---
title: "Algorithmic vs. Human Portfolio Choice"
authors:
  - name: "Béatrice Boulu-Reshef"
    affiliation: "CY Cergy Paris Université, CNRS, THEMA"
  - name: "Alexis Direr"
    affiliation: "Université d'Orléans, LEO"
  - name: "Nicole von Wilczur"
    affiliation: "Bedrock Streaming"
keywords: [robo-advisor, human-algorithm interaction, portfolio choice, behavioral household finance, MiFID II, risk profiling, algorithm aversion, anchoring]
jel_codes: [D14, G11, G23, G41, G51]
language: [en, fr]
type: research-article
---

# Algorithmic vs. Human Portfolio Choice

**Authors**
- Béatrice Boulu-Reshef — CY Cergy Paris Université, CNRS, THEMA — *beatrice.boulu-reshef@cyu.fr*
- Alexis Direr — Université d'Orléans, LEO — *alexis.direr@univ-orleans.fr*
- Nicole von Wilczur — Bedrock Streaming — *nicole.vonwilczur@bedrockstreaming.com*

**Keywords**: robo-advisor, human-algorithm interaction, portfolio choice, behavioral household finance.
**JEL codes**: D14, G11, G23, G41, G51.
**Research framework**: PREF research initiative under the aegis of the Europlace Institute of Finance — joint initiative by Yomoni and the University of Orléans.

---

## Abstract

**English.** Robo-advisors that provide investment advice using risk profiling questionnaires have recently made a breakthrough in the investment management industry. The validity of these questionnaires is crucial as profiling inaccuracies can lead to a mismatch between investment proposals and retail investors' preferences. This paper uses data from a robo-advisor that makes portfolio recommendations to its potential clients and lets them choose their risk exposure after having received this recommendation. We provide evidence that although recommendations by the robo-advisor are qualitatively aligned with portfolio theory, the recommendation is heavily based on answers about financial risk taking. A large majority of clients follow the recommendation and as a result are also strongly influenced by their declared propensity to take financial risks.

**Français.** Les robo-conseillers qui fournissent des conseils en investissement à l'aide de questionnaires de profilage de risque ont récemment marqué une avancée dans l'industrie de la gestion d'actifs. La validité de ces questionnaires est cruciale, car des imprécisions dans le profilage peuvent entraîner un décalage entre les propositions d'investissement et les préférences des investisseurs particuliers. Cet article utilise les données d'un robo-conseiller qui formule des recommandations de portefeuille à ses clients potentiels et leur permet de choisir leur niveau d'exposition au risque après avoir reçu cette recommandation. Nous montrons que, bien que les profils de risque recommandés par le robo-conseiller soient qualitativement cohérents avec la théorie des portefeuilles, la recommandation repose fortement sur les réponses relatives à la prise de risque financier. Une large majorité de clients suivent la recommandation et, par conséquent, sont également fortement influencés par leur propension déclarée à prendre des risques financiers.

---

## 1. Contributions

The paper makes three main contributions.

1. **Estimating the algorithmic recommendation function.** We document how the algorithm translates questionnaire answers into a risk profile and test the extent to which this translation is consistent with standard financial theory. The setting allows us to observe both the full decision process and the final allocation, providing a cleaner test of questionnaire informativeness and predictive validity than in the prior literature (Rice 2005; Foerster et al. 2014; Lucarelli et al. 2015).

2. **Measuring clients' reactions to the recommendation.** A majority follows the algorithm, but a significant minority deviates either toward more caution or more risk. The setting offers a high-stakes test — as opposed to experimental protocols (Dietvorst et al. 2015, 2018; Filiz et al. 2022) — of the intrinsic value clients place on retaining their decision rights (Bartling, Fehr & Herz 2014).

3. **Exploiting variables observable but not used by the algorithm.** Some information (gender, type of investment project) is recorded by the fintech and observable to the econometrician but is not incorporated into the recommendation. For gender, inclusion would amount to discrimination, which justifies its exclusion. This setup allows us to estimate how these characteristics nonetheless influence clients' final choices, and to identify the boundaries of the information set used by the algorithm.

---

## 2. Data and subscription process

**Source.** Largest robo-advisor operating in France. Period: September 2015 – December 2023.

**Volumes:**
- 136,187 algorithmic recommendations (including prospects who completed the questionnaire without subscribing) — basis for estimating the recommendation function.
- 79,874 contracts corresponding to 68,953 unique clients — basis for estimating final choices. 87.8% of clients hold a single contract.
- 70.4% men, 29.6% women. Median age: 34 years. 56.4% homeowners.

