Is the price right? Swing pricing and investor redemptions

BIS Working Papers

No 664

 

Is the price right? Swing pricing and investor redemptions

by Ulf Lewrick and Jochen Schanz

 

Monetary and Economic Department

October 2017

 

JEL classification: G01, G23, G28, C72

Keywords: Financial stability, mutual funds, regulation, market liquidity

 

BIS Working Papers are written by members of the Monetary and Economic Department of the Bank for International Settlements, and from time to time by other economists, and are published by the Bank. The papers are on subjects of topical interest and are technical in character. The views expressed in them are those of their authors and not necessarily the views of the BIS.

This publication is available on the BIS website (www.bis.org).

 

© Bank for International Settlements 2017. All rights reserved. Brief excerpts may be reproduced or translated provided the source is stated.

ISSN 1020-0959 (print)

ISSN 1682-7678 (online)

 

Is the price right? Swing pricing and investor redemptions

Ulf Lewricka, Jochen Schanza

Bank for International Settlements, Centralbahnplatz 2, CH-4002 Basel, Switzerland

 

Abstract

How effective are available policy tools in managing liquidity risks in the mutual fund industry? We assess one such tool – swing pricing – which allows funds to adjust their settlement price in response to large net flows. Our empirical analysis exploits the fact that swing pricing is available to Luxembourg funds, but not yet to U.S. funds. We show that swing pricing dampens outflows in reaction to weak fund performance, but has a limited effect during stress episodes. Furthermore, swing pricing supports fund returns, while raising accounting volatility, and may lead to lower cash buffers.

 

Keywords: Financial stability, mutual funds, regulation, market liquidity

JEL: G01, G23, G28, C72


We thank Diego Urbina for expert research assistance and the members of the Association of the Luxembourg Fund Industry’s swing pricing working group for helpful discussions. For their helpful comments, we also thank Stijn Claessens, Ingo Fender, Leslie Kapin, Gianpaolo Parise, Ilhyock Shim and Nikola Tarashev as well as seminar participants at the Bank for International Settlements and the Bank of Japan. Disclaimer: The views expressed in this article are those of the authors and do not necessarily reflect those of the Bank for International Settlements.

  • Corresponding author. Email: ulf.lewrick@bis.org. Phone: +41 61 280 94 58.
  • Email: jochen.schanz@bis.org. Phone: +41 61 280 94 57.

 

1. Introduction

The asset management industry has been growing at an exceptional pace over the past few years, reflecting a persistent shift from bank-based towards more market-based intermediation. Open-end mutual funds have been contributing to this trend, with their total financial assets increasing by more than 5.6 trillion U.S. dollars (USD) over the past 10 years in the United States alone. As a result, fund managers’ trading activities have attracted increasing attention from other market participants as well as from supervisory authorities. Based on the experiences gained from the financial crisis of 2008/09 as well as other, shorter-lived episodes of market stress, a number of structural vulnerabilities associated with fund management activities have come to the fore (Financial Stability Board (2017)).

For open-end mutual funds, financial stability concerns focus on the risks related to the liquidity mismatch that is inherent in the funds’ business model: they invest in assets that may prove difficult to liquidate under stressed market conditions, while granting fund investors the right to redeem their shares on a daily basis based on the end-of-day net asset value (NAV) per share of the fund. These risks are particularly pronounced for funds investing in relatively illiquid assets, such as corporate bonds. Fund managers are equipped with a variety of tools to manage the risk of large-scale redemptions (IOSCO (2015)). Relatively little is known, however, about the effectiveness of these tools in containing risks. This paper intends to shed some light on this issue by studying the effect of swing pricing on fund flows and other performance measures under both normal and stressed market conditions. Swing pricing is an innovative liquidity management tool that will be introduced as one of the U.S. Securities and Exchange Commission’s measures to strengthen the resilience of U.S. open-end funds.

Swing pricing allows the fund manager to adjust (“swing”) the fund’s NAV per share to reflect the estimated costs associated with investor redemptions and subscriptions. These costs arise whenever the fund manager needs to sell or buy assets in order to meet redemption requests or invest cash inflows. During tranquil market conditions, the cost of liquidating assets tends to be low, at least for transactions of limited size (Borkovec et al. (2016)). Yet during episodes of market stress, liquidation costs can suddenly spike (Dick-Nielsen et al. (2012), Friewald et al. (2012)). It is often during these times that fund investors redeem their shares to meet their liquidity needs. Absent swing pricing or other redemption charges that are redistributed to the fund, the cost of liquidating assets to satisfy redemptions will only be borne by those investors that stay with the fund. Anticipating this dilution of the NAV, investors may have a first-mover advantage in withdrawing from the fund - creating the breeding ground for a run on the fund.

Swing pricing can mitigate the first-mover advantage by levying the dilution costs on with­drawing investors. At the same time, it may induce fund managers to take on more liquidity risk and could capture investors in low-performing funds. To identify these effects, we exploit the fact that swing pricing is available to funds registered in Luxembourg, whereas U.S. funds will not be permitted to swing prices until November 2018. These countries host two of the largest mutual fund industries worldwide.

Our comparative analysis, based on a large sample of open-end bond mutual funds, yields findings that are consistent with several predictions derived from our conceptual framework. Comparing Luxembourg and U.S. funds, we show that Luxembourg fund flows are less sensitive to negative returns during normal times. This is consistent with the predicted impact of swing pricing on investor incentives. That said, we find no evidence of a dampening effect on outflows during the 2013 U.S. “taper tantrum”. We argue that current swing pricing rules, which tend to be based on applying a constant swing factor once outflows exceed a certain threshold, are unlikely to offset investor first-mover advantages in stressed market environments.

We also provide evidence that Luxembourg funds benefited from higher returns during the taper tantrum. This tallies with the prediction that swing pricing helps to contain the dilution of the fund value. Furthermore, we show that Luxembourg funds experienced a higher volatility of daily price changes. We relate this finding to our prediction that swing pricing increases the accounting volatility of funds. Finally, we assess whether swing pricing reduces fund managers’ incentives to insure against liquidity risks. Controlling for a comprehensive set of fund characteristics, we find that Luxembourg funds hold less cash. While this is generally justified by the dampening effect of swing pricing on fund outflows during normal market conditions, reduced cash holdings could aggravate investor incentives to withdraw during stress episodes. This suggests that minimum liquidity requirements for funds could strengthen the effectiveness of swing pricing as a risk management tool.

Our paper is related to a young but growing strand of the literature that studies the financial stability concerns arising from mutual fund flow dynamics. Similar to one of our research questions, Malik and Lindner (2017) discuss the effect of swing pricing on fund outflows during times of stress. Based on analysing samples of three and six individual funds, they find evidence that investor first-mover advantages pertain to swinging funds during such periods. This result tallies with one of our hypotheses, and we find supporting empirical evidence based on assessment of a large sample of funds during the taper tantrum.

