Petter N. Kolm

60 Years of portfolio optimization: Practical challenges and current trends

The concepts of portfolio optimization and diversification have been instrumental in the development and understanding of financial markets and financial decision making. In light of the 60year anniversary of Harry Markowitz’s paper “Portfolio Selection,” we review some of the approaches developed to address the challenges encountered when using portfolio optimization in practice, including the inclusion of transaction costs, portfolio management constraints, and the sensitivity to the estimates of expected returns and covariances. In addition, we selectively highlight some of the new trends and developments in the area such as diversification methods, risk-parity portfolios, the mixing of different sources of alpha, and practical multi-period portfolio optimization.

Incorporating Trading Strategies in the Black-Litterman Framework

It is well known that applying classical portfolio optimization in practice may lead to problems; in fact, the “optimal” portfolio may not be optimal at all. The problems encountered in real-world portfolio optimization include issues such as unstable portfolio weights, corner solutions, and poor performance. Some portfolio managers are using Bayesian estimation techniques and robust portfolio optimization to mitigate some of these problems. The Black-Litterman framework has become more popular among practitioners as it provides a flexible yet robust quantitative portfolio management tool, into which different trading strategies are easily incorporated. Keywords: portfolio optimization; Black-Litterman model; capital asset pricing model (CAPM); market equilibrium; momentum; trading strategies; portfolio rebalancing

Quadruple and octuple layer potentials in two dimensions I: Analytical apparatus

Abstract A detailed analysis is presented of all pseudo-differential operators of orders up to 2 encountered in classical potential theory in two dimensions. Each of the operators under investigation turns out to be a sum of one or more of standard operators (second derivative, derivative of the Hilbert transform, etc.), and an integral operator with smooth kernel. This classification leads to an extremely simple analysis of spectra of such operators, and simplifies the design of procedures for their numerical evaluation. In a sequel to this paper, the obtained apparatus will be used to construct stable discretizations of arbitrarily high order for a variety of boundary value problems for elliptic partial differential equations.

Hidden noise structure and random matrix models of stock correlations

We find a novel correlation structure in the residual noise of stock market returns that is remarkably linked to the composition and stability of the top few significant factors driving the returns, and, moreover, indicates that the noise band is composed of multiple sub-bands that do not fully mix. Our findings allow us to construct effective generalized random matrix theory market models that are closely related to correlation and eigenvector clustering. We show how to use these models in a simulation that incorporates heavy tails. Finally, we demonstrate how a subtle purely stationary risk estimation bias can arise in the conventional cleaning prescription.

A Simple Framework for Time Diversification

In this article the authors provide a simple but rigorous mathematical framework for time diversification. Based on this framework, we provide a measure of time diversification that can be computed for any return distribution model and any risk measure; this measure of time diversification can be empirically ascertained with non-parametric estimates of risk and with bootstrap techniques to simulate the return distribution. The authors argue that the critical issue of time diversification is not how to interpret time diversification in sequences of IID returns, but how to make long-term forecasts. The latter involves complex issues related to the distributional properties of returns, as well as memory effects and regime shifts. The authors then discuss how the distributional properties of stock returns, long memory, and regime shifts affect time diversification.

Multiperiod Portfolio Selection and Bayesian Dynamic Models

Techniques inspired by Bayesian statistics provide an elegant solution to the classic investment problem of optimally planning a sequence of trades in the presence of transaction costs.

New Kids on the Block

The evolution of quantitative methods in finance is changing the investment management industry. With an altered focus in finance and investment theory, theoretical concepts such as market efficiency and market equilibrium have ceded ground to econometric methods that allow a more pragmatic investigation of asset predictability. Mean-variance optimization, one of the cornerstones of classic finance theory, presents some problems in practice, and recent developments in Bayesian modeling and robust optimization techniques circumvent some of its weaknesses. Beyond the classic framework, we must model the feedback mechanisms that we know to operate in financial markets, with caution as to model risk, data snooping, and overfitting biases.

Best Practices in Research for Quantitative Equity Strategies

The authors examine the research process and principles underlying successful models used in quantitative equity strategies. They identify three key factors they see contributing to improved empirical work: 1) making research design a top priority, 2) making new, more extensive datasets available, and 3) making advances in computational areas such as econometrics, machine learning, and statistics. The authors explain these key factors and also share insights on how to integrate market dynamics, data, research design, advance modeling techniques, and economic/financial introspection into the research process.

On the Bayesian Interpretation of Black-Litterman

We present the most general model of the type considered by Black and Litterman (1991) after fully clarifying the duality between Black–Litterman optimization and Bayesian regression. Our generalization is itself a special case of a Bayesian network or graphical model. As an example, we work out in full detail the treatment of views on factor risk premia in the context of APT. We also consider a more speculative example in which the portfolio manager specifies a view on realized volatility by trading a variance swap.

Robust Portfolio Optimization

As the use of quantitative techniques has become more widespread in the investment industry, the issue of how to handle portfolio estimation and model risk has grown in importance. Robust optimization is a technique for incorporating estimation errors directly into the portfolio optimization process, and is typically applied in conjunction with robust statistical estimation methods. The robust optimization approach uses the distribution from the estimation process to find a portfolio allocation in one single optimization, while keeping the computational costs low. Robust portfolios tend to be less sensitive to estimation errors, offer some improved portfolio performance, and often have lower turnover ratios. Keywords: portfolio optimization; uncertainty sets; robust portfolio management; Bayesian methods; robust modeling; investment management; MSCI Barra Research Insights Report; Management Science