Multi-manager fund diversification: an empirical analysis
on the risks and rewards of this free lunch
Bow Mud
MSc Thesis Finance
University of Groningen
†Supervisor: J.V. Tinang Nzesseu, Ph.D
July 3, 2020
Abstract
Managing multiple managers or multiple funds is a central issue facing pension funds. Using Monte Carlo simulation with real underlying fund returns for eight asset classes, both equities and fixed income, this paper investigates the decrease in time-series volatility of the returns in excess of a specified index. The results show that the benefits of diversification dissolve after a certain number of managers because of the incremental fees and costs. Additionally, this paper finds that multi-manager funds are susceptible to a multiplication of generic factor concentration of the underlying funds, which leads to additional tail-risk and raises the consideration of passive factor investing.
Student number: S3011984, E-mail: b.d.mud@student.rug.nl
† Faculty of Economics and Business Word count: 8,938
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1. Introduction
Pension assets have been growing over the last decade, reaching USD 44 trillion worldwide at the end of 2018. The pension fund assets to GDP (%) in the Netherlands was 197% in 20171. This long-term trend is attributable to positive real net returns over the long term, and to an increase in contributions paid as more people are being covered by a pension plan. Most of these pension funds use a fiduciary management solution or delegated investment consulting which is a solution that enables pension scheme trustees to execute their long-term strategies efficiently and target better outcomes through a more effective governance structure.
One of the fiduciary managers in the Netherlands is TKP Investments which is a subsidiary of Aegon Asset Management. Fiduciary managers offer a range of investment funds in which they can use a single- or multi-manager investment strategy. Multi-management means that the fiduciary manager will build a diversified fund of a single asset class by investing in multiple underlying external funds within the same asset class, a fund-of-funds strategy. There are passively managed funds, which try to replicate the returns of a certain index, and actively managed funds, which take active positions outside of a certain index to pursue returns in excess of the index. The idea behind multi-management is that you will gain diversification benefits from investing in multiple active management funds. The question that lies before multi-managers is when a fund is diversified enough, and when will the addition of external fund managers start to dissolve excess returns? These external fund managers often have a tiered fee scheme where the fees will decrease when you place additional assets at their investment fund, this causes a certain trade-off between diversification benefits and increased overall fees.
The positive attributes of diversification are an accepted principle of modern portfolio theory and are often thought of as the only “free lunch” in Finance. Diversification is a duty of fiduciary managers which reduces risk because of the imperfect correlation of asset price movements. There is a growing amount of literature on the subject of fund of funds diversification and an important topic in the literature is the multiplication of fees that are charged to the investors of these funds. Managing multiple managers or multiple funds is a central issue facing pension funds, endowments, foundations, funds of funds, managers of multi-strategy funds and consultants. In fact, it is a central issue for all investors trading off expected return against risk. And there is a standard approach for addressing this issue. If we understand the expected return to each manager or fund, as well as their variances and covariances, we can build an optimal combination of managers or funds just as we build optimal combinations of individual securities. One problem that arises with multi-management portfolios is generic risk concentration. Multi-management portfolios concentrate generic ideas and diversify away orthogonal ideas. Many investors have not sufficiently appreciated this problem (Garvey, Kahn and Savi, 2017).
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2. Literature review and hypothesis development
William Sharpe (1991) poses the problem of overdiversification in the following manner: “If ‘active’ and ‘passive’ management styles are defined in sensible ways, it must be the case that
1. Before costs, the return on the average actively managed dollar is equal to the return on the average passively managed dollar, and
2. After costs, the return on the average actively managed dollar is less than the return on the average passively managed dollar”.
Sharpe (1991) was able to make this assertion by explaining that the market return is simply a weighted average sum of the returns from both the active and the passive segments of the market. Because the passive return equals the market return, the active return must also equal the market return
before fees, which implies that the aggregate
weighted holdings of all active managers, including individual investors, must equal the market. Since Sharpe posed his problem of active management there has been done a lot of research on the subject. Before we dive
into the research that has been done, we should develop an understanding of the definitions used in these studies and in the topic of active investment management. Actively managed funds try to add value by pursuing returns in excess of the returns of a certain specified index. The excess returns come with additional active risk which is the standard deviation of excess returns (hereafter tracking error). An active management fund can hold securities of which the weights differ substantially from the index, the absolute difference between the weights of the active manager and the index is called the active share. The different types of active management can be seen in figure 1. In addition to the performance spectrum of active management, investors have become more concerned about Environmental, Social and Governance related issues (ESG). Excluding certain companies that otherwise would have been included in an index is a form of active management, therefore active management has become even more relevant in today’s society.
