In chapter 1, I study the experimentation dynamics of a decision maker (DM) in a two-armed bandit setup ([5]), where the agent holds ambiguous beliefs regarding the distribution of the return process of one arm and is certain about the other one. The DM entertains Multiplier preferences à la [27], thus I frame the decision making environment as a twoplayer differential game against nature in continuous time. I characterize the DM’s value function and her optimal experimentation strategy that turns out to follow a cut-off rule with respect to her belief process. The belief threshold for exploring the ambiguous arm is found in closed form and is shown to be increasing with respect to the ambiguity aversion index. I then study the effect of provision of an unambiguous information source about the ambiguous arm. Interestingly, I show that the exploration threshold rises unambiguously as a result of this new information source, thereby leading to more conservatism. This analysis also sheds light on the efficient time to reach for an expert opinion. The results of this chapter has been recently published in [61].

In chapter 2, I introduce a dynamic model of random search where ex ante heterogeneous venture capitalists (investors) with unknown abilities match with a variety of startups (projects). There is incomplete yet symmetric information about investors’ types, whereas the projects’ types are publicly observable to all investors. In the unique stationary equilibrium, the matching sets, value functions and steady state distributions are endogenously determined. Interpreting the market posterior belief about the venture capitalists’ ability as their reputation, I study the outcomes of the economy when the success or failure of the projects create feedback effects: innovation spillovers and reputational externalities. When there are positive spillovers from successful early stage projects to late stage business opportunities, I show increased levels of search frictions could save the market from breakdown caused by the neglect of spillover effect. When the reputational externality is at play, namely when the deal flow of each investor is inversely impacted by the distribution of other investors’ reputation, I show the proportion of the high ability inactive investors is inefficiently high, and the projects suffer from early termination.

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.

Low-risk investing refers to a diverse collection of investment strategies that emphasize low-beta, low-volatility, low idiosyncratic risk, downside protection, or risk parity. Since the 2008 financial crisis, there has been heightened interest in low-risk investing and especially in investment strategies that apply leverage to low-risk portfolios in order to enhance expected returns.

In chapter 1, we examine the well-documented low-beta anomaly. We show that despite the fact that low-beta portfolios had lower volatility than the market portfolio, some low-beta portfolios had higher realized Sharpe ratios (over a 22-year horizon) than the market portfolio. This is can not happen in an efficient market, where long-run return is expected to be earned as a reward for bearing risk, if risk is equated with volatility. We expand the notion of risk to include higher moments of the return distribution and show that excess kurtosis can make low-beta stocks and portfolios riskier than higher beta stocks and portfolios.

In chapter 2, we show that the cumulative return to a levered strategy is determined by five elements that fit together in a simple, useful formula. A previously undocumented element is the covariance between leverage and excess return to the fully invested source portfolio underlying the strategy. In an empirical study of volatility-targeting strategies over the 84-year period 1929-2012, this covariance accounted for a reduction in return that substantially diminished the Sharpe ratio in all cases.

In chapter 3, we gauge the return-generating potential of four investment strategies: value weighted, 60/40 fixed mix, unlevered and levered risk parity. We have three main findings. First, even over periods lasting decades, the start and end dates of a backtest can have a material effect on results; second, transaction costs can reverse ranking, especially when leverage is employed; third, a statistically significant return premium does not guarantee outperformance over reasonable investment horizons.

In the first chapter, I develop a model of prospective memory, defined as the

capacity to recall actions to be carried out in the future. An agent faces some

task with stochastic cost ct , benefit b, and T periods until some exogenously

imposed deadline. The agent can only execute the task at time t if the task is

recalled in that period. The memory process exhibits the rehearsal property

that the probability of recall is lower if the task was forgotten in the recent

past. The agent sets a threshold cost each period based on her expectations

of whether she will recall and carry out the task in future periods. If the task

is recalled at time t, and the draw from the cost distribution is below this

threshold, the task is executed. We then introduce memory overconfidence

into the model, which we define as either overestimating the base likelihood

of recall in future periods or underestimating the effect of temporary forgetting

on subsequent recall. Memory overconfidence leads not only to inefficiently

low rates of task completion, but also to the prediction that the probability

of task completion may vary inversely with the length of time allocated to

completing the task. We discuss the interaction of these effects with present-biased preferences, and provide examples of economic scenarios where this

dynamic may be exploited by firms to the detriment of consumers.

In the second chapter, I introduce a new copula which simultaneously allows

fully-general correlation structures in the bulk of a multivariate distribution

and an arbitrarily high degree of dependence in the left tails. This is

ideally suited for modeling financial assets which may display moderate correlation in normal times, but which experience simultaneous left tail events,

such as during a financial crisis. The new copula is shown to be fully flexible

in the sense that the user can specify a desired structure for a sequence of

increasingly dire events in the left tail, while still retaining the same correlation

structure in the bulk. Finally, I illustrate the use of this copula with an

application to hedge fund returns.

I explicitly derive the optimal dynamic incentive contract in a general continuous time agency problem where inducing static first-best action is not always optimal. My framework generates two dynamic contracts new to the literature: (1) a ``quiet-life" arrangement and (2) a suspension-based endogenously renegotiating contract. Both contractual forms induce a mixture of first-best and non-first-best action. These contracts capture common features in many real life arrangements such as ``up-or-out", partnership, tenure, hidden compensation and suspension clauses. In applications, I explore the effects of taxes, bargaining and renegotiation on optimal contracting. My technical work produces a new type of incentive scheme I call sticky incentives which underlies the optimal, infrequent-monitoring approach to inducing a mixture of first-best and non-first-best action. Furthermore, I show how differences in patience between the principal and agent factor into optimal contracting.