Base Portfolio Research Articles

Risk optimizations on basis portfolios: The role of sorting

This paper investigates the mean–variance and diversification properties of risk-based strategies executed on style or basis portfolios. We show that the performance of these risk strategies is highly sensitive to the sorting procedure used to form the basis assets. Whereas the extant literature provides mixed support for the outperformance of smart beta strategies based on scientific diversification, our designed strategies outperform both the market model and multifactor model. Our testing framework is based on bootstrapped mean–variance spanning tests and shows valid conclusions when controlling for multiple testing, transaction costs, and luck from random basis portfolio construction rules. Economically, our results are supported by diversification-based properties. • The dependent sorting procedure improves the efficiency of basis portfolios. • Low-risk optimizations on dependent basis portfolios outperform traditional portfolios. • Maximum diversification and minimum variance deliver very strong outperformance. • Smart betas on dependent portfolios span a larger set of traditional portfolios.

Benchmarking Individual Corporate Bonds

We propose an alternative approach to the linear factor model to estimate and decompose asset risk premia in empirical asset pricing. To resolve the high-dimensional sort difficulty in forming characteristic-based benchmark portfolios, we introduce a benchmark combination model (BCM) that combines multiple basis portfolios as the pricing kernel. With a non-arbitrage objective, our approach minimizes cross-sectional pricing errors and identifies the sources of risk through the combination of basis portfolios. For a 40-year sample for U.S. corporate bonds, we find that BCM outperforms standard factor models in pricing corporate bonds. Second, our study shows that credit ratings, downside risk, and short-term reversal are primary sources of bond risk premia. Finally, incorporating machine learning forecasts into the BCM, we find strong evidence of return predictability.

Factoring characteristics into returns: A clinical study on the SMB and HML portfolio construction methods

Abstract Factor performance is highly sensitive to the number of stocks composing its long and short basis portfolios. We examine three methodological choices that have an impact on portfolio diversification: the (in)dependence and the (a)symmetry of the stock sorting procedure and the sorting breakpoints. We show that these methodological choices have to be considered jointly and that a dependent (D) sort that starts with the control variables with whole sample or “name” (N) breakpoints and that performs a symmetric (S) sort on characteristics minimizes the biases from unpriced risks. This paper also demonstrates that the biases introduced by currently popular sorting methodologies can become very severe under specific market conditions and are not driven by small capitalizations. This alternative framework generates much stronger “turn-of-the-year” size and “through-the-year” book-to-market effects than what is conventionally documented.

When Factors Do Not Span Their Basis Portfolios

To price assets with a parsimonious set of factor-mimicking portfolios, one typically identifies and weights well-diversified basis portfolios. Traditional weightings lead to factor-mimicking portfolios that are unlikely to price even the basis portfolios from which they are formed. We offer a method to combine basis portfolios into a single factor-mimicking portfolio that is closely linked to the optimal portfolio. In practice, this method improves the pricing accuracy of parsimonious factor models, even for anomaly portfolios formed from characteristics that are distinct from those underlying the basis portfolios.

Improving Factor Models

Factor-mimicking portfolios typically identify and weight well-diversified basis portfolios. Improving weightings of the basis portfolios so that they are more closely related to the optimal portfolio’s weights enhances the pricing accuracy of parsimonious factor models. In this article, the authors—one of whom was a student of Professor Stephen Ross at the Yale School of Management and later a Ross coauthor—show that this can be achieved with known ex post efficiency criteria, applied with common sense that recognizes when statistical biases are minimal. These alternatives to traditional weightings, such as equal long–short portfolios, help explain the returns of popular anomaly portfolios.

Factoring Characteristics into Returns: A Clinical Approach to Fama-French Portfolio Decomposition

Factor performance is highly sensitive to the number of stocks composing its long and short basis portfolios. We examine three methodological choices that have an impact on portfolio diversification: the (in)dependence and the (a)symmetry of the stock sorting procedure and the sorting breakpoints. We show that these methodological choices have to be considered jointly and that a dependent (D) sort that starts with the control variables with whole sample or “name” (N) breakpoints and that performs a symmetric (S) sort on characteristics minimizes the biases from unpriced risks. This paper also demonstrates that the biases introduced by currently popular sorting methodologies can become very severe under specific market conditions and are not driven by small capitalizations. This alternative framework generates much stronger “turn-of-the- year” size and “through-the-year” book-to-market effects than what is conventionally documented.

Smart Equity Investing: Implementing Risk Optimization Techniques on Strategic Beta Portfolios

This paper investigates the mean-variance and diversification properties of risk-based strategies executed on style or basis portfolios. We show that the performance of these risk strategies is highly sensitive to the sorting procedure used to form the basis assets. Whereas the extant literature provides mixed support for the outperformance of smart beta strategies based on scientific diversification, our designed strategies outperform both the market model and multifactor model. Our testing framework is based on bootstrapped mean-variance spanning tests and shows valid conclusions when controlling for multiple testing, transaction costs, and luck from random basis portfolio construction rules. Economically, our results are supported by diversification-based properties.

