# Mutual fund liquidity costs.

One dollar in purchases or redemptions generates an average cost of $0.006 for US equity mutual funds during the period 1997-2009, approximately 70% lower than prior estimates derived from older data. However, large cross-sectional differences exist between funds. Many funds have costs near zero, but funds that hold relatively illiquid equities, have relatively concentrated portfolios, and manage relatively large amounts of assets have average liquidity costs significantly greater than the full sample average. Furthermore, despite a large difference in underlying asset liquidity, US bond funds and US equity funds have similar average liquidity costs.Mutual funds offer many attractive features to investors. An otherwise small investor can gain access to a well-diversified portfolio run by a dedicated financial expert, maintaining the option to redeem his or her investment at the net asset value (NAV) at the end of each day. However, such benefits come with costs. The direct cost (i.e., the expense ratio) is readily observable, and the impact of such costs on performance has received significant study (e.g., Wermers, 2000; Gil-Bazo and Ruiz-Verdu, 2009). In this study, we consider an indirect cost. In particular, we analyze the costs associated with providing daily liquidity to investors.

Providing daily liquidity generates costs in multiple ways. There are realized costs experienced when mutual funds trade in response to actual redemption and purchase requests from investors. Those requests are driven by both the allocation decisions of long-term investors and, in some instances, short-term investors attempting to profit from return predictability created by the process funds use to set their daily NAV (e.g., Chalmers, Edelen, and Kadlec, 2001; Greene and Hodges, 2002). There are also opportunity costs experienced when a manager maintains an otherwise suboptimal portfolio in anticipation of such requests. For example, a fund offering daily liquidity may hold more cash than an otherwise identical fund that does not offer daily liquidity. In this study, we focus on how liquidity costs vary in the cross-section of funds by considering the impact of fund flows on fund returns.

We begin our analysis by extending the work of Edelen (1999) to measure the average cost of providing liquidity to investors from 1997 to 2009. Our estimates suggest one dollar in liquidity-motivated trading creates a cost of $0.006 for the average fund. That cost represents a decrease of about 70% since the late 1980s, which is consistent with the general decrease in trading costs across US equity markets over the past three decades (Hasbrouck, 2009). Subperiod analysis suggests that average liquidity costs vary during our sample period with costs being particularly high during the financial crisis.

While the changes in average liquidity costs over time are notable, our analysis focuses on how liquidity costs vary between mutual funds. Hodrick and Moulton (2009) model the level of concern a portfolio manager would have for liquidity costs based on portfolio attributes, and their work suggests several fund characteristics that could lead to cross-sectional variation in liquidity costs. We examine three key attributes based on their model. We first consider how the liquidity of a fund's equity positions impacts liquidity costs. Funds holding relatively illiquid equities have average liquidity costs two to three times greater than the full sample average, while funds that hold relatively liquid equities have near-zero costs. We then consider how the concentration of a fund's equity portfolio impacts liquidity costs. As with the liquidity of a fund's equity positions, funds with relatively concentrated portfolios have significantly greater average liquidity costs compared to the full sample average, while funds with relatively diversified portfolios have costs close to zero. Finally, we consider how a fund's total net assets impacts liquidity costs. Larger funds have greater average liquidity costs than smaller funds, but the costs are economically nontrivial for both groups. Taken as a whole, these results suggest that many funds have a low cost of providing liquidity, but that specific characteristics contribute to higher costs and drive the significant cross-sectional variation between funds.

To further examine the role of mutual fund characteristics, we also consider the cost of providing liquidity for US bond mutual funds. Like equity funds, bond funds offer daily liquidity to investors, but they primarily invest in assets with significantly less liquidity. Holding all else equal, we would expect bond funds to have greater average liquidity costs than equity funds because of the increased mismatch between the liquidity offered to investors and the liquidity of fund assets. However, as a practical matter, bond fund managers are aware of the mismatch and could take additional measures to manage liquidity (e.g., holding a larger buffer of cash-equivalent assets) to account for the relative illiquidity of their primary investments. Using the same time frame as in our prior analysis, we find that one dollar in liquidity-motivated trading costs the average bond fund about $0.004, which is economically similar and not statistically different from our estimate for equity funds. As with equity funds, subperiod analysis suggests that average liquidity costs were particularly large for bond funds during the financial crisis.

