Multivariate Performance Analysis of Firms

I framed this project around a practical finance question: when a firm has dozens of financial ratios, which underlying dimensions actually explain performance? PCA helped me move from a crowded ratio table to a smaller set of interpretable business signals. The goal was not to predict bankruptcy directly, because the bankruptcy label was excluded from the PCA inputs. The goal was to discover structure first, then test whether that structure made financial sense.

The original dataset had 96 variables, but PCA is only useful when the inputs are interpretable. I selected 14 ratios that represented the major dimensions a financial analyst would care about: profitability, liquidity, leverage, asset structure, operating efficiency, and cash flow. I also winsorized extreme values at the 1st and 99th percentiles and standardized every variable so no ratio dominated simply because of scale.

Before interpreting components, I checked whether the correlation structure supported PCA. The KMO statistic was 0.50, which is marginal but usable for exploratory work. Bartlett test was significant below 0.0001, confirming that the ratios were not independent noise. I used that evidence carefully: the data was suitable enough for exploratory PCA, but the interpretation still needed discipline.

The retention decision was one of the most important parts of the case. The Kaiser rule identified five components with eigenvalues above 1, and the 80% cumulative-variance threshold also pointed to five components. Together, those five components explained 81.1% of the total variance, giving me enough compression to simplify the dataset without throwing away the main financial structure.

The loading matrix was where the case became financial rather than purely statistical. PC1 loaded positively on net worth/assets, current ratio, quick ratio, and equity-to-liability, and negatively on debt ratio. I interpreted it as Liquidity and Solvency Strength. PC2 was dominated by profitability measures, PC3 by cash-flow variables, PC4 by fixed assets and turnover, and PC5 by receivables turnover.

I translated the five retained components into a set of analytical lenses: Liquidity and Solvency Strength, Profitability and Earnings Quality, Cash Flow Generation Capacity, Asset Structure and Capital Intensity, and Receivables Efficiency. That translation mattered because PCA outputs are only useful when decision-makers can connect the component scores back to operating reality.

After constructing the PCA without using the bankruptcy label, I compared component scores by bankruptcy status. This was the validation moment. Bankrupt firms averaged -2.847 on PC1, while non-bankrupt firms averaged +0.095, a 2.942 standard-unit gap. That result made PC1 more than a mathematical component: it behaved like a meaningful solvency signal.

The case became most useful when I translated the results into a workflow. I recommended treating PC1 as a composite solvency score, flagging firms with PC1 below -2 for enhanced review, and tracking PC1 over time as part of an early-warning dashboard. I also proposed using the five PC scores as clean, uncorrelated inputs for future supervised models such as logistic regression or random forests.

This project feels personal because it shows the kind of analyst I am trying to become. I do not want to stop at software output or a polished chart. I want to understand the data, challenge whether the method is justified, name the result in business language, and then turn the analysis into something a manager could actually use. In this case, PCA helped me move from 96 ratios to five financial dimensions that were both statistically defensible and practically readable.