Several studies on US equity mutual funds find that active fund managers who take big bets by holding concentrated portfolios perform better than fund managers who hold more diversified portfolios. Huij and Derwall (2010) found that concentrated funds with higher level of tracking error display better performance than their more broadly diversified counterparts.
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Cremers and Pareek (2014) find that high active share portfolios whose holdings differ substantially from their benchmark with patient investment strategies on average outperform with 2% per year. Tracking error is the traditional way to measure active management. It represents the volatility of the excess portfolio return.
To be able to measure the mean-variance properties of their active portfolio, investors could use a single number. Goodwin (1998) defines the information ratio, it builds on the Markowitz mean-variance paradigm, which states that the mean and variance of returns are sufficient statistics to characterize a portfolio. Calculation of the information ratio is based on standard statistical formulas for the mean and standard deviation and is closely related to the Sharpe ratio. The original Sharpe ratio is the special case of the information ratio when the risk-free asset is a shorted security. The information ratio is intended to serve as a measure of the special information that an active portfolio reveals through its return. The Sharpe ratio, however, will generally be positive even if the returns to a passive index are used. What special information is contained in an index? Logically, the information ratio of any passive benchmark is zero. Some analysts prefer to construct an information ratio from estimating least squares regression and dividing the alpha by the standard error, however, Goodwin argues that this rewards managers who take on less risk than the benchmark with higher information ratios. In addition, Goodwin argues that estimated β suffers from a well-established temporal instability and moving to a multifactor model to enhance stability only raises questions of how many and what factors are appropriate. In contrast to constructing an information ratio from estimating β by least squares regression, the simple information ratio presented in equation 1 can be thought of as an ex post, model free measure that is universally applicable and relatively stable over time. The key assumption is that the benchmark roughly matches the systemic risk of the manager, so fixing β at 1 is sensible. The information ratio is simply the ratio of the fund return in excess of the index 𝐸𝑅 and its time-series volatility (tracking error).
𝐼𝑅 = 𝐸𝑅 𝜎̂𝐸𝑅
(1)
Where 𝜎̂𝐸𝑅 is the standard error of the monthly excess returns (tracking error). The information
4 𝐴𝐸𝑅 ̅̅̅̅̅̅ = [∏ (1 + 𝑅𝑓𝑡 1 + 𝑅𝑏𝑡 ) 𝑇 𝑡=1 ] 12/𝑇 − 1 (2)
Where 𝑅𝑓𝑡 is the return of the active external fund at time t and 𝑅𝑏𝑡 is the return of the benchmark of the external fund at time t. T is the amount of months of which the performance is measured. Additionally, measuring the excess return geometrically has the desirable property that we obtain time-series data on excess returns. The benchmark of the portfolio is the weighted average combination of benchmarks of the underlying funds, so in the case of multi-management within a single asset class the funds would have the same benchmark which is the index in which the funds have an investment mandate to invest in and are presented for each asset class in table 1.
2.1 Portfolio time-series risk reduction
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reduction in the time-series of absolute returns. The theoretical reduction in time-series volatility of excess returns is similar to portfolios of securities. The time-series volatility of excess returns (tracking error) is
𝜎𝑃 = √∑ ∑ 𝜔𝑖𝜔𝑗𝜎𝑖𝑗 𝑁 𝑗=1 𝑁 𝑖=1 (3)
Where 𝜎𝑖𝑗 is the covariance between the excess returns of the ith and jth external fund in the portfolio. The tracking error of a multi-management portfolio decreases to an asymptote with the addition of n-managers as a function of the correlation between the excess returns of the managers and is therefore dependant on the opportunity set managers have in a certain asset class. The formal hypothesis is as follows:
H1: The tracking error of a multi-management portfolio decreases to an asymptote at
n-managers.
