Narrow Results

In this paper, we address the issue of how macroeconomic conditions affect corporate bond volatility. We employ the GARCH-MIDAS multiplicative two-component model of volatility that distinguishes the short-term dynamics from the long-run component of volatility. Both the in-sample and out-of-sample analysis show that recognizing the existence of a stochastic low-frequency component captured by macroeconomic and financial indicators may improve the fit of the model to actual bond return data, relative to the constant long-run component embedded in a typical GARCH model.

The following sections are included:

• Average Returns are the Main Focus
• Compound Return Facts: Tail Risks Dominate!
• Compound Returns a Function of Risk
• Big Problem: Tail Events More Frequent than Normal Distribution
• Think Tails of the Distribution: Concentrate on Normal Events
• Relative Performance Evaluation
• Investment Strategies — Asset Allocation Static Constraints are Costly
• Factors that Affect Terminal Wealth
• Measuring Tail Risk Using Market Prices
• Tail Gains/Losses from Opiton Prices
• Enhancing Compound Returns Through Dynamic Risk Management (1996—2015)
• Using Option Prices to Forecast Risk Changing Risk Proactively
• Using Option Prices to Measure Risk
• Uncertainty of the Distribution of Returns
• Adaptive Strategy — Pre and Post “2008” Crisis
• Issues

I consider the Black–Scholes–Merton option-pricing model from several angles, including personal, technical and, most importantly, from the perspective of a paradigm-shifting mathematical formula.

Recent work has documented roughness in the time series of stock market volatility and investigated its implications for option pricing. We study a strategy for trading stocks based on measures of their implied and realized roughness. A strategy that goes long the roughest-volatility stocks and short the smoothest-volatility stocks earns statistically significant excess annual returns of 6% or more, depending on the time period and strategy details. The profitability of the strategy is not explained by standard factors. We compare alternative measures of roughness in volatility and find that the profitability of the strategy is greater when we sort stocks based on implied rather than realized roughness.We interpret the profitability of the strategy as compensation for near-term idiosyncratic event risk.

The Contingent Claims Analysis (CCA) is a general approach to analyze the stakeholders of a corporation who have contingent claims on the future, uncertain cash-flows generated by the operations of the firms. The CCA allows valuing each stakeholder’s claim and also to assess the risk incurred by the stakeholders. The CCA highlights the potential conflicts of interest among the various claimholders. In this paper, we review applications of CCA including valuation of various forms of debt, rating, credit spread, probability of default and corporate events like dividends, employee stock options and M&A. The CCA framework is shown to be useful to address all these financial questions. In this approach the starting point is that the value and the risk of the firm’s assets are given. The future distribution of the assets’ rates of return is also known and given. The focus is on the liability side of the balance sheet, i.e., the funding sources of the activity of the firm, and more generally on the financial claims of the various claimholders of the firm.

Starting from humble beginnings, the use of financial options has substantially increased as an important financial tool for both speculation and hedging over the last 50 years. This chapter discusses both the theoretical and practical applications of financial options and related models. While the content is somewhat technical, we provide illustrations of their applications in simple settings. We address particular stylized features of option pricing models.

We examine time-series features of stock returns and volatility, as well as the relation between return and volatility in four of China’s stock exchanges. Variance-ratio tests reject the hypothesis that stock return follows a random walk. We find evidence of long memory of returns. Application of GARCH and EGARCH models provides strong evidence of time-varying volatility and shows volatility is highly persistent and predictable. The results of GARCH-M do not show any relation between expected returns and expected risk. Daily trading volume used as a proxy for information arrival time has no significant explanatory power for the conditional volatility of daily returns.

This study identifies nonlinear patterns of momentum profits across stocks with different levels of return volatility and skewness. It finds that momentum profits are the largest from mildly volatile and skewed stocks; this phenomenon is consistently observed for different formation/holding periods, types of examined returns, and momentum grouping. Based on the patterns, this chapter proposes a sample filtering criterion for momentum investment; the profits accrued through the sample filtering are economically enlarged. Such an enhancement of momentum profits by the filtering process is documented in various strategies, including the conventional, 52-week high, and risk-managed momentum strategies.

The following sections are included:

• Introduction
• How to Measure Systemic Risk?
• Modelling Systemic Risk
• The Situation in Europe
• The Situation of European Institutions
• Note
• References