Modeling and forecasting covariance matrices of asset returns play a crucial role in finance.The availability of high frequency intraday data enables the modeling of the realized covariance matrix directly. However, most models in the literature suffer from the curse of dimensionality. To solve the problem, we propose a factor model with a diagonal CAW model for the factor realized covariance matrices. Asymptotic theory is derived for the estimated parameters. In an extensive empirical analysis, we find that the number of parameters can be reduced significantly. Furthermore, the proposed model maintains a comparable performance with a benchmark vector autoregressive model.

Realized moments of higher order computed from intraday returns are introduced in recent years. The literature indicates that realized skewness is an important factor in explaining future asset returns. However, the literature mainly focuses on the whole market and on the monthly or weekly scale. In this paper, we conduct an extensive empirical analysis to investigate the forecasting abilities of realized skewness and realized kurtosis towards individual stock's future return and variance in the daily scale. It is found that realized kurtosis possesses significant forecasting power for the stock's future variance. In the meanwhile, realized skewness is lack of explanatory power for the future daily return for individual stocks with a short horizon, in contrast with the existing literature.

To maximize their effectiveness, environmental, social, and governance (ESG) strategies should target those ESG firms that are most capital constrained. Inherently, this involves seeking ESG firms that have irrationally high costs of capital and thus high expected return. We replicate results that find returns among ESG firms that are similar to those among non-ESG firms. In addition, we find that sorting stocks based on cost of equity capital generates significant positive return for both ESG and non-ESG firms. Investing in an ESG in Need index, which contains only high-ESG companies and tilts toward firms with high cost of capital, thus generates both higher social value and better return than investing in traditional capitalization-weighted ESG indexes.

Recently, inference about high-dimensional integrated covariance matrices (ICVs) based on noisy high-frequency data has emerged as a challenging problem. In the literature, a pre-averaging estimator (PA-RCov) is proposed to deal with the microstructure noise. Using the large-dimensional random matrix theory, it has been established that the eigenvalue distribution of the PA-RCov matrix is intimately linked to that of the ICV through the Marčenko-Pastur equation. Consequently, the spectrum of the ICV can be inferred from that of the PA-RCov. However, extensive data analyses demonstrate that the spectrum of the PA-RCov is spiked, that is, a few large eigenvalues (spikes) stay away from the others which form a rather continuous distribution with a density function (bulk). Therefore, any inference on the ICVs must take into account this spiked structure. As a methodological contribution, we propose a spiked model for the ICVs where spikes can be inferred from those of the available PA-RCov matrices. The consistency of the inference procedure is established and is checked by extensive simulation studies. In addition, we apply our method to the real data from the US and Hong Kong markets. It is found that our model clearly outperforms the existing one in predicting the existence of spikes and in mimicking the empirical PA-RCov matrices.

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