2.2 multiplication of fees in fund of fund structures
Many institutional investors, charged with outperforming a policy benchmark, hire dozens of active managers in order to diversify the particular risk associated with individual fund manager performance. They try to minimize the aggregated portfolio time-series risk but try to select external fund managers with high isolated active risk because of the performance that is associated with this high isolated risk. This logic is in line with basic portfolio theory: expected returns are linear, meaning that hiring additional managers with the same expected excess return keeps the overall expected excess return constant. At the same time, the overall level of active risk declines, boosting the top-level expected information ratio. The desire to find external fund managers with high isolated active risk, and to diversify among those managers could become problematic when taken to the extreme. McKay, Shapiro and Thomas (2018) found that many of the largest pension funds operate inefficiently, hiring too many active managers, and that diversifying capital among numerous active managers, even if those managers all have high active risk in isolation, can lead to an expensive index fund. In this case, diversification can be quite an expensive lunch.
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does not compensate investors for these fees because the individual hedge funds dominate fund of funds on a Sharpe ratio basis. They include hypothetical incentive fees in their analysis that are related to investment performance, which fund of funds pass on to their investors in the form of after-fee returns. In this case the individual performance of one external manager in the portfolio might induce an incentive fee, consequently reducing the aggregate portfolio return to an index level, or below that. Jennings and Payne (2016) expand the literature by examining the effect of incremental fees on diversifying asset classes. They consider asset classes fees as a proportion of the excess return relative to their diversification benefit and find that in some cases, the extra fees of certain asset classes overwhelm the diversification benefits. A fund may have an attractive alpha relative to its tracking error, but after the consideration of incremental fees, it would make investors think twice about the proposed investment. Moreover, they argue that the benefits of a fund of funds delegation, manager diversification, due diligence, and access may come at such a cost as to offset the benefits of the underlying funds. Jennings and Payne (2016) conclude their paper by quoting Ellis (2012) and Malkiel (2013) “investors should consider fees charged…not as a percentage of total returns, but as a percentage of the risk-adjusted incremental returns above the market.” Since investors are not able to invest directly in a certain index, the alternative to investing in an active manager would be investing in a passive manager that tracks a certain index. As passive investing is not cost-free, the performance of actively managed funds should be directly compared to passively managed funds (Ammann and Steiner, 2009). To fully capture the efficiency of active external fund managers in comparison to the passive funds, we should also account for the replication costs passive funds incur, like implementation costs. The realized alpha of an active fund would then be the differential between the excess return of an active and passive fund minus the differential in fees to be paid. We could use the average annualized geometrical underperformance of passive funds to the benchmark per asset class as a proxy for the replication costs of passive funds 𝑅𝐶𝑝. The focus of this paper is around the diversification benefits of fund of funds with an active investment strategy as an alternative to indexing after the consideration of fees and costs.
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to tail risk because they embrace common factors that tend to spike during volatile market events. The formal hypothesis is as follows:
H2: There is an optimal number of underlying funds in an active multi-manager portfolio that
manages to add value after costs on a risk adjusted basis.
2.3 Portfolios of generic ideas
Garvey, Kahn and Savi (2017) extend the theory of multi-manager diversification benefits with the problem of generic risk concentration in multi-strategy funds. They find that multi-manager portfolios act to concentrate risk into generic ideas that are a significant source of high risk and poor performance. they present this problem by considering a simple model where they assume that every underlying fund relies on a combination of orthogonal and generic insights, and so every underlying fund’s risk budget is invested partly in orthogonal insights and partly in generic insights, what fraction of the multi-management fund’s risk budget is invested in generic ideas? They assume that the active return of funds consists of generic insights and orthogonal insights and, in their simple model they assume that generic insights are 100% correlated between funds, and orthogonal insights are completely uncorrelated across funds2. They argue that multi-strategy funds that invest in several funds concentrate generic
risk and diversify away orthogonal ideas. Generic equity ideas are well-known and used, typically applicable across regions, and sometimes highly correlated across managers. Generic ideas include value, momentum, size, and the low-beta anomaly. Orthogonal ideas are not widely known or used, not always usable in every region because of data availability, unique to individual managers, and uncorrelated across managers, they show empirically that the multi-strategy funds double the exposure to risk factors of the underlying funds. During the financial crisis, generic factor correlations spiked, as did generic factor risk, this was the source of the significant rise in multi-strategy risk, which they argue to be a plausible mechanism underlying tail risk for such funds. Garvey, Kahn and Savi (2017) focus on the generic risk concentration of multi-strategy funds with combined regions. This paper will show the relation of generic risk concentration in multi-management funds that combine funds within a single asset class, indicating if these multi-manager funds give rise to additional tail risk. The formal hypothesis is as follows:
H3: The active multi-manager fund concentrates risk into generic factor ideas.