Overall, our results provide new evidence on the costs mutual funds face to provide liquidity. First, using similar methods, we show that average liquidity costs over the period 1997-2009 are significantly lower than the costs estimated by Edelen (1999) for the late 1980s. Second, we show that there is significant cross-sectional variation in liquidity costs between funds. On the one hand, funds that invest in relatively illiquid equities, funds that hold relatively concentrated equity portfolios, and funds that manage relatively large amounts of assets have average liquidity costs significantly greater than the full sample average. On the other hand, many other funds without those characteristics have average liquidity costs statistically indistinguishable from zero. Third, we show that average liquidity costs for bond funds are similar to those of equity funds despite a substantial difference in the liquidity of the primary investments of those funds.

I. Prior Work

All mutual funds have costs associated with their operations; Wermers (2000) provides a breakdown of those costs for actively managed funds investing in US equities. The average fund has costs of about 0.8% of assets per year attributable to the expense ratio and about 0.7% of assets per year attributable to nonequity holdings (such as cash). (1) Trading costs are about 0.8% of assets per year, which Edelen, Evans, and Kadlec (2013) further divide into commissions (0.14%), spreads (0.13%), and price impact (0.53%). In total, the average mutual fund has operating costs of about 2.3% per year. Considered against the 1.3% per year in gross alpha generated by a fund's equity portfolio, operating costs contribute significantly to the zero or negative net alphas observed for most funds in the literature (e.g., Barras, Scaillet, and Wermers, 2010; Fama and French, 2010).

Within those cost analyses, the impact of providing liquidity is indirectly captured. Mutual fund investors have the option to purchase and redeem shares every day at the end-of-day NAV. The provision of daily liquidity can force fund managers to trade to meet transaction requests on short notice and at potentially high cost. Compared to an otherwise identical portfolio with no requirement to provide daily liquidity, mutual funds will incur additional trading costs, which will negatively affect fund performance. Edelen (1999) estimates that one dollar of liquidity-motivated trading costs the average fund about $0.02.

However, both the Wermers (2000) and Edelen (1999) analyses focus on a time frame that includes the late 1980s, and a combination of factors have decreased the cost of trading during the past three decades. The downward trend in trading costs can be explained in part by the growth of off-exchange liquidity providers and increasing competition between brokers (Goldstein et al., 2009). (2) Changes in exchange rules have also contributed to lowering trading costs. Schultz (2000) shows trading costs decreased following a crackdown on collusion on the exchanges during the mid-1990s. Chakravarty, Panchapagesan, and Wood (2005) and Goldstein and Kavajecz (2000) show that the decimalization of equity prices also affected trading costs. Finally, electronic trading has largely overtaken US markets. Stoll (2006, p. 162) notes that with respect to commissions, spreads, price impact, and order delays, "electronic markets have reduced all these costs." Considering the market as a whole, Hasbrouck (2009) finds a significant decrease in total transaction costs across all US stock exchanges during the past three decades. (3)

We expect these trends to decrease liquidity costs for the average mutual fund, but the impact of the requirement to provide daily liquidity is not captured by average transaction costs alone. Rakowski (2010) shows that both increased daily flow volatility and large unexpected daily flows have a negative impact on fund performance. Hanouna et al. (2015) find that large redemption requests can negatively affect the liquidity of a fund's portfolio. Chen, Goldstein, and Jiang (2010) and Goldstein, Jiang, and Ng (2015) demonstrate how providing daily liquidity creates negative externalities for long-term investors in a fund.

The daily pricing necessary to provide liquidity itself generates costs for mutual funds. Funds must estimate a price for each asset to calculate their NAV, but the price could be stale or difficult to estimate for lightly traded assets. For assets trading asynchronously with US markets, the appropriate price could be difficult to determine even for heavily traded assets, in part because the price has not been recently updated or changes shortly after the fund calculates the NAV These pricing issues can create short-term predictability in fund returns, as discussed in Chalmers et al. (2001), Goetzmann, Ivkovic, and Rouwenhorst (2001), Greene and Hodges (2002), and Zitzewitz (2003, 2006). To the extent this predictability leads to additional trading, short-term investors can create additional liquidity costs for the fund. Johnson (2004) finds that the liquidity costs created by these short-term investors are greater than those created by long-term investors.

