---
title: "Les choix de portefeuille des épargnants sur le cycle boursier et le cycle de vie"
title_en: "Savers' Portfolio Choices over the Stock Market Cycle and the Life Cycle"
authors:
  - name: "Alexis Direr"
    affiliation: "Université d'Orléans, CNRS, LEO, UMR 7322; Paris School of Economics"
    email: "alexis.direr@univ-orleans.fr"
  - name: "Eric Yayi"
    affiliation: "Université d'Orléans, CNRS, LEO, UMR 7322"
date: "2014"
journal: "Économie et Statistique"
issue: "472-473"
pages: "125-152"
keywords: [household finance, portfolio choice, life-cycle investing, age effects, cohort effects, stock market cycle, retirement savings, Madelin contracts, unit-linked funds, procyclical investment, return extrapolation, Tobit, Probit]
language: fr
type: research-article
---

# Les choix de portefeuille des épargnants sur le cycle boursier et le cycle de vie

**Authors**
- Alexis Direr — Université d'Orléans, CNRS, LEO, UMR 7322; Paris School of Economics — *alexis.direr@univ-orleans.fr*
- Eric Yayi — Université d'Orléans, CNRS, LEO, UMR 7322

**Publication**: *Économie et Statistique*, N° 472-473, 2014, pp. 125-152.

**Keywords**: household finance, portfolio choice, life-cycle investing, age effects, cohort effects, stock market cycle, retirement savings, Madelin contracts, unit-linked funds, procyclical investment, return extrapolation, Tobit, Probit.

---

## Abstract

**Français (verbatim).** Les épargnants détenant des titres financiers risqués ont-ils tendance à investir à contretemps de la conjoncture boursière ? Réduisent-ils leur exposition au risque avec l'âge et à l'approche de la retraite ? Les données d'un grand assureur français répertoriant les souscriptions de contrats Madelin entre 2002 et 2009 permettent d'avancer quelques réponses. Les souscripteurs peuvent placer leur épargne dans deux types de support : des titres monétaires presque sans risque, et des fonds en unités de compte représentant des parts d'OPCVM investies en titres à risque.

La part du capital investie en unités de compte ne s'avère sensible à la conjoncture boursière qu'au moment de la souscription du contrat. Ensuite prévaut une forte inertie des choix de portefeuille, les épargnants ne modifiant que très rarement la part sélectionnée initialement. Une forte procyclicité des choix d'investissement semble s'expliquer par une extrapolation de la performance boursière récente. Ainsi les nouveaux souscripteurs détiennent-ils une part d'actifs risqués minimum en 2004, au début d'une phase de hausse de quatre ans, et maximum en 2008, au début de la chute boursière liée à la crise financière.

La part risquée décline régulièrement avec l'âge, une fois tenu compte des effets temps et sans contrôler les effets génération. Le profil par âge décline également dans la configuration inverse (avec effets génération et sans effets temps), mais la baisse est moins accentuée car elle résulte de deux mécanismes opposés : avec l'âge, le nombre d'épargnants investissant dans des actifs risqués tend à s'accroître alors que, conditionnellement à investir, la part risquée diminue. Ainsi, entre 40 et 60 ans, la probabilité de détention d'unités de compte augmente d'environ 12 points, alors que la part investie en unités de compte, conditionnellement à détenir une part positive, décroît avec l'âge d'environ 6 points, laissant subsister un risque financier à l'approche de la retraite.

> *No official English abstract is provided in the source. The contributions and results sections below are written in English.*

---

## 1. Motivation and contributions

The paper investigates two largely under-studied dimensions of individual portfolio choice using French administrative data: how households adjust the risky share of their savings (i) over the stock market cycle and (ii) over the life cycle, with particular attention to behaviour around retirement. Two theoretical motivations frame the inquiry.

First, since equity returns exhibit medium-horizon mean reversion (Campbell & Shiller 1988; Fama & French 1988; Koijen & Van Nieuwerburgh 2007), risk-averse investors can in principle exploit predictability through a counter-cyclical investment policy that raises long-run returns (Campbell & Viceira 1999). Conversely, a procyclical policy would significantly erode returns. Second, two distinct theoretical mechanisms predict a declining risky share near retirement: medium-horizon mean reversion (Samuelson 1991; Barberis 2000) and the buffering role of human capital, which loses effectiveness as the labour-income horizon shortens (Bodie, Merton & Samuelson 1992; Viceira 2001).

The paper makes three main empirical contributions.