3. Research method and data
The goal of this research is to find the number of external active fund managers that optimizes the mean-variance properties of a multi-management portfolio, when tiered fee schemes are taken into consideration. We will investigate whether the relation between the number of
2 Garvey, Kahn and Savi (2017) acknowledge that 100% correlation is extreme and also provide an
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external fund managers and the mean-variance properties are different among asset classes. Additionally, this paper will show the relation of generic risk concentration in multi-management funds. We will show how correlations between external fund managers have changed over the years, which would have an effect on the diversification benefits.
3.1 Data
To analyse the issue of overdiversification I use monthly performance data from the GIMD database which is a database containing more than 6,000 global Investment Managers and 32,000+ Investment Strategies. Monthly gross return data was obtained from the GIMD database, it includes both surviving and non-surviving funds, and has data on in which region and universe fund managers invest in. The database also contains fee scheme data on most individual fund managers and market averages which we will use for the calculation of the fee premiums that active managers charge in excess of passive fund managers. For the calculation of the fee premium we subtract the median fee of a passive fund for a given asset class from the fee of an active manager of that same asset class given the weight of the fund in the portfolio. The fees that are charged to the multi-management portfolio are segregated fees.
The scope of asset classes considered in this research are displayed in table 1. In this paper we construct multi-management portfolios that consist of multiple external active fund managers that invest in a single asset class. An emerging markets equity portfolio will consist only of active fund managers that invest in global emerging markets – equity and will have MSCI Emerging Markets as a benchmark. For equity funds it is common practice to use the MSCI indices as a benchmark, except for US equities where it is common practice to use Russell indices. The US equity funds have structural tilts towards growth and value, we screened the funds for these biases and evaluated them against the appropriate benchmarks. For emerging markets debt, we used the JP Morgan index which is a common index to use for the assessment of funds in that asset class. For the remaining fixed income funds, I used the Bank of America (BofA) indices as a benchmark. The funds that are included in this research are the funds whose self-reported benchmarks match the indices in table 1 (Petajisto, 2013; Mackay, Shapiro, and Thomas 2018).
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I collected monthly gross performance data from the GIMD database to calculate monthly excess returns, annualized excess returns and annualized tracking errors for all the funds in the asset classes that are in included the scope of this research. The monthly data on indices against which the returns where measured were obtained from DataStream. We look at the period January 2015 – January 20203 and calculated the annualized excess returns following equation
(2). Table 2 reports the descriptive statistics of our dataset with excess returns. All the returns were measured in USD.
3.2 Simulation analysis
The simulation analysis assumes that one specific fund objective meets an individual investor’s investment needs. In reality, many investors allocate their assets across equities, fixed income and alternative asset classes following a utility function of some form. The choice of a certain mix would be an arbitrary one for this simulation. The purpose of this analysis is to determine whether among funds within the same asset class, enough variability in performance is present to warrant holding several funds. I use Monte Carlo simulation to randomly draw samples of external fund managers. After finding combinations I construct equally weighted portfolios of excess returns, this process is similar to O’Neal (1997), Garvey, Kahn and Savi (2017), Brands and Gallagher (2005), and McKay, Shapiro, and Thomas (2018). For every asset class and every fixed n number of external fund managers, I simulate 1,000 portfolio time-series of excess returns for randomly selected equally weighted multi-management portfolios following a geometrical process (equation 2). By randomly selecting and equally weighing the funds I control for selection bias. The process of finding combinations and determining weights will be repeated 1,000 times for all portfolios with 2-15 underlying funds. To be able to make the best assessment of the current optimal number of external fund managers in a portfolio I will
3I look at a recent 5 year period because consultation with practitioners indicates that the funds in the
dataset could have shifted their strategy from passive to active management, and would be classified as an active management strategy at the time of the analysis while it followed a passive strategy in a prior period. I include an analysis in a different time period in the appendix.
