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arxiv: 2607.01905 · v1 · pith:LLJ4JIPCnew · submitted 2026-07-02 · 💰 econ.EM

Measuring Opportunity Cost with Stock Lifetime Value

Geoffrey Decrouez , Tobias Huelden , Paresh Nakhe , Dominik Prugger This is my paper

Pith reviewed 2026-07-03 02:15 UTC · model grok-4.3

classification 💰 econ.EM
keywords stock lifetime valueopportunity costA/B testinge-commerce metricsfashion retailinventory managementlong-term effectspricing optimization
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The pith

SLV aggregates expected profit from current inventory through its full selling lifecycle to measure true opportunity cost in short e-commerce experiments.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Stock Lifetime Value (SLV) to address how standard short-term metrics like revenue bias A/B test decisions in e-commerce. Interventions such as dynamic pricing shift consumer behavior over months, yet experiments often run only weeks due to operational needs. SLV instead projects the expected profit from existing stock items to the end of their individual selling periods. This stock-centric approach is developed for fashion retail at Zalando, where inventory constraints and seasonal cycles make short- versus long-term tradeoffs especially sharp. The metric is then applied to article- and customer-level tests, pricing optimization, and annualizing effects for financial reporting.

Core claim

SLV aggregates the expected profit from current inventory through the end of its selling lifecycle, providing a way to evaluate interventions against their true profit impact.

What carries the argument

Stock Lifetime Value (SLV), which sums projected profit contributions of each current stock unit across its remaining selling window rather than stopping at the experiment close.

If this is right

  • Article-level and customer-level A/B tests can use SLV efficiency as the primary metric and still align with realized long-term profit.
  • Pricing algorithms can optimize directly against SLV, removing the mismatch between measurement and decision objectives.
  • Treatment effects observed in short windows can be annualized into the financial reporting metrics required by business stakeholders.
  • The same framework extends to any inventory-constrained setting where value decays over time or demand shifts across periods.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • SLV might reduce the need for long-running experiments in other retail categories that face similar stock decay, such as electronics or perishables.
  • If demand shifts are strongly seasonal, SLV projections could be improved by incorporating calendar-aware adjustments without lengthening test windows.
  • The metric creates an implicit bridge between online experimentation and traditional inventory accounting, potentially allowing finance teams to treat experimental results as direct inputs to profit forecasts.

Load-bearing premise

Expected profit from current inventory through the end of its lifecycle can be estimated reliably from short experimental windows without material bias from unmodeled seasonality, demand shifts, or stock dynamics.

What would settle it

Compare SLV estimates computed from a one-week experiment against the actual realized profit of the same inventory cohort tracked over its full 18-month lifecycle and check for statistically significant divergence.

Figures

Figures reproduced from arXiv: 2607.01905 by Dominik Prugger, Geoffrey Decrouez, Paresh Nakhe, Tobias Huelden.

Figure 1
Figure 1. Figure 1: SLVi,t0 pSi,t0 q represents the total marginal profit generated from the Si,t0 “ 1000 units of sneakers i in stock at time t0, via all the Zalando channels : shop, lounge, and liquidation. Section 4 concludes with a discussion of limitations and directions for future work. 2 Methodology 2.1 Stock Lifetime Value Definition For retailers managing perishable or seasonal goods, the core operational challenge i… view at source ↗
Figure 2
Figure 2. Figure 2: Variation in nSLV (blue) for a specific model of training shoes over the course of a season [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Stationarity in operational lifecycle and pricing processes within Zalando captured as vari [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (left) Average nSLVt0 and nSLV {t0 at Zalando over the full seasonal assortment. The dotted red line represents the break even line nSLVi,t0 “ 1. The x-axis represents the number of weeks since season start. The y-axis is anonymised to keep the order of magnitude confidential at an aggregated level. (Right) Accuracy metrics WAPE and bias computed in a backtesting environment. and Bias “ ř i ´ SLV zi,t0 ´ S… view at source ↗
Figure 5
Figure 5. Figure 5: Illustration of SLV efficiency. Both plots show the cumulative marginal profit of an article [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Visualized annualization framework for a exemplary short term experiment conducted in [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Average profit cost share of revenue across calendar weeks in the past 5 years. Displayed [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Stability of the relationship between pricing strategy and revenue or profit. Colored lines [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Average profit cost share of revenue in the past 5 years. Displayed values are multiplied [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Average profit cost share of revenue across calendar weeks in the past 5 years. Displayed [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
read the original abstract

