Spectral Portfolio Theory
Economic shocks can have diverse effects on financial market dynamics at different time horizons, yet traditional portfolio management tools do not distinguish between short- and long-term components in alpha, beta, and covariance estimators. In this paper, we apply spectral analysis techniques to quantify stock-return dynamics across multiple time horizons.Using the Fourier transform, we decompose asset-return variances, correlations, alphas, and betas into distinct frequency components. These decompositions allow us to identify the relative importance of specific time horizons in determining each of these quantities, as well as to construct mean-variance-frequency optimal portfolios. Our approach can be applied to any portfolio, and is particularly useful for comparing the forecast power of multiple investment strategies. We provide several numerical and empirical examples to illustrate the practical relevance of these techniques.
Black’s Leverage Effect is Not Due to Leverage
with Jasmina Hasanhodzic,
One of the most enduring empirical regularities in equity markets is the inverse relationship between stock prices and volatility, first documented by Black (1976) who attributed it to the effects of financial leverage. As a company's stock price declines, it becomes more highly leveraged given a fixed level of debt outstanding, and this increase in leverage induces a higher equity-return volatility. In a sample of all-equity-financed companies from January 1972 to December 2008, we find that the leverage effect is just as strong if not stronger, implying that the inverse relationship between price and volatility is not driven by financial leverage.
Measuring Systemic Risk in the Finance and Insurance Sectors
with Monica Billio, Mila Getmansky, and Loriana Pelizzon,
A significant contributing factor to the Financial Crisis of 2007–2009 was the apparent interconnectedness among hedge funds, banks, brokers, and insurance companies, which amplified shocks into systemic events. In this paper, we propose five measures of systemic risk based on statistical relations among the market returns of these four types of financial institutions. Using correlations, cross-autocorrelations, principal components analysis, regime-switching models, and Granger causality tests, we find that all four sectors have become highly interrelated and less liquid over the past decade, increasing the level of systemic risk in the finance and insurance industries. These measures can also identify and quantify financial crisis periods. Our results suggest that while hedge funds can provide early indications of market dislocation, their contributions to systemic risk may not be as significant as those of banks, insurance companies, and brokers who take on risks more appropriate for hedge funds.
Is It Real, or Is It Randomized?: A Financial Turing Test
with Jasmina Hasanhodzic and Emanuele Viola,
We construct a financial "Turing test" to determine whether human subjects can differentiate between actual vs. randomized financial returns. The experiment consists of an online videogame where players are challenged to distinguish actual financial market returns from random temporal permutations of those returns. We find overwhelming statistical evidence (p-values no greater than 0.5%) that subjects can consistently distinguish between the two types of time series, thereby refuting the widespread belief that financial markets "look random". A key feature of the experiment is that subjects are given immediate feedback regarding the validity of their choices, allowing them to learn and adapt. We suggest that such novel interfaces can harness human capabilities to process and extract information from financial data in ways that computers cannot
Agent-Based Models of Financial Markets: A Comparison with Experimental Markets
with Nicholas Chan, Blake LeBaron, and Tomaso Poggio,
We construct a computer simulation of a repeated double-auction market, designed to match those in experimental-market settings with human subjects, to model complex interactions among artificially-intelligent traders endowed with varying degrees of learning capabilities. In the course of six different experimental designs, we investigate a number of features of our agent-based model: the price efficiency of the market, the speed at which prices converge to the rational expectations equilibrium price, the dynamics of the distribution of wealth among the different types of AI-agents, trading volume, bid/ask spreads, and other aspects of market dynamics. We are able to replicate several findings of human-based experimental markets, however, we also find intriguing differences between agent-based and human-based experiments.