Our work also builds on Chen et al. (2010), who develop a model showing how costly redemptions dilute a fund’s NAV per share, creating an incentive for investors to run on the fund. In line with their model, they provide evidence that equity funds investing in less liquid assets experience greater outflows in response to poor performance. Goldstein et al. (forthcoming) show that this effect is even more pronounced for corporate bond funds, given the higher cost of liquidating the underlying assets. Furthermore, their results imply a concave shape of the flow-to-performance relation for corporate bond funds, which means that - in contrast to the case of equity funds - bond fund outflows are more sensitive to bad performance than inflows are to good performance. This points to the risk of self-reinforcing redemptions during periods of weak fund performance. Our findings confirm the concave flow-to-performance relation for U.S. bond funds, while suggesting that flows for Luxembourg funds are less susceptible to bad performance.

Another part of this literature focuses on how funds manage their cash holdings, which provide a first line of defence against large redemption requests. The work of Chernenko and Sunderam (2016) illustrates how U.S. equity and long-term corporate bond funds use their cash buffers to accommodate fund flows rather than transacting in the assets they are invested in. They argue that cash, including cash substitutes (e.g., short-term debt securities), is the primary liquidity management tool of these funds. Other tools, such as redemption fees or lines of credit, are found to be of minor importance. In line with this, the authors show that funds investing in less liquid assets hold more cash. This is consistent with the results of Wang (2015), who shows that large cash buffers reduce investor incentives to run on corporate bond funds. Zeng (2017), by comparison, points to the dilemma that fund managers may face in using their cash. Accommodating redemptions by running down the fund’s cash position today might force the fund to sell assets in future periods in order to replenish the cash buffer. Rational investors anticipate these future sales and the associated dilution of the fund’s NAV and hence choose to run today. Our paper adds to this work by analysing how the design of swing pricing can complement cash buffers in reducing the redemption risks.

Morris et al. (2017) broaden the perspective on this issue by developing a model in which the fund manager can choose between liquidating assets in expectation of future redemptions and selling them at a fire-sale discount in response to actual redemption requests. This implies that fund managers may decide to sells assets in advance of fund outflows (i.e., “hoard” cash) if the associated costs are sufficiently low relative to the fire-sale discount. Based on a sample of global bond funds, Morris et al. (2017) and Shek et al. (2015) find support for advance selling by fund managers, pointing to a potential amplifying effect on market downturns.

Understanding how fund managers respond to market shocks is key to assessing their poten­tial contribution to systemic risks. The study by Banegas et al. (2016) emphasises the impact of monetary policy shocks on fund flows. The authors show that an unexpected tightening of monetary policy induces persistent outflows from bond funds. Given the associated dilution effect on funds’ NAV, this aggravates the first-mover advantage that funds investing in illiquid assets are exposed to. Feroli et al. (2014) illustrate how a growing fund industry may intensify the risk of concerted selling by fund managers in response to a perceived tightening of mon­etary policy, such as during the taper tantrum. These concerns echo the findings in studies on the herding behaviour of institutional investors (e.g., Cai et al. (2016)), and the references therein), which may propagate illiquidity across financial markets as documented in, for exam­ple, Manconi et al. (2012) or Jotikasthira et al. (2012). While our paper is not concerned with interactions among fund managers, our conceptual framework takes into account the adverse effect of fund sales on market liquidity. Indeed, a number of bond market trends suggest that such effects may have further increased in recent years (Committee on the Global Financial

System (2014, 2016)). One issue is reduced availability of liquidity services from dealer-banks, which implies that fund managers may need to accept higher discounts if they are forced to sell during episodes of market stress (Bao et al. (2016), Fender and Lewrick (2015)).

Finally, our paper connects with the literature on the design and effect of mutual fund fees or charges. Chordia (1996) develops a model to explain the diversity of open-end fund charges. His model predicts that fund managers can dissuade investor redemptions by charging front­or back-end load fees. As a result, funds charging such fees attract more long-term investors allowing the fund manager to hold less liquid assets in order to raise fund returns. Nanda et al. (2000), by comparison, focus on the interaction between load fees and management fees as well as fund manager skills. Similar to the result in Chordia (1996), their model suggests that the more skilled fund managers, who can generate higher returns, seek to attract long­term investors by charging low management fees, while charging a load fee to disincentivise subscriptions by short-term investors with high liquidity needs. In Lewrick and Schanz (2017), we develop a model showing that trading frictions and investors’ liquidity needs determine the fund manager’s ability to swing the settlement price in the presence of no-arbitrage conditions. Based on this, we derive welfare-optimal swing pricing policies.

Several empirical studies consider the dilution of fund value that arises from mutual fund flows. For one, Edelen (1999), using monthly flow data finds that liquidity-motivated trading has a significant adverse effect on open-end U.S. equity fund performance. Greene and Hodges (2002) confirm this result for international funds based on daily flow data, but find no significant effect for other fund categories. Greene et al. (2007) study the effect of redemption fees on fund flows. Their results point to a sizeable reduction in flows for funds that introduce redemption fees, with daily flows for U.S. bond funds declining by as much as 77%. This suggests that swing pricing could exert a powerful influence on investor behaviour since, as discussed in the next section, swing pricing and redemption fees affect investor payoffs in a similar manner.

The rest of the paper is organised in three sections. Section 2 presents the rationale for swing pricing, including the challenges associated with its implementation in practice. This provides the conceptual background to derive a number of testable predictions. We apply these predictions to the data in Section 3, where we assess the impact of swing pricing on several fund performance measures, highlighting the differences between the impact under normal market conditions and during the 2013 taper tantrum. Section 4 concludes.

2. The basics of swing pricing

This section presents a conceptual framework to organise our assessment of swing pricing. We start by illustrating the rationale for swing pricing and how funds implement it in practice. Based on this, we derive five testable hypotheses of the effect of swing pricing. We motivate these hypotheses by focusing on economic intuition, while also presenting a formal motivation based on a global games model in the appendix of this paper.

2.1. How swing pricing reduces fund dilution

Our analysis builds on the observation that net fund flows dilute the value of the fund when­ever they prompt the fund manager to trade securities. To see why this matters for investor behaviour, we consider a stylised example of how the NAV per share of an open-end mutual fund is determined. At the end of each period t (typically a trading day), the fund manager calculates the NAV of the fund per outstanding share at t and collects all customer orders in terms of the number of shares to redeem or issue. Whenever redemptions exceed subscriptions to the fund (i.e., net fund inflows are negative), the fund manager sells securities in the next period (t + 1) to raise enough cash to pay out investors. Likewise, the manager buys securities in t + 1 in response to having received net inflows. In both cases, the fund manager incurs transaction costs (e.g., commissions, fees). When selling securities, the fund also faces liquida­tion costs. These are equal to the difference between the prices of the securities that are used in the calculation of the NAV at t (typically the mid-price at the end of period t) and the prices at which the securities are effectively sold at t + 1. Liquidation costs arise if the price of the securities falls from t to t + 1. But even in the absence of changes in the market price, the fund manager will usually not be able to sell at the mid-price, but only at the price offered by her market-maker (e.g., a dealer-bank), which will charge a spread for the liquidity service. This spread will often increase with the size of the trade, suggesting that the price moves against the fund manager if she wishes to sell a larger amount of securities.

