No-Arbitrage Factor Geometry: Identification in High-Dimensional Instrumented Asset Pricing

Instrumented asset pricing models use large sets of firm characteristics to identify latent sources of systematic risk. As the number of available characteristics continues to grow, a natural question is whether additional instruments provide genuinely new information or instead repackage existing information in higher-dimensional form. This thesis-based work studies that question from a geometric perspective, building on Instrumented Principal Component Analysis and the characteristic-based asset pricing literature.

Using a broad panel of equity characteristics, I document that the effective dimensionality of the characteristic space is substantially lower than the raw instrument count suggests, and that the resulting long-run geometry is highly anisotropic. In such a space, conventional Euclidean notions of orthogonality can be misleading, allowing latent and observable factor directions to overlap. Motivated by this observation, I develop a no-arbitrage geometric extension of IPCA that incorporates empirical characteristic geometry through a QZ-based metric and an economically disciplined identification structure. Preliminary evidence suggests that accounting for this geometry is important for factor identification and is associated with improved cross-sectional pricing relative to standard Euclidean IPCA specifications.