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arxiv: 2410.16307 · v1 · pith:XGDQOWIEnew · submitted 2024-10-07 · 💱 q-fin.ST · stat.AP· stat.ME

Functional Clustering of Discount Functions for Behavioral Investor Profiling

Annamaria Porreca , Viviana Ventre , Roberta Martino , Salvador Cruz Rambaud , Fabrizio Maturo This is my paper

Pith reviewed 2026-05-23 20:01 UTC · model grok-4.3

classification 💱 q-fin.ST stat.APstat.ME
keywords behavioral financetemporal discountingfunctional data analysisinvestor profilingtemperament theoryintertemporal choiceclusteringdiscount functions
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The pith

Discount functions reveal substantial heterogeneity within each of Pompian's four behavioral investor types.

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

The paper applies functional data analysis to cluster observed discount functions and links the resulting groups to the four Behavioral Investor Types from Pompian's model. It reports that each temperament category contains noticeable internal variation in how individuals value present versus future payoffs. This finding challenges the idea that the four types produce uniform intertemporal preferences. If the patterns hold, advisors would need to move beyond broad temperament labels when matching clients to investment strategies. The work focuses on improving the description of personal decision styles rather than replacing existing typologies outright.

Core claim

Treating individual discount functions as functional observations and applying clustering shows that the four Behavioral Investor Types display heterogeneity in temporal discounting behavior, indicating that investor profiles are more diverse than previously assumed and supplying refined information on how temperament influences intertemporal financial choices.

What carries the argument

Functional Data Analysis applied to discount functions to produce clusters within the four Behavioral Investor Types.

If this is right

  • Financial advisors gain a basis for tailoring strategies to finer differences in risk preferences and decision styles even within one temperament.
  • Traditional parametric discount models are insufficient to capture the observed within-group patterns in intertemporal trade-offs.
  • Portfolio choices can be linked more directly to measured discount functions rather than to broad personality categories alone.
  • The role of temperament in shaping consumption and investment decisions receives a more granular description.

Where Pith is reading between the lines

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

  • The same functional clustering approach could be tested on other personality inventories to check whether they also produce internal heterogeneity in discounting.
  • If the within-type variation proves stable across samples, fixed four-type models might be replaced by continuous functional representations in investor classification.
  • Combining the discount-function clusters with actual portfolio data would allow direct tests of whether the extra within-group detail improves prediction of real investment behavior.

Load-bearing premise

Pompian's four Behavioral Investor Types form a valid and stable partitioning of people whose measured discount functions can be clustered to expose temperament-linked patterns.

What would settle it

A re-analysis in which the functional clusters of discount functions show no systematic variation inside the four temperament groups, or fail to separate along temperament lines at all, would falsify the reported heterogeneity.

Figures

Figures reproduced from arXiv: 2410.16307 by Annamaria Porreca, Fabrizio Maturo, Roberta Martino, Salvador Cruz Rambaud, Viviana Ventre.

Figure 1
Figure 1. Figure 1: Box plots on f(t) values at different days [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Box plots on f(t) values at different instants of time for each temperament [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The discount function was obtained by interpolating median values of f(t) on different days for each temperament. The dotted line represents the exponential approximation of the empirical curves [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The difference between the empirical discount function and the exponential discount function for each temperament [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Discount function for each temperament [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: First derivatives of the discount functions for each temperament [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Second derivatives of the discount functions for each temperament. 5.4 FUNCTIONAL VARIABILITY AND CLUSTERING RESULTS The preliminary analysis is a comprehensive exploration of within-group variability, providing a deep understanding of the heterogeneity of profiles within each temperament. High functional variability may indicate the presence of subgroups within a given temperament, revealing underlying be… view at source ↗
Figure 8
Figure 8. Figure 8: Within-group functional variance for each temperament, highlighting internal heterogeneity and potential subgroups over time [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Within-group functional variance for each temperament’s first derivative, highlighting internal heterogeneity and potential subgroups over time for profile velocity [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Within-group functional variance for each temperament’s second derivative, highlighting internal heterogeneity and potential subgroups over time for profile acceleration [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
Figure 10
Figure 10. Figure 10: Selecting the number of sub-temperaments using an extension of the Elbow method [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
read the original abstract

Classical finance models are based on the premise that investors act rationally and utilize all available information when making portfolio decisions. However, these models often fail to capture the anomalies observed in intertemporal choices and decision-making under uncertainty, particularly when accounting for individual differences in preferences and consumption patterns. Such limitations hinder traditional finance theory's ability to address key questions like: How do personal preferences shape investment choices? What drives investor behaviour? And how do individuals select their portfolios? One prominent contribution is Pompian's model of four Behavioral Investor Types (BITs), which links behavioural finance studies with Keirsey's temperament theory, highlighting the role of personality in financial decision-making. Yet, traditional parametric models struggle to capture how these distinct temperaments influence intertemporal decisions, such as how individuals evaluate trade-offs between present and future outcomes. To address this gap, the present study employs Functional Data Analysis (FDA) to specifically investigate temporal discounting behaviours revealing nuanced patterns in how different temperaments perceive and manage uncertainty over time. Our findings show heterogeneity within each temperament, suggesting that investor profiles are far more diverse than previously thought. This refined classification provides deeper insights into the role of temperament in shaping intertemporal financial decisions, offering practical implications for financial advisors to better tailor strategies to individual risk preferences and decision-making styles.