**Regulatory framework.** The questionnaire complies with MiFID II requirements, which mandate client profiling before any investment recommendation.

**Questionnaire (administered in French)** — three blocks:
1. Investment project: goal, initial and recurring amounts, horizon, saving capacity.
2. Socio-demographic and economic situation: age, fiscal residency, dependent children, income, financial and property wealth, rents or mortgage repayments, homeownership.
3. Risk aversion, liquidity needs, financial knowledge and experience.

**Subscription process.** The algorithm computes a weighted score and presents a recommended profile from 1 to 10. If the client wishes to deviate by more than 2 points (in absolute value) from the recommendation, the company's staff may contact them to verify that the implications of the additional risk taken are well understood.

### Asset allocation by risk profile

| Profile | Money market | Bond ETFs | Stock ETFs |
|:---:|:---:|:---:|:---:|
| 1 (least risky) | 100% | 0% | 0% |
| 2 | 80% | 10% | 10% |
| 3 | 60% | 20% | 20% |
| 4 | 40% | 30% | 30% |
| 5 | 20% | 40% | 40% |
| 6 | 0% | 50% | 50% |
| 7 | 0% | 40% | 60% |
| 8 | 0% | 30% | 70% |
| 9 | 0% | 20% | 80% |
| 10 (riskiest) | 0% | 0% | 100% |

Fees range between 0.9% and 1.6% of assets under management, deducted annually.

---

## 3. Econometric strategy

| Table | Model | Dependent variable | Sample |
|---|---|---|---|
| A1 | OLS | Algorithmic profile recommendation | 136,187 recommendations |
| A2 | OLS | Profile chosen by the client (with out-of-algorithm variables) | 79,784 contracts |
| A3 | Logit (average marginal effects) | Compliance with the recommendation (1/0) | 79,784 contracts |
| A4a | Logit (AME) | Upward deviation (riskier profile) | 75,419 (profile 10 excluded) |
| A4b | Logit (AME) | Downward deviation (safer profile) | 79,147 (profile 1 excluded) |

Identification rests on the fact that all respondents receive a recommendation and that additional information (gender, profession, marital status, account type, market performance) is observed without being incorporated into the recommendation.

---

## 4. Results

### 4.1 Determinants of the algorithmic recommendation (Table A1)

The OLS R² reaches **0.84**, indicating that questionnaire answers reconstruct almost the entire recommendation function.

**Most influential variables:**

1. **Risk Q2** (gain/loss trade-off over a 10-year horizon) — by far the most important determinant. Selecting the most conservative scenario (20% expected gain, 5% loss risk) rather than the riskiest (70% / >15%) reduces the recommended profile by **3.45 points**.
2. **Project "Saving in case of hardship"** — reduces the profile by **2.68 points**, consistent with the literature on precautionary savings (Guiso, Jappelli & Terlizzese 1996; Fagereng, Gottlieb & Guiso 2017).
3. **Short horizon (1–3 years)** — reduces the profile by **1.57 points** relative to the 10–14 year reference, in line with life-cycle portfolio theory (Samuelson 1969; Merton 1969; Bodie, Merton & Samuelson 1992; Barberis 2000).

**Moderate influence:** financial wealth (+0.52 to +0.80 points across brackets), property wealth, mortgage repayments, annual income, Risk Q1 (numerical gain/loss trade-offs), Risk Q3 (response to a 10% drop), Risk Q4 (past loss experience), liquidity needs, age, number of dependent children.

**Weak or no influence:** rents, financial knowledge questions (the quiz appears more pedagogical than discriminating).

> **Authors' critical reading.** Although the orientation of coefficients is consistent with theory, the quantitative weight of Risk Q2 appears disproportionate. The recommendation rests heavily on a single declarative answer, which raises concerns about the robustness of profiling and underscores the importance of careful questionnaire design.

### 4.2 Clients' choices (Table A2)

R² = 0.62. The determinants of the algorithmic recommendation remain largely validated by human choices, with a few discrepancies:
- The "hardship" project effect is dampened (−2.14 vs. −2.68 in the algorithm).
- The Risk Q1 effect is amplified (up to −0.71 vs. −0.24 in the algorithm).

