Journal of Derivatives & Hedge Funds

, Volume 17, Issue 3, pp 253–265

Flow-induced redemption costs in funds of funds

Original Article

DOI: 10.1057/jdhf.2011.12

Cite this article as:
Stein, M. & Rachev, S. J Deriv Hedge Funds (2011) 17: 253. doi:10.1057/jdhf.2011.12

Abstract

We show that funds of fund managers are best advised to carefully track the possible costs from selling target funds with redemption fees when facing outflows. In this study, we show how different the costs to be incurred may be. While a static approach of estimating the costs to be incurred in the presence of a liquidity shock delivers insight on the span of possible costs at one point of time, a dynamic approach with path-dependent cost effects takes into account the possibility of successive periods of fund cash-flows and the resulting cost effects.

Keywords

liquidity risk liquidity costs redemption costs back-end load fees funds of funds 

INTRODUCTION

The recent crisis has clearly demonstrated that the direction and magnitude of capital flows are crucial to the survivorship and performance of financial market assets. While the years following the dotcom crisis were characterized by very low costs of capital, the global economy and the financial markets were flooded with excess liquidity. Until the sub-prime mortgage crisis unfolded and triggered the worst economic slump since the Great Depression, along with the worst year for global stock market performance, capital was available in huge lot sizes and at both low borrowing costs and low restrictions. As this period came to an end and money was withdrawn from investments with unprecedented speed and strength, the problems surrounding cash-flows and liquidity management came back into the discussions in the financial world and academia.

As many fund management companies try to find ways to protect themselves from new problems caused by capital flows, the appropriate handling of load fees, or redemption fees, is crucial for investors. Especially when investors in funds are themselves exposed to capital flows they cannot control, as are most funds of funds (FoFs in the following), the holding of funds that may not be redeemed without costs calls for appropriate tracking of the cost that may be incurred when funds must be sold. In this study, we show how this may be done in two differing ways. While a static view calculating the costs to be incurred in the presence of a liquidity shock delivers insight on the span of possible costs at one point of time, a dynamic approach with path-dependent cost effects takes into account the possibility of successive periods of fund cash-flows and the resulting cost effects.

FUND FLOWS, LIQUIDITY RISK AND LIQUIDITY COSTS IN FUNDS (OF FUNDS)

The topic of fund flows and liquidity risk has been researched in the past, with studies concerning mutual fund flows by Ippolito,1 Sirri and Tufano,2 Hendricks et al,3 Warther,4 Zheng5 and Greene et al6 being significant, among others. Nanda et al7 model the interaction of flows, performance and load structure for mutual funds. Although the primary focus of many theoretical and empirical studies has been on determining factors driving fund flows and how investors are affected by the loads and fees that are charged by the respective mutual funds, the management of flow-induced liquidity and flow-induced selling of target investments on the fund side has also been studied. While Edelen8 finds that flow-induced trades lower fund performances, Chan and Lakonishok9 and Keim and Madhavan10 focus on the fact that trading costs increase with the size of the trades that are necessary to meet unexpected redemptions.

However, the majority of studies focused on funds rather than on FoFs, the latter having a special problem. As many FoFs invest at least part of their capital in funds that may not be redeemed at net asset value, they face the danger of performance losses when outflows occur and they have to sell off costly funds. The practical relevance of these problems is very high, and the lessons learned from the recent crisis imply that this will be amplified in the future.

The problem in practice was that in the upswing of financial markets, the management of liquidity and the costs and risks that come along with it were ignored or at least were in minor positions in the priorities of asset managers. Caused by steady and growing capital flows, the markets grew and prospered, along with the ignorance of market players concerning the potential risks associated with leverage and consequences that would come should the funding sources run dry. The consequence was excessive leverage not only on the balance sheets of banks and households, but in asset management firms as well. Firms such as hedge funds and private equity funds that traditionally use large amounts of debt were heavily leveraged in the hunt for stellar returns and in a market that was pushed upward only with huge pressure on market participants not to fall behind their successful peers.

In what has become a downturn in financial markets called the sub-prime crisis and the following credit crunch, the globally increasing interest rates and the burst of the housing price bubble in the United States has ended the spree and money was withdrawn from all kinds of investments. Of course this severely affected the asset management industry as well. A large number of funds had to close business or at least turned out to be unable to fulfil the redemption wishes of their investors and had to lock these in. ‘If everybody panics, panic first’ was the phrase that best described the mood in the industry, with investors withdrawing huge amounts from investments that were or could in any way be affected by the crisis.

