While financial economics is still in its infancy when compared to the mathematical and natural sciences, it has enjoyed a spectacular period of growth over the past three decades, thanks in part to the mathematical machinery that Wiener, Ito, and others pioneered. In this review article, I shall present a survey of some recent research in this exciting area—more specifically, in empirical finance and financial econometrics—including a discussion of the random walk hypothesis, long-term memory in stock market prices, performance evaluation, and the statistical estimation of diffusion processes. It is my hope that such a survey will serve both as a tribute to the amazing reach of Nobert Wiener's research, and as an enticement to those in the "hard" sciences to take on some of the challenges of modern finance.

The practice of risk management starts with an understanding of the statistical behavior of financial asset prices over time. Models such as the random walk hypothesis, the martingale model, and geometric Brownian motion are fundamental to any analysis of financial risks and rewards, particularly for longer investment horizons. Recent empirical evidence has cast doubt on some of these models, and this article provides an overview of such evidence. I begin with a review of the random walk hypothesis and related models, including a discussion of why such models perform so poorly, and then turn to some current research on alternative models such as long-term memory models and stable distributions.

Artificial intelligence has transformed financial technology in many ways and in this review article, three of the most promising applications are discussed: neural networks, data mining, and pattern recognition. Just as indexes are meant to facilitate the summary and extraction of information in an efficient manner, sophisticated automated algorithms can now perform similar functions but at higher and more powerful levels. In some cases, artificial intelligence can save us from natural stupidity.

Despite the collapse of Long-Term Capital Management less than five years ago, the memories of those troubled times are apparently gone, replaced by concerns about the economic climate and the dearth of attractive investment opportunities. Not surprisingly, interest in alternative investments has skyrocketed. Along with opportunities for the alternative investments industry, institutional investors bring new challenges, underscoring the gap between them and hedge fund managers. The challenges revolve around risk  management — after all, outsized returns are usually accompanied by outsized risks — and fall into three categories: determining investors’ risk preferences, developing risk models for alternative investments, and blending quantitative and qualitative approaches to manager selection and capital allocation. Any complete risk management protocol should address each of these.

In this article, we attempt to quantify the potential impact of hedge funds on systemic risk by developing a number of new risk measures for hedge funds and applying them to individual and aggregate hedge-fund returns data. These measures include: illiquidity risk exposure, nonlinear factor models for hedge-fund and banking-sector indexes, logistic regression analysis of hedge-fund liquidation probabilities, and aggregate measures of volatility and distress based on regime-switching models. Our preliminary findings suggest that the hedge-fund industry may be heading into a challenging period of lower expected returns, and that systemic risk is currently on the rise. This is a redacted version of our paper "Systemic Risk and Hedge Funds".

In this article, we attempt to quantify the potential impact of hedge funds on systemic risk by developing a number of new risk measures for hedge funds and applying them to individual and aggregate hedge-fund returns data. These measures include: illiquidity risk exposure, nonlinear factor models for hedge-fund and banking-sector indexes, logistic regression analysis of hedge-fund liquidation probabilities, and aggregate measures of volatility and distress based on regime-switching models. Our preliminary findings suggest that the hedge-fund industry may be heading into a challenging period of lower expected returns, and that systemic risk is currently on the rise.

The Efficient Markets Hypothesis (EMH) refers to the notion that market prices fully reflects all available information. Developed independently by Paul A. Samuelson and Eugene F. Fama in the 1960's, this idea has been applied extensively to theoretical models and empirical studies of financial securities prices, generating considerable controversy as well as fundamental insights into the price-discovery process. The most enduring critique comes from psychologists and behavioral economists who argue that the EMH is based on counterfactual assumptions regarding human behavior, i.e., rationality. Recent advances in evolutionary psychology and the cognitive neurosciences may be able to reconcile the EMH with behavioral anomalies.

Trading volume is an important aspect of the economic interactions in financial markets among various investors. Both volume and prices are driven by underlying economic forces, and thus convey important information about the workings of the market. This chapter focuses on the empirical characteristics of prices and volume in stock markets. The interactions between prices and quantities in an equilibrium yield a rich set of implications for any asset pricing model, when an explicit link between economic fundamentals and the dynamic properties of asset returns and volume are derived. By exploiting the relation between prices and volume in the dynamic equilibrium model, one can identify and construct the hedging portfolio, which can be used by all investors to hedge against changes in market conditions. This hedging portfolio has considerable forecast power in predicting future returns of the market portfolio and its abilities to explain cross-sectional variation in expected returns is comparable to other popular risk factors such as market betas, the Fama and French SMB factor, and optimal forecast portfolios. The presence of market frictions, such as transactions costs, can influence the level of trading volume and serve as a bridge between the market microstructure literature and the broader equilibrium asset pricing literature.

The recent financial crisis has generated many distinct perspectives from various quarters. In this article, I review a diverse set of 21 books on the crisis, 11 written by academics, and 10 written by journalists and one former Treasury Secretary. No single narrative emerges from this broad and often contradictory collection of interpretations, but the sheer variety of conclusions is informative, and underscores the desperate need for the economics profession to establish a single set of facts from which more accurate inferences and narratives can be constructed.

We develop a dynamic equilibrium model of an asset market with multiple securities in which investors trade to share risks and smooth consumption over time, and investigate the empirical implications for the cross-sectional characteristics of trading volume and the dynamic volume-return relation. We extend the model to include fixed transactions costs, and when calibrated to aggregate data, the model implies realistic levels of trading volume. We also evaluate the efficacy of technical analysis in capturing the relation between prices and volume heuristically.