The CDS‐Bond Basis Arbitrage and the Cross Section of Corporate Bond Returns

We provide a comprehensive empirical analysis on the implication of CDS‐Bond basis arbitrage for the pricing of corporate bonds. Basis arbitrageurs introduce new risks such as funding liquidity and counterparty risk into the corporate bond market, which was dominated by passive investors before the existence of credit default swap (CDS). We show that a basis factor, constructed as the return differential between LOW and HIGH quintile basis portfolios, is a superior empirical proxy that captures the new risks. In the cross section of investment grade bond returns, the basis factor carries an annual risk premium of about 3% in normal periods. © 2017 Wiley Periodicals, Inc. Jrl Fut Mark 37:836–861, 2017

When Factors Don't Span Their Basis Portfolios

To price assets with a parsimonious set of factor-mimicking portfolios, one typically identifies and weights well-diversified basis portfolios - assets grouped by a set of characteristics. Traditional weightings - like long-short return spreads - lead to factors that are unlikely to price even the basis portfolios they are formed from. This is because the number of true factors likely exceeds the number of factor-mimicking portfolios. To avoid generating non-zero alphas for spurious reasons, we offer a method to combine basis portfolios into a single factor that tends to span the optimal portfolio, thereby producing zero alphas. In practice, this adjustment significantly improves the pricing accuracy of parsimonious factor models, even for investment strategies that have long been regarded as having abnormal returns.

The CDS-Bond Basis Arbitrage and the Cross Section of Corporate Bond Returns

We provide a comprehensive empirical analysis on the implication of CDS-Bond basis arbitrage for the pricing of corporate bonds. Basis arbitrageurs introduce new risks such as funding liquidity and counterparty risk into the corporate bond market, which was dominated by passive investors before the existence of CDS. We show that a basis factor, constructed as the return differential between LOW and HIGH quintile basis portfolios, is a superior empirical proxy that captures the new risks. In the cross section of investment grade bond returns, the basis factor carries an annual risk premium of about 3% in normal periods. However, speculative grade bonds are not affected by the basis factor as they are not widely used in the basis arbitrage.

The CDS-Bond Basis and the Cross Section of Corporate Bond Returns

The CDS/Bond basis trade has played an important role in the current financial crisis. Many banks and hedge funds, such as Deutsche Bank, Merrill Lynch, and Citadel, have lost billions of dollars in this trade. The widening of the basis has also created significant disruptions in the credit market. In this paper, we provide a comprehensive empirical analysis on the CDS/bond basis and the impact of the basis on expected corporate bond returns. We construct the basis based on CDS spreads from Markit and bond prices from TRACE and NAIC from 2001 to 2008. We find that on average the basis of investment grade bonds is negative during our entire sample and that bonds with lower basis tend to be older and have lower rating, longer maturity, higher duration and convexity. We also find that low basis bonds tend to have higher future returns than high basis bonds and that the basis can predict future returns of individual bonds and bond portfolios. Most important, we find that the basis factor, constructed as the return differential between low and high basis portfolios, helps explaining the cross-sectional differences in the expected returns of corporate bonds even after controlling for most known systematic risk factors.

Factor representing portfolios in large asset markets

We study the properties of mimicking portfolios in an intertemporal APT model, in which the conditional mean and covariance matrix of returns vary in an interdependent manner. We use a signal extraction approach, and relate the efficiency of (possibly) dynamic basis portfolios to mean square error minimisation. We prove that many portfolios converge to the factors as the number of assets increases, but show that the conditional Kalman filter portfolios are the ones with both minimum tracking error variability, and maximum correlation with the common factors. We also show that our conclusions are unlikely to change when using parameter estimates.

Diversification and the Optimal Construction of Basis Portfolios

Nontrivial diversification possibilities arise when a factor model describes security returns. This paper catalogs the merits of alternative strategies for constructing basis portfolios to mimic the common factors. We show how to use the 𝜒2 statistic for the joint significance of mean basis portfolio returns to rank alternative procedures and the bootstrap to perform inferences on the disparity between 𝜒2 statistics across portfolio formation procedure, estimation method, cross-section size, and number of factors. Our main conclusion is that maximum likelihood factor analysis coupled with minimum idiosyncratic risk portfolio formation yields economically and statistically superior basis portfolios compared with those derived from asymptotic principal components.

Factor Representing Portfolios in Large Asset Markets

We study the properties of mimicking portfolios in an intertemporal APT model, in which the conditional mean and covariance matrix of returns vary in an interdependent manner. We use a signal extraction approach, and relate the efficiency of (possibly) dynamic basis portfolios to mean square error minimisation. We prove that many portfolios converge to the factors as the number of assets increases, but show that the conditional Kalman filter portfolios are the ones with both minimum tracking error variability, and maximum correlation with the common factors. We also show that our conclusions are unlikely to change when using parameter estimates.

The empirical foundations of the arbitrage pricing theory

Abstract This paper uses maximum-likelihood factor analysis of large cross-sections to examine the validity of the arbitrage pricing theory (APT). We are unable to explain the expected returns on firm size portfolios, although we do explain the expected returns on portfolios formed on the basis of dividend yield and own variance, where risk adjustment using the usual CAPM market proxies fails. We also compare alternate versions of the APT and sharply reject the hypothesis that basis portfolios formed to mimic the factors span the mean-variance frontier of the individual assets.