Measuring the long-term opportunity cost of interventions remains a critical challenge in e-commerce A/B testing. While strategic levers (such as dynamic pricing, ranking algorithms, and promotional campaigns) trigger shifts in consumer behaviour that persist over months, operational constraints necessitate fast decision-making cycles that are typically limited to weekly experimental windows. Standard metrics like revenue and conversion are inherently short-sighted, biasing decisions toward immediate gains. We introduce Stock Lifetime Value (SLV), a stock-centric metric that captures long-term opportunity cost within short experiments by aggregating expected profit from current inventory through the end of its selling lifecycle. We develop the methodology in the context of fashion e-commerce at Zalando, where stock constraints and seasonal lifecycles make the trade off between short-term and long-term outcomes particularly relevant. SLV aggregates the expected profit from current inventory through the end of its selling lifecycle, providing a way to evaluate interventions against their true profit impact. We discuss three applications: (a) SLV efficiency as a metric for article-level and customer-level A/B tests, validated against realized 18-month lifecycle outcomes; (b) SLV as an optimization target for pricing algorithms, aligning the metric used for measurement with the objective used for decision-making; and (c) a framework for annualizing treatment effects into financial reporting metrics required by business stakeholders. While our empirical setting is fashion retail, the framework applies broadly to any inventory-constrained environment where value decays over time or interventions shift demand across periods.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces Stock Lifetime Value (SLV), a stock-centric metric that aggregates expected profit from current inventory through the end of its selling lifecycle to measure the long-term opportunity cost of interventions in e-commerce A/B testing. Developed in the fashion retail setting at Zalando, it presents three applications: (a) use of SLV efficiency in article- and customer-level A/B tests with claimed validation against realized 18-month outcomes; (b) SLV as an optimization target for pricing algorithms; and (c) a framework for annualizing treatment effects into financial reporting metrics. The approach is positioned as applicable to any inventory-constrained environment with time-decaying value.

Significance. If the SLV construction and extrapolation can be shown to deliver unbiased long-term profit estimates from short windows, the metric would address a practical gap in aligning experimental design with inventory-constrained profit maximization, potentially improving decision quality in retail A/B testing and pricing.

major comments (2)
  1. [Abstract] Abstract: The claim of validation against realized 18-month lifecycle outcomes supplies no derivation, functional form for the extrapolation, data description, or error analysis. This is load-bearing for the central assertion that SLV captures true profit impact without material bias.
  2. [Abstract] Abstract: The methodology for estimating expected profit from short experimental windows is not specified, leaving unaddressed whether the aggregation relies on untested assumptions about demand stability, seasonality, or stock dynamics over the full lifecycle. This directly affects the reliability of all three applications.
minor comments (1)
  1. [Abstract] The sentence describing SLV aggregation is repeated verbatim in the abstract; this should be consolidated for conciseness.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on the abstract. The points raised are valid regarding the level of detail provided in the abstract itself. We address each below and will revise the abstract accordingly while preserving the manuscript's core contributions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim of validation against realized 18-month lifecycle outcomes supplies no derivation, functional form for the extrapolation, data description, or error analysis. This is load-bearing for the central assertion that SLV captures true profit impact without material bias.

    Authors: We agree the abstract is too concise on this point. The full manuscript provides the derivation and functional form for extrapolating from short windows to 18-month outcomes (in the validation subsection of the applications), describes the Zalando fashion retail dataset used, and reports error metrics comparing SLV-based predictions to realized profits. We will revise the abstract to briefly reference the validation approach and direct readers to the relevant sections. revision: yes

  2. Referee: [Abstract] Abstract: The methodology for estimating expected profit from short experimental windows is not specified, leaving unaddressed whether the aggregation relies on untested assumptions about demand stability, seasonality, or stock dynamics over the full lifecycle. This directly affects the reliability of all three applications.

    Authors: The abstract does not detail the estimation process. The main text specifies the methodology, including models for expected profit that incorporate historical sales patterns, seasonality adjustments, and stock depletion dynamics, along with a discussion of assumptions (e.g., in the limitations section). We will revise the abstract to include a high-level description of the estimation and note the key assumptions. revision: yes

Circularity Check

0 steps flagged

No circularity: SLV introduced as conceptual aggregation without equations reducing to fitted inputs or self-citations

full rationale

The provided abstract and description introduce SLV as a stock-centric metric that aggregates expected profit from current inventory through end-of-lifecycle, with applications validated against 18-month outcomes. No equations, functional forms, fitting procedures, or self-citations are visible that would allow any derivation step to reduce by construction to its own inputs. The central claim remains a definitional proposal for a new metric rather than a fitted prediction or self-referential uniqueness theorem. This is the most common honest finding when no load-bearing reductions are exhibited.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies insufficient technical detail to identify free parameters, axioms, or invented entities.

pith-pipeline@v0.9.1-grok · 5798 in / 992 out tokens · 39669 ms · 2026-07-03T02:15:55.385322+00:00 · methodology

discussion (0)

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