Individuals asset class choice behavior in their pension fund individual account appear consistent with the use of naive learning rules. Preliminary results from joint work with Felix Villatoro, Olga Fuentes and Pamela Searle.

1. Mislearning and Performance of
Individual Investors*
Olga Fuentes, Julio Riutort, Pamela Searle y Félix Villatoro
Universidad de Los Andes, May 2019
*Our opinions do not necesarily represent the Superintendencia de Pensiones’ views.

2. Introduction
Motivation
• We study the determinants and performance of individual investors
making active investment decisions with their pension plan. Focusing
on the potential feedback effects from performance (i.e. learning-by-
doing).
• Individuals are faced with complex investment decisions which have a
direct effect on their expected pension.
• Pension savings currently amount to 19% of total financial assets for
the average individual in an OECD country.
 In Chile, this figure is 43% and AUM are 70% of GDP.

3. Introduction
Institutional Setup in Chile
• DC system since 1981.
• 75% coverage of working-age population.
• AFPs – single purpose pension fund managers (PFM)
• AUM about 70% of GDP.
• Members get to choose:
 PFM: currently 6 (soon 7).
 Fund type: Fund A (80%), Fund B (60%), Fund C (40%), Fund D
(20%), Fund E (5%).
• At PFM offices or online; within 4 days; no direct fees.

4. Introduction
Performance and Investment Decisions Literature
• Average individual investor has poor performance and trades too much
(Odean, 1999, Barber and Odean, 2000, 2001, Calvet et al., 2007).
 Nevertheless, there is considerable heterogeneity in results (Grinblatt
et al., 2001).
• Average individual member of pension plan displays inertia (Madrian and
Shea, 2001, Agnew et al., 2003, Mitchell et al., 2006, Bilas et al., 2010, Tang
et al., 2012)
 Overall, there is less availability of evidence for pension plan members.
 When they are actively involved they fail to diversify (Tang et al., 2010).
 Heterogeneity in involvement: high wealth and income
 In Chile: younger, men, low income, low financial knowledge “choose”
default (Kristjanpoller and Olson, 2014)

5. Introduction
Learning Literature
• Past performance seems to affect future frequency of investment
decisions (Glaser and Weber, 2007, Meyer et al., 2012, Barber et al.,
2014).
 In some cases, performance improves with gained experience
(Nicolosi et al., 2009, Ser et al., 2009, Meyer et al., 2012).
 While in others, individuals stop trading after discovering their lack
of ability (Seru et al., 2009).
 This can be rationalized by the existence of learning-by-trading
(Mahani and Bernhardt, 2007, Linnainmaa, 2011).

6. Introduction
Our Approach
• Investment ability is unknown so it must be estimated (“learning-by-
trading”).
 Our dataset allows us to determine patterns of fund changes and
estimate performance.
• We explore the existence of a feedback between past performance
and subsequent fund changes.

7. Introduction
Contributions
1. We provide new evidence on the effects of investment decisions 0n
performance within a large pension system.
 Active investors poor performance is not robust across sample periods.
2. The more members make active investment decisions the more
likely they are to obtain worst performance.
 Market timers perform poorly
3. We provide evidence on a potential mechanism behind investors’
behavior.
 Feedback effects through the use of naïve learning rules

8. Introduction
Main Results and Policy Implications
• Performance of average individual that makes fund changes tends to
be poor, specially with higher frequency of changes and for “market
timers”.
• Robust evidence of learning and feedback effects for naïve ability-
updating rule.
• Tension between investment flexibility and outcome. Can we improve
the way in which individuals evaluate their investment decisions?

