We propose a new performance attribution framework that decomposes a constrained portfolio’s holdings, expected returns, variance, expected utility, and realized returns into components at- attributable to: (1) the unconstrained mean-variance optimal portfolio; (2) individual static constraints; and (3) information, if any, arising from those constraints. A key contribution of our framework is the recognition that constraints may contain information that is correlated with returns, in which case imposing such constraints can affect performance. We extend our framework to accommodate estimation risk in portfolio construction using Bayesian portfolio analysis, which allows one to select constraints that improve—or are least detrimental to—future performance. We provide simulations and empirical examples involving constraints on ESG portfolios. Under certain scenarios, constraints may improve portfolio performance relative to a passive benchmark that does not account for the information contained in these constraints.

A tribute to John (Jack) C. Bogle, founder of The Vanguard Group, who passed away on January 16, 2019.

We represent risk factors as sums of orthogonal components capturing fluctuations with cycles of different length. The representation leads to novel spectral factor models in which systematic risk is allowed—without being forced—to vary across frequencies. Frequency- specific systematic risk is captured by a notion of spectral beta. We show that traditional factor models restrict the spectral betas to be constant across frequencies. The restriction can hide horizon-specific pricing effects that spectral factor models are designed to re- veal. We illustrate how the methods may lead to economically meaningful dimensionality reduction in the factor space.

The value added by an active investor is traditionally measured using alpha, tracking error, and the information ratio. However, these measures do not characterize the dynamic component of investor activity, nor do they consider the time horizons over which weights are changed. In this paper, we propose a technique to measure the value of active investment that captures both the static and dynamic contributions of an investment process. This dynamic alpha is based on the decomposition of a portfolio’s expected return into its frequency components using spectral analysis. The result is a static component that measures the portion of a portfolio’s expected return resulting from passive investments and security selection and a dynamic component that captures the manager’s timing ability across a range of time horizons. Our framework can be universally applied to any portfolio and is a useful method for comparing the forecast power of different investment processes. Several analytical and empirical examples are provided to illustrate the practical relevance of this decomposition.

We use a new dataset of hedge fund returns from a separate account platform to examine (1) how much of hedge fund return smoothing is due to main-fund specific factors, such as managerial reporting discretion (2) the costs of removing hedge fund share restrictions. These accounts trade pari passu with matching hedge funds but feature third-party reporting and permissive share restrictions. We use these properties to estimate that 33% of reported smoothing is due to managerial reporting methods. The platform's fund-level liquidity is associated with costs of 1.7% annually. Investor flows chase monthly past performance on the platform but not in the associated funds.

Moderator Martin Leibowitz asked a panel of industry experts—Andrew W. Lo, Robert C. Merton, Stephen A. Ross, and Jeremy Siegel—what they saw as the most important issues in finance, especially as those issues relate to practitioners. Drawing on their vast knowledge, these panelists addressed topics such as regulation, technology, and financing society’s challenges; opacity and trust; the social value of finance; and future expected returns.

WSJ Wealth Expert Andrew W. Lo of MIT says robo advisers are the rotary phones to today’s iPhone--technology that has great potential but it still immature.

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.

Technological advances in telecommunications, securities exchanges, and algorithmic trading have facilitated a host of new investment products that resemble theme-based passive indexes but which depart from traditional market-cap-weighted portfolios. I propose broadening the definition of an index using a functional perspective—any portfolio strategy that satisfies three properties should be considered an index: (1) it is completely transparent; (2) it is investable; and (3) it is systematic, i.e., it is entirely rules-based and contains no judgment or unique investment skill. Portfolios satisfying these properties that are not market-cap-weighted are given a new name: “dynamic indexes.” This functional definition widens the universe of possibilities and, most importantly, decouples risk management from alpha generation. Passive strategies can and should be actively risk managed, and I provide a simple example of how this can be achieved. Dynamic indexes also create new challenges of which the most significant is backtest bias, and I conclude with a proposal for managing this risk.

