NATIONALEKONOMISKA INSTITUTIONEN Uppsala universitet
Examensarbete C
Författare: Thomas Frööjd & Olof Rydström Handledare: Edward Palmer
VT 2005
Is free choice efficient?
Will the large number of funds in the Swedish individual accounts system make individuals choose non-effectively?
Abstract
The Swedish individual accounts system incorporates a rebate system to capture economies of scale in fund management. Do clients in the system make inefficient choices among the large number of funds? A limited number of fund groups is examined using data from five years. Their performance, as measured by the information ratio IR (alpha-omega ratio), is adjusted to fund size to create a fee adjusted performance IRf which is then related to the net assets attracted in the system. All studied groups proved not inefficient, except for the groups with very few funds.
Keywords
PPA, Premium Pension Authority, The Swedish Individual Accounts System, fund managment, fund efficiency, fund choice, fund size, alpha-omega ratio, information ratio, IR, IRf, fee adjusted performance, pension fund, economies of scale, limit choice, efficient choice.
This essay would not have been possible without the creative input of Professor Edward Palmer at Uppsala University and suggestions from Anna Westerberg at the Swedish Finance Ministry. Anja Helms and Lars Oderbeck at Swedish Social Insurance Administration provided us with necessary data and information. Kim Santala at PPA answered many of our technical questions concerning the definition of variables.
Content
1 Introduction ____________________________________________________________ 4 1.1 Purpose ___________________________________________________________ 5 2 Information aspects in fund selection _________________________________________ 6 2.1 Information and Choice _______________________________________________ 6 2.2 Problems related to freedom of choice ____________________________________ 7 3 Organizing individual accounts______________________________________________ 8 3.1 Economies of scale in fund management __________________________________ 8 3.2 Retail market compared to investing through an institution ___________________ 10 3.3 How to capture institutional rates_______________________________________ 11 4 Organization of individual accounts in Sweden_________________________________ 12 4.1 Overview _________________________________________________________ 12 4.2 Rebate structure ____________________________________________________ 15 5 Measuring Efficiency ____________________________________________________ 16 5.1 The information ratio ________________________________________________ 16 5.2 Comparing performance using fund fees _________________________________ 17 5.3 Comparing fee adjusted performance between similar funds __________________ 17 5.4 The test __________________________________________________________ 18 5.5 Data _____________________________________________________________ 19 6 Testing for inefficient choice ______________________________________________ 20 6.1 Evaluating the results ________________________________________________ 20 6.2 Sweden___________________________________________________________ 20 6.3 Europe ___________________________________________________________ 22 6.4 North America and USA _____________________________________________ 24 6.5 Asia _____________________________________________________________ 25 6.6 Conclusion ________________________________________________________ 27 7 Summary _____________________________________________________________ 28 7.1 Ideas for future research______________________________________________ 28 8 References ____________________________________________________________ 29
1 Introduction
The Swedish individual accounts system was constructed as a complement to the old pay-as-you- go system. Palmer (2000) stresses four goals set out by the Swedish authorities: 1
• Fair treatment of persons with different contribution histories.
• Transparent redistribution.
• Financial stability.
• Financial saving managed by private financial institutions.
The goal of the reform was to construct a pension system where the pension depended on the individual’s income throughout the whole life and were the final pension were not decided until retirement. It was designed as a two tier system, the bulk of the savings are made in a traditional Pay-as-you-go (NDC) system and as a complement there is a mandatory individual accounts system (FDC). The FDC scheme was designed with free entry for fund managers with a price ceiling and as a result of this the number of funds is very large. The large number of funds has been questioned by Palme & Sundén for being very costly to administer as well as possibly confusing the investors and creating a passive investment attitude.2 In the article
‘Premiepensionen I det reformerade pensionssystemet – är det önskvärt att välja mellan 663 fonder’ they propose the following three changes to the design of the system.3
1. A redesign of the government owned fund ‘Premiesparfonden’ to a fund where the ratio between bonds and stocks are decided on the individual investor’s age. This is for people who don’t want to make an active investment decision.
2. A number of predetermined portfolios for investors who wants to make an active choice but don’t have the knowledge to construct a portfolio from scratch.
3. A system similar to the one used today for individuals who wants complete control of their portfolio but with a smaller number of funds to choose from to keep the costs down.
1Palmer, 2000, p 2-3
2 Palme & Sundén, 2004, p 9
3 Ibid, p 15
Palme & Sundén further states that there is a problem how to determine which funds that should be allowed in the system since proposal no 3 suggests that the current large number has to be narrowed down somehow.4 This implies that the system will not longer have free entry for funds but that the funds have to be selected by the PPA monopoly.
