Knowledge-Based Systems 2022 · Semantic Models of Financial Markets

Stock Portfolio Selection Balancing Variance and Tail Risk via Stock Vector Representation Acquired from Price Data and Texts

Xin Du · Kumiko Tanaka-Ishii

An inner-product space over event distributions unifies stocks, news, and prices. Textual records of rare events become portfolio risk geometry, explicitly improving negative-return tails beyond variance risk.

Paper · DOI Research · Semantic Models of Financial Markets

Why Covariance Does Not See All Risk

The Markowitz model compresses asset risk into historical return covariance. This has clear geometry for approximately stationary fluctuations with enough samples, but financial losses are heavy-tailed. The extreme events that determine long-run risk appear only rarely in finite price histories and are systematically underestimated by covariance.

News has the opposite sampling mechanism. Small daily moves may not be reported, while crises, policy shocks, accidents, and supply-chain interruptions are recorded disproportionately. Text is therefore not a noisy substitute for prices but a biased and useful observation of the tail. The technical problem is to place prices, articles, firms, and events—heterogeneous objects—inside one interpretable risk geometry rather than concatenate sentiment scores as arbitrary features.

NESTED: A Hilbert Space Induced by Event Distributions

NESTED, NEws-STock space with Event Distribution, represents stocks, articles, and latent events in one inner-product space $\mathcal H$ . Stock vectors are determined jointly by text and prices through event distributions rather than fixed sector labels. For stocks $s_i,s_j\in\mathcal H$ ,

G_{ij}=\langle s_i,s_j\rangle_{\mathcal H},

where $G$ is their Gram matrix. A large inner product indicates similar semantic exposure to events. Heterogeneous data thus become a geometric object that can enter the same quadratic optimization as covariance without predefining labels for every event type.

There is also a theoretical connection. Covariance is an inner product between random variables in an $L^2$ space; NESTED generalizes “returns move together” to “market objects respond together under an event distribution.” Stock vectors are not auxiliary features but an extension of the Markowitz risk space.

Balancing Variance and Tail Risk in One Objective

The classical portfolio problem is

\min_w\; w^\top\Sigma w, \qquad w^\top r=E,\quad w^\top\mathbf 1=1.

NESTED supplements or reconstructs the risk matrix with the semantic Gram matrix. Price covariance primarily captures frequent, non-tail co-movement; event semantics use sparse but concentrated news evidence of extreme conditions. The two sources remain interpretable components of portfolio geometry rather than being hidden in one prediction score.

If portfolio loss $L$ has tail behaviour

\Pr(L>x)\propto x^{-\alpha},

a larger Pareto index $\alpha$ means a lighter extreme-loss tail. The paper therefore evaluates negative-return tails and risk-adjusted return in addition to average return, distinguishing higher return from apparent performance purchased with heavier tail exposure.

Consistent Evidence across Three Markets

Experiments cover 24 news–price datasets in three markets and learn stock representations from news and price history. NESTED increases the Pareto index of portfolio negative returns in all three markets. The text representation is therefore capturing risk associated with extreme-event exposure rather than only ordinary covariance.

When balancing tail and non-tail risks, the largest observed improvements are 45.5% in return and 59.4% in information ratio. The main evidence is not a single best run but the consistent direction of the tail metric across all three markets: news semantics contributes risk information outside a finite price sample.

Conclusion and Boundary

NESTED provides a mathematical interface between financial NLP and modern portfolio theory. News is elevated from an input to a prediction model into a component of the risk space, allowing semantic representations to support extreme-event management rather than only direction classification.

The representation still depends on news coverage, the text encoder, and the training window. Selective reporting may omit hidden risks or amplify attention rather than fundamentals, and vector inner products describe shared exposure rather than causal influence. Practical deployment must also include transaction costs, liquidity, short-sale constraints, and changing market regimes. A central next question is how the semantic space evolves over time and whether spectral transitions in its Gram matrix precede crises.

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