1. **Procyclicality of portfolio choice at contract subscription.** Using a panel of subscribers covering a complete stock cycle (2002–2009), the paper shows that the unit-linked (UC) share is highly sensitive to recent market performance — but only at the moment the contract is opened. The behaviour is consistent with extrapolative expectations of recent returns (Greenwood & Shleifer 2013; Nagel & Malmendier 2011) and parallels findings on the US housing bubble (Case, Shiller & Thompson 2012).

2. **Inertia of portfolio choices over the contract's life.** Once the initial UC share is chosen, savers very rarely rebalance. The aggregate procyclicality of the average risky share is therefore driven almost entirely by new subscribers, while existing contract holders adopt a buy-and-hold strategy even during sharp downturns. This complements US evidence on portfolio inertia in 401(k) plans (Ameriks & Zeldes 2004; Agnew, Balduzzi & Sunden 2003).

3. **Decomposition of age effects into extensive and intensive margins under alternative identification assumptions.** The paper estimates Tobit and Probit models on UC participation and UC share, varying which of the age/cohort/time effects is excluded (the standard identification problem). The preferred specification — which excludes pure time effects and retains cohort and subscription-year controls — yields opposing margins: the *probability* of holding UC rises with age (+12pp between 40 and 60), while the UC share *conditional on investing* falls with age (−6pp between 40 and 60). The total margin is mildly declining, leaving non-negligible financial risk near retirement.

---

## 2. Data and institutional setting

**Source.** Administrative data from a large French insurer covering Madelin retirement contracts subscribed between March 2002 and April 2009 and not yet liquidated as of January 2010. Approximately 8,000 contracts; 34,188 panel observations enter the regressions.

**Madelin contracts (institutional context).** Created in 1994, these are tax-advantaged retirement savings contracts for non-agricultural self-employed professionals. Contributions are deductible from taxable income up to a ceiling, and accumulated capital must be converted into a life annuity at retirement. They totalled €2 billion in 2009 over 834,000 active contracts (FFSA), with a mean annual contribution of €2,400 and a 57% participation rate within the eligible population — high relative to the ~8% of employees holding an equivalent retirement plan. The deductibility regime and the annuitisation rule are identical for the euro fund and the UC compartments.

**Investment vehicles.** Subscribers split contributions between (i) a euro fund composed mainly of monetary instruments with capital guarantee and (ii) unit-linked (UC) funds — equity, balanced, or bond UCITS.

**Variables observed.** Subscriber characteristics (sex, year of birth, département, occupation, two marketing-segmentation indicators for income and wealth) and contract characteristics (distribution channel, subscription date, dates and amounts of contributions). Year-end UC share is observed each 31 December from 2002 to 2009, except 2006 (missing from the database, interpolated for older contracts).

**Headline descriptive statistics.**

| Statistic | Value |
|:---|:---:|
| Mean UC share (full sample) | 35% |
| Share of savers investing any positive UC amount | 84% |
| Share investing in UC in the comparable life-insurance population (Direr & Visser 2013) | 42% |
| Mean annual contribution (sample) | ~€2,500 |
| Mean annual contribution (FFSA, all Madelin) | €2,400 |
| Mean annual contribution on PERP/employee plans (Carbonnier et al. 2014) | ~€1,700 |

The Madelin population is wealthier than the general life-insurance population and has a longer investment horizon, both of which favour equity exposure.

### Historical fund returns (annual, %)

| Fund | 2007 | 2008 | 2009 | 2010 | 2011 | Geometric mean | Std. dev. |
|:---|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
| Euro fund | 4.45 | 4.20 | 3.85 | 3.70 | 3.50 | 3.94 | 0.38 |
| Equity fund | 0.42 | −37.62 | 25.06 | 8.84 | −0.85 | −3.30 | 23.02 |
| International balanced | −0.20 | −22.91 | 16.50 | 8.36 | −3.88 | −1.37 | 14.84 |
| International equity | 2.96 | −48.69 | 18.91 | 10.26 | −9.24 | −8.87 | 26.43 |
| European equity | 6.33 | −45.09 | 26.81 | 2.49 | −15.99 | −8.61 | 27.04 |
| Eurozone fund | 9.52 | −17.71 | −19.27 | 12.27 | 2.29 | −3.53 | 14.98 |
| Energy equity | 17.11 | −54.02 | 50.05 | −54.02 | 17.11 | −15.33 | 46.94 |
| Inflation-linked bonds | 3.46 | 4.09 | 6.96 | 1.01 | 0.92 | 3.26 | 2.50 |

---

## 3. Econometric strategy

The age, cohort, and time effects cannot be jointly identified because of the linear identity *time = year of birth + age*. The paper estimates the age profile under four alternative sets of controls, each excluding one of the colinear effects:

| Set | Cohort dummies | Time dummies | Subscription-year dummies | Tenure dummies | Additional sociodemographic controls |
|:---:|:---:|:---:|:---:|:---:|:---:|
| (a) | Yes | No | Yes | Yes | No |
| (b) | Yes | No | Yes | Yes | Yes |
| (c) | No | Yes | Yes | No | No |
| (d) | No | Yes | Yes | No | Yes |

