19, 271–275) and find a highly significant role for β risk in the UK stock market when we allow for correlation amongst idiosyncratic returns.

This paper gives a solution to the problem of estimating coefficients of index models, through the estimation of the density-weighted average derivative of a general regression function. A normalized version of the density-weighted average derivative can be estimated by certain linear instrumental variables coefficients. The estimators, based on sample analogies of the product moment representation of the average derivative, are constructed using nonparametric kernel estimators of the density of the regressors. Consistent estimators of the asymptotic variance-covariance matrices of the estimators are given, and a limited Monte Carlo simulation is used to study the practical performance of the procedures.

T HE model presented in this paper is a system of recursive linear regression equations, the parameters of which are esti-mated from monthly series of data covering the

We test both the unconditional and conditional Mean Variance Efficiency of the UK stockmarket, paying particular attention to choosing a suitable set of instruments for the conditional version of the model. By considering more carefully than previous authors the pricing of economic risk within the mean-variance framework we show that certain instruments can enhance the basic model structure. Given the tendency for financial market data to display non-constancy in variance and non-normality we employ the GMM procedure described in Hansen (1982), which requires much weaker distributional assumptions than the more traditional OLS techniques. We discuss forming portfolios of stocks using both size and dividend yield as a criterion to achieve a suitable spread of risk and return, and find that our conclusions are sensitive both to the method of portfolio formation and to the choice of estimator. This is an important finding given the problem of thin trading associated with the size ordering of UK stocks. We find some support for both the unconditional and conditional version of the CAPM, though we are cautious about our conclusions given the instability of the parameter estimates.

We present an economic model of systemic risk in which undercapitalization of the financial sector as a whole is assumed to harm the real economy, leading to a systemic risk externality. Each financial institution's contribution to systemic risk can be measured as its systemic expected shortfall (SES), that is, its propensity to be undercapitalized when the system as a whole is undercapitalized. SES increases in the institution's leverage and its marginal expected shortfall (MES), that is, its losses in the tail of the system's loss distribution. We demonstrate empirically the ability of components of SES to predict emerging systemic risk during the financial crisis of 2007-2009.

We provide the first evidence after Regulation G on firms’ non-GAAP EPS denominator choices and whether they are informative or opportunistic. From 2013 to 2019, 17 percent of annual non-GAAP EPS numbers use denominators different from that of GAAP diluted EPS, which makes denominator adjustments among the most prevalent individual types of non-GAAP adjustments. For firms reporting GAAP and non-GAAP profits or GAAP losses and non-GAAP profits, we provide evidence consistent with denominator adjustments increasing non-GAAP EPS informativeness. Our evidence also suggests that opportunism in denominator choices is concentrated in firms reporting GAAP losses and non-GAAP profits and failing to adjust the denominator. Such nonadjustment is inconsistent with SEC requirements to report non-GAAP EPS “on a diluted basis” because the EPS denominator for a GAAP loss excludes dilutive claims. Although the SEC largely overlooks such firms, they are more likely, on average, to report non-GAAP EPS that analysts consider inflated.