Markowitz defined portfolio risk as an internal property, built from the covariance among a book's own holdings rather than the distance to any index. Seventy years of simplification reversed that. The market beta of CAPM, the fixed style and industry axes of Barra-type models, and the promotion of benchmark deviation to the definition of risk all traded the inward view for an external one. Risk became distance from an index. For a fund that fits no benchmark, that trade fails. A global book concentrated in a few markets and a few innovation sectors has no natural index to deviate from, and the active-risk number it produces measures the mismatch, not the risk. We return to the covariance. Principal component analysis (PCA) recovers the systematic structure inside the portfolio directly from its own returns. PCA has always carried one cost: its factors resist a plain-English reading. We clear that with a generative-AI labelling layer. It names the leading factors, ranked by their actual contribution to risk rather than by universe variance, and a deterministic rubric keeps it from inventing structure the loadings do not contain. Around this sit four independent signals. Density-based clustering with a mismatch ratio flags groups whose risk outruns their capital. A sign-invariant PCA Risk Score (PRS) marks the names that build the dominant factor bets. A standalone Bleed score catches the slow capital destroyers PCA cannot see. A trailing-return timing gate routes disagreements between the risk signals and recent price action to human judgment. We run the full engine on a proxy global-innovation book of thirty names over one year.
Hedge ratios, factor models and diversified portfolios all rest on an estimate of which firms move together. That estimate is not stable: firms migrate between the groupings the market treats as coherent, and when enough migrate the organizing axes of the cross-section turn. We measure the rate of that turning as the mean squared sine of the principal angles between subdominant eigenspaces of consecutive twelve-month S&P 500 correlation matrices. A typical month rewrites a fifth of the structure and carries four-fifths forward. That rate is priced: it couples to the aggregate variance risk premium at t = 5.40, no level measure correlates above 0.32, and the implied-correlation surface spans at most 6.7 percent of it. Only the persistent component is priced - the premium compensates the pace of revision, not the distance traveled. The mechanism is prepayment: implied variance rises on impact, volatility follows two to three quarters later (simulated-null p<0.03 at h = 1-9), and the premium converges as it arrives. Three pre-registered boundaries hold: no timing alpha, no crash protection, and a downside version inseparable from intensity. The premium is, in part, rent on exposure held over a map still being redrawn.
Structured retail products are unsecured bonds subject to the default risk of the issuer. We analyze the price‐setting policy of issuers with respect to this default risk. Using a long‐term data set of discount certificates in the German market, we apply a time series IVX‐approach to find that (i) quoted prices do depend on issuer default risk, but (ii) this dependency is under‐proportional. Hence, retail investors are only partially compensated for bearing issuer default risk. A long‐term analysis covering the global financial crisis, the European debt crisis, and the succeeding calm period, as well as supporting evidence from the coronavirus crisis, provides patterns consistent with a fading attention hypothesis: When default risk has left the focus of retail investors, they are no longer compensated for it, even if it becomes substantial, as in the early months of the coronavirus crisis.
R. Baule, Falk Jensen· Journal of futures markets· 0 citations
In mean-variance portfolio analysis, the efficient frontier represents the optimal trade-off between expected return and risk, assuming stable underlying parameters. This paper investigates portfolio fragility: the instability of optimal weights, risk-adjusted performance, and diversification when model inputs and construction choices are jointly perturbed. Combining constrained Markowitz optimization with variance-based global sensitivity analysis (Sobol indices), we map out how input uncertainty and portfolio-construction choices propagate along the target-return dimension. Using an empirical universe of multi-asset exchange-traded funds (ETFs), we find a distinct transition in the sensitivity structure: in the baseline experiment, lower target returns are dominated by l2 regularization, whereas aggressive return requirements become increasingly sen- sitive to the weight cap and expected-return perturbations. This shift coincides with a sharp drop in effective diversification and a rise in weight dispersion. We extend the analysis to a multi-universe fragility atlas, showing that under a com- mon absolute concentration rule, the smallest universe is weight-cap-driven in the aggressive return region, while larger sampled universes remain more often regularization-driven. The fragile frontier serves as a direct diagnostic tool to evaluate the structural robustness of constrained optimizers without altering the underlying allocation rule.
Stefano Pellegrino, Giulia Vannucci, R. Siciliano· 0 citations
Nigerian investors diversifying into international markets face a significant obstacle in the form
of foreign exchange risk, but there is a startling lack of empirical data on its effects. This study
closes this gap by carefully examining the impact of Naira volatility (NGN/USD, NGN/GBP, and
NGN/EUR) on the risk-adjusted performance of international portfolios. We use comparative
hedging simulations and multivariate regression using monthly data from 2010–2023, which
includes Nigeria’s 2016 capital liberalisation, several currency crises, and the 2023 Naira float.
Key findings show that oil price fluctuations and inflation discrepancies increase losses, and that
a 1% increase in forex volatility lowers real risk-adjusted returns (Sortino ratio) by 0.62% (*p*
< 0.001). Importantly, despite transaction costs, forward contracts through Nigeria's Investors' &
Exporters' window prove to be the best hedge, providing net returns during crises that are 10.8
percentage points higher than unhedged portfolios.
Isibor Areghan PhD· Journal of Accounting and Fi...· 0 citations
In the context of normalized volatility in the A-share market, traditional VaR models are unable to effectively capture the tail risk of extreme market conditions, while Expected Shortfall (ES) can make up for this deficiency. This paper selects 12 A-shares from two equally weighted stock portfolios within and outside the CSI 300 index, with a sample period from May 2022 to April 2026. It uses three methods—historical simulation, parametric method (normal), and GARCH (1,1)-t—to estimate VaR and ES, and conducts backtesting using the Kupiec POFF test, the Christoffersen conditional coverage test, and the Acerbi-Székely Z2 test. The results show that GARCH (1,1)-t can more accurately characterize tail risk at a 99% confidence level. The historical simulation method is generally robust, while the normal parameter method tends to underestimate systematic risk. ES is greater than VaR in all scenarios, which verifies its stronger ability to capture extreme losses. The conclusion remains unchanged after replacing the confidence level and portfolio weights. This paper recommends that A-share investors and regulatory agencies use ES as an important supplementary indicator to VaR, and prioritize the use of GARCH-t or historical simulation methods for risk measurement.
Yuhui Gao· Advances in Economics, Manag...· 0 citations
This paper presents a comprehensive review of two foundational portfolio models in modern finance: the Markowitz mean-variance model and the Sharpe single-index model. The study systematically examines their theoretical frameworks, computational requirements, empirical performance, and practical applicability. The Markowitz model, as a model-free optimisation framework, aims to achieve theoretically optimal risk-return trade-offs by fully considering pairwise covariances among assets. However, its high sensitivity to estimation errors and intensive data requirements often limit its empirical usefulness, particularly for large portfolios. In contrast, the index model simplifies covariance estimation by attributing asset return variations to a common market factor, thereby reducing parameter dimensionality and enhancing computational efficiency. Multi-factor extensions further improve explanatory power while maintaining practical feasibility. By reviewing existing literature and empirical evidence, this paper highlights the strengths, limitations, and appropriate application scenarios of both models. The findings provide guidance for investors, portfolio managers, and researchers in selecting or integrating portfolio models to balance theoretical rigor with empirical robustness and operational efficiency.