Pioneered by the Nobel Prize–winning economist Harry Markowitz over half a century ago, portfolio theory is one of the oldest branches of modern financial economics. It addresses the fundamental question faced by an investor: how should money best be allocated across a number of possible investment choices? That is, what collection or portfolio of financial assets should be chosen? In this article, we describe the fundamentals of portfolio theory and methods for its practical implementation. We focus on a fixed time horizon for investment, which we generally take to be a year, but the period may be as short as days or as long as several years. We summarize many important innovations over the past several decades, including techniques for better understanding how financial prices behave, robust methods for estimating input parameters, Bayesian methods, and resampling techniques.

We apply spectral techniques to analyze the volatility and correlation of U.S. common-stock returns across multiple time horizons at the aggregate-market and individual-firm level. Using the cross-periodogram to construct frequency bandlimited measures of variance, correlation and beta, we find that volatilities and correlations change not only in magnitude over time, but also in frequency. Factors that may be responsible for these trends are proposed and their implications for portfolio construction are explored.

In Brennan and Lo (2010), a mean-variance efficient frontier is defined as “impossible” if every portfolio on that frontier has negative weights, which is incompatible with the Capital Asset Pricing Model (CAPM) requirement that the market portfolio is mean-variance efficient. We prove that as the number of assets n grows, the probability that a randomly chosen frontier is impossible tends to one at a geometric rate, implying that the set of parameters for which the CAPM holds is extremely rare. Levy and Roll (2014) argue that while such “possible”frontiers are rare, they are ubiquitous. In this reply, we show that this is not the case; possible frontiers are not only rare,but they occupy an isolated region of mean-variance parameter space that becomes increasingly remote as n increases. Ingersoll (2014) observes that parameter restrictions can rule out impossible frontiers, but in many cases these restrictions contradict empirical fact and must be questioned rather than blindly imposed.

The hedge-fund industry has grown rapidly over the past two decades, offering investors unique investment opportunities that often reflect more complex risk exposures than those of traditional investments. In this article, we present a selective review of the recent academic literature on hedge funds as well as updated empirical results for this industry. Our review is written from several distinct perspectives: the investor’s, the portfolio manager’s, the regulator’s, and the academic’s. Each of these perspectives offers a different set of insights into the financial system, and the combination provides surprisingly rich implications for the Efficient Markets Hypothesis, investment management, systemic risk, financial regulation, and other aspects of financial theory and practice.

Some economic events are so major and unsettling that they “change everything.” Such is the case with the financial crisis that started in the summer of 2007 and is still a drag on the world economy. Yet enough time has now elapsed for economists to consider questions that run deeper than the usual focus on the immediate causes and consequences of the crisis. How have these stunning events changed our thinking about the role of the financial system in the economy, about the costs and benefits of financial innovation, about the efficiency of financial markets, and about the role the government should play in regulating finance? In Rethinking the Financial Crisis, some of the nation’s most renowned economists share their assessments of particular aspects of the crisis and reconsider the way we think about the financial system and its role in the economy.

The portfolio optimization problem has attracted researchers from many disciplines to resolve the issue of poor out-of-sample performance due to estimation errors in the expected returns. A practical method for portfolio construction is to use assets’ ordering information, expressed in the form of preferences over the stocks, instead of the exact expected returns. Due to the fact that the ranking itself is often described with uncertainty, we introduce a generic robust ranking model and apply it to portfolio optimization. In this problem, there are n objects whose ranking is in a discrete uncertainty set. We want to find a weight vector that maximizes some generic objective function for the worst realization of the ranking. This robust ranking problem is a mixed integer minimax problem and is very difficult to solve in general. To solve this robust ranking problem, we apply the constraint generation method, where constraints are efficiently generated by solving a network flow problem. For empirical tests, we use post-earnings-announcement drifts to obtain ranking uncertainty sets for the stocks in the DJIA index. We demonstrate that our robust portfolios produce smaller risk compared to their non-robust counterparts.