1.1 Purpose
The purpose of this paper is to see whether there may be a reason to limit the number of funds in the Swedish individual accounts system as proposed by Palme & Sundén. The reason being that the larger number of funds might confuse the clients and make them act unrational. Our hypothesis is that larger funds should be more efficient, ceteris paribus, due to economies of scale. If this is the case, the question becomes, do consumers choose rationally by choosing more efficient funds? That is, if the larger funds attract investors because of better fee adjusted
performance. We will then compare the results with the individual accounts system rebate scheme. We will use data for the performance and fee structures of a limited number of fund categories in the individual accounts system obtained from the Premium Pension Authority (PPA) and the Swedish Social Insurance Administration. The test will be restricted to equity funds with at least five years of data available.
To measure cost effectiveness we will use the Information Ratio as presented by Goodwin (1998) adjusted for fund management fees as an indicator of risk adjusted performance per unit of fee.
We will then relate this to the assets in the system of the funds in question and compare the result between the different fund types. We will also give the reader a brief overview of current research about design and evaluation of individual account systems.
The disposition of this paper is as follows: An introduction to the economic theories of choice and a discussion of effects of the large number of funds in the Swedish individual accounts system. This is followed by an introduction to the theory behind organization of individual account systems and an explanation of the design of Swedish FDC system and its rebate scheme.
A statistical test is then conducted on how well the clients’ choices adapt to the fee adjusted performance before and after the rebate.
4 Palme & Sundén, 2004, p 15
2 Information aspects in fund selection
2.1 Information and Choice
In order to make an informed choice the consumer needs to have access to correct and complete information concerning the product. How do individual decision-makers form their decisions with regard to information? Boland (1986) states: ‘If everyone uses the same ‘set of information’
and everyone uses the same means of processing that information, the theorist might be able to predict and possibly explain what everyone is doing.’5 If this is correct a careful study of the available information at the time of choice may explain the consumer behavior.
It is not evident what is meant by the term information. Information is of limited value if the consumer is unable to understand, misinterpret or only understands part of the information.
Phelps (1985) concludes: ‘The resulting focus of this modern theory is on the roles of imperfect information and incomplete knowledge in the performance of the market economy /…/Each participant in the market, according to modern theory, has to rely on his beliefs about the desires and capacities of those he deals with’6 The reason one needs information is to be able to
correctly assess the costs and benefits of a particular choice. The very term cost may be used in two different ways with regard to choice. Buchanan (1978) states: ‘It is this “cost” consequent to choice which helps to create a part of the confusion between cost in the predictive theory and cost in the logic of choice’7 There are two variables of choice, one of which is difficult to measure. Buchanan concludes: ’Cost, then is purely subjective in any theory of choice, whereas cost is objective in any theory that involves genuine prediction’8
How is cost related to information? Louis Phlips (1989) concludes: ‘Getting information on prices charged for particular brands by particular shops then involves costs of information, which depend on the information technology (the existence of consumer reports, specialized journals, advertising etc.), the number of brands and shops available and one’s a priori knowledge. These costs are mostly in terms of the time spent searching: Time is more valuable for the “rich” than for the “poor”. Rich customers are therefore said to be “high cost,” and poor customers are said
5 Boland, 1986, p 120
6 Phelps, 1985, p 180
7 Buchanan, 1978, p 44
8 Ibid, p 43
to be “low cost.” Other things equal, the former should search less than the latter.’9 Thus the time spent searching for information is costly and there is a need for an objective way to compare different choices.
However there is also a psychological aspect to be considered. Loewenstein (1999) summaries the benefits and costs of an expansion of choice: ‘Expanded choices are beneficial when they satisfy people’s highly varied wants and needs and when they promote competition that lowers price or improves quality. The gains from competition are best realized when consumers are well-
informed, and when price and quality are easy to compare. Expanded choices are inadvisable when they require expertise that people don’t possess. In such situations: (1) the benefits from competition are likely to be minimal; (2) the decisions are likely to take considerable time to make; (3) people are more likely to make bad decisions; and (4) decision making is likely to be a considerable source of anxiety and anticipated regret.’10 This should apply especially to the private investor facing the diversity of the fund market where price and quality is hard to assess.
Palme and Sundén (2004)11 state a number of problems involving free choice in fund
management. They fear the large number of alternatives may create a passive attitude instead of promoting choice because individuals have difficulty comparing investments to risk tolerance resulting in:
• Lack of diversification of investments; there is a risk for home bias in the country one lives in or sector one works in.
• A risk that investment strategies do not change over time, therefore not adapting to the individuals changing risk preference during her lifecycle.