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construct portfolios in the period January 2015 – January 2020. The funds that are included in the stratified sample are funds with a full return history4 in this period. Table 3 reports the first and third quartiles of the correlation matrix of excess returns in each asset class and the dispersion of excess returns.
The fixed income managers in our sample haver higher correlations of excess returns on average than the equity managers, they have less opportunities to outperform their index and are overweighed in risk. The fund managers in the US market are having difficulties beating their benchmark because the market is more efficient. The funds in the Global equity and US asset classes are less correlated than the funds in the European and emerging markets because their opportunity set is larger, they have more alternatives to invest in.
3.3 Time-series risk reduction
After the Monte Carlo simulation, the portfolios will be examined for the hypothesized relationship of decreasing portfolio tracking error to an asymptote as diversification increases. To derive some estimate of the manner in which the active risk variation will be reduced as the number of external fund managers in the portfolio increased, I follow a testing process in the spirit of Evans (1968). I perform t-tests on successive mean portfolio tracking errors, which indicate on average the significance of successive increases in external fund managers, and F-tests on successive standard deviations about the mean portfolio standard deviation, which tend to indicate convergence of the individual observations on the mean value5.
4 We take a stratified subsample where we exclude funds with only a few monthly returns, this exclusion
is reasonable because these funds would not have been included in an institutional investor’s portfolio after a sound due diligence process. This sample also includes the non-surviving funds that stopped reporting their performance figures after January 2020.
5 The necessary assumption of normality of the distribution of the actual observations around the mean was sufficiently met.
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3.4 multiplication of fees in fund of funds structures
Since the focus of this research is to find the efficiency of investing in multiple active managers instead of tracking the index, we should also account for the fees that active managers charge in excess of the fees that passive managers charge. When we account for active management fee premiums, we obtain the excess portfolio return for a multi-management fund
𝑅𝑚𝑚 = 𝑅𝑢− ∑ 𝜗𝑖
𝑁
𝑖=1 (4)
Where 𝜗𝑖 is the median fee premium of an active manager to the median fee of passively
managed funds in the same asset class as the manager6, 𝑅𝑢 is the annualized excess return of the underlying funds after costs, and 𝑅𝑚𝑚 is the annualized excess return of the multi-management fund after paying active fee premiums to the underlying funds. For individual external active managers, it is preferable that they have a higher tracking error in isolation, because it is associated with higher performance. But on an aggregate portfolio level, it is preferable to reduce the amount of risk, keeping the excess return constant, increasing the overall portfolio information ratio. The information ratio tells us that it would be attractive to keep adding uncorrelated external fund managers, but there is another factor in the equation and that is tiered fee schemes, Jennings and Payne (2016) account for these tiered fee schemes by considering different types of investors with different amounts of assets under management (AuM). From a fee perspective, it is beneficial to place at least a certain amount of assets at one external fund manager to minimize the portfolio costs because an external fund manager will charge lower fees if an investor places more assets with them. Tiered fee schemes change the function of excess returns with the addition of n-managers from a linear to a non-linear one. When an investor places his assets at too many external managers, he will have too few assets at the individual managers placing him in the highest tier, effectively deteriorating the annualized excess portfolio returns and lowering the annualized portfolio information ratio of the multi-management fund.