The large outflows that the asset management world was facing were redemptions of shares by both retail investors and institutional investors. While the massive withdrawals of money took place in every kind of financial asset class, we will focus on the problems of FoFs in the presence of share redemptions. While funds investing in stocks or bonds, for example, may have the problem that their underlyings are turning illiquid or a high spread is charged, FoFs have to sell target funds and may face the problem of redemption costs or back-end load fees. With many asset management companies now taking actions to prevent problems induced by share redemptions, one can expect to see increased use of redemption fees, causing fund investors to be conscious of the possible cost consequences of their investments.

Of course, the discussion of flows in mutual funds and the fee structure of the funds with front-end and back-end load fees is highly relevant when it comes to investment and divestment decisions, as well as concerning performance expectations. Among others, Ippolito,11 Elton et al12 Gruber,13 Zheng,5 and Alves and Mendes14 investigate the performance differences between load and no-load funds, with the latter reporting the back-end load fees being influential on investor (non-)reaction to poor performance. Therefore, an assessment of the possible costs that are incurred by an investment when being sold should be in line with the possible benefits of that particular investment when FoF managers select their target funds.

Generally, the focus has been on assessing the differences in funds with and without load fees, investigating the differing performances, and how the flow-induced trading filters through to the funds. However, there has been no detailed analysis of the inside of the funds, that is, of how the flows and the costs incurred may be seen as a risk factor to the fund liquidity. Nor has there been an analysis of how FoFs may deal with load fees when faced with flows on their own side. Although the current crisis has shown the immediate need of dealing with liquidity shocks, there appear to be few approaches that enable portfolio managers to track the risks appropriately when investing in shares that may not be redeemed at book value. We will show in the following sections how different the effects of redemption fees can be, with an example of time-dependent back-end load fees.

THE STATIC FRAMEWORK: LIQUIDITY SHOCK ANALYSIS

In this section, we show a slim approach that can be used by FoF managers to track the effects of their investments with respect to costs when needing liquidity due to outflows from their FoF. We suggest that FoF managers track their portfolio of investments according to time spans and fund volume spans as the baseline. This is straightforward, as some target funds held by FoFs can only be redeemed at a cost (for example, back-end load fees), after lock-up periods or a combination of both (time-dependent discounts when redeeming shares). Of course, the costs to be incurred when reducing positions in the respective funds have changing magnitudes with regard to the volume of the FoF when redeeming and to the size of the redemption.

While born out of practical considerations for FoFs facing redemption costs, the analysis of costs when facing capital outflows is crucial for other effects as well. For example, during times where target funds turn illiquid and suspend the redemption of shares, FoF managers may be forced into secondary markets, where funds are often traded at discounts to their net asset value (NAV), the discount being a result of the illiquidity and the expectation concerning the NAV at a future date when the fund shares may be redeemed at NAV. This holds true even for open-end funds, if these need to (temporarily) suspend the redemption of shares or introduce restrictions.

In this section, we consider a one-off redemption of shares for an FoF, and use an example to show how an FoF may be affected by costs that are caused by the forced selling to meet investors’ demand for capital. Consider the following example.

An FoF currently has US$500 million of assets under management. The FoF has invested in several target funds with back-end load fees. To keep the analysis tractable and transparent, we set all funds with a back-end load fee to charge 5, 3 and 1 per cent for shares held less than 1 year, 2 years and 3 years, respectively. This means that for any time point after the first investment in a back-end load fee fund, we are able to calculate which costs at this point of time would have to be incurred depending on the amount of the redemption and the time held. Of course, these costs have a direct impact on the FoF performance, with the magnitude depending on the size of the FoF at the time the shares are sold.

Table 1 shows the investments made by an FoF. The example FoF has invested a total of $100 million or 20 per cent of the fund volume, in funds that may charge a cost when positions are reduced, depending on the time of selling.
Table 1

Investment schedule of the FoF

Investment number

Amount (in US$)

Date

Time passed (in years)

Cost (in US$)

Cost (in % of fund volume)

 1

20 million

1 March 2007

3.0

0

0.00

 2

10 million

1 April 2007

2.9

100.000

0.02

 3

10 million

1 June 2007

2.8

100.000

0.02

 4

5 million

1 September 2007

2.5

50.000

0.01

 5

10 million

1 September 2007

2,.5

100.000

0.02

 6

5 million

1 November 2007

2.3

50.000

0.01

 7

5 million

1 January 2008

2.2

50.000

0.01

 8

20 million

1 January 2008

2.2

200.000

0.04

 9

10 million

1 July 2008

1.7

300.000

0.06

10

5 million

1 January 2009

1.2

150.000

0.03

Note: Date under consideration: 1 March 2010. Fund volume on date for relative cost in percentage: US$500 million.