2.2 Problems related to freedom of choice
How do clients in the Swedish individual accounts system handle their choices? Research by Sundén (2004) concerning the clients choices emphasizes that people do choose a lot, however their choices may not always be as rational as they are mathematically simple: ‘Among
participants who made an active investment choice in 2000, the average number of funds selected was 3.4. However, almost one-third of participants chose five funds, the maximum allowed /…/
Experience with investing in 401(k) plans has shown that participants often fall back on simple
9 Phlips, 1989, p 23
10 Loewenstein, 1999, p 3-4
11 Palme & Sundén, 2004, p 9-12
rules of thumb. One such rule is the 1/n heuristic which means that participants divide their contributions equally among the available investment options. The results indicate that a significant share of the Swedish participants appear to follow this type of rule by choosing five funds. A consequence of the 1/n heuristic is that participants tend to invest too much in equities when the number of choices increases.’12 Sundén further concludes that people who have
selected their own portfolio have higher fees than those who have chosen to remain in the default fund, many portfolios were undiversified; there was a geographic bias to Sweden, but no sector bias; there are indications of rational choices with regard to unemployment risk and safer funds, however many people with low income have too risky portfolios.13
Yet unpublished research by Palmer (2005) concludes that the Swedish system may create problems due to the rebate principles supporting larger funds: ’As the system works today, funds with the highest returns compared to relevant alternatives tend to attract relatively more clients, while the PPM rebate system drives down the allowable price for services as funds grow in volume. This mechanism steers clients into high return funds, while forcing down prices charged by these funds , thereby created a sort of pseudo optimizing behavior, given participant risk and portfolio choice preferences.’14 Thus there are reasons for questioning the principles of choice in the Swedish individual accounts system.
3 Organizing individual accounts
The purpose of this chapter is to give the reader an idea of the fundamental economical questions about markets’ that constitutes the premises for individual accounts systems. We will also present the various ways to design such a system.
3.1 Economies of scale in fund management
There may be good reasons why one should expect economies of scale in fund management. The fund fees depend on a number of variables. James, Smalhout & Vittas (2001) present a model for the administration costs15 as the sum of startup costs, record-keeping and communication costs, investment cost and marketing costs. Since these costs are mainly fixed they are faced by large as
12 Sundén, 2004, p 9
13 Ibid, p 13
14 Palmer, 2005, p13
15 James, Smalhout & Vittas, 2001, p 256
well as small funds. Thus one may suspect that larger funds are more efficient, simply because they can divide these fixed costs on a large number of clients.
If one assumes economies of scale it may be justified to create a rebate system that encourages clients to select larger funds and fund managers to share the economies of scale to the investors.
However a rebate structure as this makes it more difficult for new companies to enter the market:
‘It makes considerable difference whether newcomers can enter an industry at will or whether there are barriers to entry./…/Moreover, if the product is differentiated, you will have to spend a lot on advertising to force your way into the market and if you fall, you will have nothing to show for this investment.’16 Thus a rebate-system that supports economies of scale (even if proved effective to the consumer) may harm competition. The question is how much will the
competition suffer and how much will consumer gain from a system like this? It is assumed that
‘Economic agents do not suffer from money illusions.’17
This can not be separated from the question of whether an individual account system is efficient in the economic sense18: That there is no other possible situation that would improve conditions for at least one client without harming another (or the weaker version were the loser could be compensated by the winner with an overall increase in utility – Kaldor-Hicks). In this case there may be other ways to organize the premium pension system.
The aim to maximize the clients’ efficiency of choices raises the question of what we mean by efficiency with regard to the individual client? There is a return and a risk (variance) associated with each fund. These figures, however, are known only in retrospect. The fee, on the other hand, is more or less well known and presented by the manager. It is evident that all consumers wish to maximize their return on each unit of risk. A fee is a kind of cost and should be treated as one. Thus to maximize the benefit of the fee; the client must maximize the return/risk-ratio on each unit of fee.
The question is whether high-fee funds perform better then low-fee funds. The research so far gives no straight answers. Engström (2001) summarizes the research: ‘The evidence from U.S.
data is somewhat mixed. On the one hand, Ippolito (1989) finds that high-fee U.S. funds also
16 Reynolds, 1988, p 131
17 Miller & Pulsinelli, 1986, p 70
18 Werin, 1993, p 66
perform relatively well – even well enough to offset the higher fees. However, in their
reinterpretation of this evidence, Elton, Gruber, Das and Hlavka (1993) and Carhart (1997) argue that high-fee funds do not perform as well as low-fee funds.’19 Thus, there have been some researches concerning fees; though the results are debated among scientist. However, Engström generally concludes that: ‘our results indicate that the measured performance is negatively related to fees, that is, high-fee funds seem not to perform as well as low-fee funds.’20
3.2 Retail market compared to investing through an institution
In the previous section we concluded that there are certain economies-of-scale to fund management which can be captured in an organized individual account system.James, Smalhout and Vittas (2001), find two ways to organizing fee structure and have further investigated their cost-effectiveness
1. ‘investing through the retail market in which workers choose their own pension fund, open entry is subject to regulations, and the fund sets prices…
2. …investing through the institutional market under conditions in which entry and price are negotiated for a larger group or for the entire covered labor force and group choice constrains workers choice’21
Empirical evidence22 suggests that both these systems capture the economies of scale in asset management but have different benefits and disadvantages. Investing through the institutional market seems to be a more cost-effective way and the final pensions in the study were 10-20 %23 higher than if they would be managed through the retail market. There is however certain problems that should be accounted for. “Potential pitfalls inherent in the institutional approach include the increased probability of corruption, collusion, regulatory capture, decreased
performance incentives, re-bidding problems and inflexibility in the face of unforeseen contingencies.”24 The cost reduction in the institutional system should therefore be weighted again the benefits of the retail approach.