12 𝑅𝑚𝑚 = 𝑅𝑢 − ∑ 𝜔𝑖𝜗𝑖 𝑁 𝑖=1 𝜗𝑖 = { 𝜗𝑖1 𝑖𝑓 50𝑚 ≤ 𝜔𝑖 < 100𝑚 𝜗𝑖2 𝑖𝑓 100𝑚 ≤ 𝜔𝑖 < 250𝑚 𝜗𝑖3 𝑖𝑓 250𝑚 ≤ 𝜔𝑖 < 500𝑚 𝜗𝑖4 𝑖𝑓 500𝑚 ≤ 𝜔𝑖 𝑤𝑖𝑡ℎ 𝜗𝑖1 > 𝜗𝑖2 > 𝜗𝑖3 > 𝜗𝑖4 (5)
𝜔𝑖 is the weight of the ith external fund manager in the multi-management portfolio which is fixed by the investor and restricted by the underlying funds to a minimum investment of $50 million to be able to build an efficient portfolio. Ammann and Steiner (2009) argue that to fully capture the efficiency of active external fund managers in comparison to the passive funds, we should also account for the replication costs passive funds incur in following the index, like implementation costs. The realized excess return of an active multi-management fund would then be the differential between the excess return of an active and passive fund minus the differential in fees to be paid. We could use the average of geometrical annualized underperformances of passive funds to the benchmark per asset class as a proxy for the replication costs of passive funds 𝑅𝐶𝑝. Additionally, we should subtract the due diligence costs 𝐷𝐷 incurred by multi-management funds by implementing additional underlying funds7.
𝑅𝑚𝑚= 𝑅𝑢− 𝑅𝐶𝑝− 𝐷𝐷 − ∑ 𝜔𝑖𝜗𝑖
𝑁
𝑖=1
(6)
The fees will increase with the addition of other external managers, according to the quoted tiered fee schemes of that managers. The passive fee median of that asset class will be subtracted from the active fee median to arrive at the active management fee premium 𝜗𝑖. Table
4 reports the active fee premiums of each asset class and the replication costs that passive funds have in following the benchmark 𝑅𝐶𝑝.
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To measure what the risk-adjusted added value 𝑅𝐴𝑉 is of an active multi-management fund we divide the realized multi-management excess return by the tracking error of the portfolio.
𝑅𝐴𝑉 =𝑅𝑚𝑚
𝜎𝑝 (7)
For each asset class we construct 1,000 portfolios of four different sizes with the following amount of Assets under Management (AuM) 500 million, 1 billion, 2 billion and 3 billion. For each size and asset class we sample portfolios with 2-15 managers8, this means that our simulated samples consist of 408,000 diversified multi-management portfolios in total. After sampling the portfolios, we calculate the risk-adjusted added value of each portfolio following equation 7 which will indicate the added value of multi-management portfolios on average.
3.5 Portfolios of generic ideas
To determine if the multi-management portfolios are susceptible to generic idea concentration, I follow the methodology of Garvey, Kahn and Savi (2017), they use a factor investing approach to determine the proportion of generic idea concentration. Factor investing is quite established in equities, but there is much less academic consensus and a much shorter track record when it comes to fixed income asset classes. Therefore, I will focus the empirical research on the equity asset classes but I will include the fixed income classes in the simple model they propose. After the Monte Carlo simulation of the multi-management portfolios, I will focus on the four generic insights contained in the Fama-French (1992) and Carhartt (1997) models: market beta, size, value, and momentum. By regressing the active returns of the underlying funds of our simulated portfolios against the Fama-French-Carhart factors (specific for each asset class) one at a time, the R2 statistic provides the fraction of the active variance attributable to each isolated factor. I then assign a sign to this result based on the sign of the
8 For the funds of 0,5 billion assets under management we sample up to 10 managers since the minimum investment is restricted to 50 million.
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regression coefficient. For example, a growth fund may have a negative exposure to value. To see the impact of the management fund structure, I compare the fraction of multi-management fund-risk in a factor to the average fraction of underlying funds. The comparison will be made by a linear regression of the active variance of the fund-of-funds attributable to the risk factor (R2 fund-of-funds), and the average active variance of the underlying funds
attributable to that risk factor (R2 underlying funds). This analysis will be performed on 1,000
multi-management portfolios of 5 and 10 managers on 4 equity asset classes: US large caps, World Equity, Emerging markets equity and European equity. Additionally, I will run a regression on all four factors to determine what the total portion of generic risk concentration in the portfolio is (adjusted R2 fund-of-funds).
