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Author: Ivchenko, Oleh Affiliation: Odessa National Polytechnic University Series: AI Portfolio Optimisation Year: 2025

Abstract

Portfolio decision quality degrades when environmental entropy — the degree of unpredictability in the market system — exceeds the capacity of available information to characterize it. This paper formalizes the concept of environmental entropy in the context of pharmaceutical portfolio management and demonstrates its impact on Decision Readiness Index (DRI) dimension R5 (temporal stability). We analyze the Ukrainian pharmaceutical market from 2020 to 2025, a period that encompassed pandemic-driven demand shocks, supply chain disruptions, and full-scale military conflict — providing an extreme-case empirical study of entropy-driven decision readiness collapse. We show that aggregate DRI scores for Ukrainian pharmaceutical portfolios declined sharply following entropy-generating events, validating R5 as a leading indicator of portfolio management degradation. Implications for crisis-period portfolio governance are discussed.

1. Introduction

In information theory, entropy measures the unpredictability of a random variable: high entropy indicates that outcomes are spread across many possibilities and difficult to predict from historical patterns. This concept has direct relevance to portfolio decision-making: when the environment generating market data becomes highly entropic — unpredictable, structurally unstable, or discontinuously changing — historical data loses predictive validity and optimization models built on that data become unreliable.

The Holistic Portfolio Framework (HPF) operationalises this insight through the R5 (temporal stability) dimension of the Decision Readiness Index (DRI). R5 captures the degree to which the data-generating process has remained stable over the relevant historical horizon. High R5 values indicate a stable, predictable environment where historical patterns are likely to persist. Low R5 values indicate that structural breaks have occurred and historical data should be discounted or disregarded.

Ukraine’s pharmaceutical market between 2020 and 2025 provides an exceptional empirical context for studying R5 dynamics. During this period, the market experienced three distinct entropy-generating shocks: the COVID-19 pandemic (2020–2021), post-pandemic normalization turbulence (2021–2022), and full-scale military conflict beginning in February 2022. Each shock produced measurable increases in environmental entropy that are reflected in DRI/R5 trajectories.

2. Theoretical Framework: Environmental Entropy

2.1 Definition

We define environmental entropy $H(s,t)$ for portfolio segment $s$ at time $t$ as:

$$H(s,t) = -\sum{k} pk(s,t) \log p_k(s,t)$$

where $p_k(s,t)$ represents the probability of outcome $k$ under current environmental conditions. In practice, this is estimated through a composite of observable entropy indicators:

$$H(s,t) = \alpha1 \cdot H{demand}(s,t) + \alpha2 \cdot H{supply}(s,t) + \alpha3 \cdot H{macro}(s,t) + \alpha4 \cdot H{geo}(s,t)$$

with default weights $\alpha_i = 0.25$.

2.2 Entropy Components

$H_{demand}$ (demand entropy): Measured through the coefficient of variation of demand, the frequency of structural breaks in the demand series, and the forecast error ratio (actual vs. predicted). High demand entropy indicates that future demand patterns cannot be reliably inferred from historical data.

$H_{supply}$ (supply entropy): Measured through supplier availability uncertainty, lead time variability, and supply chain disruption frequency. High supply entropy indicates that inventory and availability planning is unreliable.

$H_{macro}$ (macroeconomic entropy): Measured through GDP volatility, inflation rate instability, currency exchange rate volatility, and credit risk indicators. High macroeconomic entropy affects pricing, costs, and financial planning.

$H_{geo}$ (geopolitical entropy): Measured through territorial control stability, infrastructure integrity indicators, trade route disruption, and regulatory continuity. This component is typically near zero in stable markets but becomes dominant during conflict.

2.3 Connection to R5

R5 is derived from $H(s,t)$ through an exponential decay function:

$$R5(s,t) = \exp(-\kappa \cdot H_{norm}(s,t))$$

where $H_{norm}$ is the normalized entropy (scaled to [0,1] against a historical maximum) and $\kappa = 1.5$ (default). This produces R5 scores that decline rapidly under high-entropy conditions, ensuring that the DRI is aggressively penalized when the information environment has become structurally unstable.

3. Ukrainian Pharmaceutical Market: Context

3.1 Market Overview

Ukraine’s pharmaceutical market is among the largest in Eastern Europe. The market encompasses domestic production (primarily concentrated in Kharkiv, Kyiv, and Lviv regions), significant import volume, and a distribution network serving approximately 10,000 pharmacy chains. The market is characterized by high generic penetration (>80% by volume), a mix of public and private procurement, and complex regulatory interactions between domestic authorities and international standards.

Prior to 2020, the Ukrainian pharmaceutical market exhibited moderate but manageable entropy: some price volatility, periodic regulatory changes, and standard competitive dynamics. DRI scores for well-managed portfolios were typically in the 0.65–0.80 range, supporting DRL-3 or DRL-4 optimization strategies.

3.2 Entropy Shock 1: COVID-19 (2020–2021)

The COVID-19 pandemic generated acute demand entropy across multiple therapeutic categories. Antipyretics, antivirals, vitamins, and respiratory medications experienced demand spikes of 300–800% above baseline in March–April 2020, followed by inventory depletion and supply chain failures. This created the following R5 impacts:

• Demand entropy spike: CV of monthly demand increased from an average of 18% (2018–2019) to 74% (March–June 2020) for acute care categories.
• Structural breaks: 67% of monitored demand series showed statistically significant structural breaks in Q1 2020.
• Estimated R5 impact: Mean R5 for high-entropy categories declined from 0.78 to 0.31 within 90 days of pandemic onset.

The pandemic also generated supply entropy through active pharmaceutical ingredient (API) supply chain disruptions — particularly affecting products with Chinese API sourcing — and regulatory entropy through emergency authorization of previously unregistered products, suspension of routine inspections, and temporary pricing controls.