19 Engström, 2001, p 16
20 Ibid, p 19
21 James, Smalhout & Vittas, p 254
22 Ibid, p 255
23 Ibid, p 256
24 Ibid
3.3 How to capture institutional rates
An institutional system can be designed in different ways which will have an impact on the cost- effectiveness. A model that is used in Bolivia is to simply auction the opportunity to manage the system to the lowest bidder.25 This will constrain the choice for the individuals considerably since there is only one fund that is mandatory (In Bolivia actually two since there were two winners). A system like this would probably not fulfill the requirements for diversification and risk
management in a more developed country. It will also pose substantial risk for corruption and the other issues of the institutional approach outlined earlier. Setting this aside Bolivia’s IA system has been a success and managed to greatly reduce the administration costs (especially when taking consideration for the country’s bad infrastructure and undeveloped financial markets).
On the other extreme we have the Swedish individual accounts system. Funds are free to enter the market through a government agency, the PPA, as long they comply to offer a certain rebate on the PPA funds they manage.26 This results in a very big number of funds offering plenty of diversification opportunities. The free entry approach, while offering cost-reduction over the retail system has still been criticized for generating unnecessarily high administration costs due to the large number of funds that will enter the system. This approach also has the drawback of generating high start-up costs in the early years of the system.
Palmer (2005)27 has proposed a different model to further reduce the administration costs where the institution uses its monopoly power to purchase the services of a limited number of funds.
This system would, at least in theory, provide a supply of funds large enough to satisfy the individuals need for diversification and option to choose appropriate level of risk according to risk preference. However, by limiting the number of funds, through an auction process, the administration costs would decrease as the average fund would be larger.
Braff (1969) concludes: ‘Where economies of scale indicate that a given market could be served considerably more efficiently by a single producer than by many smaller firms, the situation is often identified as a natural monopoly.’28 A monopoly purchaser can hold down costs to
themselves as well as to the clients of the system. However, these two goals may differ. Friedman
25 Ibid, p 286
26 Sundén, 2004, p 2
27 Palmer, 2005, p 13
28 Braff, 1969, p 163
(1980) emphasizes the need for individual choices as – or someone else (who might have other preferences) will spend the money for you29. If one, despite this argument, assumes that the PPA focuses on the clients, there are ways for them to reduce consumer costs by economies of scales through promoting larger funds.
One way is to simply exclude undesirable funds; that is funds that perform in ways that do not meet certain criteria. The question is then what criteria are suitable? One may even argue that all rules restrict the principles of market economy. One may use other methods to exclude funds.
One way would be to simply not allow for new funds to enter the system during a period.
Another example of exclusion would be to allow all funds to compete to be part of the system, allowing only a few funds that offer the best conditions. A third alternative is to impose fees or a rebate system, supporting funds with good performance. An alternative to this is to impose a fee or rebate system as above, but letting the consumer face the extra cost/rebate directly.
To summarize the above discussion we can conclude that in the design of a FDC system there is a tradeoff between maximizing the cost-reduction and the number of funds in the system. Since we earlier discussed how a number of funds above a certain threshold may create passivity among the investors instead of promoting choice there seems to be more of a danger in having to many funds than too few since there are two negative effects to account for. A properly designed system has to be customized to its users with regard to the demand for options among the investors (financial literacy, financial infrastructure, need for diversification).
4 Organization of individual accounts in Sweden
4.1 Overview
The system with individual accounts for all workers was introduced in 1998 as a part of the reconstruction of the earlier pay-as-you go system. The goal was to introduce a pension system where the pension depended on the individual’s income throughout the whole life and not on the years with the highest income that was the case with the previous scheme.30 At the moment all Swedish employees fund the pension system with 18.5 % of their earnings, 16 % are put in a pay-
29 Friedman, 1980, p116-
30 SOU 1997:131, p 47
as-you-go arrangement and the remaining 2.5 %31 are used to fund individual accounts. The individual is then free to decide how the contribution will be invested by choosing from a large number of domestic and international funds. These funds are in general privately run and are also traded in the retail fund market. All fund managers that have the legal right to manage a fund in Sweden have the right to enter the individual accounts system as long as they comply with regulations on rebate, withdrawal fees and reporting.32 The free entry has caused a large number of funds to enter the system and there are currently 702 equity, bond and mixed funds workers in Sweden can choose from.33 For those individuals that don’t want to make a choice there is also a state administrated fund.34 The administration of fees and trading in the system is managed by a separate authority, the Premium Pension Authority (PPA). There are two fees the individuals pay in the Swedish individual accounts system, one for the fund management to the fund companies and one to PPM that will cover the administrative costs.