Fund managers could attempt to mitigate some of the costs associated with providing liquidity through cash and cash-equivalent holdings. Chernenko and Sunderam (2015) show that cash and cash-equivalent holdings play a key role in maintaining liquidity for shareholders. Fund managers could also attempt to mitigate some of the costs through the use of redemption fees. Greene, Hodges, and Rakowski (2007) find that redemption fees reduce the volatility of daily fund flows, presumably by limiting the trading activity of short-term investors. (4)

Given that liquidity costs are a general concern for fund managers, a natural question is whether such costs vary between funds and whether certain fund characteristics systematically drive that variation. Hodrick and Moulton (2009) model the extent to which a manager's portfolio creates liquidity considerations along three dimensions: pricing, timing, and quantity. Pricing is the manager's ability to transact near the fair-value price. Timing is the ability of the manager to wait to transact at the fair-value price. Quantity is the manager's ability to transact using orders of desired sizes. Because all mutual funds offer daily liquidity, the timing dimension is limited for all mutual fund managers, and the model predicts additional shadow costs because of that timing restriction.

However, the shadow costs resulting from the pricing and quantity dimensions should vary between mutual funds. With respect to the pricing dimension, different funds face different levels of uncertainty about execution price. Funds with investment styles that require holding equities that are difficult to trade at the fair-value price could incur greater costs when managing redemption and purchase requests. Part of that transaction difficulty arises from price impact, which is a key part of liquidity and varies significantly between equities (Amihud, 2002; Goyenko, Holden, and Trzcinka, 2009). Another part of that difficulty comes from heterogeneity in bid-ask spreads due to several factors (Easley, Hvidkjaer, and O'Hara, 2002). With respect to the quantity dimension, Keim and Madhavan (1997) show that transaction costs for institutional traders increase with trade size, so funds with characteristics that are likely to increase the size of individual transactions (e.g., relatively large amounts of assets or relatively concentrated equity positions) could incur greater costs to meet a redemption. Sapp and Yan (2008) attribute part of the relative underperformance of concentrated mutual funds to liquidity problems associated with holding a small number of equities.

Our study contributes to the above literature in three ways. First, we provide an estimate of average liquidity costs for US equity mutual funds operating in the lower cost environment described by Hasbrouck (2009). More importantly, we consider cross-sectional differences in liquidity costs driven by the quantity and pricing dimensions of Hodrick and Moulton (2009). For the pricing dimension, we consider the liquidity of a fund's equity positions, specifically focusing on the Amihud (2002) liquidity and the average bid-ask spread. For the quantity dimension, we consider the impact of a fund's total net assets and the concentration of a fund's equity portfolio. Finally, we provide an estimate of average liquidity costs for US bond mutual funds, which has not been documented in any prior work.

II. Data

We build our sample of US equity mutual funds using the Center for Research in Security Prices (CRSP) Survivor-Bias-Free Mutual Fund Database. Only funds with a traditional US equity style, at least 80% of their portfolio invested in equities, and more than $20 million in assets are included in the sample. (5) Any fund that CRSP identifies as an index fund is removed from the sample, and we also search fund names for key terms to further remove index funds and any fund not following a traditional US equity strategy. (6) We collapse multiple share classes of a fund into a single fund. To mitigate the incubation bias discussed in Evans (2010), we exclude a fund from the sample until its oldest share class is at least two years old. In our analysis of cross-sectional differences in liquidity costs, we use measures of average equity liquidity and equity portfolio concentration derived from the Thomson Reuters Mutual Fund Holdings Database. Those measures are merged to our CRSP sample using MFLINKS. We do not require these data for a fund to be part of the final sample, but it is available for 88% of our observations.

To obtain the data on gross mutual fund flows and fund trading activity necessary to estimate liquidity costs, we use Form N-SAR filings from the Securities and Exchange Commission's Edgar Web site. We first match those filings to our CRSP sample algorifhmically using fund names and assets. We then manually confirm and expand that match. More than 95% of the initial CRSP sample is matched to the Form N-SAR filings. The portion of the CRSP sample not matched is excluded from the final sample because the N-SAR data are essential. Our final sample has 125,034 fund-month observations across 2,124 unique funds over the period 1997-2009.

