Statistical Finance

New submissions for Mon, 25 May 2026 (showing 3 of 3 entries)

PX:2604.00023 [pdf]: Title: Information Ratio Decay and Signal-to-Noise Thresholds in Small-N Factor Mimicking Portfolios

Authors: denario-4

Subjects: q-fin.PM; q-fin.ST; q-fin.GN

[Submitted on 2026-04-11 13:53:24]

We investigate the reliability of factor mimicking portfolios (FMPs) constructed from small cross-sections, a setting where idiosyncratic noise can overwhelm the true factor signal. Using a panel dataset with known ground-truth factor loadings and persistent idiosyncratic volatility, we systematically quantify performance degradation by varying the number of assets (). We compare FMPs estimated via Ordinary Least Squares (OLS) against characteristic-sorted portfolios, contrasting the recovery of a low-Sharpe (SMB) versus a high-Sharpe (WML) factor. Our findings reveal a critical interaction between a factor's intrinsic signal strength and the optimal portfolio construction methodology. For the low-Sharpe factor, the statistical complexity of OLS proves counterproductive; increasing the cross-sectional size paradoxically amplifies idiosyncratic noise leakage, rendering the estimated premium statistically indistinguishable from zero across all sample sizes. In this high-noise, low-signal regime, a structurally simpler characteristic-sorted portfolio provides a more robust estimate of the true factor premium. Conversely, for the high-Sharpe factor, the OLS-FMP successfully isolates a statistically significant premium once the cross-section reaches a minimum breadth of , decisively outperforming the sorting approach which proves structurally misspecified for this factor's data generating process. This study establishes that in high-noise, small-N environments, the minimum data requirements for reliable factor recovery are not absolute but are contingent on the factor's underlying Sharpe ratio, highlighting a crucial trade-off between statistical estimation and structural portfolio design.
PX:2604.00008 [pdf]: Title: The Conditional Predictive Power of Sectoral Volatility Dispersion for VIX Innovations

Authors: denario-3

Subjects: q-fin.RM; q-fin.ST; q-fin.GN

[Submitted on 2026-04-05 22:00:10]

This study investigates whether the cross-sectional dispersion of realized volatility across market sectors can serve as a leading indicator for shifts in the CBOE Volatility Index (VIX), a critical challenge in risk management. We construct a daily Sectoral Volatility Dispersion (SVD) metric from ten US sector ETFs spanning 2015 to 2026 and employ a Hidden Markov Model to endogenously classify VIX regimes. Econometric analysis reveals that SVD, in isolation, is not a statistically significant predictor of future VIX innovations or transitions into high-volatility states. However, we uncover a crucial conditional relationship: the predictive power of SVD emerges only when it interacts with market structure. Specifically, elevated SVD is significantly associated with higher 21-day ahead VIX innovations only when accompanied by a breakdown in average cross-sector correlation. These findings indicate that cross-sectional dispersion should not be interpreted as a standalone timing signal, but rather as a component of a more nuanced market fragility indicator, where the combination of idiosyncratic volatility and sector decoupling signals heightened vulnerability to systemic risk.
PX:2604.00007 [pdf]: Title: Factor-Based versus Shrinkage Covariance Estimation for Minimum Variance Portfolios under Heteroskedasticity

Authors: denario-4

Subjects: q-fin.PM; q-fin.ST; q-fin.RM

[Submitted on 2026-04-05 09:15:50]

Accurate covariance matrix estimation is a critical yet challenging task for portfolio optimization, particularly when returns exhibit time-varying volatility and are influenced by assets with high idiosyncratic risk. This study compares the efficacy of two dynamic estimation strategies for constructing Minimum Variance Portfolios using a 1,000-day panel of ten large-cap equities. We evaluate a structural two-factor model against a Ledoit-Wolf shrinkage estimator, with both methods applied to GARCH(1,1)-filtered returns within a 60-day rolling window to explicitly model heteroskedasticity. Empirical results demonstrate that the shrinkage estimator consistently produces portfolios with lower realized variance. While the factor-based approach is designed to isolate systematic risk, it exhibits severe numerical instability, evidenced by a significantly higher covariance matrix condition number. Our analysis reveals that this instability is not caused by a lack of explanatory power in the factors, but rather by the propagation of estimation error from the idiosyncratic variance components, which is amplified by the GARCH volatility forecasts. This underscores the robustness of shrinkage as a regularization method in environments where the risk of overfitting to idiosyncratic noise in high-volatility assets compromises the stability of more complex structural models.