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This thesis focuses on three research questions in the areas of empirical asset pricing and corporate finance. I introduce the overview in the first chapter and conclude in the final chapter. In the second chapter, we investigate the impact of the beta's statistical significance on the performance of the betting against beta (BAB) portfolios in the U.S. and major international markets. After dropping stocks with statistically insignificant betas, we find that a betting against statistically significant beta strategy reduces the monthly alphas of BAB portfolios by 20% - 50%, depending on beta estimation methods. If we replace the value of statistically insignificant beta by zero, a refined BAB strategy can generate a higher alpha than the original BAB strategy. In the third chapter, we find a negative relationship between abnormal investment and future stock performance in the U.S. market. This negative relation is mainly driven by firm under-investment, not over-investment. Our explanations can be that market investors may not react promptly to the fundamental information contained in under-investment about a firm's future profitability, asset growth, and financial distress probability. Alternatively, the negative relation between underinvestment and future stock returns is more pronounced for firms with lower investor monitoring and higher agency costs. In the fourth chapter, we identify a positive link between peer firms' investment and focal firm's value of cash holding in the U.S. market. This effect is likely to result from the positive externalities brought by peer investment which are reflected in young and growing industries with ample investment opportunities that are shared by the focal firms. We find little evidence to support either the precautionary hypothesis or the learning hypothesis. Our further analyses show that firms increase their level of cash holdings while peer investment increases. Meanwhile, firms are less willing to use cash for dividend payments while they are more willing to use it for capital expenditure and R&D investment.

Expanders are well-connected graphs. They have numerous applications in constructions of error correcting codes, metric embedding, derandomization, sampling algorithms, etc. Local-spectral expanders (HDXes) are a generalization of expander graphs to hypergraphs. They have recently received more attention due to their applications to agreement tests [24], locally testable codes [28, 99, 75, 27], hardness of SoS refutation [25, 59], and connections with local sampling algorithms [5]. In comparison to expanders we have very limited understanding of HDXes: there are abundant random or explicit constructions of sparse expander graphs such as random d-regular graphs [50], algebraic expanders [92, 51], the zig-zag product [101], etc. In contrast, we know only two general constructions of sparse HDXes: the LSV complexes [90] and thecoset construction [66]. In this thesis, we take two approaches to tackle the construction problem. The first approach is taking graph products of sparse expander graphs. This is inspired by the zig-zag product. However, this construction fails to give good local-spectral expansion. The second approach is inspired by the following question: does any continuous space have the local-spectral expansion property? We show that the answer is affirmative for high-dimensional spheres. More precisely, we show that 3-uniform hypergraphs sampled randomly over high-dimensional spheres are (relatively sparse) local-spectral expanders. Furthermore, tight isoperimetric inequalities of local-spectral expanders have remained elusive. Intuitively, isoperimetric inequalities provide a lower bound on the probability that a random walk leaves a subset of vertices in the graph. A tight bound on this probability is crucial for applications to agreement testing. In this thesis, we explore this problem and give an improved bound for good local-spectral expanders.

Event time series are sequences of events occurring in continuous time. They arise in many real-world problems and may represent, for example, posts in social media, administrations of medications to patients, or adverse events, such as episodes of atrial fibrillation or earthquakes. In this work, we study and develop methods for prediction and anomaly detection on event time series. We study two general approaches. The first approach converts event time series to regular time series of counts via time discretization. We develop methods relying on (a) nonparametric time series decomposition and (b) dynamic linear models for regular time series. The second approach models the events in continuous time directly. We develop methods relying on point processes. For prediction, we develop a new model based on point processes to combine the advantages of existing models. It is flexible enough to capture complex dependency structures between events, while not sacrificing applicability in common scenarios. For anomaly detection, we develop methods that can detect new types of anomalies in continuous time and that show advantages compared to time discretization.

How can we bridge the gap between the lack of construction land and the sustained rapid urban population growth in China? This is a social problem China need to solve in the near future. ‘Land [Fill] The Gap’ is an investigation of the possibility of utilizing existing landfills in Beijing for urban construction in order to accommodate inhabitants, remove landfills and generate electricity from trash.