9. Empirical Analysis
Data
• Administrative records: 2007 to 2016.
 Individual level: fund, day of change, balance, income, contributions, etc.
 Fund level: daily fund NAVs, daily fund return.
• Representative sample of 62,865 individuals already enrolled in 2007.
 Changed funds at least once: 4,157 (6.6%)
 Roughly 18,000 fund changes in total
• Do not distinguish between fund changes within and across PFMs.
• Treat both mandatory and voluntary account fund changes the same.
• Types of fund changes:
1. Change  1(fund change in the month)
2. More Risk  1(fund change increased equity exposure)
3. Less Risk  1(fund change decreased equity exposure)

10. Empirical Analysis
Data – Investor Behavior Classification
• Four groups according to their fund switching behavior.
 Group 1 (Passive). Did not make any voluntary fund changes.
58,708 individuals (93,4%).
 Group 2 (Non-Timers). All their fund changes were in the same
direction. 1,671 individuals (2,7%).
 Group 3 (Moderate Timers). Two or more fund changes with both
increases and decreases in equity exposure. 1,202 individuals
(1,9%).
 Group 4 (Market Timers). At least two fund changes in both
directions between funds A and E. 1,284 individuals (2,0%).

11. Empirical Analysis
Descriptive Statistics (Mean)
Variable Group 1 (Passive) Group 2 (Non-Timer) Group 3 (Mod. Timer) Group 4 (Mkt Timer)
Age 41.212 40.194*** 41.656*** 38.74***
Log(Balance) 14.675 15.729*** 16.099*** 16.158***
Log(Income) 12.174 12.982*** 13.29*** 13.549***
VPS 0.034 0.087*** 0.169*** 0.258***
Male 0.55 0.593*** 0.569*** 0.685***
Change 0 0.013*** 0.037*** 0.098***
More Risk 0 0.000*** 0.015*** 0.047***
Less Risk 0 0.013*** 0.022*** 0.051***
Equity 49.365 56.734*** 55.532*** 55.537***
Deltar -0.098 -0.098 -0.098 -0.098
Volatility 3.678 3.678 3.678 3.678
Change PFM 0.004 0.006*** 0.012*** 0.014***
Web Password 0.066 0.17*** 0.35*** 0.49***
N 58,708 1,671 1,202 1,284

12. Empirical Analysis
Monthly Fund Changes

13. Empirical Analysis
Performance
 Raw returns. Compare raw average (geometric) returns across
individuals’ fund change groups.
 Jensen’s Alpha. Adjust for differential market risk loadings and
compare alphas across individuals’ fund change groups.
𝑅𝑖,𝑡 − 𝑅𝑓,𝑡 = 𝛼 + 𝛽 𝑅 𝑚,𝑡 − 𝑅𝑓,𝑡 + 𝑢 𝑡
𝑅𝑖,𝑡: real return of individual 𝑖 in month 𝑡.
𝑅𝑓,𝑡: short-term inflation-adjusted interest rate in Chile.
𝑅 𝑚,𝑡: real return of the MSCI Chile index in month 𝑡.

14. Empirical Analysis
Investors and Pension Fund Performance (%)
Group 2 (Non-timers) Group 3 (Moderate timers) Group 4 (Market timers)
Return SD Alpha Return SD Alpha Return SD Alpha
P5 2.300 4.908 2.298 P5 1.503 4.876 1.337 P5 0.209 5.596 0.184
P25 2.629 6.641 2.699 P25 2.361 7.055 2.378 P25 1.794 7.569 1.791
Mean 3.140 8.092 2.972 Mean 2.881 8.157 2.736 Mean 2.376 8.703 2.278
P75 3.538 10.619 3.227 P75 3.432 10.090 3.198 P75 3.071 10.257 2.925
P95 4.019 10.912 3.623 P95 4.054 10.779 3.727 P95 4.038 10.701 3.828
Pension Funds
Return SD Alpha
F A 2.678 10.923 2.790
F B 3.314 7.904 3.083
F C 4.013 5.136 3.575
F D 4.433 2.893 3.960
F E 4.817 1.723 4.390

15. Empirical Analysis
Performance - Luck or Skill?
• True market timing ability should eventually show up as high
performance of individuals with a high number of fund changes.
• We examine the number of fund changes across performance
quartiles, both in raw returns and alphas.
• Split the subsample of individuals with at least one fund change according to
raw return or alpha quartiles