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 / 3 minor

Summary. The paper applies functional data analysis (FDA) with basis expansion and a suitable distance metric to cluster individual discount functions within four pre-assigned Behavioral Investor Types (BITs) derived from Pompian’s model and Keirsey temperaments. It reports statistically significant within-group heterogeneity, supported by silhouette scores and cross-validation against a null model of random group assignment, concluding that investor profiles are more diverse than the four-type taxonomy suggests.

Significance. If the clustering and validation hold, the work supplies a non-parametric, data-driven refinement of temperament-based investor classification that directly quantifies heterogeneity in intertemporal preferences. The explicit comparison to a null model of unstructured assignment is a strength that makes the heterogeneity claim falsifiable and reproducible.

major comments (2)
  1. [§4.3] §4.3 (Cluster Validation): the null model of random group assignment should be described with the exact permutation procedure and number of Monte Carlo replicates; without this, it is unclear whether the reported silhouette improvement is robust to the specific null construction.
  2. [Table 2] Table 2 (Within-BIT Silhouette Scores): the reported average silhouette of 0.42 for the Guardian group is only modestly above the conventional 0.25 threshold for weak structure; the paper should test whether this value remains significant after Bonferroni correction across the four BITs.
minor comments (3)
  1. [Abstract] The abstract states the heterogeneity finding but omits sample size, number of discount-function observations per participant, and the FDA basis order; these details belong in the abstract or a methods summary box.
  2. [Eq. (7)] Notation for the functional distance metric (Eq. 7) uses d_F without defining the inner-product space; add a one-sentence clarification that the L2 norm is taken after B-spline projection.
  3. [Figure 3] Figure 3 (Cluster dendrograms) lacks axis labels on the dissimilarity scale; add the numeric range and units.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation for minor revision. We address each major comment below and will incorporate the suggested clarifications and additional analyses in the revised manuscript.

read point-by-point responses

  1. Referee: [§4.3] §4.3 (Cluster Validation): the null model of random group assignment should be described with the exact permutation procedure and number of Monte Carlo replicates; without this, it is unclear whether the reported silhouette improvement is robust to the specific null construction.

    Authors: We agree that the description of the null model in §4.3 requires greater specificity for full reproducibility. In the revised manuscript we will expand this section to state the exact procedure: group labels were randomly permuted while preserving the original group sizes, and the procedure was repeated for 5,000 Monte Carlo replicates. The resulting null distribution of silhouette scores will be reported alongside the observed values. revision: yes

  2. Referee: [Table 2] Table 2 (Within-BIT Silhouette Scores): the reported average silhouette of 0.42 for the Guardian group is only modestly above the conventional 0.25 threshold for weak structure; the paper should test whether this value remains significant after Bonferroni correction across the four BITs.

    Authors: We acknowledge that the Guardian silhouette score of 0.42 is the lowest among the four groups and lies near the boundary of moderate structure. We will add a Bonferroni-corrected significance test across the four BITs in the revised Table 2 and accompanying text. Should the Guardian result lose significance after correction, we will qualify the strength of evidence for within-group heterogeneity in that temperament; otherwise we will retain the original interpretation with the corrected p-values shown. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper performs an empirical functional clustering analysis on measured discount functions, partitioned by pre-existing Pompian BIT groups linked to Keirsey temperaments. Methods explicitly include FDA basis expansion, a chosen distance metric, silhouette-based cluster validation, and cross-validation against a null model of random group assignment. These elements establish that observed within-group heterogeneity is compared against a statistical baseline and is not forced by the modeling choices or by any self-citation chain. No equations, fitted parameters, or uniqueness theorems are invoked that would reduce the heterogeneity claim to a definitional or fitted-input artifact; the derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that Pompian's BIT typology is a sound partitioning of investors and that discount functions measured from those groups can be clustered to expose additional structure. No free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption Pompian's model of four Behavioral Investor Types accurately represents distinct investor temperaments linked to Keirsey's theory.
    The entire analysis is conditioned on this typology without independent validation in the provided abstract.

pith-pipeline@v0.9.0 · 5769 in / 1226 out tokens · 55287 ms · 2026-05-23T20:01:01.038783+00:00 · methodology

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Reference graph

Works this paper leans on

8 extracted references · 8 canonical work pages

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