Specifications (a)–(b) identify age effects under the assumption that there are no pure time effects (cohort effects retained); (c)–(d) reverse the assumption (time retained, cohorts excluded). All four sets retain subscription-year dummies because the descriptive analysis showed that the year a contract is opened durably shapes the UC share for the rest of the contract's life.

| Outcome | Model | Sample (N) |
|:---|:---|:---:|
| UC share (censored at 0) | Tobit | 34,188 |
| Probability of holding any UC | Probit | 34,188 |
| UC share conditional on holding UC | Tobit on positive sub-sample | 28,496 |

Marginal effects of discrete (dummy) variables are computed as $em_i(X_k) = E(Y_i \mid X_i^k=1) - E(Y_i \mid X_i^k=0)$ averaged across the sample (see paper's Appendix 2). Additional sociodemographic controls in (b) and (d) include sex, marital status, number of children, occupation, marketing segmentation, income indicator, wealth-profile indicator, distribution channel, annualised contribution, number of contributions per year, and département dummies.

---

## 4. Results

### 4.1 Procyclicality at subscription, inertia thereafter

The aggregate UC share co-moves strongly and positively with the DJ EuroStoxx 50: the average UC share fell from 31% in 2003 to 27% in 2004, rose to 38% in 2008, then declined to 35% in 2010. The pattern is procyclical in the sense that the risky share is *minimum* (27%) at the start of the 2004–2008 boom and *maximum* (38%) at the onset of the 2008 crash.

Decomposition into the extensive and intensive margins:

- **Extensive margin (share of savers holding any UC):** 71% in 2003 → 87% in 2007–2008 (+16pp), then back to ~76% by 2010.
- **Intensive margin (UC share conditional on holding):** ~38% in 2005 → ~44% in 2007–2008 (+6pp).

Because the extensive margin is independent of return realisations, it cannot be explained by mechanical drift in fund values — it reflects deliberate participation choices. Decomposing the UC share by year of subscription shows that:

- The 11pp rise in the average UC share between 2004 and 2008 is attributable *entirely* to new subscribers' choices.
- For savers who subscribed in 2002, the UC share fell by ~4pp over the same period. For 2003 subscribers, it fell by ~2pp.
- The participation rate among new subscribers rose by ~23pp during 2004–2007 and fell by ~43pp (from 93% to 50%) during 2008–2009, closely tracking the stock cycle.

> **Authors' interpretation.** A few years of bad or good market performance suffice to radically change new savers' participation. Once the initial UC share is chosen, however, it is rarely revised — savers adopt a buy-and-hold policy and do not sell their UC even when markets fall. The *Cour des Comptes* (2012) reports a similar pattern in life-insurance contracts, where the UC share peaked at 21.3% in 2000 and again at 21.7% in 2007, both at market peaks.

### 4.2 Age profile of the UC share (total margin, Tobit)

Marginal effects of age dummies (reference category: 38 years old):

| Identification | Slope (~pp per decade) | Significance |
|:---|:---:|:---:|
| (a)–(b): cohort retained, time excluded | ~−1.5 pp/decade | Not significant when additional controls are included |
| (c)–(d): time retained, cohort excluded | ~−7 pp/decade | Significant (except at 39–40 years) |

In both configurations the age profile is *declining*, but the slope is much steeper when time effects are retained and cohorts excluded. Adding sociodemographic controls shifts the level of the profile but not its slope.

### 4.3 Age profile of UC participation (Probit)

This is where the two identification strategies diverge most sharply.

| Identification | Probability of holding UC, age 38 → ~60 |
|:---|:---:|
| Cohort retained, time excluded | ~34% → ~52% (**+18pp, increasing**) |
| Time retained, cohort excluded | ~40% → ~15% (**−25pp, decreasing**) |

The discrepancy reflects a cohort effect: older generations participate less often, plausibly because of lower wealth and lower formal education levels (consistent with Guiso, Haliassos & Jappelli 2003 on European stockholding; Campbell 2006 for the US; and the financial-literacy evidence of Maarten et al. 2011). Under the cohort-controlled specification, this generational gap is removed and the residual age effect is positive.

### 4.4 Age profile of the UC share conditional on investing (Tobit)

Conditional on holding any UC, the age profile is *declining in both configurations*:

- Time retained, cohort excluded: ~−6 pp per decade.
- Cohort retained, time excluded: ~−3 pp per decade.