16. Empirical Analysis
Number of Voluntary Fund Changes and Performance
Group 2 (Non-Timers) Group 3 (Moderate Timers) Group 4 (Market Timers)
Return Category N Num. Changes N Num. Changes N Num. Changes
Cat. 1 (r < 2.37%) 144 1.514 328 5.02 569 12.596
Cat. 2 (2.37% < r < 2.95%) 461 1.356*** 299 4.040*** 280 11.136***
Cat. 3 (2.95% < r < 3.37%) 565 1.483*** 307 3.886 167 10.012**
Cat. 4 (3.37% < r) 501 1.956*** 350 4.683*** 187 11.166*
Group 2 (Non-Timers) Group 3 (Moderate Timers) Group 4 (Market Timers)
Alpha Category N Num. Changes N Num. Changes N Num. Changes
Cat. 1 (α < 2.37%) 123 1.634 313 5.217 605 13.091
Cat. 2 (2.37% < α < 2.82%) 469 1.380*** 325 4.105*** 246 9.996***
Cat. 3 (2.82% < α < 3.16%) 601 1.539*** 292 4.010 146 9.788**
Cat. 4 (3.16% < α) 478 1.858*** 354 4.404* 206 10.859*

17. Empirical Analysis
Why Change Funds? Detecting Learning
• No liquidity or tax motivated motive for trading. Life cycle (unidirectional?) and market
timing remain.
• Posible learning from investment experience (update ability estimate).
• Success is defined as:
 Definition 1 (counter-factual): r with change r w/o change.
 Definition 2 (naive): r of selected fund > 0.
 Definition 3 (market timing): r of selected fund is the highest.
• Alternative definitions (based on day of change, net number of successful changes) don't
change qualitative results.
• Ability is the proportion of successful over total accumulated changes, 0.5 initial value.
• Correlations b/w Ability and Number of fund changes. Counter-factual (0.17), Naïve
(0.45), Market-timing (-0.38)

18. Empirical Analysis
Density of Ability and Sample End –Counter-factual

19. Empirical Analysis
Density of Ability at Sampel End – Naive

20. Empirical Analysis
Density of Ability at Sample End – Market timing

21. Empirical Analysis
Detecting Learning – Regression Analysis
• We prioritized simpler (consistent) models: lineal panel with
individual fixed effects and probit models.
• Models:
𝑌𝑖,𝑡 = Г𝑋𝑖,𝑡 + 𝛾𝑖 + 𝜖𝑖,𝑡
 𝑌𝑖,𝑡: 1(Change); 1(More Risk); 1(Less Risk)
 𝑋𝑖,𝑡: ability and controls (age, balance, income, voluntary savings,
lagged returns, lagged A-E return gap, gender, gender interactions,
A volatility, PFM change, password, trend)

22. Panel Regression Results: Dep Var Change
Variable (1) Counter-factual (2) Naive (3) Market-timing
Age -0.000531*** -0.000344*** -0.000382***
Log(Balance) 0.000625*** 0.000574*** 0.000779***
Log(Income) -0.000021*** -0.000020*** -0.000026***
VPS 0.0121*** 0.00918*** 0.00929***
rt-1 0.000224*** 0.000234*** 0.000263***
Deltar -0.000155*** -0.000168*** -0.000181***
Male X Deltar -0.000028*** -0.000034*** -0.000028***
Volatility 0.000125*** 0.000126*** 0.000137***
Male X Volatility -0.000046** -0.000008 -0.000051**
Change PFM 0.0368*** 0.0360*** 0.0360***
Web Password 0.0229*** 0.0179*** 0.0210***
Trend 0.000067*** 0.000043*** 0.000044***
Ability 0.138*** 0.312*** -0.223***
Male X Ability 0.0448** 0.0423** 0.00263
Constant -0.0727*** -0.165*** 0.112***
R2 (%) 1.8 4.0 2.3
N 7,404,158 7,404,158 7,404,158
Age (2) Naive: 3.4 bp
In our 10 year sample,
frequency of change was:
• 1.3% non-timers
• 3.7% mod. timers
• 9.7% market timers
Balance (3) MT: 7.8 bp
increase in prob of change
for 1% increase in balance.
Ability (2) Naive: a 1 sd
increase in ability
increases the prob of
change by 156 (177) bp for
females (males).