Since trading is costly, net fund flows in t dilute the NAV of the fund. Yet the dilution does not show up before the calculation of the NAV per share in t + 1. This is because the NAV at t does not reflect the future transaction and liquidation costs associated with net cash flows in t. The dilution is particularly pronounced if the fund sells relatively illiquid assets. Hence, funds that invest in thinly traded assets (e.g., high-yield corporate bonds) are more exposed to dilution than those investing in liquid assets (e.g,. government bonds of major economies). In addition, the cost of trading can spike during periods of elevated market uncertainty, when market-makers curtail their liquidity provision to mitigate their risks. These episodes are typically characterised by large net fund outflows, as investors seek to redeem their shares to meet their own liquidity needs or become more pessimistic about the future value of the fund.

Informed investors will anticipate that fund managers facing large net outflows in period t will be forced to sell securities - possibly at a large discount - in the next period, which will drive down the NAV per share in t +1. Particularly under strained market conditions, investors may also suspect that the prices of relatively illiquid assets that are used to calculate the NAV at t do not yet factor in the latest information (i.e., they are “stale”) and could prove to be significantly higher than the prices at which the fund manager can actually sell the assets. Since the cost of liquidating assets is exclusively borne by the investors that remain with the fund, each individual investor may thus be tempted to withdraw from the fund, hoping to benefit from a first-mover advantage.

Swing pricing offers one policy option to reduce the dilution effect and the implied first­mover advantage. It allows the fund manager to reduce or raise the NAV per share (pt) by the swing factor (st) in response to large net fund outflows and inflows, respectively. If the NAV per share is swung, all transactions are settled at price pit, the “swung” NAV per share:

The sign of the swing factor depends on the sign of total net fund flows in that period. If the fund manager applies a full swing pricing policy, she sets a positive (negative) swing factor whenever the fund experiences net outflows (inflows), while the swing factor is only equal to zero if fund flows net out. Given the operational cost of determining whether or not to activate the swing factor, a partial swing pricing policy is common in practice (ALFI (2015b)). In this case, the swing factor is positive (negative) only if total net outflows (inflows) exceed a specified threshold. To keep investors from gaming the swing pricing policy, most funds do not disclose the threshold, whereas the swing factor is typically made available upon investor request.

Swing pricing partly, or fully, offsets the dilution that arises from net fund flows. There are several effects at work. First, for given net flows, a positive (negative) swing factor reduces (raises) the amount of cash the fund manager pays out to (receives from) trading investors. This effect raises the value of the fund, compared with the case of not swinging, regardless of the direction of net fund flows. Second, a positive (negative) swing factor reduces (raises) the amount of assets the fund manager sells (buys) in the next period to accommodate net flows today. For the case of net outflows, the reduction in the amount of assets that need to be sold reduces the dilution effect that arises from liquidation costs. For the case of net inflows, by contrast, the increase in the amount of assets purchased by the fund results in additional transaction costs, partly offsetting the anti-dilution effect.

In practice, as confirmed by anecdotal evidence from industry experts, funds set the swing factor equal to the approximate cost of selling securities under normal market conditions. While some funds apply different swing factors depending on the amount of net outflows, most funds tend to set a uniform swing factor which is periodically reviewed by the fund company. Fur­thermore, many funds commit to not raising the swing factor above a maximum value, often around 2% of the NAV per share for bond funds (ALFI (2015a,b)). These design choices reflect the trade-off between approximating dilution effects, which may be difficult to attribute to in­dividual investor transactions, and the need for operationally efficient and transparent rules of application.

 2.2. How swing pricing affects investor behaviour and fund manager incentives

We derive five testable predictions that follow from the application of swing pricing. The first one stems from the effect of swing pricing on investor incentives to withdraw from the fund. As noted above, swing pricing affects these incentives in two ways. First, a positive swing factor reduces the payout to redeeming investors, which discourages investors from withdrawing from the fund. Second, for any given amount of net outflows, a positive swing factor reduces the dilution of the fund value, which, in turn, raises the expected return from remaining invested in the fund. We expect these effects to be strongest when past fund performance is weak. This is because, for bond funds, weak performance has been found to predict future fund outflows, whereas strong performance has only a moderate effect on inflows (e.g., Goldstein et al. (forthcoming)). Investors in a fund that performs badly are thus likely to expect other fund investors to withdraw, which would prompt the fund to swing the NAV downwards in order to contain dilution. As a result, investors in a fund that applies swing pricing would have fewer incentives to withdraw than those invested in a fund that does not swing. We summarise these consideration in Hypothesis 1:

Hypothesis 1. Swing pricing reduces fund outflows in response to weak fund performance.

We illustrate the above effects in Figure 1. Here, we assume that each investor receives a noisy private signal (di) about the future returns of the fund (see the appendix for details). If the signal is low (i.e., moving towards the left on the horizontal axis), the investor expects low future returns and predicts that a large number of investors will redeem their shares, which further reduces the expected payoff (shown on the vertical axis) due to dilution of the fund. The solid red line depicts the payoff that results from staying invested for the case of a non-swinging fund, given the investor’s beliefs about the behaviour of all other invertors. The investor compares this payoff with the one resulting from withdrawing from the fund. The latter is given by the dashed red horizontal line, which highlights that future returns do not affect the investor’s payoff if she redeems. If the investor receives the signal d^, she is exactly indifferent between withdrawing and remaining invested, as shown by the intersection of both red lines at point A. Swing pricing shifts this point based on the two effects discussed above. First, it lowers the payout to redeeming investors as shown by the downward shift in the horizontal line, moving the point of indifference to B. Second, it mitigates the dilution of the fund. This raises the expected payoff of remaining investors as depicted by the upward shift in the solid line, shifting the intersection of the two payoffs (black lines) to point C. The investor would thus remain invested even if her signal is lower than Oa as long as her signal is at least 0*. This implies that swing pricing reduces fund outflows for any given expected return of the fund. Note that the difference between the two payoffs from remaining invested (solid lines) increases as the signal becomes lower. This is because the dilution of the fund rises as a larger share of investors is expected to redeem due to the increasingly weak outlook on fund performance. The effect of swing pricing on fund outflows is thus expected to become stronger as the expected fund performance weakens. To the extent that past performance is a good predictor of future performance, we expect swing pricing to dampen outflows in response to weak fund performance as stated in Hypothesis 1.

Our second hypothesis is concerned with the effectiveness of swing pricing as a financial stability tool given its current application in practice:

Hypothesis 2. Swing factors that are calibrated to normal market conditions may fail to offset investor first-mover advantages during periods of market stress.

Since liquidation costs rise under stressed market conditions (e.g., Committee on the Global Financial System (2014)), fund managers would need to raise their swing factors to offset the first-mover advantage. In practice, however, swing pricing rules tend to be simple and swing factors to be confined to relatively low values.

