We have reason to believe that negatively-skewed assets are commonly overvalued, despite having significant downside risk. This paper investigates how the skewness of returns should change investors’ evaluation of and allocation to hedge funds. We first provide evidence to support the claim that many hedge funds have negatively skewed returns. We then propose a new evaluation benchmark for negatively-skewed funds. Finally, we discuss how investors can construct portfolios that take into account the skew of the underlying assets. We find that many common hedge fund indices have return distributions that resemble the shape of short put option payoffs, which are known to be left-skewed. We argue that when choosing a benchmark against which to measure a fund’s performance, investors should choose one with similar skew. Therefore, instead of measuring hedge fund performance relative to the S&P 500, we propose that funds be compared to a strategy of shorting monthly put options on the S&P 500. Not only should skew affect the way investors evaluate hedge fund performance, but it should also influence their capital allocation. We solve a mean-variance-skewness (MVS) portfolio optimization problem to construct an optimal portfolio across common hedge fund indices. We compare this optimal portfolio to the traditional Markowitz portfolio containing the same assets. The differences between these two portfolios provide evidence that incorporating skew in portfolio optimization should change how investors optimally allocate to hedge funds.

Political Polarization is a growing issue in the US, and undermines the stability of our democracy. Linguistic Polarization is the manifestation of political polarization in the language used by ideological groups, and can serve to deepen ideological divides. In this thesis, we investigate two forms of linguistic polarization: lexical polarization and semantic polarization. Lexical Polarization focuses on vocabulary differences between ideological groups, while semantic polarization captures shifts in the meanings of words. We examine four corpora of Reddit data, collected from r/democrats and r/Republican in 2019 and 2023. We use frequency and embedding-based analysis methods to characterize the language polarization in our datasets. This allows us to identify polarizing issues and political figures, and identify any communication gaps between the two sides of the ideological spectrum that may be exacerbating overall polarization.

\indent The 2021 Texas blackouts exposed the vulnerability of ERCOT’s deregulated electricity grid to extreme weather and price volatility, and these risks intensify with climate change, electrification, and rising electricity demand. At the same time, residential distributed energy resources (DERs)—rooftop solar, home batteries, and electric vehicles—are becoming more widespread and capable of providing valuable grid flexibility. Virtual Power Plants (VPPs) aggregate these resources to bid into wholesale markets, but typically rely on opaque, automated platforms that offer users little visibility or control. As a result, most households lack tools to understand or optimize their DERs for financial benefit.

This thesis presents a transparent, data-driven framework that enables household DERs to actively participate in ERCOT’s two-settlement electricity market, where day-ahead bids must anticipate uncertainty in real-time prices and solar generation. We combine probabilistic forecasting with two-stage stochastic optimization to model household market decisions. Quantile LSTM (QLSTM) models, trained on historical price and solar data, generate scenario-based forecasts that feed into a two-stage optimization model capturing DER dynamics, including battery degradation, EV availability, and flexible load scheduling. To align forecasts with downstream outcomes, we fine-tune the QLSTM using a decision-focused learning (DFL) loss that minimizes regret in the two-stage problem.

Simulations across four Texas cities and three levels of residential load profiles show that the baseline predict-then-optimize strategy consistently recovers most of the profit achievable under perfect foresight, while DFL improves robustness under volatile conditions. This work demonstrates how machine learning and optimization approaches can empower households to participate meaningfully in electricity markets by offering a user-centric alternative to DER optimization and supporting a more distributed, resilient, and responsive energy grid.