23. Panel Regression Results: Dep Var More Risk and Less Risk
Variable M: (1) C-F M: (2) Naive M: (3) M-T L: (1) C-F L: (2) Naive L: (3) M-T
Age -0.000269*** -0.000173*** -0.000204*** -0.000262*** -0.000172*** -0.000178***
Log(Balance) 0.000246*** 0.000236*** 0.000319*** 0.000379*** 0.000337*** 0.000460***
Log(Income) -0.000011*** -0.000011*** -0.000014*** -0.000010** -0.000009** -0.000012**
VPS 0.00548*** 0.00422*** 0.00474*** 0.00665*** 0.00497*** 0.00454***
rt-1 0.000003 0.000011 0.000021* 0.000221*** 0.000223*** 0.000242***
Deltar -0.000016** 0.000008 0.000004 -0.000171*** -0.000175*** -0.000184***
Male X Deltar -0.000009*** -0.000012** -0.000010* -0.000018*** -0.000021*** -0.000019***
Volatility 0.000037*** 0.000040*** 0.000045*** 0.000087*** 0.000087*** 0.000092***
Male X Volatility -0.000025*** -0.000006 -0.000027*** -0.000022*** -0.000002 -0.000024
Change PFM 0.0218*** 0.0215*** 0.0216*** 0.0149*** 0.0145*** 0.0144***
Web Password 0.00887*** 0.00671*** 0.00854*** 0.0140*** 0.0112*** 0.0125***
Trend 0.000029*** 0.000017*** 0.000020*** 0.000038*** 0.000026*** 0.000024***
Ability 0.0930*** 0.141*** -0.0711*** 0.0449*** 0.171*** -0.0152***
Male X Ability 0.0233** 0.0259** -0.00281 0.0215* 0.0165 0.00544
Constant -0.0471*** -0.0751*** 0.0388*** -0.0255*** -0.0896*** 0.0734***
R2 (%) 1.1 2.0 0.8 0.8 1.9 1.4
N 7,404,158 7,404,158 7,404,158 7,404,158 7,404,158 7,404,158
Ability (1) Counter-factual:
a 1 sd increase in ability.
 Increases the prob of
More Risk change by 71
(84) bp for females
(males).
 Increases the prob of
Less Risk change by 22 bp
for females and males.
Ability (2) Naive: a 1 sd
increase in ability.
 Increases the prob of
More Risk change by 71
(84) bp for females
(males).
 Increases the prob of
Less Risk change by 86 bp
for females and males.

24. Empirical Analysis
Takeaways
• Propensity of making changes declines with age.
• Wealth and income have opposite effects, though the former
dominates in magnitude.
• Making VPS has a strong (and robust) effect on propensity of making
changes.
• Potential gains from MT (proxied by volatility) lead to more changes
(specially reducing equity exposure).
• Regarding gender, a clear pattern emerges with males showing
stronger response to perceived ability.

25. Empirical Analysis
Robustness: Exclude 2007-2008
• We evaluate performance during the 2009-2016 period.
• Since the large losses of 2008 are left out, fund A (E) is the best
(worst) performing pension fund.
• Since it continues to be true that individuals are mostly on funds A
through C, performance looks better.
• Nevertheless, performance continues to be negatively related to
number of changes and market-timers mostly obtain poor
performance.

26. Empirical Analysis
Robustness: Simulated Performance
• Using multinomial regression models we estimate the “investment
rules” followed by different groups: full sample, best/worst
performers, market timers/non market timers.
• Caveat: limited set of independent variables.
• Nevertheless, rules replicate in-sample behavior (i.e. more extreme
changes for market timers).
• Difference in performance obtained in simulations is negligible
between groups, questioning the existence of ability.

27. Conclusions
• Performance seems to be poor for individuals who make fund
changes.
• Moreover, we find robust evidence showing that performance
decreases with the number of fund changes.
• We document the existence of feedback effect between self-assessed
ability and the frequency of fund changes.
• This effect increases fund changes for the naïve and counter-factual
ability performance measures.

