arXiv subjects

Lisa R. Goldberg

Publications and source records attributed to Lisa R. Goldberg.

7 recordsLinked to original sources

arXiv2026

Principal component error in high-dimensional factor models

In a statistical factor model, principal components (or eigenvectors) of a sample covariance matrix serve as estimates of {\it principal directions}, the true drivers of co-movement of a collection of observed variables. We write the often substantial error in these estimates as a sum of two interpretable terms, which we show have almost sure asymptotic limits as the number of variables grows with sample size bounded. This scenario is commonplace in financial economics, genomics, machine learning and signal processing. {\it Out-of-subspace error} measures the distance from an estimate to the subspace spanned by population factor exposures. It can be expressed in terms of data, providing an estimable floor for error. {\it In-subspace error} arises from the fixed sample size of the latent factor returns and cannot be estimated from data alone. We illustrate our error analysis with a three-factor simulation of the US public equity market, showing the dependence of the magnitude of the error and its components on dimension and sample size. In that simulation, out-of-subspace error dominates. Researchers who rely on principal component analysis to estimate factor models can use our results to quantify errors in model-based predictions and attributions.

math.ST↗

arXiv2026

A Levered ETF Anomaly Explained

Counterintuitively, the S&P 500 Index rose between January 1, 2022, and December 29, 2023, while exchange-traded funds (ETFs) seeking to deliver 2x and 3x daily returns of the index delivered substantially negative returns. Roughly two-thirds of the difference between the returns of the index and the levered ETFs can be attributed to compounding and volatility. The remaining difference is explained by the covariance between the ETFs' deviations from constant leverage and the index's return.

q-fin.PM↗

arXiv2023

Sustainable Investing and the Cross-Section of Returns and Maximum Drawdown

We use supervised learning to identify factors that predict the cross-section of returns and maximum drawdown for stocks in the US equity market. Our data run from January 1970 to December 2019 and our analysis includes ordinary least squares, penalized linear regressions, tree-based models, and neural networks. We find that the most important predictors tended to be consistent across models, and that non-linear models had better predictive power than linear models. Predictive power was higher in calm periods than in stressed periods. Environmental, social, and governance indicators marginally impacted the predictive power of non-linear models in our data, despite their negative correlation with maximum drawdown and positive correlation with returns. Upon exploring whether ESG variables are captured by some models, we find that ESG data contribute to the prediction nonetheless.

q-fin.ST↗

arXiv2017

Do Steph Curry and Klay Thompson Have Hot Hands?

Star Golden State Warriors Steph Curry, Klay Thompson, and Kevin Durant are great shooters but they are not streak shooters. Only rarely do they show signs of a hot hand. This conclusion is based on an empirical analysis of field goal and free throw data from the 82 regular season and 17 postseason games played by the Warriors in 2016--2017. Our analysis is inspired by the iconic 1985 hot-hand study by Thomas Gilovitch, Robert Vallone and Amos Tversky, but uses a permutation test to automatically account for Josh Miller and Adam Sanjurjo's recent small sample correction. In this study we show how long standing problems can be reexamined using nonparametric statistics to avoid faulty hypothesis tests due to misspecified distributions.

stat.AP↗

arXiv2016

Drawdown: From Practice to Theory and Back Again

Maximum drawdown, the largest cumulative loss from peak to trough, is one of the most widely used indicators of risk in the fund management industry, but one of the least developed in the context of measures of risk. We formalize drawdown risk as Conditional Expected Drawdown (CED), which is the tail mean of maximum drawdown distributions. We show that CED is a degree one positive homogenous risk measure, so that it can be linearly attributed to factors; and convex, so that it can be used in quantitative optimization. We empirically explore the differences in risk attributions based on CED, Expected Shortfall (ES) and volatility. An important feature of CED is its sensitivity to serial correlation. In an empirical study that fits AR(1) models to US Equity and US Bonds, we find substantially higher correlation between the autoregressive parameter and CED than with ES or with volatility.

q-fin.PM↗

arXiv2013

Risk Without Return

Risk-only investment strategies have been growing in popularity as traditional in- vestment strategies have fallen short of return targets over the last decade. However, risk-based investors should be aware of four things. First, theoretical considerations and empirical studies show that apparently dictinct risk-based investment strategies are manifestations of a single effect. Second, turnover and associated transaction costs can be a substantial drag on return. Third, capital diversification benefits may be reduced. Fourth, there is an apparent connection between performance and risk diversification. To analyze risk diversification benefits in a consistent way, we introduce the Risk Diversification Index (RDI) which measures risk concentrations and complements the Herfindahl-Herschman Index (HHI) for capital concentrations.

q-fin.ST↗

arXiv2013

Minimizing Shortfall

This paper describes an empirical study of shortfall optimization with Barra Extreme Risk. We compare minimum shortfall to minimum variance portfolios in the US, UK, and Japanese equity markets using Barra Style Factors (Value, Growth, Momentum, etc.). We show that minimizing shortfall generally improves performance over minimizing variance, especially during down-markets, over the period 1985-2010. The outperformance of shortfall is due to intuitive tilts towards protective factors like Value, and away from aggressive factors like Growth and Momentum. The outperformance is largest for the shortfall that measures overall asymmetry rather than the extreme losses.

q-fin.PM↗