We illustrate in Figure 2, based on a stylised example, the difference between how swing factors are typically calibrated in practice and how they would need to be set in order to fully offset the first-mover advantage. The red (dotted) line shows an example of a typical swing pricing rule, where the swing factor is set to 1% of the NAV per share whenever net outflows exceed 2% of the fund’s total net assets (TNA) and is zero otherwise. The swing factor is calibrated so that it corresponds to the cost of liquidating 2% of the fund’s TNA. At this level of outflows, the red line touches the black (dashed) line, which represents the cost of liquidating securities. This cost increases with the amount of outflows because of the adverse price impact the fund manager faces when having to sell large amounts of securities (Borkovec et al. (2016)).

The blue line, finally, depicts the swing factor that follows from an outflow-dependent policy. It ensures that investors withdraw if, and only if, they expect the fund returns to be negative (i.e., less than the outside option of holding cash). We derive this policy formally in the appendix. The main characteristic of this policy is that it fully offsets the first-mover advantage by reducing the payout to investors in response to larger outflows. We note that the swing factor is lower than corresponding liquidation costs. Thus, under this policy, outflows dilute the value of the fund. Yet because of the dual effect of swing pricing on investor payoffs, this swing factor still keeps investors that expect small positive returns from redeeming.

There are three regions of interest in Figure 2. The first one concerns outflows of up to 2% of TNA. Here, the dilution effect is weak so that the two swing pricing rules generate very similar outcomes. The second region is for outflows equivalent to 2% to 8% of TNA. In this region, a fund that applies a 1% swing factor taxes redemptions by more than what would be necessary to address the first-mover advantage. As a result, there may be “captured” investors that (e.g., given private information) expect negative fund returns but remain invested because of the swing factor. It is in this region of moderate outflows that we would expect swing pricing, as applied in practice, to have a relatively strong dampening effect on outflows if compared with funds that do not swing. The third region covers outflows exceeding 8% of TNA, where the outflow-dependent rule implies a swing factor above 1%. As outflows increase, the gap between the two rules widens, suggesting that a 1% swing factor becomes increasingly ineffective in addressing the first-mover advantage. As a result, fund flows would become more sensitive to expected fund returns.

Our third prediction relates to the effect of swing pricing on the fund’s returns:

Hypothesis 3. Swing pricing raises measured fund returns by reducing fund dilution, particu­larly during periods of large fund outflows.

This is because the fund reduces the payout to redeeming investors by adjusting the NAV downwards. In addition, the fund incurs lower liquidation costs since it needs to sell fewer securities to service redemptions. The results in BlackRock (2011) indicate that such effects can be sizeable. For the period from July 2010 to June 2011, the study finds an increase in annual fund returns by up to 2.5 percentage points with funds swinging on up to 72 days. While we expect swing pricing to support fund returns whenever the fund swings the NAV, the effect should be strongest when liquidation costs are high such as during stressed periods.

Our fourth hypothesis concerns the impact of swing pricing on the volatility of fund returns. There are two considerations in the context of swing pricing. The first one is its effect on the volatility of the published (i.e., swung) fund prices, often referred to as accounting volatility (ALFI (2015a)). The second, more indirect one, is the effect of swing pricing on the volatility of the fund’s portfolio. The overall effect of swing pricing on the variance of the NAV per share is then given by:

 

where we denote by pf the (counterfactual) price per share that would prevail in the absence of swing pricing. The first two terms on the right-hand side of equation (2) summarise the effect of swing pricing on the variance of the NAV per share. Var[st pt] represents the additional variation in the NAV per share that is due to the up- and downward adjustment of the share price by the swing factor (st). The covariance term, in turn, captures the comovement of the swing factor with the NAV per share. The sign of this term depends on the contemporaneous correlation of net fund flows, which determine the sign of the swing factor, and the fund’s (unswung) share price (pt). If the price of the fund’s portfolio is positively correlated with net fund flows, the covariance term will be negative, raising the accounting volatility of the swinging fund. In our empirical analysis (see Section 3.3), we provide some evidence to support this claim, by showing that weak fund performance induces fund outflows, which in turn may prompt the fund manager to swing the NAV downwards (i.e., s > 0).

The difference between the last two terms on the right-hand side of equation (2) represents the effect of swing pricing on the variance of the fund’s underlying portfolio. It is difficult to sign this effect because of the hypothetical nature of the comparison. The two terms cancel out if swinging has no effect on the composition of the fund’s portfolio. To the extent that swing pricing induces the fund to raise its holdings of risky assets (see below), we would expect the volatility of the underlying portfolio to increase. Taking the two effects together, we predict that:

Hypothesis 4. Swing pricing raises a fund’s accounting volatility.

This effect is expected to be strongest during times of large net fund flows, when the swing factors are triggered most often.

Our last prediction relates to the effect of swing pricing on fund manager incentives to insure against liquidity risks. We argue that:

Hypothesis 5. Swing pricing reduces funds’ liquid asset holdings.

Swing pricing, by discouraging investors from redeeming their shares, would allow the fund manager to take on more liquidity risk if compared with a non-swinging fund. Compensation schemes that are linked to fund performance, for example, provide a strong incentive to reduce the fund’s holdings of low-yielding liquid assets. In line with this hypothesis, Chernenko and Sunderam (2016) show that variable annuity funds hold less cash than similar open-end funds because their fund in- and outflows are less volatile. The flip side of reduced cash holdings is that they raise the average cost of liquidating the fund’s assets. This raises the implied dilution of investor redemptions, which, in turn, could reduce the dampening effect of swing pricing on fund outflows, particularly under strained market conditions when liquidity concerns come to the fore.

3. Empirical analysis

This section presents the empirical analysis to test the five hypotheses that follow from our conceptual framework. The section starts with a description of the data. Guided by our predictions, we analyse the effect of swing pricing by comparing fund flow dynamics as well as other fund metrics of U.S. open-end bond funds with those of comparable Luxembourg funds. We consider developments for the entire period of observation (2012-16) before turning to developments during the taper tantrum, which was marked by significant fund outflows. To conclude, we assess how swing pricing affects funds’ cash holdings.

3.1. Data

Our analysis builds on 1,719 mutual bond funds for which we gather monthly data from Lipper and daily data on funds’ NAV from Bloomberg. To construct our sample, we first select all actively managed open-end mutual bond funds available from Lipper that are domiciled in the United States or Luxembourg. Data are available at the level of the individual fund’s share classes. We keep only the primary share class of each fund to avoid bias from intra-fund reallocations or subsidisation. Hence, we can refer to each fund share class as representing a unique fund. Data coverage for Luxembourg funds improves significantly as of 2012, which is why we base our analysis on the period from January 2012 to May 2016.

All funds in the sample need to meet two criteria. First, based on the Lipper fund clas­sification (henceforth referred to as the fund style), we keep only funds that can be allocated to a style for which we observe both U.S. and Luxembourg funds. This is to ensure that we are comparing funds with similar investment focus. Second, we exclude all funds that invest mainly in advanced economy sovereign debt for which liquidation costs are low and, as a result, the first-mover advantage should be small. Overall, our sample consists of 1,000 U.S. funds and 719 Luxembourg funds, split across ten different styles such as Bond USD Corporates or Bond USD High Yield.