In the individual accounts system the individuals are free to make changes in their fund portfolio at any time. On a daily basis PPA then aggregates all changes in its client’s portfolio and makes the corresponding trades with shares in the funds so that the organizations portfolio is consistent with the sum of all of its investors’ portfolios. As a consequence of this institutional arrangement the funds in the system lack information about the individual investors.
The PPA35 sorts the funds into categories based on stock funds, bond funds or a mix of the two.
The mixed funds are sorted into generally mixed funds and generation funds. In the next level funds with sector preferences or regional preferences are grouped together. Generation funds, however, are sorted into categories based on time to retirement.
The stock funds are sorted into categories as well as subcategories. The categories are Sweden funds, with at least 75 % Swedish stocks. Regional funds, with at least 75% stocks in normally at least two countries, Country funds, with at least 75% in another country than Sweden. And finally there are sector funds, with at least 75% in a specific sector worldwide.
31Homepage PPA 20050331
32 SOU 1997:131, p 12
33 Homepage PPA, 20050331
34 Palmer, 2000, p 38
35 PPA fund catalogue 2005
• Interest rate funds
o Sweden, short time o Sweden, long time o Sweden real interest rate o Europe and Euro land o Other foreign
• Mixed funds
o Swedish stocks and interests o Swedish and foreign stocks and o Swedish interest rates
• Generation funds
o Pension in less than 10 years funds o Pension in less than 20 years funds o Pension in more than 20 years funds
• Stock funds
o Sweden funds
Sweden
Sweden, small business
Sweden, index o Regional funds
Swedish and foreign stocks
Scandinavian
European
Euro land
Europe, Euro land, small business
Europe, Euro land, index
North America and USA
Asia and Foreign East
Global
New markets
East Europe o Country funds
Japan
Other countries o Sector funds
IT and communication
Medical
Other sectors
As the above table points out the fund supply is geographically biased to Sweden. Many of the funds also have a similar investment strategy investing mainly in Swedish large cap stocks,
therefore almost replicating the index. Worth noticing is the lack of sector funds for other sectors than high risk branches like IT and life science. While the system offers its investors reasonable capabilities in geographical diversification it doesn’t emphasize differences in investment strategies and between sectors.
4.2 Rebate structure
To lower the asset management costs for the participants the Swedish individual accounts system includes a rebate system that the funds wishing to participate have to agree too. The fee schedule is designed to mimic the cost function of the fund manager and separate the record-keeping and communication costs from other costs for running the fund.36 The idea is that the PPA, by using economies of scale, will be able to charge a lower fee for administration than the individual fund would on the retail market. The rebate is recalculated every day and follows a formula further explained by Palmer (2000). For funds with fixed administrative charges the administrative cost reduction becomes37:
Reduction= [NC-(Free+(1-R)(NC-Free))] (Asset in PPA System) (1)
NC = Fund manager’s normal fee charge
Free =Flat rebate for an asset interval, tabulated value.
R = Incremental rebate for an asset interval, tabulated value.
A few fundamentals of the formula should be noted:
• The rebate depends on the amount of contributions the fund is attracting from the PPA system; more popular funds are forced to give a larger rebate.
• The rebate depends on the fee charged by the fund in the retail market; higher fees require a higher rebate to the PPA customers.
• A sliding scale is used to mimic the benefits for the fund manager of economies of scale.
36 James, Smalhout & Vittas, 2001, p 291
37 Palmer, 2000, p 41-42
In the year 2003 the average investor contributed 0.43 % of their total savings as fees to the fund manager while paying a fixed fee to PPM of 0.3 % for administration. Sundén has stated about the administrative fee that ‘this fee is relatively high compared to, for example the U.S.
government Thrift Savings Plan, which has expense ratios of 0.1 percent of assets’.38 The current high fee is related to startup costs of the system and is expected to decrease in the future.
As the Swedish FDC rebate system tries to simulate the actual costs faced by the funds it also disregards some parameters hard to quantify, the most important of those being the different costs of different investment strategies. An actively managed fund with high research cost is treated almost the same as a low cost index fund with comparable size. While some of those differences are included because the model accounts for the fund fee on the retail market, the model is still not completely fair.
5 Measuring Efficiency
This section explains how efficiency can be measured. We adapt standard mathematical measurements slightly to serve our needs.
5.1 The information ratio
The Information Ratio, called IR or alpha-omega ratio, measures the average excess return per unit volatility in excess return. It determines the quality of the manager’s information discounted by the residual risk.39
dER
IR = ER (2)
Where
∑
−= T
R
ER Rpt bt (3)
Rpt = Return on an active portfolio in period t
Rbt = Return on a benchmark portfolio or security in period t
As a benchmark one may use a non-risk value, in our case we used Swedish Treasury Bonds.