As an example we have chosen 1 March 2010. At this point the first investment in the synthetic FoF already may be redeemed without charge of costs due to an expired minimum holding period. However, it is even more interesting to see how these positions influence the potential costs over time and over different fund volumes. As the fund volume in the future is far from certain, one is best advised to calculate possible effects form redemption costs up front.

From Figure 1, we can see the time- and fund volume-dependent costs that would have to be incurred when being faced with redemptions, thereby assuming that the redemptions are made on an allocation-neutral basis (for example, an outflow of capital of 10 per cent of the FoF volume would lead to a 10 per cent reduction in the positions in funds that charge redemption fees).
Figure 1

Costs of redemptions over time and fund volume spans. Assumption of redemption according to fund volume reduction (allocation neutral), that is if the FoF has outflows of 10 per cent, the respective share of 10 per cent of funds with redemption fees is sold. Costs calculated into new fund volume, after outflows.

It is obvious that the differing investment points determine the locations of the peaks in the possible costs from redeeming, and that performance effects of over 5 per cent are possible even though the maximum charged is 5 per cent. This is a result of the fact that a large outflow of capital that leads to a fund volume that is even smaller than the total share of capital allocated to funds with redemptions fees would leverage the costs on a relative basis. For example, a reduction of $450 million (90 per cent of the original fund volume) would lead to a fund volume of $50 million. The redemptions of costly funds would be $90 million (90 per cent of the invested $100 million) and one would have to pay costs that would be calculated into the new fund volume of $50 million in the next period. Admittedly, it is a very strong scenario that there will be a hit in the fund with outflows of 90 per cent of the fund volume, but this can be seen as a stress-test with a very high magnitude of possible flows.

In addition, FoFs normally have notifications of redemptions and can sell off target funds before the outflows are booked, that is, the costs are calculated into the fund volume at the time the outflows occur, rather than afterwards. One the one hand, this is done to be able to serve all liquidity demands by FoF investors; on the other hand, waiting to sell assets and then pay the costs on the new fund volume is both more performance damaging and punishes remaining investors. The significance of the influence of direct selling can be seen in Figure 2, where the dimension of resulting fund volume is irrelevant as costs have to be incurred by the fund volume of $500 million when the liquidity shock occurs, as here the effects are less severe than in Figure 1.
Figure 2

Costs of redemptions over time. Assumption of redemption according to fund volume reduction (allocation neutral), that is if the FoF has outflows of 10 per cent, the respective share of 10 per cent of funds with redemption fees is sold. Costs calculated into old fund volume, that is US$500 million.

Apart from the extreme events, the plane of costs over time and possible fund volumes (the line when selling directly) is informative with regard to the potential costs that have to be incurred when liquidity is needed owing to own outflows of capital. Note that even the moderate share of 20 per cent of assets invested in costly funds may lead to large costs (especially in the case of high outflows and when selling may be possible only after outflows have occurred, as can be seen in Figure 1). However, the assumption underlying this kind of static overview is that there is a single hit at the specified time point. A more realistic view is to see how the costs would affect the portfolio when there are several periods of outflows, that is the fund volume changes from time to time and the FoF management must liquidate positions in target funds in tranches. This brings us to a path-dependent view of the liquidity costs, where the process of forced redemptions is gradual, rather than a one-off event in the preceding baseline example.

THE DYNAMIC FRAMEWORK: PATH-DEPENDENT ANALYSIS

In this section, we take a look at the path-dependent costs, thereby modelling the fund volume with Monte Carlo simulations for possible flow patterns.

For problems related to the analysis of liquidity and cash-flows, the modelling of cash-flows is crucial. While from a general viewpoint the modelling of the expected cash-flows seems to be highly desirable, their very nature makes this a complicated process. Inflows and outflows into and from investments are caused by a large variety of factors. Not only do market (participant) expectations, general economic surroundings, historic performance and observable information heavily influence the cash-flow patterns, but with the institutionalization of the asset management industry, sales power, mutual agreements, contracting, communication and marketing, and executive decision making play a major role when it comes to the direction and magnitude of fund flows. This makes an extrapolation of historic cash-flows inappropriate for the vast majority of investments, even if there are data available. If a fund or FoF is erased from a recommendation list of a wealth management company, for example, or if a distribution arm is lost in the course of a restructuring process, any historic data become useless, as the driving fundamentals changed significantly.