4.
Results
This section discusses the results of the study. Section 4.1 covers the time-series risk reduction of excess returns in a multi-management portfolio answering hypothesis 1. Subsequently, section 4.2 covers the main focus of this paper, presenting the results of the risk-adjusted added value that multi-manager funds produce at a given number of underlying funds. Section 4.3 presents how the addition of successive underlying funds in a multi-manager portfolio gives rise to a multiplication of generic factor concentration inducing additional tail risk.
4.1 Time-series risk reduction
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4.2 Risk-adjusted added value after the multiplication of incremental fees.
To analyse the efficiency of investing in multiple active managers instead of tracking an index I calculated the added value of investing in multiple active managers following equation 6. To measure the diversification benefits of these portfolios on a risk-adjusted basis I divided this return by the tracking error of the portfolio. Table 6 reports the results of the analysis of risk-adjusted added value after the multiplication of incremental fees and costs. The results show that the diversification benefits first increase due to the significant decrease in portfolio tracking error, as discussed in section 4.1, but at a certain point start to dissolve by the incremental fees and costs incurred by the multi-manager fund, at a certain point, the marginal decrease of the tracking error will not compensate the additional costs and fees. We observe scale-advantages which arise from the tiered fee schemes of the underlying funds, a fund with more AUM will have the ability to place enough assets at one underlying fund to achieve a lower fee. When we look at the average values of the risk-adjusted added value, we observe an inverted U-shape curve with an optimum which supports hypothesis 2, for an emerging markets equity fund with 2 billion AUM the most diversification benefits on average would be achieved with 5 underlying funds. When we look at the 95th percentiles of the sampled portfolios we observe a decreasing function with the successive addition of underlying funds, this would mean that a portfolio manager with superior selection skills would only suffer from adding additional funds to the portfolio. In the US asset classes it is difficult to obtain returns in excess of the index on average, because the market is more efficient, in those asset classes it would be a more economical choice to invest in a passive fund that tracks the index. The active emerging markets funds have the ability to outperform the market on average, however, this excess return is almost completely dissolved by the fees they charge. The risk-adjusted added value ratios in some of the fixed income asset classes are higher than the equity classes, this is mainly because of the lower tracking errors in the fixed income classes and the lower fees.
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4.3 Portfolios of generic ideas
Table 7 reports the results of the regression on the active variance attributable to each factor of the underlying funds, and the active variance attributable to each factor of the multi-management fund. For Emerging Markets Equity, we observe that in a portfolio of 5 managers the active variance attributable to the value factor is 1.46 times as high as it is for the underlying funds which supports hypothesis 3. The median of the isolated value factor concentrations is negative for emerging markets equity, which indicates that the portfolios are mostly invested in growth stocks. Overall, we observe that the multi-manager portfolios in all the asset classes double the concentration in generic factors as opposed to the underlying factor concentration, which is consistent with Garvey, Kahn and Savi (2017). Increasing the number of underlying funds in the portfolio only further increases this multiplication of generic factor concentration, giving rise to more tail risk. I repeated the analysis on all the factors of the four-factor model via multiple regression to determine the total variance attributable to the all factors (adjusted R2) for 1,000 5-fund portfolios. The results of the total factor concentration are roughly consistent with the simple model proposed by Garvey, Kahn and Savi (2017). The regression output for each isolated factor concentration is included in appendix A.
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Additionally, due to a lack of academic consensus on fixed income factor models this paper includes Table 8 which reports the results of generic factor concentration in the simple model of Garvey, Kahn and Savi (2017). In the simple model we assume that generic insights are 100% correlated across funds and orthogonal insights are 0% correlated. The results of this simple model are roughly consistent with the empirical Fama-French-Carhart four-factor model. The median of total factor concentration in a 5-fund portfolio for European equities is 60.75% in the empirical model and the median proportion of generic idea concentration in the simple model is 0.61 (or 61%). We observe an increase in generic idea concentration as the number of underlying funds in a portfolio increases. The excess returns of active fixed income managers are more correlated than for the active equity funds because of the limited opportunity set fixed income managers have, this leads to an increase in the proportion of generic idea concentration which can be a source of tail risk. When we look at the correlation of excess returns through time (appendix B) we observe that the correlations for equity funds did not change that much, but the correlations of fixed income managers spiked during the financial crisis, indicating that the fixed income managers are even more susceptible to tail risk in periods of volatile market movements.