We present a brief overview of our sample in Table I. The average mutual fund manages about $1.7 billion in assets, although the median fund manages only $288 million. Consistent with prior studies, the average Carhart (1997) alpha is small and negative (-0.02% per month). (7) Looking at trading activity, the average fund makes annual purchases worth 143% of assets and annual sales worth 145% of assets. The average gross inflow is 3.0% per month while the average gross outflow is 3.1% per month, implying that the average fund experiences a small net outflow during our sample period. (8)

III. The Average Cost of Providing Liquidity

Edelen (1999, p. 441) examines the relation between monthly returns and gross flows and finds "a statistically and economically significant relation between a mutual fund's risk-adjusted return and its measured volume of liquidity-motivated trading." He measures the cost of providing liquidity in two steps. In the first step, he estimates the amount of trading generated by gross flows. Inflows and outflows can offset and do not necessarily lead to transactions. He estimates that about $0.70 of every dollar in gross flows generates a liquidity-motivated transaction. In the second step, he estimates the effect of liquidity-motivated trading on risk-adjusted returns. His final estimation of average costs ranges from $0,017 to $0,022 for every dollar in liquidity-motivated trading. In this section, we describe and implement the estimation procedure of Edelen (1999) to evaluate the cost of providing liquidity using our sample.

A. Modeling the Average Cost of Providing Liquidity

We briefly explain how we estimate liquidity costs below. Our procedure follows Edelen (1999), so we refer readers to that study for a detailed description of the model and its assumptions. We use Equation (2) from Edelen (1999) as our base model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

where A[R.sub.j,t] is the abnormal return for mutual fund j in month t, [??] is the liquidity-motivated trading for fund j in month t, and [??] is the discretionary trading for fund j in month t. We estimate the abnormal return for fund j in month t as the alpha from a Carhart (1997) four-factor regression on fund j's full sample of net monthly returns plus month t's residual. Liquidity-motivated trading ([??]) is defined as c([Inflow.sub.j,t] + [Outflow.sub.j,t]), in which c is the estimate of the percentage of gross flows that generate a transaction (i.e., the trade-to-flow ratio). Discretionary trading ([??]) is defined as the sum of purchases and sales less liquidity-motivated trading ([??]).

There are two significant obstacles in estimating this model. First, it requires an estimate for the trade-to-flow ratio. Edelen (1999) estimates that c = 0.7 by modeling purchases and sales as a function of inflows and outflows in several specifications. However, Dubofsky (2010) and our own untabulated results both suggest a wide range of possible values for c. Given those results, we use c = 0.7 in our base specification to be consistent with Edelen, but we also present our initial results using alternative values of c to illustrate the functional impact of this assumption.

The second obstacle arises from the endogeneity of flows and returns. A mutual fund's return in the first half of the month can influence the flows in the second half of the month, so regressing month t returns on month t flows produces biased estimates. An instrument for flows is introduced to correct this bias. In particular, we construct a lagged flow instrument by first estimating Equation (3) from Edelen (1999) each month:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

We then use [??] as our instrument for flows in our calculation of the amount of liquidity-motivated trading, where b is the average [b.sub.t] across the full time period estimated with total gross flows.

B. Estimating the Average Cost of Providing Liquidity

We estimate Equation (1) using a Fama-MacBeth regression and present the results in Table II. For convenience, we label the coefficient [lambda] as "Liquidity trading" and the coefficient [delta] as "Discretionary trading." We suppress the coefficients associated with the lagged measures of abnormal return and annualize all the data to ease interpretation. Our base specification in Panel A assumes that 70% of gross flows generate trades (c = 0.7) but also presents estimates using alternative values (c = 1.0, 0.4, and 0.1) to demonstrate the impact of this assumption.

We find that liquidity-motivated trades have a statistically significant, negative impact on mutual fund returns. With c equal to 0.7, one dollar in liquidity-motivated trading will cost the average fund about $0.006 (t-stat = -2.46). Notably, this estimate is significantly smaller than the lowest estimate of $0.017 from the Edelen (1999) sample period. Alternative values of c produce significant variation in cost, from a low of $0.005 for c = 1 to a high of $0.048 for c = 0.1. However, unless the average liquidity-motivated trade forces funds to transact at very disadvantageous terms, the highest estimate is unlikely given that Edelen, Evans, and Kadlec (2007) estimate total fund transaction costs are approximately equal to the fund expense ratio (around 1%). The practical maximum is more likely the $0.011 observed when c = 0.4.

The above results suggest that the cost of liquidity-motivated trading has decreased since the late 1980s, but we also find the cost of liquidity-motivated trading varies during our time period. Panel B estimates the model using c equal to 0.7 during five distinct time periods (1997-1998, 1999-2001, 2002-2004, 2005-2007, and 2008-2009). The average cost of liquidity-motivated trading is not statistically different from zero in three of the five time periods, but the cost is statistically significant and economically large during two turbulent market periods (2002-2004 and 2008-2009). One dollar in liquidity-motivated trading during the period that includes the financial crisis costs the average mutual fund about $0.009, which is 50% greater than the average cost in the full sample.