38 Sundén 2004, p 2
39 Goodwin, 1998, p 34-35
dER = Standard deviation of (Rpt-Rbt) under period 1 through T)
In order to evaluate ER, a t-statistic is formed40:
T d t ER
ER
StatER = (4)
This variable has a t-distribution with (T-1) degrees of freedom. If tStatER exceeds the tabulated value41 the manager’s excess return is positive under the tabulated probability. This test can also be used to create thresholds to be compares to the IR.
5.2 Comparing performance using fund fees
The fund fees may vary a lot. To ensure that the test is neutral with regard to fees, we created a modified IR-test, called IRf. If one divides the IR by the fund fee, one can create a measurement of fund efficiency with regard to the fee:
fee
IRf = IR (5)
By comparing the IRf to fund size, S, it is possible to tell if larger funds provide more risk adjusted performance with regard to a fee.
5.3 Comparing fee adjusted performance between similar funds
A plot of these variables will thus give IRf on the y-axis and S on the x-axis. If the slope, β, is statistically significant, it would be possible to conclude that the size is indeed an important factor to be considered in fund managing with regard to risk adjusted turnover.The β -value is evaluated by standard statistical methods42. If βe is the estimated β43:
40 Ibid, p 37
41 Blom, 1984, p 319
42 Maddala, 1988, p 46
43 Blom, 1984, p 319
) * SE(
n t )
* SE(
n
-t( −2) βe < βe < ( −2) βe , 95%level (6)
Where SE(βe) is the standard error of the determination coefficient
It would be possible to determine whether fund size is an important factor in studying fund fees.
The β-coefficient should, in that case, not be a random variable for the linear model.
5.4 The test
By using standard regression equations for linear regression we will examine if Size S and Fee adjusted performance IRf are related. The regression formulas are:
ε β
α+ +
= e IRf
S * (7)
The null-hypothesis H0 is that βe=0 This would imply that we can not determine whether clients choose rationally in the sense that they optimize their fee adjusted performance.
The alternative hypothesis H1 is that βe ≠0 This implies that there is a connection of some kind between clients choices and the fee adjusted performance.
For each group examined a t-statistic for βe will be calculated. The hypothesis H0 was rejected44 based on this computer t-statistic. This was a double sided test on the 5%-level. Thus the probability of wrongly accepting H0 was maximum 5%.
By using a standard Cartesian diagram plotting fund size, S, on the y-axis and fee adjusted performance, IRf, on the x-axis one will be able to graphically display the variable
However, if large funds have economies of scale due to their size and this is the prime reason for their efficiency – one may argue that an increasing number of clients may cause more efficiency.
In that case size may implicate efficiency - not only the other way around. The causality between IRf and S is not self evident. IRf may implicate S – in the sense that clients make their choices based on IRf.. But many clients (a high S) may create economies of scale and thus create a high IRf.. The high IRf may however attract other clients. Thus if one accepts that there may be
44 Edling & Hedström, 2003, p 125
economies of scale in fund management; this fact can not be separated from the hypothesis that IRf implicates S. Our test simply tells us whether IRf implicates S. We do not test whether S implicates IRf, since this implication can not be separated from the hypothesis that IRf, implicates S. This should not be interpreted as a dismissal of economies of scale, but simply an attempt to find a connection between IRf and S, to see if we find evidence that clients act inefficiently.
Recently attempts have been made to modify the IR to provide correct rankings when excess returns are negative45. However, we decided to divide the data into different groups. The fee adjusted performance, measured as IRf,, can thus be both positive and negative they can not be compared to each other and hence we divide our samples into negative and positive groups. For a negative group a observation with low IRf implies better fee adjusted performance than another observation in the same group with a higher value. The opposite is true for a group with positive values where a high IRf value implies better performance than a low. This is thus an attempt to capture some of the essential parameters of consumer information by a single formula. In doing so, we try to evaluate whether consumer choose funds based on available information.
5.5 Data
The data are from the years 2000-2004 since this was the data the PPA could provide us with.
The database only captures a few aspects of the clients’ choices namely the same the clients use in the PPA Fund Catalogue. Other aspects that may be important to their choices, such as
unemployment rate, expected inflation, expected income, changes in income, etc., were ignored.
These facts may affect the clients’ choices. In times of uncertainty one may suspect that people choose less risky funds. Since the study only includes five years, this aspect should perhaps have been considered. However, we ignored it to minimize the model.
We only used funds that were a part of the system during this period. Many of the groups contained a very small number of funds. To improve the statistical significance we limited our study to groups with more than 20 funds. In the test for regression groups with less than four funds were eliminated, since there would be no point calculating a linear model for those cases.