28. Conclusions
• Maintaining the possibility of making fund adjustments could be
desirable in the presence of heterogeneity among individuals.
• Nevertheless, negative and unintended consequences may be
present.
• The results suggest that increased efforts should be made in order to
understand how individuals learn from past decisions and also in
improving the way in which the results of fund changes is informed.

29. Appendix
Model

30. Model
Preferences
• We model a representative individual 𝑖 who only cares about his
wealth at retirement, 𝑊𝑇.
• Preferences over 𝑊𝑇 are standard 𝑢′
𝑊𝑇 > 0 and 𝑢′′
𝑊𝑇 ≤ 0 .
• Elements that are left out (for now):
 Choice regarding amount of savings (reasonable for our data set
and doesn't interfere with empirical results).
 Retirement age (it seems likely that this is an exogenous variable in
many cases).
 General equilibrium effects (i.e. impact of trading on asset prices).
 Changes in the way in which agents learn.

31. Model
Investment Choice
• Two risky assets: 𝑎1 and 𝑎2.
• Every 𝑡, 𝑟1,𝑡 > 𝑟2,𝑡 or 𝑟1,𝑡 > 𝑟2,𝑡, with probability 𝜋 and 1 − 𝜋 ,
respectively.
• For expositional purposes, we assume that pdf of both assets is the
same.
• Therefore, ex-ante individuals would be indifferent between these
two assets.

32. Model
Private Information and Market Timing
• In exchange for incurring in a cost 𝑐𝑖 , 𝑖 receives a signal 𝜑𝑖,𝑡.
• This signal can take two values: 𝜑 𝑔,𝑡 or 𝜑 𝑏,𝑡.
𝑃𝑟 𝜑𝑖,𝑡 = 𝜑 𝑔,𝑡|𝑟𝑖,𝑡 = 𝑟𝑔 = 𝑃𝑖
𝑃𝑟 𝜑𝑖,𝑡 = 𝜑 𝑔,𝑡|𝑟𝑖,𝑡 = 𝑟𝑏 = 1 − 𝑃𝑖
• We assume that 𝑃𝑖 𝜖 1
2
, 1 : lower (upper) limit implies no (perfect)
market-timing ability.

33. Model
Learning
• 𝑃𝑖 is rationally estimated as the ratio of successful investment
decisions over total number of decisions (consistent with 𝑃𝑖 following
beta distribution).
• Also, 𝑖 can only learn about his ability if he engages in market timing.
• If there is no market timing, assessed ability remains unchanged
(nothing new is learned and there is no “depreciation” of previous
learning).
• Each period 𝑖 decides between engaging in market timing or following
a passive investment strategy.

34. Model
Optimal Learning
• Bellman equation 𝑉𝑖,𝑡 𝑃𝑖,𝑡 states that 𝑖 chooses the max between no
MT:
𝛿 0.5𝑉𝑖,𝑡+1 𝑟𝑔, 𝑃𝑖,𝑡 + 0.5𝑉𝑖,𝑡+1 𝑟𝑏, 𝑃𝑖,𝑡
and MT:
−𝑐𝑖 + 𝛿 𝑃𝑖,𝑡 𝑉𝑖,𝑡+1 𝑟𝑔, 𝑃𝑖,𝑡 + 1 − 𝑃𝑖,𝑡 𝑉𝑖,𝑡+1 𝑟𝑏, 𝑃𝑖,𝑡

35. Model
Optimal Learning
• We are interested in the determinants of 𝑃𝑖,𝑡
∗
: the assessed ability that
makes 𝑖 indifferent between no MT and MT.
• For the last period, 𝑇 − 1 (results qualitatively similar for t < 𝑇 − 1)
𝑃𝑖,𝑇−1
∗
=
1
2
+
𝑐𝑖
𝛿𝑖 𝑢 𝑊𝑇−1 1 + 𝑟𝑔 − 𝑢 𝑊𝑇−1 1 + 𝑟𝑏
• 𝑃𝑖,𝑇−1
∗
decreases with: 𝑟𝑔, 𝛿𝑖 and 𝑊 (with low risk aversion).
• 𝑃𝑖,𝑇−1
∗
increases with: 𝑟𝑏, 𝑐𝑖 and 𝑊 (with high risk aversion).