Disaster and fortune risk in asset returns

Do Disaster risk and Fortune risk fetch a premium or discount in the pricing of individual assets? Disaster risk and Fortune risk are measures for the co-movement of individual stocks with the market, given that the state of the world is extremely bad and extremely good, respectively. To address this question measures of Disaster risk and Fortune risk, derived from statistical Extreme Value Theory, are constructed. The measures are non-parametric and the number of order statistics to be used in the analysis is based on the Kolmogorov-Smirnov distance. This alleviates the problem of an arbitrarily chosen extreme region. The extreme dependence measures are used in Fama-MacBeth cross-sectional asset pricing regressions including Market, Fama-French, Liquidity and Momentum factors. I find that Disaster risk fetches a significant premium of 0.43% for the average stock

Tail index estimation: quantile driven threshold selection

The selection of upper order statistics in tail estimation is notoriously difficult. Most methods are based on asymptotic arguments, like minimizing the asymptotic mse, that do not perform well in finite samples. Here we advance a data driven method that minimizes the maximum distance between the fitted Pareto type tail and the observed quantile. To analyse the finite sample properties of the metric we organize a horse race between the other methods. In most cases the finite sample based methods perform best. To demonstrate the economic relevance of choosing the proper methodology we use daily equity return data from the CRSP database and find economic relevant variation between the tail index estimates

Extreme downside risk in asset returns

Does extreme downside risk require a risk premium in the pricing of individual assets? Extreme downside risk is a conditional measure for the co-movement of individual stocks with the market, given that the state of the world is extremely bad. This measure, derived from statistical extreme value theory, is non-parametric. Extreme down-side risk is used in double-sorted portfolios, where I control for the five Fama-French and various non-linear asset pricing factors. I find that the average annual excess return between high- and lowexposure stocks is around 3.5%

Extreme downside risk in the cross-section of asset returns

Extreme movements in financial markets are not always reflected equally in individual stocks. Identifying which firms are unable to absorb shocks is a challenge. This paper considers extreme downside risk, an extension to Ang et al.’s (2006) downside risk framework, and the value in separating the sensitivity between extreme and non-extreme downside risk. I find that the cross-sectional average annual excess return between high and low extreme downside exposure stocks is around 3.9%. The extension differentiates itself for young firms or firms that have not experienced a severe crisis, where the risk premium ranges from 2.4% to 10.4%

Strategic uncertainty in financial markets: Evidence from a consensus pricing service

This paper measures valuation and strategic uncertainty in an over-the-counter market. The analysis uses a novel data set of price estimates that major financial institutions provide to a consensus pricing service. We model these institutions as Bayesian agents that learn from consensus prices about market conditions. Our uncertainty measures are derived from their beliefs through a structural estimation. The main contribution of the consensus pricing service is to reduce strategic uncertainty in the most opaque market segments. This stresses the importance of public data, such as financial benchmarks, for a shared understanding of market conditions in markets with limited price transparency

Covariates hiding in the tails

Scaling behavior measured in cross-sectional studies through the tail index of a power law is prone to a bias. This hampers inference; in particular, time variation in estimated tail indices may be erroneous. In the case of a linear factor model, the factor biases the tail indices in the left and right tail in opposite directions. This fact can be exploited to reduce the bias. We show how this bias arises from the factor, how to remedy for the bias and how to apply our methods to financial data and geographic location data

Challenges in implementing worst-case analysis

Worst-case analysis is used among financial regulators in the wake of the recent financial crisis to gauge the tail risk. We provide insight into worst-case analysis and provide guidance on how to estimate it. We derive the bias for the non-parametric heavy-tailed order statistics and contrast it with the semi-parametric extreme value theory (EVT) approach. We find that if the return distribution has a heavy tail, the non-parametric worstcase analysis, i.e. the minimum of the sample, is always downwards biased and hence is overly conservative. Relying on semi-parametric EVT reduces the bias considerably in the case of relatively heavy tails. But for the less-heavy tails this relationship is reversed. Estimates for a large sample of US stock returns indicate that this pattern in the bias is indeed present in financial data. With respect to risk management, this induces an overly conservative capital allocation if the worst case is estimated incorrectly

Tail index estimation: Quantile-driven threshold selection

The selection of upper order statistics in tail estimation is notoriously difficult. Methods that are based on asymptotic arguments, like minimizing the asymptotic MSE, do not perform well in finite samples. Here, we advance a data-driven method that minimizes the maximum distance between the fitted Pareto type tail and the observed quantile. To analyze the finite sample properties of the metric, we perform rigorous simulation studies. In most cases, the finite sample-based methods perform best. To demonstrate the economic relevance of choosing the proper methodology, we use daily equity return data from the CRSP database and find economically relevant variation between the tail index estimates