The rise of quantitative investment strategies has been driven by increased data availability and advancements in financial modeling. This thesis introduces Causal Factor Investing (CFI), a novel approach that integrates causality and machine learning to enhance the performance and explainability of factor investing strategies. Traditional factor investing often suffers from specification errors due to its reliance on correlations rather than causal relationships, and machine learning methods are frequently criticized for their `black box' nature. CFI addresses these issues by using causal discovery methods, which are based on the mathematical properties of graph theory, to identify factors that have a cause-effect relationship with asset returns. These causal factors are then utilized as features in machine learning models to predict future returns, serving as investment signals for portfolio construction.

Our empirical analysis in the European corporate bond market utilized causal discovery algorithms including Fast Causal Inference (FCI) and Greedy Equivalence Search (GES). The use of GES in CFI improves portfolio performance compared to traditional factor investing, while FCI led to insufficient causal graphs. For the portfolios constructed with neural networks in CFI, the use of causal factors resulted in the best-performing portfolio.

Altogether, CFI contributes to the field of quantitative finance by offering an explainable and profitable approach to factor investing. For further research, we suggest exploring alternative causal discovery algorithms, including time-series causal discovery methods and other algorithms that account for hidden confounders to increase the accuracy of the causal graphs. Additionally, a practical improvement would be including transaction costs and adjust the model for risk constraints through optimization approaches.

In this bachelor thesis we use a stochastic model to aspire to explain biodiversity patterns in different ecosystems with selection advantage. The stochastic model we use is an extension of the mean­-field voter model where we include a selection factor. In the model individuals with two different types of alleles in two different ecosystems are considered. The model is a stochastic Markov process that describes interactions of individuals with each­other over time. This means that the ratio of individuals with certain alleles stochastically drifts over time. The main goal of this bachelor thesis is investigate whether is it possible that individuals with two different types of alleles can coexist (a stable equi­librium) in two populations. We do this by taking the limit of this Markov process such that we can show convergence to ordinary differential equations. By studying these differential equations we ob­tain results: vector fields with equilibrium points. We conclude that, under certain conditions and with a selection advantage, coexistence of individuals with two different alleles in two different ecosystems is possible (see Section 4.4) in the form of a stable equilibrium. Furthermore we claim that the typical time to absorption, reaching an absorbing state where all the individuals have the same allele, of the two­-dimensional mean­-field voter model with selection scales exponentially with the system size.