The choice of distribution is crucial to the outcomes of the analysis, and any risk manager or portfolio manager applying the analysis needs to select the distribution type that best fits the nature of the flows and/or the needs and aims of the analysis. We model daily flows with a chi squared distribution, using 1 and 3 degrees of freedom for the random number generation, and to obtain both positive and negative flows, we multiply the number generated with the sign of a random number from a normal distribution. Flows are modelled on a daily basis, and a time span of 1000 trading days begins on 1 January 2009 when the last investment in shares charging costs was made. Of course, there are large differences between the paths the fund volume may take due to the random flow patterns. While the restrictions on holding period-based redemption fees are generally based on calendar days rather than trading days, we left out the weekend days following 5 trading days. Of course, the choice of the appropriate frequency is left to managers and should be made in accordance with the respective product structures. For redemptions, we use a first in-first out premise, an assumption that is not very strong, as we model the funds to be equal. In practice, one would simply adjust for first in-first out for each of the respective funds.

Our approach yields a considerably large span of possible outcomes, with the paths to the final outcomes differing significantly, as well as the final volume of the simulated FoF.

We employ two different strategies. One is a conservative strategy, where inflows do not lead to successive investments in the funds with redemption fees; this means that the management successively reduces the cost-prone investments when there are outflows, but does not buy shares when there are inflows.

The second strategy is an allocation-neutral strategy, such that if there is a decrease in capital, the respective share is divested, and if there is an increase, the additional capital is invested proportionally in ‘costly funds’; this means that the 20 per cent share is maintained throughout the analysis.

STRATEGY 1: THE CONSERVATIVE STRATEGY

The rationale behind the conservative strategy in the presence of flow-forced rebalancing may be, for example, an FoF whose management expects that there will be more outflows than inflows in the future, and therefore the positions in cost-prone investments are reduced.

In this section, we show the results that were obtained from the path-dependent analysis using the conservative approach, where inflows are not invested in funds that charge back-end load fees but where for each outflow the same proportion of ‘costly’ target funds is redeemed. As this means that over time the allocation into such funds decreases owing to a pessimistic outlook, we can expect that the relative performance effects from redemption costs that have to be incurred decrease for two reasons. First, the holdings are decreased successively, and second, increasing amounts of shares may be sold at no cost after minimum holding periods have expired.

We need to keep in mind that even when there is a fund volume of, for example, $2 billion an outflow of x per cent of the total volume leads to a reduction in the respective costly positions of x per cent as well, a very pessimistic approach. However, this is in line with several policies, guidelines and management rules that have been implemented throughout the industry, to face the redemption and liquidity risks, especially during the recent crisis. First, this is to ensure that all investors are treated equally, that is to prevent the problem of the losses being loaded on remaining investors only; and second, to prevent high relative costs from being incurred when selling off at reduced fund volumes later on.

Figure 3 shows the example for 5 of the 10 000 simulated paths. As expected, the different paths lead to very different costs that have to be incurred over time. The earlier outflows occur, the higher are the fees that have to be paid, and if large outflows occur at the end of the 1000-day analysis, the additional costs are only marginal or tend to zero.
Figure 3

Fund volume paths and resulting costs of redemptions over time (conservative strategy, 1 degree of freedom). Assumption of redemption according to outflows, with no new investments in inflow periods, that is if the FoF has outflows of 10 per cent, the respective share of 10 per cent of funds with redemption fees is sold; an inflow of 10 per cent does not lead to buying. Five examples from 10 000 simulations.

As we can see from Figure 7, in the top left graph, in the distribution of the total percentage costs, that is performance effects, while these are diverse regarding the magnitude, no path led to total costs of even 1 per cent with the parameters used. The performance effects are therefore considerably small for just over 2.5 years, meaning that less than approximately a third of one percentage point is lost per year.
Figure 7

Total percentage of costs of redemptions over time, distribution comparison. Histograms of total costs of 10 000 simulations. Conservative strategy on the left, allocation-neutral strategy at the right. Simulations with 1 degree of freedom on top, results using 3 degrees at the bottom.

How influential the pessimistic or conservative strategy is on the costs to be incurred can be seen in Figure 4 and in the bottom left graph of Figure 7. Although the magnitude of the flows is greatly enlarged, the strategy of selling proportionally but not re-investing when receiving inflows of capital limits the performance effects such that still over 90 per cent of the paths do not lead to total costs of one per cent or above for the 1000-day period. This has strong implications for the selection of investments in cost-prone target funds, as the 20 per cent share has an implied outperformance requirement of less than 1 per cent over approximately 2.5 years to justify its selection with respect to additional gains for additional (possible) costs.
Figure 4

Fund volume paths and resulting costs of redemptions over time (conservative strategy, 3 degrees of freedom). Assumption of redemption according to outflows, with no new investments in inflow periods, that is if the FoF has outflows of 10 per cent, the respective share of 10 per cent of funds with redemption fees is sold; an inflow of 10 per cent does not lead to buying. Five examples from 10 000 simulations.