**Significant out-of-algorithm variables:**

- **Gender.** Men choose riskier profiles (+0.098 point), despite a gender-blind algorithm. Consistent with the literature on gender differences in risk-taking (Byrnes, Miller & Schafer 1999; Sunden & Surette 1998; Agnew, Balduzzi & Sunden 2003).
- **Project type** (other than "hardship") — coefficients are statistically significant but hard to interpret once other questionnaire variables are controlled for.
- **Saving capacity** — positively correlated with risk-taking, weak quantitative effect.
- **Marital status, account type** (assurance-vie vs. regular securities account), **recent MSCI World performance** — weak or non-significant effects.

### 4.3 Compliance with the recommendation (Table A3)

**64.8% of clients follow the algorithmic recommendation.** Of the 35.2% who deviate:
- 57.0% choose a **safer** profile (mean distance: −2.14)
- 43.0% choose a **riskier** profile (mean distance: +1.90)

**More likely to comply:** older clients (+9.8 pp for >69 vs. 30–39), clients with limited financial knowledge, retirement (+4.6 pp) or children's studies (+5.9 pp) projects, clients with mortgage repayments, single individuals.

**More likely to deviate:** clients with high financial wealth (−9.2 pp for €250k–€1M), long horizons, homeowners (−2.7 pp), men (−1.4 pp), high saving capacity, real estate project (−6.7 pp), high financial knowledge.

### 4.4 Direction of deviations (Tables A4a and A4b)

Separate logit regressions for upward and downward deviations reveal a marked asymmetry:

**Increase risk-taking relative to the recommendation:**
- **Men (+3.7 pp)**, long horizon (>25 years: +7.6 pp), young clients (18–29: +2.4 pp), high saving capacity (+1.7 to +2.7 pp), real estate project (+4.1 pp), declared tolerance for losses.

**Decrease risk-taking relative to the recommendation:**
- High financial wealth (**+12.4 pp** probability of downward deviation for the €250k–€1M bracket), high property wealth, homeownership, presence of children, past experience with financial losses, inheritance project (+2.6 pp), men **less** likely to deviate downward (−2.4 pp).

**Special case — real estate project.** It increases *both* the probability of moving up (+4.1 pp) *and* down (+3.0 pp) in risk, suggesting polarized behavior likely depending on the time horizon of the planned purchase.

**Financial knowledge.** Clients with lower knowledge deviate *less* in both directions: they comply more with the algorithmic recommendation, which amplifies the practical impact of any algorithmic bias on this population.

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## 5. Conclusion

Three main takeaways.

**First — the algorithmic recommendation is qualitatively consistent with portfolio theory.** The recommended profile increases with declared risk propensity, absence of short-term liquidity needs, long horizon, financial knowledge, market experience and financial ease. However, a small set of variables — in particular *one single* risk-return trade-off question (Risk Q2) — exerts disproportionate influence.

**Second — little evidence of algorithm aversion, but several explanations remain open.** 64.8% of clients accept the recommendation. This level of acceptance could reflect:
- genuine agreement with the recommendation,
- an **anchoring** effect on the value proposed by the algorithm,
- general deference to advice perceived as expert (even when the expert is an algorithm),
- the fact that the algorithm only proposes a profile, with asset management remaining handled by humans.

This widespread acceptance reinforces the importance of questionnaire and algorithm design: any embedded bias is transmitted directly to investors' portfolios.

**Third — deviations are predictable and structured.** Variables related to the capacity to bear risk (age, children, financial wealth, attitudes toward risk, liquidity needs) predict both the probability and the direction of deviations.

### Limitations and research extensions

The analysis covers profile choices **immediately after the questionnaire**, which by construction excludes later adjustments driven by changes in personal circumstances or the economic environment. This choice strengthens identification but limits scope. A natural extension would be to study profile adjustments **over time**.

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## Acknowledgments

The authors thank for useful comments François Langot, Olivier L'Haridon, Christophe Hurlin, Sébastien Saurin, and participants of the Laboratoire d'Économie d'Orléans seminar, the Risk Forum in Paris, the LFIN Seminar at Louvain-la-Neuve, the *Investor Emotions & Asset Pricing* workshop in Lille, the AFFI (French Finance Association) Conference, the ANR AESOP workshop at the University of Rennes, and the Paris IdR PREF workshop on Household Finance held at the Institut Louis Bachelier. The authors also thank the two anonymous referees for their useful comments and suggestions. This research has been conducted within the PREF research initiative under the aegis of the Europlace Institute of Finance, a joint initiative by Yomoni and the University of Orléans.

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## Main references

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*The full reference list appears in the PDF.*