Further the group ‘Other Countries’ was eliminated since it was not a group with a common reason for being grouped together. The remaining fund groups were:
• Sweden (positive & negative IRf)
45 Israelsen, 2005
• Europe (only negative IRf)
• North America (only negative IRf)
• Asia (positive & negative IRf)
To compute the IR a risk free interest rate have to be estimated, for this we used the annual return for the Swedish 6-month Treasury bill.46
6 Testing for inefficient choice
6.1 Evaluating the results
If we are to find a positive relation between the net assets of the funds in a given group and the fee adjusted performance we can make a case that:
• Investors choose funds in a rational way
• Larger funds are more efficient in the Swedish individual accounts system because the rebate manages to capture economies of scale
If instead the results do not show a significant relation it would mean that the Swedish individual accounts system is flawed because the individual investors do not take advantage of the rebate.
A comparison between the results with and without the rebate accounted for will also show if the rebate really affects investor choice. A large difference in significance would mean that the clients were able to comprehend the information when conducting a choice. However, the tests with and without rebate can not be compared directly since the IRf values where defined differently.
Without a rebate a fund may not have been chosen.
6.2 Sweden
The Sweden group consisted of 24 observations with negative performances and 4 observations with positive performances. After constructing the regression equation we plotted the
observations with regression line and the 95% confidence interval of the determination
46 Ecowin
coefficient. Since the positive performances had no statistical significance we refrained from analysing them further.
Table 1
Regression analysis of Irf impact on Net assets of funds in the Swedish individual accounts system, Sweden
Negative performances (24 observations)
Positive performances (4 observations)
Before rebate After rebate Before rebate After rebate Determination
Coefficient -1617 -1756 531 3206
Std. Error of Det.
Coef. 592 397 8673 4796
t-Statistic -2.73 -4.42 0.06 0.67
Prob. (β=0) 0.0122 0.0002 0.9568 0.5727
R-squared 0.253 0.470 0.002 0.183
Std. Error of
Regression 286 241 2544 2302
0 400 800 1200 1600
-.5 -.4 -.3 -.2 -.1 .0
IRf before rebate
PPA Assets (Msek)
Sweden negative performances before rebate
-400 0 400 800 1200 1600
-.6 -.5 -.4 -.3 -.2 -.1 .0 IRf after rebate
PPA Assets (Msek)
Sweden negative performances after rebate
Table 2
95% Confidence interval of determination coefficient, Sweden
<
Determination
coefficient <
Before rebate -2843 -1617 -391 After rebate -2579 -1756 -933
In both cases with negative performance the t-statistic shows that there is a connection between the fee adjusted performance and the net size in the individual accounts system. This connection is clear when testing both before and after the rebate. This connection is significant on the 5 % level and therefore we conclude that the IRf effects the choice of funds in the Sweden group.
Note also how the explained variance (R-squared) differs in the two tests, the test after the rebate shows a much higher explained variance.
A similar test on the positive performers in the Sweden group shows no significance in the regression coefficient and thus we can not conclude anything. This may be due to too few observations.
6.3 Europe
The Europe group consisted of 31 observations with negative performances and no positive performances. The first table presents the descriptive statistics of the regression equation. The following graph is the plot of the observations and the last table is the 95% confidence interval of the determination coefficient.
Table 3
Regression analysis of Irf impact on Net assets of funds in the Swedish individual accounts system, Europe
Negative performance (31 observations)
Before rebate After rebate Determination
Coefficient -502 -487
Std. Error of
Det. Coef. 187 80
t-Statistic -2.69 -6.10
Prob. (β=0) 0.0118 0.0000
R-squared 0.20 0.56
Std. Error of
Regression 134 99
-100 0 100 200 300 400 500 600
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 IRf after rebate
IRf before rebate
Europe negative performances after rebate
-100 0 100 200 300 400 500 600
-.7 -.6 -.5 -.4 -.3 -.2 -.1 .0 IRf before rebate
PPA Assets (Msek)
Europe negative performances before rebate
Table 4
95% Confidence interval of Determination coefficient Europe
<
Determination
coefficient <
Before rebate
-
884 -502 - 119
After rebate -
650 -487 - 323
Since the Europe group lacked any funds with positive performance we only conducted the test on negative values. Both tests show that there is a connection between the fee adjusted
performance and the net size in the individual accounts system independent of the rebate or not.
This connection is clear when testing both before and after the rebate. This connection is significant on the 5 % level and therefore we conclude that the IRf variable may affect the choice of funds in the Europe group.
6.4 North America and USA
The North America and USA group consisted of 32 observations with negative performances and no positive performances. The first table presents the descriptive statistics of the regression equation. The following graph is the plot of the observations and the last table is the 95%
confidence interval of the determination coefficient.