Fund flows as well as other fund characteristics are fairly similar for the U.S. and Luxem­bourg funds, highlighting the similarity of their investment strategies and investor basis. Figure 3 depicts the aggregate fund flows as a percentage of TNA (left-hand panel), and TNA by country (right-hand panel). At this level, fund flows of U.S. and Luxembourg funds as well as their TNA are highly correlated, with correlation coefficients of 0.78 and 0.94, respectively.

The period from May to early July 2013, highlighted by the grey-shaded region, marks a clear break in the flow patterns for both countries. This period was characterised by a sharp increase in bond yields, following signs of a possible tapering of the U.S. Federal Reserve’s monetary policy accommodation. During this taper tantrum, credit spreads on corporate bonds and emerging market economy debt increased significantly, resulting in sizeable valuation losses for the type of funds in our sample (Bank for International Settlements (2013)). This suggests that this period of strained market conditions be specifically accounted for in our empirical analysis.

Even though U.S. and Luxembourg funds share many common features, some notable differences exist. To provide a comprehensive comparison, we show the summary statistics of each country sample in Table 1. One apparent difference is the size of the funds, as measured by their TNA. U.S. funds, on average, are 5.4 times as large as their Luxembourg counterparts in the sample. Furthermore, U.S. funds exhibit somewhat higher and less volatile returns, on average, during the period of observation. Fund flows, by comparison, appear broadly similar across both groups, supporting the patterns shown in Figure 3. About 60% of the funds report a benchmark index to evaluate their performance. These funds tightly manage their performance against the benchmark, as is evident from the low standard deviation and small range of the reported market-adjusted returns, which are given by the difference between the funds’ returns and those of the benchmark. We will exploit this fact when comparing the performance of funds during the taper tantrum (see Section 3.4 below). Finally, we note that only about one out of eight U.S. funds applies redemption charges, which is consistent with the results in Chernenko and Sunderam (2016). Luxembourg funds make even less use of redemption charges. This is not surprising, given the widespread use of swing pricing, which provides a similar means of levying liquidation costs on redeeming investors.

Other studies using the CRSP database, which only contains data for U.S. funds, provide a welcome benchmark for our sample selection. Our summary statistics, for example, tally with those presented by Goldstein et al. (forthcoming) for a sample of 4,679 fund share classes (1,660 corporate bond funds) from 1992 to 2014. For one, their study reports a median and standard deviation for cash holdings of 2.81% and 10.04, as compared with our values of 2.20% and 14.80, respectively. Likewise, they report the use of redemption charges only for the 80th percentile of U.S. funds (75th in our sample).

3.2. Methodological approach

Our methodological approach builds on the premise that investors subscribe to funds or redeem their shares based on the information they have about a fund at any given point in time. In this sense, we presume that investors in Luxembourg funds are aware of the risk of the NAV being swung and adjust their trading behaviour accordingly. This information, often supplemented by a commitment to a maximum swing factor, is available from the fund’s prospectus. In some cases, investors may also know the swing factor that is currently applied if the fund manager swings the NAV, which is typically available at the request of the investor. That said, the threshold at which the swing factor kicks in is not disclosed by the fund, nor can investors observe whether the NAV was actually swung.

Investor expectations are a key determinant of investor behaviour. Yet the set of information that is used by individual investors to form their expectations is unknown. Recent information on past fund returns, however, is likely to be a pivotal component of investors’ information set. Our empirical analysis thus builds on using past fund returns as a gauge of investors’ return

expectations, in line with the literature studying the relation of fund flows and past returns.

Our empirical analysis also presumes that U.S. and Luxembourg funds are comparable across the main parameters of interest to investors. Indeed, with the exception of swing pricing, U.S. and Luxembourg fund managers can resort to the same set of policy tools to address redemption pressures (IOSCO (2015)). At the same time, it appears unlikely that the ability to swing prices has any meaningful impact on the fund company's decision whether to register a fund in the United States or in Luxembourg. Other considerations, such as having established a renowned brand name in the region, are likely to be far more important. Thus, we can consider the ability of the fund to swing as largely exogenous. Controlling for other fund characteristics, we can therefore gauge whether differences in the fund performance of U.S. and Luxembourg funds are consistent with the predictions from the Section 2.2.

3.3. Differences in the flow-to-performance relation of U.S. and Luxembourg funds

​​​​​​​We start with testing Hypothesis 1 by analysing whether Luxembourg fund flows are less sen­sitive to weak performance than those of their U.S. peers. To do so, we run several variants of the following baseline regression:

where flowit represents the value of fund i’s net inflows as a percentage of TNA in month t. Xit-1 is the vector of p predictors, is a p x 4 matrix of coefficients, S is the 4 x 1 vector of interaction dummies. Furthermore, ai represents the time-invariant individual fund effect, whereas Yet captures country-month fixed effects to account for, e.g., tax-loss selling before year-end. eit is the error term.

Xit-1 comprises all time-varying fund characteristics based on those shown in Table 1. In addition, we construct a variable of returns interacted with an indicator variable that is equal to one if returns are negative. This allows us to account for the potential non-linearity in the flow-to-performance relation, following the approach proposed by Goldstein et al. (forthcoming). That is, we control for the possibility that flows respond differently to negative returns than to positive ones. Our main results are based on the first lag of monthly fund returns (annualised, in per cent). This performance metric is available to investors when taking their decision whether to sell or buy shares. It also addresses potential endogeneity concerns that would be associated with using current returns. Furthermore, relying on nominal returns is consistent with the findings in, e.g., Fulkerson et al. (2013), who make the case that investors focus on simple return measures, largely neglecting any risk adjustment. All that said, we consider a variety of alternative return measures to confirm the robustness of our results (see below). Other fund-level controls are the first lag of (log) TNA, (log) age, flow value and of the expense ratio.

The interaction vector, 5, consists of four indicator variables, allowing us to distinguish the impact of the predictors for four different cases: (i) U.S. funds (the reference case); (ii) Lux­embourg funds (indicated by LUX); (iii) U.S. funds during the taper tantrum (TT); and (iv) Luxembourg funds during the taper tantrum (TT x LUX).

As a reference point, we consider a fund fixed-effect regression based on using only U.S. funds and omitting any interaction terms for the taper tantrum. We highlight the slope coefficients on returns and negative returns in Column 1 of Table 2. The estimates support the findings in Goldstein et al. (forthcoming): inflows into bond funds are less sensitive to good performance than outflows are to weak performance as indicated by the much larger coefficient on negative returns than the one on (all) returns. Based on the point estimates in Column 1, a U.S. fund with annualised returns of +10% in the preceding month (roughly equivalent to the 75th percentile of the U.S. funds’ returns in our sample) would experience additional inflows of only 0.01% of TNA in the current month, with the effect not being statistically significant. Had the fund, by comparison, returned —10% (roughly equivalent to the 10th percentile of the U.S. fund returns, Table 1) it would have been subject to additional net outflows of 0.52% of TNA (10 x (0.001 + 0.051)). To put these numbers into perspective, we recall that average cash holdings of U.S. funds were 1.75% of TNA.