While our estimate of the cost per dollar of liquidity-motivated trading is significantly less than previous estimates using older data, we note that the total cost depends on both the cost per dollar and the quantity of dollars traded. Edelen (1999) reports average gross flows (inflows plus outflows) of 113% of assets per year. Assuming that c is equal to 0.7, liquidity-motivated trades would then average 79% of assets per year in the late 1980s. Our sample has an average gross flow of about 73% of assets per year, which suggests that liquidity-motivated trades average only 51% of assets during our time period of study. Hence, the total cost of liquidity-motivated trading for the average mutual fund has decreased since the 1980s because of both a lower cost per dollar and a lower quantity of dollars traded as a percentage of assets.

IV. Cross-Sectional Differences in the Cost of Providing Liquidity

The results in Section III show the average cost for US equity mutual funds to provide liquidity to investors. In this section, we explore cross-sectional variation between equity funds in the cost of providing liquidity using differences in fund characteristics. Hodrick and Moulton (2009) suggest that a portfolio manager's concern about liquidity costs will depend on portfolio characteristics that affect three dimensions of liquidity: pricing, timing, and quantity. As discussed in Section I, all funds in our sample face the same timing constraint, so we focus on fund characteristics affecting the quantity and pricing dimensions. For pricing, we consider the liquidity of the equities held by the fund. For quantity, we consider the concentration of the fund's equity portfolio and the total net assets managed by the fund.

We test the impact of each characteristic on the cost of providing liquidity by introducing a dummy variable into Equation (1). The dummy variable takes on a value of one if a specified condition is met, else zero. We interact this dummy variable with all right-hand-side variables in the original model. Specifically, we estimate:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where D[V.sub.j,t] is the dummy variable for mutual fund j in month t. In this model, [[lambda].sub.2] represents the incremental increase in the cost of liquidity-motivated trading for a fund that meets the condition specified by the dummy variable.

A. Liquidity of the Equities Held by the Fund

The first characteristic we consider is the liquidity of the equities in a mutual fund's portfolio. Funds that invest in relatively illiquid equities (e.g., lightly traded, small companies) should face higher transaction costs to buy or sell a given amount of assets compared to funds that invest in relatively liquid equities (e.g., S&P 500 components). Therefore, holding all else equal, a fund holding relatively illiquid equities should incur a greater cost to provide liquidity to investors.

We construct two measures of portfolio liquidity using position-level data on mutual fund equity holdings. Both measures are designed to capture the cost of buying or selling one dollar of a cross-section of a fund's equity portfolio. The first measure is the position-size weighted average Amihud (2002) liquidity of the equity positions, and the second measure is the positionsize weighted average bid-ask spread of the equity positions. There is significant variation in both fund-level measures with, for example, the average bid-ask spread being 0.38% and the standard deviation of bid-ask spreads being 0.40%.

We test the impact of equity liquidity on fund liquidity costs by setting the dummy variable in Equation (3) equal to one if the equity liquidity measure for a given mutual fund is among the lowest 20% (most illiquid) at the beginning of a month. Results from that model are presented in Table III. We present the base coefficients and the interaction coefficients side-by-side to ease comparison. For the funds that hold relatively liquid equities, the average cost of providing liquidity is economically and statistically zero. In comparison, using the Amihud (2002) liquidity measure, funds that hold relatively illiquid equities incur an average cost of about $0.014 ( = -0.0129 + -0.0015) per dollar of liquidity-motivated trading. The estimate is even larger using the bid-ask spread measure ($0.019 = -0.0177 + -0.0008). These results suggest that while the average cost of providing liquidity is very small for most funds, such costs can be large for funds that invest in relatively illiquid equities.

B. Concentration of a Fund's Equity Portfolio

The second characteristic we consider is equity portfolio concentration. Mutual funds with relatively concentrated equity portfolios have less opportunity to spread liquidity-motivated trades over many equities compared to funds with relatively diversified equity portfolios. Keim and Madhavan (1997) show that transaction costs for institutional traders increase with trade size, so holding all else equal, a fund with a relatively concentrated equity portfolio should incur a greater cost to provide liquidity to investors. We construct two measures of equity portfolio concentration using position-level data on fund equity holdings. The first measure is the Herfindahl-Hirschman index (HHI) of the weights on the equity positions, and the second measure is the total weight given to the ten largest equity positions in the portfolio. There is significant variation in both measures of concentration. For example, the average total weight given to the ten largest equity positions is 31% and the standard deviation is 13%.

