The Applications of Graph Theory to Investing

Abstract: How can graph theory be applied to investing in the stock market? The answer may help investors realize the true risks of their investments, help prevent recessions like that of 2008, and increase financial literacy amongst students. Using several original Python programs, we take a correlation matrix with correlations between the stock prices and then transform that into a graphable binary adjacency matrix. From this graph, we take a graph in which each edge represents weak correlations between two stocks. Finding the largest complete graph will produce a diversified portfolio. Numerous trials have shown that diversified portfolios consistently outperform the market during times of economic stability, but undiversified portfolios prove to be riskier and more unpredictable, either producing huge profits or even larger losses. Furthermore, once deciding among which stocks our portfolio would consist of, how do we know when to invest in each stock to maximize profits? Can taking stock price data and shifting values help predict how a stock will perform today if another stock performs a certain way n days prior? It was found that this method of predicting the optimal time to investment failed to improve returns when based solely on correlations. Although a trial with random stocks with varied correlations produced more profits than continuously investing.