The relation of fund flows and past returns differs for U.S. and Luxembourg funds, sup­porting Hypothesis 1. As we move from Column 1 to Column 2 in Table 2, we include the Luxembourg funds to assess the differences with their U.S. peers. What stands out is the Lux­embourg funds’ lower sensitivity to negative returns, which more than compensates for their higher sensitivity to performance more generally. Our point estimates in Column 2 suggest that, on average, a Luxembourg fund with a pre-month return of —10% witnessed additional net outflows of 0.25% of TNA (—10 x (0.001 + 0.053 + 0.021 — 0.050)). The same fund, by com­parison, received additional net inflows of 0.22% of TNA (10 x (0.001 + 0.021)) if its annualised pre-month return was +10%. The reduction in outflows that can be linked to swing pricing follows from the sum of the slope coefficients on returns and negative returns of Luxembourg funds (0.021 — 0.050). Conditional on returns being negative, outflows are reduced by nearly 0.03% of TNA for every percentage point decline in returns.

As a next step, we control for additional fund characteristics that may affect investor redemptions. First, we take account of redemption charges, which, similar to swing pricing, should disincentive investor redemptions. Column 3 in Table 2 reports the coefficients estimates that result from excluding all funds with redemption charges, which predominantly reduces the number of U.S. funds in the sample. Following this adjustment, the absolute value of the coefficient on negative returns interacted with the Luxembourg dummy increases. Thus, Luxembourg fund flows are, in relative terms, even less sensitive to past weak performance if we compare them only with U.S. funds that do not impose redemption charges.

Second, we account for differences in the funds' cash holdings in order to control for an­ticipated dilution costs. We recall from the conceptual framework that higher liquidation costs increase the dilution effect of investor redemptions, reducing investor incentives to stay with the fund. Cash holdings serve as a useful gauge of liquidation costs. As a direct effect, lower (higher) cash holdings raise (reduce) the average costs of liquidating the fund portfolio. Second, funds with lower cash holdings may have to respond more promptly to net outflows, suggesting that they have less leeway in timing their sales and may need to make higher price concessions when liquidating securities. Column 4 in Table 2 presents the slope coefficients for the return measures based on including lagged cash holdings in the set of predictors. We consider the changes in the estimates line by line. First, our estimates reinforce the earlier finding of a con­cave flow-to-performance relation for bond funds. Positive returns induce a modest net inflow into funds, with the coefficient estimate now being statistically significant. Negative returns, however, prompt much larger net outflows - to the tune of four times more (in absolute value) than the response to positive returns.

Once controlling for differences in cash holdings, we also find that net flows into Luxembourg funds are as responsive to positive returns as for their U.S. peers, with the slope coefficient (Returnt-1x LUX) becoming close to zero and statistically insignificant. One interpretation of this result is that Luxembourg fund managers have little incentive to dampen inflows into their funds by making active use of swing pricing (i.e., by adjusting the NAV per share upward).

The reaction of fund flows to negative returns, by contrast, differs across the two groups. Consistent with our earlier findings and the predicted impact of swing pricing, Luxembourg funds that yield negative returns are less susceptible to outflows than their U.S. peers. The difference is not only significant statistically, but also in terms of its magnitude. The marginal effect of negative returns on outflows is reduced by roughly 0.04% of TNA per percentage point of return.

Hypothesis 2 suggests that swing pricing, given its current design, is unlikely to offset investor first-mover advantages if markets are under stress. The taper tantrum interaction terms, indicated by TT in Table 2, allow us to indirectly test this prediction, even though we cannot measure such advantages directly. We focus on the specification in Column 4, discussed above, which includes controls for cash holdings and excludes funds with redemption charges. We take the sum of all eight slope coefficients for returns and negative returns reported in

Column 4, including those interacted with the taper tantrum interaction term, to calculate the flow-to-performance relation for Luxembourg funds during the taper tantrum. This yields of TNA per percentage point change in (negative) returns, more than twice the value we found for normal market conditions. Had swing pricing policies fully offset first-mover advantages during the taper tantrum, there should have been no significant increase in the flow-to-performance relation. Our finding thus lends some indirect support to Hypothesis 2 and tallies with the results of Malik and Lindner (2017), who study first-mover advantages for a small sample of individual funds. We note, however, that the additional impact on Luxembourg fund flows during the taper tantrum is not statistically significant (see the coefficient estimates in the last two rows of Table 2), given the comparatively large standard errors.

We assess the robustness of our results by considering alternative return measures. As a first check, we regress fund flows on the same set of predictors as in Column 4, Table 2, but vary the measure of fund returns. Specifically, we consider the impact of using cumulative returns over the preceding three months (Column 5) and six months (Column 6), respectively. This adjustment assumes that investors not only factor in the most recent returns to assess future fund performance, but also consider the fund’s medium-term performance in their assessment. One rationale for such an approach is the presumption that skilled fund managers perform well on average, but may nevertheless fail to generate returns in individual months (Kacperczyk et al. (2014)).

Our main takeaway from the results shown in Columns 5 and 6 is that they lend further support to Hypothesis 1. First, we find additional evidence that negative returns induce fewer outflows from Luxembourg funds than from their U.S. peers. Intuitively, the difference becomes larger as we lengthen the range of returns that we assume investors are factoring into their decisions. Comparing a U.S. and Luxembourg fund with negative returns over the past three months, we find that the Luxembourg fund benefits from reduced outflows of about 0.08% of TNA per percentage point change in (negative) returns (Column 5). If, by comparison, the return of both funds was negative, on average, over the past six months, the benefit amounts to as much as 0.16% of TNA (Column 6).

As a second robustness check, we consider whether potential differences in investors’ cur­rency of account affect our results. One concern with the above regressions could be that investors from different regions evaluate fund performance based on their home currency. Since an appreciation (depreciation) of the USD against the investor’s home currency raises (reduces) the fund’s return in home-currency terms, investors using different currencies of account could respond differently to past fund returns. While information on investors’ currency of account is generally not available, a rough approximation is that investors are more likely to evaluate U.S. fund performance in USD terms and Luxembourg fund performance in euro (EUR), for example, because investors are biased towards investing in funds domiciled in their home region. In Columns 1 to 3 of Table 3, we show the slope coefficients for Luxembourg funds based on measuring U.S. fund returns in USD (as throughout the paper), but swapping Luxembourg fund returns into EUR terms based on spot exchange rates shown in the left-hand panel of Figure As before, we consider results based on using monthly returns (Column 1), three-month (Column 2) and six-month returns (Column 3). We find that the estimates are little changed if compared with the corresponding estimates in Columns 4 to 6 in Table 2.