While equity portfolio concentration relates to the overall liquidity of a mutual fund's portfolio, it differs from the average liquidity of the equities held by the fund because it acknowledges nonlinearity in transaction costs. For example, two funds of the same size could hold equities with the same average Amihud (2002) liquidity. However, if one of those funds holds significantly fewer positions than the other, then we would expect the relatively concentrated fund to have greater liquidity costs because it will have to make larger, and hence more expensive on a per-dollar basis, trades to generate the same amount of cash as the relatively diversified fund.

We test the impact of equity portfolio concentration by setting the dummy variable in Equation (3) equal to one if a given mutual fund's equity portfolio concentration is among the highest 20% (most concentrated) at the beginning of a month. Results from that model are presented in Table IV. For funds with relatively diversified portfolios, the average cost of providing liquidity is economically smaller than the full sample average and not statistically different from zero. In comparison, the average cost of providing liquidity for funds with relatively concentrated equity portfolios ranges from $0.013 to $0.015 per dollar of liquidity-motivated trading. Like the equity liquidity results above, the average cost of providing liquidity appears to be small for most funds but substantial for funds with relatively concentrated equity portfolios.

C. Total Net Assets

The last characteristic we consider is total net assets managed by the mutual fund. Chen et al. (2004) find that fund performance decreases as fund size increases and attribute that result to diseconomies of scale. While the diseconomies could come in many forms, the cost of providing liquidity could be one channel through which performance is negatively affected. Larger funds receive larger flows, which leads them to execute larger transactions. As discussed before, transactions costs for institutional traders increase with trade size, so holding all else equal, we expect the cost of providing liquidity will be greater for funds that manage more assets. For example, converting 1% of an equity portfolio into cash requires $1 million in transactions for a $100 million equity portfolio but $10 million in transactions for a $1 billion equity portfolio.

Even if both portfolios have equal measures of equity liquidity and concentration, the larger portfolio will face greater liquidity costs than the smaller portfolio because it will have to make larger, more expensive per-dollar trades to generate the cash.

We test the impact of total net assets by setting the dummy variable in Equation (3) equal to one if a given mutual fund is among the largest 20% at the beginning of a month. Results from the model are presented in Table V. For relatively large funds, the average cost of providing liquidity is $0.016 (= -0.0108 + -0.0055) per dollar of liquidity-motivated trading. In comparison, the average cost of providing liquidity is only $0.0055 for relatively small funds. These results suggest that the cost of providing liquidity is nontrivial regardless of the total net assets of the fund, but that significant diseconomies of scale in providing liquidity do exist for the largest funds.

V. The Average Cost of Providing Liquidity for US Bond Mutual Funds

US bond mutual funds offer the same daily liquidity as US equity funds but make their primary investments in assets with lower liquidity. Given that fact alone, we would expect bond funds to have a greater average cost of providing liquidity to investors compared to equity funds. However, the managers of bond funds are aware of the relative illiquidity of their primary investments and could take additional measures to manage their liquidity costs. For example, Chernenko and Sunderam (2015) show that bond funds hold greater amounts of combined cash and cash-equivalent assets compared to equity funds. While such measures could have an indirect liquidity cost, they could also mitigate a potential difference in the impact of actual redemptions and purchases. In this section, we complement our earlier analysis of the average liquidity costs of US equity funds by extending our analysis to the average liquidity costs of US bond funds.

To construct our sample of US bond mutual funds, we start with all funds that CRSP identifies as actively managed and following a municipal, high-yield, corporate, federal, or general bond style. We apply the same age and size constraints as in our US equity fund sample, and we exclude any fund that invests more than 20% of their assets in equities or more than 20% of their assets in cash and cash equivalents. This sample of funds is then algorithmically matched to N-SAR filings using fund names and assets. Our final sample of bond funds has 38,478 fund-month observations across 525 unique funds and covers the same time period as our equity fund analysis, 1997-2009.

