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Essays on the Price of Risk

Abstract

This dissertation explores how risk is priced across different sectors of the economy. In particular, Chapter 1 focuses on equity markets while Chapters 2 and 3 look at the commercial banking sector.In Chapter 1 I develop an information-geometric framework for selecting priced risk factors from a high-dimensional candidate set. The stochastic discount factor is cast as a point on a statistical manifold of exponential-affine pricing kernels, and the manifold's dual flatness yields an exact Pythagorean decomposition of Kullback-Leibler divergence across nested SDFs. The decomposition drives a greedy forward-selection algorithm that is isomorphic to the portfolio problem of an investor with multiplier preferences. The investor's ranking of candidates by worst-case welfare loss coincides with the statistical ranking by KL divergence, and the Hansen-Jagannathan distance emerges as a leading-order approximation. A Wald test on estimated risk prices and an entropy bound calibrated to the investor's detection-error probability provide distinct stopping criteria. Applied to a rich set of asset returns, the algorithm selects a parsimonious SDF spanning roughly nine thematic categories. Debt issuance, quality, and profit growth form a stable core; accruals is absent from every specification. Selected factors derive a substantial share of their pricing content from non-Gaussian features of the return distribution.Chapter 2 introduces a novel dataset of bank resolution terms constructed from over forty years of FDIC press releases to analyze the determinants of franchise value in failed bank auctions. Using a structural model of the auction process that encompasses both the liability and asset sides of the failed bank's balance sheet, I characterize the deposit franchise as a wasting asset and endogenize the acquirer's optimal asset take-up decision as a function of comparative advantage relative to the FDIC's own resolution technology. The ``Toxic Ratio'', the proportion of assets retained by the FDIC in receivership, emerges as the dominant driver of resolution outcomes across the pricing, cost, and selection channels. Because the retained asset share and the deposit premium are jointly determined at the auction, I instrument the realized toxic ratio with the pre-failure loan-loss provision (LLP) ratio. The headline cost result is that a one percentage point increase in the loan-loss provision ratio raises the cost to the Deposit Insurance Fund by approximately 86 basis points of total assets, making asset quality the dominant quantitative determinant of fiscal exposure. Accelerated deposit runoff prior to failure further reduces bid premiums and increases resolution costs, consistent with the franchise-value mechanism. This trade-off highlights a shift in regulatory technology from liquidation to financial engineering, with significant implications for moral hazard and the "Too-Big-To-Fail'' doctrine.Finally, Chapter 3 investigates the competitive distortions introduced by "Too-Big-To-Fail" (TBTF) guarantees within the U.S. banking sector, specifically examining the flight-to-safety dynamic that redistributes funding during periods of systemic distress. To formalize the mechanism through which implicit government backstops alter deposit market competition, I develop a continuous-time structural model that integrates spatial differentiation with endogenous default risk. The model yields a ``scissors'' dynamic, predicting that while distressed small banks must compress margins to retain uninsured depositors, TBTF incumbents strategically widen spreads to monetize their perceived safety. To empirically test these predictions across the entire size spectrum of the banking system, I construct a novel, continuous measure of default probability for the universe of regional and local banks using a Weighted Ensemble machine learning framework. Utilizing a difference-in-differences identification strategy, I find robust evidence of a post-GFC regime shift: uninsured deposit demand has become highly elastic to bank solvency, but with a stark size hierarchy. A one-percentage-point increase in default probability is associated with an approximately 48 percent increase in uninsured deposit share for Global Systemically Important Banks (GSIBs), while local banks experience an essentially flat or slightly negative relationship. These findings suggest that regulatory reforms have not eliminated the TBTF subsidy but have instead repriced it, allowing systemic institutions to act as liquidity sinks that absorb franchise value from smaller competitors during economic contractions.