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5. Conclusion
This paper provides empirical evidence about the diversification properties of active multi manager portfolios that diversify within a single asset class. The paper focuses on excess return time-series risk reduction and finds that the tracking error significantly decreases by adding additional funds to a portfolio. These results are consistent with the literature on stock diversification in equity portfolios. For multi-manager equity funds the tracking error decreases with greater magnitude and significance up and until a higher addition of successive underlying funds than for the fixed income funds. The magnitude of time-series risk reduction is higher for the active equity funds than it is for the active fixed income funds. The results of the analysis support our hypothesis. On average the tracking error of multi-manager funds decrease to an asymptote with 10 underlying funds, while the fixed income portfolios reach this asymptote around five underlying managers.
This paper presents an analysis of the added value of a multi-manager fund investing in multiple underlying active funds instead of tracking an index by investing in a passively managed fund. There is an optimal number of underlying funds which is obtained by measuring the decreasing tracking error against the excess return after increasing costs and fees incurred by the successive addition of underlying funds. This paper shows that there is a mean-variance optimum on average of the number of underlying funds which differs among asset classes and is dependant on: the efficiency of the market (the ability of active managers to obtain excess returns), the correlation of excess returns within an asset class (the opportunity set of the active managers), the costs that the active funds charge within a certain asset class and, the size of the multi-management fund (scale advantages). At a certain point, the marginal decrease of the tracking error will not compensate for the additional fees and costs incurred by hiring an additional fund manager. Our analysis shows that multi-manager funds are able to add value in certain asset classes, even after a large portion of the excess returns are dissolved by incremental fees and costs of the underlying funds. In some asset classes active managers are able to obtain excess returns, but these excess returns are completely dissolved by the incremental fees that are charged to small investors which is consistent with the results of Jennings and Payne (2016). Investors in efficient asset classes like US equity large caps would be better off on average by investing in a single passively managed fund.
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results from the analysis should be the justification of investing in multiple active managers while there are passive managers available that specify in factor investing at lower fees than a combination of active managers. The risk-adjusted added value of a European equity portfolio with 5 underlying funds is one of the highest in our samples, but when we consider the total variation that is explained by generic factors (60,75%) investors might think twice about following an active management strategy. Therefore, portfolio managers of multi-manager funds should also account for generic factor risk concentration when considering adding additional funds to their portfolio. The findings of this study are primarily of interest to pension funds, endowments, foundations, funds of funds, managers of multi-manager funds and consultants.
A limitation of this paper is that the results are based on randomly simulated hypothetical combinations of underlying funds. The data on the underlying funds was obtained from Mercer and is based on realized returns, there was no data available on multi-manager strategies. However, this approach of simulating fund-of-funds combinations has been performed in prior academic research (O’Neal, 1997; Brands and Gallagher, 2005; Garvey, Kahn and Savi, 2017; and McKay, Shapiro, and Thomas 2018). An additional limitation to this paper is that due to data availability the fees are based on survey data that the funds filled in themselves, the analysis might be more representative when we included negotiated fees. Lastly, the results of the study are dependent on the time-period under research, although we could argue that by looking at excess returns, we control for systemic risk in volatile market periods. Additionally, a sizeable part of the analysis includes fees as a variable, including current fees in a prior period would not result in representative results.
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Appendix A factor regression output
Beta Size Value Momentum
Beta Size Value Momentum
Emerging Market Equity multi-manager multiplication of generic factor risk.
5 managers:
25
Beta Size Value Momentum
Beta Size Value Momentum
5 managers:
10 managers:
26
Beta Size Value Momentum
Beta Size Value Momentum
5 managers:
10 managers:
27
Beta Size Value Momentum
Beta Size Value Momentum
5 managers:
10 managers:
28