We present a brief overview of this sample in Table VI. The average bond mutual fund manages about $790 million in assets, which is significantly smaller in size than the average equity fund ($1.7 billion). However, the median bond fund manages about $204 million, which is comparable to the median equity fund ($288 million). Alpha for bond funds is estimated using the five-factor bond model developed in Fama and French (1993) and is economically small at 0.06% per month. (9) Average purchases, sales, gross inflows, and gross outflows for bond funds are similar in magnitude to those of equity funds.

We estimate liquidity costs for our sample of bond mutual funds following the same Edelen (1999) procedure discussed in Section III.A. Because bond funds might not trade in response to flows at the same rate as equity funds, we estimate a new value for c for this sample. Using several different specifications like those in Edelen (1999), we find values for c ranging from 0.3 to 0.5, so we adopt 0.4 as our assumption for bond funds. We then estimate Equation (1) using the instrumented flows derived from a new estimation of Equation (2). We present results from this model in Table VII.

The cost of providing liquidity for US bond mutual funds is similar to the cost for equity funds. One dollar in liquidity-motivated trading creates $0.004 in costs for bond funds, compared to $0.006 for equity funds. In untabulated tests, we find that those costs are statistically indistinguishable at any typical confidence level. However, the cost of providing liquidity for bond funds is economically small for the majority of our sample period. Liquidity costs first become economically large in 2002-2004 with one dollar in liquidity-motivated trading creating an average cost of $0.003. Then during the period that contains the financial crisis, 2008-2009, the average cost associated with one dollar in liquidity-motivated trading increases to $0.022, which is several times the full sample average. During that same period, the average cost of one dollar of liquidity-motivated trading for equity funds is $0.009.

VI. Conclusions

An attractive feature of mutual funds is the offer of daily liquidity. However, this benefit is not without cost. Using a sample of US equity funds covering 1997-2009, we estimate one dollar in liquidity trading generates an average cost to the fund of about $0.006. This estimate is significantly lower than the costs Edelen (1999) observes for the late 1980s using similar methods, but it remains economically meaningful. When we extend the same analysis to US bond funds, we find an average cost of similar magnitude. For both groups of funds, the average cost varies over time with costs being particularly high during the financial crisis.

While the average liquidity cost estimates are informative, we show that cross-sectional differences in the characteristics of US equity mutual funds have a significant impact on the cost of providing liquidity. On the one hand, funds that hold relatively illiquid equities, funds with relatively concentrated equity portfolios, and funds that manage relatively large amounts of assets experience liquidity costs that are considerably greater than the full sample average. On the other hand, funds that hold relatively liquid equities and funds with relatively diversified equity portfolios experience liquidity costs that are economically small and statistically indistinguishable from zero. Taken as a whole, these results suggest that high average liquidity costs are confined to funds with specific characteristics and that the majority of funds have relatively low average liquidity costs.

While we show the average direct cost of providing liquidity for mutual funds has decreased since the late 1980s and that costs are low for many funds, we do not argue that the cost of providing liquidity is a decreasing concern. There remain indirect costs of providing liquidity, which are not captured in our analysis. Among other studies, Chen et al. (2010) and Goldstein et al. (2015) demonstrate that providing liquidity can create financial fragility; Hanouna et al. (2015) find providing liquidity can negatively impact the liquidity of a fund's portfolio; and Chernenko and Sunderam (2015) show that funds maintain large cash and cash-equivalent holdings to help mitigate the cost of providing liquidity, despite the drag it creates on fund performance. Hence, while the direct costs of providing liquidity often appear low, we cannot rule out that funds continue to incur significant indirect costs.

Further, our analysis focuses on per-dollar liquidity costs and treats every dollar equally, but the costs associated with a given flow could vary depending on the predictability of that flow from the fund's perspective. All else being equal, the cost of a large expected redemption request should be less than the cost of a large unexpected redemption request of the same size. However, the managers of mutual funds with highly volatile flows could take measures to manage that potential greater cost. For example, Hanouna et al. (2015) show that funds with more volatile flows hold more cash and portfolios that are more liquid. Both of those measures could have indirect liquidity costs but should also mitigate, at least in part, the greater direct liquidity costs associated with more volatile flows. Therefore, it is unclear whether funds with more volatile flows should be expected to incur significantly greater liquidity costs as defined in the Edelen (1999) model. We leave the analysis of the relation between flow volatility and such liquidity costs to future work.

