Professor Baeho Kim of Korea University Business School received the SK Award for March 2026 for his research that improves the accuracy of risk estimation in high-dimensional portfolios using long-history data.

This paper, for which I served as the corresponding author, was first conceived during my first sabbatical at UC Berkeley in 2016. After returning to Korea, I took on administrative roles as part of the Business School administration and later assumed responsibilities related to the Business Analytics program. While dedicating myself to these duties, financial data analysis techniques relevant to this research topic advanced rapidly, and I faced the challenge of having to fundamentally revise the study’s direction and core methodology.

Nevertheless, thanks to the understanding and support of my co-authors, I did not give up and continued my research efforts. Ultimately, through my second sabbatical in 2023, which allowed me to revisit UC Berkeley, and with the support of Korea University’s flexible semester system, I was able to bring the research to fruition. I would like to express my sincere gratitude to Korea University Business School for providing opportunities for sustained international collaborative research. 

• Title of Paper : Long-History Principal Component Analysis in a Dynamic Factor Model with Weak Loadings  

• Journal : Operations Research  

• Publication Date : March 11, 2026 (online publication; Articles in Advance, forthcoming in print)  

• Summary of Key Findings : 

This study proposes an innovative framework to address the persistent issue of “second-order risk (SOR)” bias in high-dimensional portfolio management. Second-order risk refers to the discrepancy between a portfolio’s predicted risk and its realized performance, which is primarily driven by estimation errors in the covariance and precision matrices of asset returns.

In traditional financial practice, it has been standard practice to use relatively short data histories—typically around one year (approximately 250 days)—to capture rapidly changing market conditions and industry dynamics.

However, this study shows that such conventional approaches can misinterpret random noise as genuine market signals, thereby inducing “excess dispersion bias” in estimated factor loadings. As a result, optimized portfolios may appear safer than they actually are, exposing investors to unforeseen risks and ultimately undermining risk management.

This study formally demonstrates this mechanism through a mathematical theoretical model. Specifically, even in dynamic environments where factor loadings vary over time, or in “weak loadings” settings where effects are concentrated in specific sectors, the study proves that extending the data history for covariance estimation to six years (approximately 1,500 days) and applying a Long-History PCA approach ensures the statistically consistent convergence of covariance and precision matrix estimates. In other words, sufficiently long historical data act as a crucial stabilizer that helps mitigate market instability.

These theoretical findings are strongly supported by both Monte Carlo simulations and empirical analyses using real stock market data from the United States and Europe. In simulations designed to reflect realistic volatility structures and sector-specific risk factors, LH-PCA achieved a substantial reduction in SOR bias compared to conventional PCA methods based on one-year data, the Ledoit-Wolf shrinkage estimator, and GPS correction techniques. Empirical results from the U.S. (CRSP) and European (EURO) markets further confirm that the use of long data histories substantially improves the accuracy of covariance structure estimation and portfolio volatility prediction.

In conclusion, the LH-PCA framework proposed in this study provides a robust and rigorous foundation for constructing more resilient and well-diversified portfolios in modern data-driven risk management. 

▶ Read the full paper: Long-History Principal Component Analysis in a Dynamic Factor Model with Weak Loadings