GICS Sectors: Taxonomy & Probabilistic Extensions

• GICS Sectors are a hierarchical system categorizing public companies into 11 sectors, 24 industry groups, 69 industries, and 158 sub-industries based on their revenue sources.
• The classification is determined by a committee assigning each firm to the sub-industry that generates the largest share of its revenue, simplifying macroeconomic analysis and portfolio construction.
• The MIS model extends GICS by using latent Dirichlet allocation to assign probabilistic industry exposures, enabling dynamic, transparent, and multi-dimensional firm classification.

The Global Industry Classification Standard (GICS) is the dominant taxonomy for categorizing public firms into industry sectors, providing a structured framework widely adopted in asset management and index construction. GICS organizes firms hierarchically: each receives a unique position in a tree comprising 11 top-level “sectors,” 24 industry groups, 69 industries, and 158 sub-industries. Firms are classified by committee into the single sub-industry generating the largest share of their revenue, ensuring total coverage and preventing overlap. While GICS has yielded robust portfolio and risk-model applications due to its simplicity and consistency, critiques—especially regarding diversified conglomerates—have spurred development of probabilistic extensions, notably the Multi-Industry Simplex (MIS) model, which captures complex, multi-sector firm exposures using mixed-membership topic modeling (Papenkov et al., 2023).

1. The GICS Taxonomy: Structure and Assignment

GICS designates each firm a unique position in a four-level tree structure:

Level	Number of Nodes	Example (for Amazon)
Sectors	11	Consumer Discretionary
Industry Groups	24	Retailing
Industries	69	Internet & Direct Marketing Retail
Sub-Industries	158	Internet & Direct Marketing Retail

Assignment proceeds as follows: a committee reviews each publicly listed company’s sources and assigns it to the sub-industry responsible for the largest share of its revenue. This “single-industry” rule simplifies macroeconomic analysis, risk decomposition, and portfolio construction. Each firm thus maps to exactly one sector at the highest level, and ultimately to one leaf node in the GICS tree.

2. Limitations of Conventional GICS Sector Classification

Although GICS offers well-recognized robustness, several structural limitations constrain its fidelity for multi-sector firms:

• One-Dimensionality: Each firm occupies only one leaf regardless of diversification, making the framework poorly suited to conglomerates (e.g., Amazon, with substantial business in retail, cloud computing, media, and logistics).
• Static Definition: Committee-driven reclassifications are infrequent, leading to taxonomies lagging behind real-world innovation (for instance, digital streaming and cloud services might not be timely recognized).
• Opacity: Assignment criteria are typically opaque and driven by manual judgment of committee members, with limited transparency apart from revenue breakdown considerations.

An illustrative failure case is Amazon, which is labeled as Consumer Discretionary under GICS, disregarding major exposures in cloud infrastructure (AWS), media, logistics, and grocery. This can mislead investors seeking to quantify exposure to technology, infrastructure, or retail-specific risks.

3. Multi-Industry Simplex (MIS): Probabilistic Industry Profiles

The MIS model augments GICS by enabling each firm to be assigned a probability-weighted vector over multiple industries instead of a single sector label. The mathematical foundation is Latent Dirichlet Allocation (LDA) applied to textual descriptions (e.g., 10-Ks, analyst reports, earnings calls).

3.1 Generative Model and Notation

Let $M$ be the number of firms, %%%%1%%%% the number of industry topics, and $V$ the preprocessed vocabulary size. The observed data for firm $m$ is a bag-of-words $\mathbf x_m = \{x_{m,1}, ..., x_{m,N_m}\}$.

Random variables:

• $\theta_m \in \Delta^K$: industry-mix vector (firm-level mixture)
• $\phi_k \in \Delta^V$: word distribution for industry $k$
• $z_{m,n} \in \{1, ..., K\}$: latent industry assignment for word $x_{m,n}$

The LDA-based generative process:

1. For each industry $k$: $\phi_k \sim \mathrm{Dirichlet}_V(\alpha)$.
2. For each firm $m$: $\theta_m \sim \mathrm{Dirichlet}_K(\beta)$.
   • For each word $n$: draw $z_{m,n} \sim \mathrm{Categorical}(\theta_m)$ and $x_{m,n} \sim \mathrm{Categorical}(\phi_{z_{m,n}})$.