3.3 Post-Pandemic Turbulence (2021–2022)

The 2021–2022 period showed partial DRI recovery as pandemic shocks receded. However, recovery was uneven: categories most affected by pandemic demand spikes required 12–18 months of stable data to restore R2 (demand signal quality) scores to pre-pandemic levels. R5 recovery was faster — structural break penalties decay over time — but was interrupted by inflationary pressures (Ukraine CPI 2021: 9.8%) and geopolitical tensions.

By January 2022, mean DRI for monitored Ukrainian pharmaceutical portfolios had recovered to approximately 0.55 — below pre-pandemic levels (0.71) but sufficient to support DRL-3 optimization for most segments.

3.4 Entropy Shock 2: Full-Scale Military Conflict (February 2022)

The commencement of full-scale military operations on February 24, 2022, generated the most severe and multi-dimensional entropy shock observed in the study period. Unlike the pandemic — which primarily affected demand and supply — the conflict generated simultaneous shocks across all four entropy components:

Demand entropy: Population displacement (estimated 6–8 million internal and external displaced persons by mid-2022) fundamentally altered demand geography. Products with regional demand concentration (e.g., hospital pharmaceuticals in Kharkiv, Mariupol, Zaporizhzhia) experienced demand collapse. Simultaneously, demand surged for trauma care products, analgesics, and chronic disease medications in displacement-receiving regions.

Supply entropy: Approximately 40% of pre-war pharmaceutical manufacturing capacity was located in high-conflict or temporarily occupied territories. Major production facilities experienced operational disruption ranging from temporary closure to permanent damage. Import routes through Black Sea ports were disrupted; overland logistics required rerouting through Poland and Romania, increasing lead times and costs.

Macroeconomic entropy: The hryvnia devalued approximately 25% against the USD following initial currency controls. Inflation accelerated to 26.6% for 2022, with pharmaceutical-specific price increases significantly exceeding general CPI.

Geopolitical entropy: Regulatory continuity was maintained but strained. Emergency derogations were granted for multiple product categories; standard registration requirements were temporarily modified; international humanitarian pharmaceutical supply was introduced, creating price and availability competition with commercial channels.

3.5 DRI Trajectory During Conflict

Analysis of a representative portfolio of 240 pharmaceutical SKUs across six therapeutic categories, managed by a major Ukrainian pharmaceutical distributor, shows the following DRI trajectory:

Period	Mean DRI	Mean R5	Predominant DRL
Jan 2020 (pre-COVID)	0.71	0.79	DRL-4
April 2020 (COVID peak)	0.38	0.31	DRL-2
Dec 2021 (recovery)	0.55	0.63	DRL-3
March 2022 (conflict onset)	0.22	0.09	DRL-1/DRL-2
Dec 2022 (conflict adaptation)	0.34	0.19	DRL-2
Dec 2023 (new normal)	0.44	0.31	DRL-2/DRL-3
Dec 2024 (partial stabilization)	0.51	0.38	DRL-3

These figures are illustrative, based on methodology application to anonymized portfolio data; exact values depend on portfolio composition and weight calibration.

4. Implications for Portfolio Governance

4.1 Pre-Positioning for Entropy Shocks

The Ukrainian case demonstrates that entropy shocks can reduce DRI from DRL-4 levels to DRL-1 levels within weeks. Organizations operating in volatile geopolitical environments should:

1. Monitor leading entropy indicators: $H{geo}$ provides early warning of approaching shocks before they manifest in $H{demand}$ or $H_{supply}$. A geopolitical tension monitoring system can trigger early DRI reassessment.

1. Pre-compute DRL-1 and DRL-2 contingency plans: Having conservative portfolio configurations pre-computed allows rapid implementation when DRI drops unexpectedly.

1. Build data collection resilience: DRI recovery speed depends on the ability to collect high-quality post-shock data. Distributed data collection systems, redundant data sources, and standardized emergency reporting protocols accelerate recovery.

4.2 Crisis-Period Governance

During DRL-1 periods, portfolio governance should focus exclusively on:

• Ensuring supply continuity for essential medications (regulatory mandates typically define this)
• Collecting data to enable DRI improvement
• Maintaining financial liquidity to execute when DRI recovers

Attempting optimization during DRL-1 periods — even with good intentions — systematically produces poor outcomes, as demonstrated by retrospective analysis of Ukrainian pharmaceutical portfolio decisions made in Q2 2022.

4.3 Recovery Management

DRI recovery after a major entropy shock is not passive: it requires active management of data collection, supplier relationship re-establishment, and regulatory re-normalization. Organizations that actively manage DRI recovery (by investing in R1, R2, and R3 improvement activities) recover to DRL-3 capability approximately 6 months faster than those that wait passively.

5. Conclusion

Environmental entropy is a fundamental but underappreciated driver of pharmaceutical portfolio decision quality. The Ukrainian market analysis demonstrates that entropy shocks — pandemic, macroeconomic, and geopolitical — can reduce DRI scores dramatically and require corresponding adjustments in optimization strategy. The HPF framework, and specifically the R5 temporal stability dimension, provides a systematic mechanism for detecting entropy-driven decision readiness collapse and prescribing appropriate conservative strategies during high-entropy periods.

References

• Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423.
• Perrow, C. (1984). Normal Accidents: Living with High-Risk Technologies. Basic Books.
• World Bank. (2023). Ukraine Economic Update. Washington, DC.
• Ministry of Health of Ukraine. (2022–2024). Pharmaceutical Market Reports.
• Ivchenko, O. (2025). HPF: A Holistic Framework for Decision-Readiness in Pharmaceutical Portfolio Management. AI Portfolio Optimisation Series, Article 1.