Finally, we consider alternative measures of investors’ opportunity costs. Thus far, we have implicitly assumed that investors respond differently to negative returns than to positive returns because a natural alternative to investing in funds - at least in the short term - is to hold cash, which yields zero nominal return. In Columns 4 to 6 of Table 3, we alter this assumption and consider how our results change if we assume that investors benchmark fund returns against the corresponding risk-free rates. Columns 4 to 6 show the coefficient estimates for Luxembourg funds based on using monthly returns, three-month and six-month returns, respectively, subtracting the euro-currency market interest rates with the corresponding term for Luxembourg funds, while using the corresponding yields on the U.S. Treasury bills for US funds.

Overall, the impact of these changes is fairly limited. This is not surprising since risk­free rates hovered around zero throughout most of the period of observation, as shown for the example of three-month rates in the right-hand panel of Figure 4. If anything, the results lend further support to accepting the hypothesis that swing pricing dampens fund outflows in response to negative returns during normal times. During the taper tantrum, by contrast, we find no evidence of a meaningful reduction in the sensitivity of fund flows to weak performance. To shed more light on this issue, we study fund flows, returns and volatility during the taper tantrum in more detail in Section 3.4.

3.4. Fund performance during the taper tantrum​​​​​​​

We assess differences in fund performance between U.S. and Luxembourg funds to gauge the effects of swing pricing during the taper tantrum. Complementing the previous analysis on the flow-to-performance relation, we match individual Luxembourg funds with U.S. funds based on a variety of fund characteristics available to investors in the run-up to the taper tantrum. Overall, we detect little evidence of systematic differences in net fund flows of U.S. and Luxembourg funds during this episode. That said, our results suggest that Luxembourg funds which were subject to outflows benefitted from higher market-adjusted returns than their U.S. peers. This is consistent with the anti-dilution effect of swing pricing (Hypothesis 3). Furthermore, we find signs of increased (accounting) volatility for Luxembourg funds, supporting Hypothesis 4.

We estimate the average treatment effect of Luxembourg funds, the treated funds (ATET), to identify the effects of swing pricing. We consider the ATET of three different measures. The top rows of Table 4 present results for the cumulative net fund flows from May to June 2013.

The rows in the middle report estimates for market-adjusted returns. These are calculated as the difference between each fund's annualised returns and those of the fund's benchmark from May to June 2013. We use this measure, rather than nominal returns, to account for differences in the riskiness of fund portfolios. We recall that the funds in our sample deviate very little from their benchmarks (see also Table 1), suggesting that this adjustment provides a useful control for differences across fund returns that are not related to swing pricing.

The bottom rows, finally, report the ATET for the annualised volatility of daily fund returns based on the reported NAV per share. We calculate the volatility for the period from 2 May to 5 July 2013, which represents the beginning and end of the 2013 bond market sell-off (Adrian and Fleming (2013)). Because we expect funds to swing only if they experience large outflows during this period, we compare the returns and volatility based on using only funds that experience net outflows. In all specifications, we exclude funds that impose redemption charges to support the precision of measuring the impact of swing pricing on fund performance.

We apply several alternative matching algorithms to evaluate the effect of swing pricing. Columns 1 to 3 in Table 4 report the ATET using nearest-neighbour matching. We match each Luxembourg fund with four U.S. funds, using the number of neighbours recommended in Abadie and Imbens (2011). For the results in Column 1, we match funds based on their age as well as their average returns, net flows and total assets in the three months preceding the taper tantrum (February to April 2013). To account for differences between funds that cater more to retail than to institutional investors, we also include an indicator variable that is equal to one if the minimum required investment is below USD 10,000. In addition, we require that funds are only matched with funds that have the same fund style.

Luxembourg funds do not appear to have experienced fewer outflows than their U.S. coun­terparts during the taper tantrum. The first row of Column 1 depicts the ATET for cumulative net fund flows during the taper tantrum. We find no statistically significant impact.

Because investors' incentives to redeem depend on the liquidation costs of the fund, high (low) cash holdings in the run-up to the taper tantrum should dampen (amplify) net outflows. We thus refine our matching by including an indicator variable in the set of covariates which indicates whether the fund, in April 2013, had cash holdings below or above the median of funds that use the same benchmark. This takes into account that funds investing in different asset classes may be exposed to different liquidation costs and, as a result, will generally hold different cash buffers. The downside of this refinement is that it reduces the number of observations because data on cash holdings are not available for all funds. Column 2 in Table 4 shows the results, with the coefficient estimate turning out to be even lower, but remaining statistically insignificant.

Funds manage their performance tightly against the benchmark they commit to. Matching funds based on the same benchmark thus provides a very close match. Column 3 presents the results when using the same set of covariates as before (including cash holdings) and matching benchmarks exactly. For this specification, the ATET turns positive indicating reduced outflows from Luxembourg funds when compared with their U.S. peers. The number of available obser­vations, however, becomes too small to draw any statistical inference, highlighting the trade-off between selecting a close match and the number of matchable funds.

To gain some further insights into the ATET, we develop an alternative matching algorithm based on the correlation of daily fund returns. This approach builds on the presumption that funds with similar portfolio allocations should be characterised by a high correlation of their returns. For each Luxembourg fund, we calculate the pairwise correlation coefficient of daily returns with each individual U.S. fund over the three months preceding the taper tantrum. Since Luxembourg funds experienced relatively steady inflows during these months (see also the left-hand panel of Figure 3), we do not expect their measured returns to be much affected by swing pricing activity. To further increase the precision of our comparison, we keep only correlation coefficients that are based on at least 30 observations per fund during this period, which gives us a maximum of 390 Luxembourg funds. Next, we match each Luxembourg fund with the U.S. fund for which we observe the highest correlation.

The corresponding ATET for the funds’ net flows provides no evidence of a significant effect on Luxembourg fund outflows during the taper tantrum as shown in Column 4 of Table 4. While the effect points to a reduction in outflows, it is neither statistically significant nor of meaningful magnitude.

To assess the robustness of this matching algorithm, we also show the ATET that follows from matching each Luxembourg fund with the four U.S. funds that exhibit the highest cor­relation with this fund in Column 5. This specification confirms our earlier results, suggesting that, overall, Luxembourg funds were as exposed to outflows during the taper tantrum as their U.S. peers. These findings lend some support to Hypothesis 2, suggesting that swing factors, as applied in practice, are too low to have a meaningful impact on investor decisions during episodes of market stress.

We now turn to the assessment of market-adjusted returns to test whether Luxembourg funds managed to mitigate the dilution implied by fund outflows. Consistent with Hypothesis 3, we find evidence that Luxembourg funds generated higher returns than their U.S. peers during the taper tantrum. Columns 1 to 3 (centre rows) report the ATET based on using nearest- neighbour matching. These estimates point to additional returns in a range of about 37 to 52 basis points on an annualised basis - a sizeable effect, given that average market-adjusted returns hovered around zero when considering the entire period of observation (see Table 1). Matching funds based on their daily returns yields qualitatively similar results, although suggesting a somewhat lower effect at around 17 to 30 basis points (Columns 4 and 5).

