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Essays in Risk Management and Financial Econometrics

  • Author(s): Liu, Haoyang
  • Advisor(s): Wallace, Nancy
  • Palmer, Christopher
  • et al.
Abstract

This dissertation consists of three chapters that concern risk management and financial econometrics. Fannie Mae and Freddie Mac’s implicit government guarantee is widely argued to cause irresponsible risk taking. Despite moral-hazard concerns, this paper presents evidence that Fannie Mae and Freddie Mac (the GSEs) more effectively managed home price risks during the 2000-2006 housing boom than private insurers. Mortgage origination data reveal that the GSEs were selecting loans with increasingly higher percentage of down payments, or lower loan to value ratios (LTVs), in boom areas than in other areas. Furthermore, the decline of LTVs in boom areas stems entirely from the segment insured by the GSEs only, and none of the decline stems from the segment co-insured by private mortgage insurers. Private mortgage insurers also did not lower their exposure to home price risks along other dimensions, including the percentage of high LTV GSE loans they insured. To quantify how the GSEs’ portfolios would have performed under alternative home price scenarios, I build an insurance valuation model based on competing-risk hazard regressions, calibrated Hull and White term-structure model, and forecasting prepayment and default speeds. I find that the GSEs’ risk management would have been sufficient for the historically average 32% mean reversion but insufficient for the realized 95% mean reversion between 2006 and 2011. My results highlight that post-crisis reform of the mortgage insurance industry should carefully consider additional factors besides moral hazard, such as mortgage insurers’ future home price assumptions.

The second chapter studies high dimensional time series, with application to estimating the mean variance frontier. One persistent challenge in macroeconmics and finance is how to draw inference from data with a large cross section but short time series. Financial econometric techniques all are designed for large time series and small cross-sections. However, financial data typically has a large cross section and short time series (large-N small-T). One particular large-N small-T impact is the underestimation of risk in the mean variance frontier. We propose a correction for the finite sample bias when the underlying returns are high dimensional linear time series. Our algorithm first corrects for the bias in eigenvalues of the asset return covariance matrix, and then estimate the contribution of each leading factor to the mean variance frontier. A cross validation method is employed to select the optimal number of leading factors. Performance of the proposed methods is examined through extensive simulation studies.

The third chapter studies how expected home prices affect borrowers’ default behavior. One of the penalties mortgage defaulters face is being locked out of the mortgage market and missing the home price appreciation. I find that this penalty deters some borrowers from defaulting. A higher future home price growth implies a lower ex-ante default probability. Furthermore, high credit score borrowers react more to past home price declines and future home price appreciation than low credit score borrowers. This suggests that high credit score borrowers are more likely to be strategic defaulters. A model is built to study the effect of changing the cooling off period. In high expected home price appreciation areas, a longer cooling-off period amplifies the impact of each foreclosure. In low expected home price appreciation areas, a longer cooling-off period reduces the number of foreclosures.

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