The conditional profile is statistically significant from age 41 onward when time is retained, and from age 43 onward when cohorts are retained.

### 4.5 Authors' preferred specification and interpretation

The paper argues that pure time effects, *once subscription-year effects are absorbed*, have no compelling economic interpretation: access costs to financial markets fell over the 2000s with the rise of index funds and online brokerage (Bogan 2008), the tax regime of Madelin contracts did not change in a way that differentiated UC from euro shares, and contractual fees were fixed at subscription. The residual time profile in the data is small (≤ 1pp on the conditional UC share) and economically uninterpretable.

The preferred specification is therefore the cohort-retained, time-excluded one. Under this configuration, between ages 40 and 60:

- Probability of holding UC: **+12pp** (extensive margin rising).
- UC share conditional on holding UC: **−6pp** (intensive margin falling).
- Total UC share: mildly declining (the two effects partly offset).

> **Authors' critical reading.** The amplitude of the conditional decline is insufficient to bring the risky share to zero by retirement. Self-employed savers in Madelin contracts retain meaningful financial risk at the moment their capital is converted into a life annuity — a moment at which they have no smoothing margin other than postponing retirement, since annuity payments are calculated from the capital value at liquidation.

---

## 5. Conclusion

The panel evidence from a French insurer's Madelin contract database (2002–2009) yields three main findings.

First, savers' portfolio choices are highly sensitive to recent stock market performance — but only at the moment of subscription. New subscribers' UC share follows the cycle closely, peaking in 2008 just before the crash and bottoming in 2004 just before a four-year boom. After subscription, savers very rarely rebalance.

Second, the aggregate procyclicality of the average UC share is therefore driven by a flow of extrapolative new subscribers rather than by active rebalancing of existing portfolios. This is consistent with Nagel & Malmendier (2011) on the persistent influence of recent macro-financial experience on risk-taking.

Third, the age profile of the risky share depends critically on how the age/cohort/time identification problem is resolved. Under the authors' preferred configuration (cohort retained, time excluded, subscription-year controls included), participation rises with age (+12pp between 40 and 60) while the conditional risky share falls (−6pp), yielding a mildly declining total profile. The decline is too slow to bring the risky share near zero by retirement, which leaves self-employed Madelin contract holders exposed to financial risk at the moment of mandatory annuitisation.

### Limitations and research extensions

- The sample is restricted to self-employed Madelin contract holders, who are wealthier and have less stable income than the general salaried population (Evain & Amar 2006). Results may not generalise to PERP holders or to broader household portfolios.
- The data report only the Madelin contract; total household wealth is not observed, so the analysis cannot control for the share that Madelin savings represent within total wealth.
- The 2006 wave of UC shares is missing and was interpolated for older contracts, which may attenuate within-contract variation in that year.
- The age/cohort/time identification problem is not formally solved: the authors' preferred specification rests on the *plausibility* argument that pure time effects have no clear interpretation once subscription-year is absorbed.
- The accumulation phase only is observed; decumulation behaviour after annuitisation is not (see Coile & Milligan 2009 for related US evidence).

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## Acknowledgments

The authors thank the insurance company that made the data available, as well as the staff who assisted with the construction and use of the database. They also thank Christophe Boucher, Nicolas Debarsy, Christophe Hurlin, and Hélène Raymond for their advice, and the participants at the INFER and GdRE conferences and the LEO seminar.

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## Main references

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Ameriks, J., & Zeldes, S. (2004). How do household portfolio shares vary with age? Working paper, Columbia University.

Arrondel, L., & Masson, A. (2003). Stockholding in France. In *Stockholding in Europe* (Guiso, Haliassos & Jappelli, eds.), Palgrave Macmillan, 75–109.

Barberis, N. (2000). Investing for the long-run when returns are predictable. *Journal of Finance* 55(1), 225–264.

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Campbell, J., & Viceira, L. (1999). Consumption and portfolio decisions when expected returns are time varying. *Quarterly Journal of Economics* 114(2), 433–495.

Greenwood, R., & Shleifer, A. (2013). Expectation of returns and expected returns. NBER Working Paper 18686.

Malmendier, U., & Nagel, S. (2011). Depression babies: do macroeconomic experiences affect risk-taking? *Quarterly Journal of Economics* 126(1), 373–416.

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Samuelson, P. (1969). Lifetime portfolio selection by dynamic stochastic programming. *Review of Economics and Statistics* 51, 239–246.

Samuelson, P. (1991). Long-run risk tolerance when equity returns are mean regressing. In *Money, Macroeconomics and Economic Policy* (Brainard, Nordhaus & Watts, eds.), MIT Press, 181–200.

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*The full reference list appears in the published article.*