We test whether the difference in market-adjusted returns is not an artefact of matching generally more profitable Luxembourg funds with less profitable U.S. funds. To do so, we estimate the ATET for the matched funds for each month over the entire period of observation based on comparing (annualised) market-adjusted returns for the latest two months. The left- hand panel of Figure 5 depicts the corresponding ATET as well as its 95% confidence interval based on the matching approach applied for the results in Column 2 of Table 4, which appears to strike a good balance between the number of matched funds and the stringency of the matching requirements. We find that the ATET tends to hover around zero, but spikes during the taper tantrum (highlighted by the grey-shaded region). This lends further support to our interpretation that swing pricing helped Luxembourg funds to contain dilution during the taper tantrum.

Finally, we evaluate whether Luxembourg funds that experienced outflows also exhibited higher volatility of their daily returns during the taper tantrum. The bottom rows of Table 4 show the ATET for each of our five specifications. Overall, the estimates support Hypothesis 4 that swing pricing raises the fund's accounting volatility, particularly when considering the narrowly matched specifications in Columns 2 and 3. As for the comparison of returns, we consider to what extent the difference between U.S. and Luxembourg funds is specific to the taper tantrum episodes. The right-hand panel in Figure 5 illustrates the ATET and correspond­ing 95% confidence interval, using the matching approach as in Column 2 of Table 4 for each month in our sample. For consistency, we calculate the annualised volatility based on two-month rolling intervals of daily returns. The results indicate a positive ATET on average, at around 1.5 percentage points of annualised volatility. Yet during the taper tantrum (highlighted by the grey-shaded region) we record a spike in the ATET, with the estimate rising significantly above its average value. One interpretation is that, consistent with the predicted impact, swing pricing tends to raise funds' accounting volatility, with the effect being amplified during periods of market stress.

3.5. Cash holdings in the presence of swing pricing​​​​​​​

We conclude this section by comparing U.S. and Luxembourg funds' cash holdings to gauge their exposure to liquidity risks and test Hypothesis 5. Our conceptual framework highlighted that swing pricing could encourage fund managers to reduce cash holdings in order to raise returns. At first glance, the summary statistics of funds' cash holdings in Table 1 provide no support for this prediction. The picture changes, however, once we control for differences in fund characteristics. Indeed, we find evidence that Luxembourg funds hold less cash than their U.S. peers. This is consistent with fund manager incentives to insure less against redemption risks if the fund can discourage investor withdrawals by committing to swing the NAV when facing outflows.

We run several regressions to estimate the differences in funds' cash holdings as reported in Table 5. Column 1 presents the main coefficient estimates for a regression of cash holdings (as a percentage of fund value) on a variety of lagged time-varying (Xit-1) and time-invariant
(Zi) fund controls:

 

where cashit measure fund i’s cash holdings as a percentage of TNA in month t. We include a full set of country and taper tantrum interaction terms (summarised in 5), as in equation (3), as well as fixed effects for the respective month (+t) and the reported benchmark (+b) of the fund (not reported). One issue with funds’ reported cash holdings is that highly levered funds or those with significant derivative positions, which tend to exhibit cash holdings in the tail ends of the sample distribution, could drive the results. To control for this, we winsorise cash holdings at 20% which excludes all funds with negative reported cash holdings.

Our main interest is in the coefficient on the indicator variable for funds domiciled in Luxembourg (LUX, Table 5, Row 1). We find that Luxembourg funds, on average, hold 0.98 percentage points less cash than those domiciled in the United States. The difference is large if compared with the funds’ average cash holdings of 3.3% of TNA in the winsorised sample.

To further investigate the robustness of our results, we define an indicator variable that is equal to one whenever a fund has cash holdings above the median of those of other funds using the same benchmark and zero otherwise. Applying the comprehensive set of fund controls mentioned above, Columns 2 and 3 of Table 5 show the marginal effects (at the means) for a logit and probit regression based on using this indicator variable. Column 4, in turn, provides the marginal effects for a logit regression if we exclude all fund observations with negative reported cash holdings. For each of these specifications, the predicted probability of above-median cash holdings is lower for Luxembourg funds, in a range of 45% to 47%. This lends further support to Hypothesis 5 that Luxembourg funds hold less cash than comparable U.S. funds.

Table 5 provides several additional insights into the drivers of funds’ cash management decisions. For one, we find that funds accommodate past flows by adjusting their cash positions, supporting the results in Chernenko and Sunderam (2016). Net outflows in the previous month, for example, are associated with lower cash holdings, suggesting that fund managers run down cash buffers to meet redemptions. Furthermore, funds with low annual charges (i.e., below the sample median) hold less cash on average. This is consistent with the predictions in the models of Chordia (1996) or Nanda et al. (2000), suggesting that fund managers attract long-term investors by charging low annual fees, which, in turn, allows the fund to hold less cash.

4. Concluding remarks​​​​​​​

In this paper, we develop a conceptual framework to explore the effects of swing pricing. This framework yields several predictions to guide our empirical analysis of how swing pricing af­fects investor behaviour and fund manager incentives. Our identification strategy is based on comparing Luxembourg funds, which are allowed to apply swing pricing, with similar funds from the United States, where swing pricing is not yet available to fund managers. To this end, we construct a sample of 1,719 actively managed open-end mutual bond funds. Next to
considering a comprehensive set of fund controls, we apply different matching approaches to ensure the comparability of Luxembourg funds with their U.S. peers.

Our main findings can be summarised as follows. Consistent with the predictions from the conceptual framework, we observe that negative returns prompt larger outflows from U.S. funds than from their Luxembourg counterparts. This observation holds during normal market conditions. Yet during the 2013 U.S. taper tantrum, a period of marked declines in bond prices, U.S. and Luxembourg funds appear to have been equally exposed to investor redemptions. This supports the view that current swing pricing rules, which tend to apply a constant swing factor if outflows exceed a certain threshold, fail to offset investor first-mover advantages in more stressed markets.

In terms of the effect of swing pricing on other fund performance measures, we show that Luxembourg funds generated higher returns during the taper tantrum. This tallies with the predicted anti-dilution effect of swing pricing, which is based on the redistribution of liquida­tion costs from remaining investors to those deciding to redeem their shares. In addition, we document that Luxembourg funds, relative to their U.S. counterparts, experienced an increase in the volatility of daily returns during the taper tantrum. This finding is consistent with our framework's prediction that swing pricing increases funds' accounting volatility.

Finally, we find evidence that Luxembourg funds hold less cash than comparable U.S. funds. By reducing redemption risks, at least under normal market conditions, the introduction of swing pricing encourages funds to seek higher returns by lowering their cash buffers. This weakens any stabilising effect of swing pricing on the underlying markets. Regulatory responses to address vulnerabilities in the mutual fund industry can thus be enhanced by taking the interaction of policy tools into account, such as combining swing pricing with minimum liquidity requirements for funds or liquidity stress testing. That said, more research is needed to assess the underlying risks in this industry in order to inform the design of risk management tools and regulatory frameworks.

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