Change-Point Testing and Estimation for Risk Measures in Time Series

We investigate methods of change-point testing and confidence interval construction for nonparametric estimators of expected shortfall and related risk measures in weakly dependent time series. A key aspect of our work is the ability to detect general multiple structural changes in the tails of time series marginal distributions. Unlike extant approaches for detecting tail structural changes using quantities such as tail index, our approach does not require parametric modeling of the tail and detects more general changes in the tail. Additionally, our methods are based on the recently introduced self-normalization technique for time series, allowing for statistical analysis without the issues of consistent standard error estimation. The theoretical foundation for our methods are functional central limit theorems, which we develop under weak assumptions. An empirical study of S&P 500 returns and US 30-Year Treasury bonds illustrates the practical use of our methods in detecting and quantifying market instability via the tails of financial time series during times of financial crisis

Inference for Large Panel Data with Many Covariates

This paper proposes a novel testing procedure for selecting a sparse set of covariates that explains a large dimensional panel. Our selection method provides correct false detection control while having higher power than existing approaches. We develop the inferential theory for large panels with many covariates by combining post-selection inference with a novel multiple testing adjustment. Our data-driven hypotheses are conditional on the sparse covariate selection. We control for family-wise error rates for covariate discovery for large cross-sections. As an easy-to-use and practically relevant procedure, we propose Panel-PoSI, which combines the data-driven adjustment for panel multiple testing with valid post-selection p-values of a generalized LASSO, that allows us to incorporate priors. In an empirical study, we select a small number of asset pricing factors that explain a large cross-section of investment strategies. Our method dominates the benchmarks out-of-sample due to its better size and power

Deep Learning Statistical Arbitrage

Statistical arbitrage identifies and exploits temporal price differences between similar assets. We propose a unifying conceptual framework for statistical arbitrage and develop a novel deep learning solution, which finds commonality and time-series patterns from large panels in a data-driven and flexible way. First, we construct arbitrage portfolios of similar assets as residual portfolios from conditional latent asset pricing factors. Second, we extract the time series signals of these residual portfolios with one of the most powerful machine learning time-series solutions, a convolutional transformer. Last, we use these signals to form an optimal trading policy, that maximizes risk-adjusted returns under constraints. We conduct a comprehensive empirical comparison study with daily large cap U.S. stocks. Our optimal trading strategy obtains a consistently high out-of-sample Sharpe ratio and substantially outperforms all benchmark approaches. It is orthogonal to common risk factors, and exploits asymmetric local trend and reversion patterns. Our strategies remain profitable after taking into account trading frictions and costs. Our findings suggest a high compensation for arbitrageurs to enforce the law of one price

Essays in Financial Econometrics, Asset Pricing and Corporate Finance

My dissertation explores how tail risk and systematic risk affects various aspects of risk management and asset pricing. My research contributions are in econometric and statistical theory, in finance theory and empirical data analysis. In Chapter 1 I develop the statistical inferential theory for high-frequency factor modeling. In Chapter 2 I apply these methods in an extensive empirical study. In Chapter 3 I analyze the effect of jumps on asset pricing in arbitrage-free markets. Chapter 4 develops a general structural credit risk model with endogenous default and tail risk and analyzes the incentive effects of contingent capital. Chapter 5 derives various evaluation models for contingent capital with tail risk.Chapter 1 develops a statistical theory to estimate an unknown factor structure based on financial high-frequency data. I derive a new estimator for the number of factors and derive consistent and asymptotically mixed-normal estimators of the loadings and factors under the assumption of a large number of cross-sectional and high-frequency observations. The estimation approach can separate factors for normal "continuous" and rare jump risk. The estimators for the loadings and factors are based on the principal component analysis of the quadratic covariation matrix. The estimator for the number of factors uses a perturbed eigenvalue ratio statistic. The results are obtained under general conditions, that allow for a very rich class of stochastic processes and for serial and cross-sectional correlation in the idiosyncratic components.Chapter 2 is an empirical application of my high-frequency factor estimation techniques. Under a large dimensional approximate factor model for asset returns, I use high-frequency data for the S&P 500 firms to estimate the latent continuous and jump factors. I estimate four very persistent continuous systematic factors for 2007 to 2012 and three from 2003 to 2006. These four continuous factors can be approximated very well by a market, an oil, a finance and an electricity portfolio. The value, size and momentum factors play no significant role in explaining these factors. For the time period 2003 to 2006 the finance factor seems to disappear. There exists only one persistent jump factor, namely a market jump factor. Using implied volatilities from option price data, I analyze the systematic factor structure of the volatilities. There is only one persistent market volatility factor, while during the financial crisis an additional temporary banking volatility factor appears. Based on the estimated factors, I can decompose the leverage effect, i.e. the correlation of the asset return with its volatility, into a systematic and an idiosyncratic component. The negative leverage effect is mainly driven by the systematic component, while it can be non-existent for idiosyncratic risk.In Chapter 3 I analyze the effect of jumps on asset pricing in arbitrage-free markets and I show that jumps have to come as a surprise in an arbitrage-free market. I model asset prices in the most general sensible form as special semimartingales. This approach allows me to also include jumps in the asset price process. I show that the existence of an equivalent martingale measure, which is essentially equivalent to no-arbitrage, implies that the asset prices cannot exhibit predictable jumps. Hence, in arbitrage-free markets the occurrence and the size of any jump of the asset price cannot be known before it happens. In practical applications it is basically not possible to distinguish between predictable and unpredictable discontinuities in the price process. The empirical literature has typically assumed as an identification condition that there are no predictable jumps. My result shows that this identification condition follows from the existence of an equivalent martingale measure, and hence essentially comes for free in arbitrage-free markets.Chapter 4 is joint work with Behzad Nouri, Nan Chen and Paul Glasserman. Contingent capital in the form of debt that converts to equity as a bank approaches financial distress offers a potential solution to the problem of banks that are too big to fail. This chapter studies the design of contingent convertible bonds and their incentive effects in a structural model with endogenous default, debt rollover, and tail risk in the form of downward jumps in asset value. We show that once a firm issues contingent convertibles, the shareholders’ optimal bankruptcy boundary can be at one of two levels: a lower level with a lower default risk or a higher level at which default precedes conversion. An increase in the firm’s total debt load can move the firm from the first regime to the second, a phenomenon we call debt-induced collapse because it is accompanied by a sharp drop in equity value. We show that setting the contractual trigger for conversion sufficiently high avoids this hazard. With this condition in place, we investigate the effect of contingent capital and debt maturity on capital structure, debt overhang, and asset substitution. We also calibrate the model to past data on the largest U.S. bank holding companies to see what impact contingent convertible debt might have had under the conditions of the financial crisis.Chapter 5 develops and compares different modeling approaches for contingent capital with tail risk, debt rollover and endogenous default. In order to apply contingent convertible capital in practice it is desirable to base the conversion on observable market prices that can constantly adjust to new information in contrast to accounting triggers. I show how to use credit spreads and the risk premium of credit default swaps to construct the conversion trigger and to evaluate the contracts under this specification