Table 5
Regression analysis of Irf impact on Net assets of funds in the Swedish individual accounts system, North America and USA
Negative performance (32 observations)
Before rebate After rebate Determination
Coefficient -160 -172
Std. Error of
Det. Coef. 31 24
t-Statistic -5.23 -7.16
Prob. (β=0) 0.0000 0.0000
R-squared 0.48 0.63
Std. Error of
Regression 81 68
Table 6
95% Confidence interval of determination coefficient, North America and USA
<
Determination coefficient <
Before rebate -223 -160 -98 After rebate -221 -172 -123
The North America and USA had no funds with positive performance. Therefore there were no tests to be made for positive values of IRf. As in the previous cases we could find a significant dependency on the 5 % level between the fee adjusted performance and the net size in the individual accounts system independent of the rebate or not. The regressions showed high explained variances and high t-statistics.
6.5 Asia
The Asia group consisted of 20 observations with negative performances and 5 observations with positive performances. After constructing the regression equation we plotted the observations with regression line and the 95% confidence interval of the determination coefficient. Since the positive performances had no statistical significance we refrained from analysing them further.
-100 0 100 200 300 400 500
-2.8 -2.4 -2.0 -1.6 -1.2 -0.8 -0.4 0.0 IRf after rebate
PPA Assets (Msek)
USA and North America negative performances after rebate
-100 0 100 200 300 400 500
-2.8 -2.4 -2.0 -1.6 -1.2 -0.8 -0.4 0.0 IRf before rebate
PPA Assets (Msek)
USA and North America negative performances before rebate
Table 7
Regression analysis of Irf impact on Net assets of funds in the swedish individual accounts system, Asia
Negative performance (20 observations)
Positive performance (5 observations)
Before rebate After rebate Before rebate After rebate Determination
Coefficient -198 -159 618 364
Std. Error of
Det. Coef. 56 37 414 232
t-Statistic -3.52 -4.28 1.49 1.57
Prob. (β=0) 0.0024 0.0004 0.2322 0.2140
R-squared 0.41 0.51 0.43 0.45
Std. Error of
Regression 40 36 54 53
-40 0 40 80 120 160 200
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 IRf after rebate
PPA Assets (Msek)
Asia negative performances after rebate
-40 0 40 80 120 160 200
-.8 -.7 -.6 -.5 -.4 -.3 -.2 -.1 .0 IRf before rebate
PPA Assets (Msek)
Asia negative performances before rebate
Table 8
95% Confidence interval of determination coefficient, North America and USA
<
Determination
coefficient <
Before rebate
-
317 -198
- 80
After rebate
-
236 -159
- 81
The Asia group had both positive and negative performance and was therefore divided in two.
The number of samples in the positive group was only five and therefore we can not make any strong conclusions based on this test. The negative group did however show the same type of connection between fee adjusted performance and the net size in the individual accounts system at the 5 % level, both with or without the rebate. The explained variances were quite high (0.41 and 0.51).
6.6 Conclusion
The statistical tests show clearly that the Swedish individual accounts system manages to capture economies of scale in fund management and that larger funds seem to perform better than smaller funds when adjusted for fee in all groups we tested. The assets in the system seem not to be distributed in a irrational way with regard to fee adjusted performance both before and after the rebate. We therefore conclude that the system does not seem to be inefficient in reality and the claims that the large number of funds makes investors behave irrationally is exaggerated.
However, it is not possible to state that they acted rationally, since there may be economies of scale that may cause the fee adjusted performance to improve.
We can not draw any conclusions about the diversification and risk management issues that have been discussed earlier since that is outside the scope of the test. A study of the confidence intervals for the determination coefficient showed that the determination coefficient of the significant fund categories were well separated from value 0 thus indicating a strong connection between fee adjusted fund performance and size at the 5 % level. Once again we stress that the tests with and without rebate can not be compared directly since the IRf values where defined differently.
7 Summary
We started with a general discussion on how a large number of options, while generally being desirable can have negative effects on the individuals’ ability to make an effective choice. This was then related to the Swedish individual account system in particular and how the large number of funds may create passivity among the investors instead of leading to better choices.
Further we presented theory and research about how fund management is an industry with large economies of scale. The most cost effective way of capturing these in an individual accounts system is by taking a institutional approach were the government either select a number of funds, for example through an auction process or setup a market free to enter as long as the fund managers comply to certain rebate arrangements. In Sweden the later model has been chosen resulting in a large number of funds in the system.
To see if the funds choose by the individual investors really were cost effective we conducted a regression analysis on the fee adjusted performance in relation to the amounts of assets inside the system the funds acquired. The result showed that that there seem to be reasonably strong correlation between the amounts of assets a fund had attracted in the system and the performance. By this we can conclude that even if the large number of funds may confuse investors they as an entirety seems to be acting rational.
7.1 Ideas for future research
To further examine the effect of options to choose from versus effectiveness in individual accounts system we suggest a comparison with another country that has chosen the monopoly model of arranging institutional individual accounts systems. To make a successful comparison an indicator of cost effectiveness in relation to funds in the system has to be developed.
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