STRATEGY 2: THE ALLOCATION-NEUTRAL STRATEGY

The rationale behind an allocation-neutral strategy in the presence of flow-forced rebalancing may be, for example, an FoF product structure that needs to be maintained, when product characteristics of target funds with and without redemption fees may be different.

In this section, we show the results that were obtained from the path-dependent analysis using the allocation-neutral approach, where inflows are invested in funds that charge back-end load fees, as for each outflow the same proportion of ‘costly’ target funds is redeemed. Therefore, a constant proportion of 20 per cent of costly funds is maintained, regardless of the fund volume. This means that over time, we can expect that the relative performance effects from redemption costs that have to be incurred over time will remain fairly stable, apart from some major steps owing to expiration of holding periods from the initially invested tranches of larger lot sizes and the first in-first out assumption.

Figure 5 shows the example for five of the 10 000 simulated paths. As in the conservative framework, the different paths lead to very different costs that have to be incurred over time. However, as expected, the timing of the flows is not as influential, because inflows are invested in cost-prone funds and therefore costs when facing outflows have to be incurred even in later stages of the analysis.
Figure 5

Fund volume paths and resulting costs of redemptions over time (allocation-neutral strategy, 1 degree of freedom). Assumption of redemption according to outflows and new investments in inflow periods, that is if the FoF has outflows of 10 per cent, the respective share of 10 per cent of funds with redemption fees is sold; an inflow of 10 per cent leads to buying. Five examples from 10 000 simulations.

Of course, the allocation-neutral strategy results in considerably higher total costs over the simulation span, with the majority of the total percentage effects being between 2.5 per cent and 4 per cent, as seen in the top right graph of Figure 7. This implies that any of the invested shares of back-end load fee funds should annually yield over 1 per cent more than other funds to justify the investment. Naturally, the magnitude of the costs to be paid is greater for the analysis using 3 degrees of freedom (Figure 6), with the majority of the simulation paths resulting in 9 per cent to 12 per cent performance losses, as can be seen on the bottom right of Figure 7, where the implied required outperformance of the restricted funds versus other funds is becoming vast.
Figure 6

Fund volume paths and resulting costs of redemptions over time (allocation-neutral strategy, 3 degrees of freedom). Assumption of redemption according to outflows and new investments in inflow periods, that is if the FoF has outflows of 10 per cent, the respective share of 10 per cent of funds with redemption fees is sold, an inflow of 10 per cent leads to buying. Five examples from 10 000 simulations.

CONCLUSIONS

FoF managers that invest in funds that may charge redemption fees need to appropriately track the costs that may be incurred when target funds need to be sold. This is necessary both for existing positions and for new investments to be made. Especially in times of strong outflows of capital, the effects from flow-induced redemptions of target funds may be severe for a fund portfolio. We therefore suggest that FoF managers adequately mirror their risks over time and over possible fund volumes.

Our analysis using the static approach yields insight into how an FoF is affected by a liquidity shock owing to a large outflow of capital and delivers direct information on how severe performance effects may be in the future. This information may be best processed as part of a risk analysis, as well as part of investment selection, with the possible cost-induced performance drain implying how large the outperformance of cost-prone investments versus other holdings should be for an investment to be justified.

The dynamic, path-dependent analysis of the influence of flows on the costs that have to be incurred by an FoF investing in funds with time-dependent redemption fees has shown that a very conservative strategy leads to considerable small performance effects, even in the presence of large changes in the fund volume. However, if a pessimistic approach is not demanded, for example owing to additional gains to be expected from the back-end load fee funds if they are differing in nature from the other funds, the costs heavily increase in an allocation-neutral approach. Therefore, both FoF managers and risk managers are best advised to closely model the possible performance effects of investments and holdings of cost-prone target funds over time.

Acknowledgements

The authors thank Stephan Brünner and Frank J. Fabozzi for helpful comments. They bear responsibility for any remaining errors. The views expressed herein are those of the authors and do not necessarily represent those of Credit Suisse.

Copyright information

© Palgrave Macmillan, a division of Macmillan Publishers Ltd 2011

Authors and Affiliations

  1. 1.Karlsruhe Institute of Technology (KIT), Kollegium am SchlossPostfachGermany