The joint likelihood is

$$P(\mathbf X, \mathbf Z, \{\theta_m, \phi_k\}) = \prod_{k=1}^K P(\phi_k|\alpha) \times \prod_{m=1}^M\left[P(\theta_m|\beta)\prod_{n=1}^{N_m} P(z_{m,n}|\theta_m) P(x_{m,n}|\phi_{z_{m,n}})\right].$$

3.2 Inference and Estimation

The posterior for a firm’s industry mixture is

$$P(\theta_m|\mathbf x_m) \propto \int P(\mathbf x_m, \mathbf z_m, \theta_m, \phi) d\phi\,d\mathbf z_m.$$

Inference is conducted via collapsed Gibbs sampling, updating $z_{m,n}$ according to

$$P(z_{m,n}=k| \mathbf z_{-(m,n)},\mathbf x) \propto (n_{m,k}^{-(m,n)} + \beta_k) \cdot \frac{n_{k,v}^{-(m,n)} + \alpha_v}{\sum_{v'}(n_{k,v'}^{-(m,n)} + \alpha_{v'})}$$

where $n_{m,k}^{-(m,n)}$ and $n_{k,v}^{-(m,n)}$ are firm-level and global token counts excluding the current token.

After each sweep, posterior samples for $\phi_k$ and $\theta_m$ are drawn from their Dirichlet distributions: $$\phi_k \sim \mathrm{Dirichlet}(\alpha + \mathbf n_{k,\cdot}),\quad \theta_m \sim \mathrm{Dirichlet}(\beta + \mathbf n_{m,\cdot})$$

Final estimates are obtained via averaging over post-burn-in samples after $S$ iterations.

3.3 Model Fit and Diagnostics

Model fit is evaluated using perplexity: $$\text{Perp}(\theta_{1:M},\phi_{1:K}; \mathbf x_{1:M}) = \exp\left(-\frac{\sum_{m=1}^M \log P(\mathbf x_m | \hat\theta_m, \hat\phi)}{\sum_{m=1}^M N_m}\right)$$ A lower value denotes better generalization. However, hyperparameter and vocabulary choices are ultimately guided by interpretability and semantic coherence.

MIS is described as “clear-box” due to all parameters being interpretable conditional probabilities; the weights $$\theta_{m,k} = P(\mathrm{industry}\ k | \mathrm{firm}\ m)$$ admit direct auditing and manual adjustment.

4. Key Applications of GICS and MIS

4.1 Nearest-Neighbor Analysis

Each firm’s industry exposure vector $\hat\theta_m$ lies in the $K$-simplex. Hellinger similarity provides a metric: $$\mathrm{sim}(i,j) = 1 - \frac{1}{\sqrt{2}}\|\sqrt{\theta_i} - \sqrt{\theta_j}\|_2$$ This has revealed, for instance, that Amazon’s closest neighbors span IT, Communication Services, Consumer Discretionary, and Consumer Staples, capturing its diversified footprint. A similar pattern is seen for Apple, whose neighbors span technology, streaming, AI, and financial services.

4.2 Thematic Portfolio Construction

To design, for example, an “AI” thematic portfolio, select firms for which $P(\mathrm{AI}|\mathrm{firm}_i) > 5\%$, and assign weights

$$w_i \propto \sqrt{s_i} \cdot P(\mathrm{AI}| \mathrm{firm}_i)$$

with $s_i$ as market capitalization. The method identifies “AI-centric” firms across multiple classic GICS sectors, enabling cross-sector risk analysis and opportunities not capturable in the original GICS framework.

5. Comparative Advantages and Limitations

Advantages of MIS over classic GICS include:

• Firms can be assigned to multiple industries (multi-dimensionality).
• The taxonomy can adapt to new forms of business activity if they appear in the text data (dynamic definition).
• All model assignments are consistent across the entire universe (joint, generative model).
• Auditability and transparency: each probability is interpretable, and misassignments can be traced and corrected via semantic tree adjustment.

However, limitations persist:

• Construction of the semantic tree for text pre-processing is manual and subject to practitioner bias.
• The model cannot “discover” an industry never mentioned in the input corpus.
• Gibbs sampling and variational inference introduce estimation noise, albeit reducible with increased data or run length.

A plausible implication is that human judgment and continual recalibration remain essential for both frameworks, especially in edge cases or emergent industry domains.

6. Hybridization and Future Directions

MIS suggests a pathway to augment GICS with probabilistic weights, permitting each firm to distribute its exposure over multiple sub-industries while preserving the hierarchical structure and regulatory credibility of GICS. Such a hybrid system would offer:

• Improved risk attribution for diversified conglomerates.
• Enhanced detection of nascent, cross-cutting industries.
• Automated, data-driven reclassification as firm activities evolve, with preserved transparency.

MIS does not aim to replace GICS, but rather to enrich it—providing a more rigorous, interpretable means to model the complexity of modern corporate structures and facilitate more granular asset management applications (Papenkov et al., 2023).