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Jon A. Fulkerson and Timothy B. Riley (*)

Part of this research was funded by a grant from the Sellinger Fund for Excellence. We thank Brad Jordan, Tuugi Chuluun, Sergey Chernenko, participants at the 2014 Southern Finance Association Annual Meeting and the 2015 Eastern Finance Association Annual Meeting, members of the Analytical Research in Investments Group at the Securities and Exchange Commission, an anonymous reviewer, and Marc Lipson (Editor), for their helpful comments and suggestions. All errors are our own.

(*) Jon A. Fulkerson is an Associate Professor of Finance in the Sellinger School of Business & Management at Loyola University Maryland in Baltimore, MD. Timothy B. Riley is an Assistant Professor of Finance in the Sam M. Walton College of Business at the University of Arkansas in Fayetteville, AR.

(1) The nonequity holdings of an actively managed US equity mutual fund may, in part, represent an opportunity cost driven by the need to provide daily liquidity to investors.

(2) Examples of early work in off-exchange liquidity includes Bessembinder (2003) and Barclay, Hendershott, and Mc-Cormick (2003). The recent literature focuses on dark pools. Topics include the impact on price discovery and quality (e.g., Zhu, 2014; Comerton-Forde and Putnins, 2015), exchange fragmentation and information linkages (e.g., Nimalendran and Ray, 2014; Kwan, Masulis, and McInish, 2015), and trade quality (e.g., Buti, Rindi, and Werner, 2015). In a comparison of dark and lit trading, Garvey, Huang, and Wu (2016) find that dark orders tend to have lower spreads and receive better prices relative to lit orders but are executed slower and with a lower fill rate.

(3) While average costs have decreased, Lesmond, Ogden, and Trzcinka (1999) and Hasbrouck (2009) both find significant cross-sectional variation in costs depending on equity characteristics.

(4) The US Securities and Exchange Commission adopted a rule in 2005 that allowed funds to use redemption fees to help recover some of the costs incurred as a result of short-term trading. The higher liquidity costs estimates in Edelen's ( 1999) sample may be due, in part, to greater use of short-term trading designed to exploit NAV predictability during that time period.

(5) Once a mutual fund reaches 80% equity and $20 million in assets, it remains in the sample even if it falls below those benchmarks. Equity allocation data are missing in CRSP for some parts of 1999-2002. We first front-fill missing allocation data using the last known allocation, and if a fund still has missing allocation data, we back-fill using the closest future allocation.

(6) The list of key terms we use in the mutual fund name search is available upon request.

(7) The Carhart (1997) model is the Fama and French (1993) three-factor model, which includes pricing factors related to size and value, augmented with a momentum pricing factor motivated by Jegadeesh and Titman (1993).

(8) The exclusion of the first two years of a mutual fund's history biases the average net flow downward. New funds often grow very rapidly (Evans, 2010).

(9) The Fama-French bond model adds two additional factors to the Fama-French three-factor equity model. The first additional factor captures the slope of the treasury yield curve, and the second additional factor captures the difference in return between long-term corporate bonds and long-term treasuries.

Table I. Characteristics of US Equity Mutual Funds This table presents summary statistics for our sample of US equity mutual funds. TNA is the total net assets reported in millions of dollars. Alpha is the monthly Carhart (1997) four-factor alpha reported as a percentage. Purchases and Sales are the annualized gross purchases and sales from the most recently available N-SAR filing. Both are measured over the six months prior to the filing and are scaled by TNA at the beginning of the reporting period. Inflow and Outflow are gross monthly inflows and outflows scaled by TNA at the beginning of the month. The sample covers 125,034 fund-months across 2,124 unique funds during the period 1997-2009. Variables Mean SD 25th Percentile TNA (millions of dollars) 1,655 6,154 96 Alpha (%) -0.02 0.25 -0.15 Purchases (% of TNA) 143 129 56 Sales (% of TNA) 145 137 53 Inflow (% of TNA) 2.99 4.48 0.78 Outflow (% of TNA) 3.11 4.10 1.33 Variables 50th Percentile 75th Percentile TNA (millions of dollars) 288 961 Alpha (%) -0.03 0.10 Purchases (% of TNA) 106 189 Sales (% of TNA) 103 190 Inflow (% of TNA) 1.66 3.47 Outflow (% of TNA) 2.15 3.47 Table II. Estimating Average Liquidity Costs for US Equity Mutual Funds This table presents results from estimating Equation (1): [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where A[R.sub.j,t] is the abnormal return for mutual fund j in month t, [??] is the liquidity-motivated trading for fund j in month t, and [??] is the discretionary trading for fundy in month t. We estimate the abnormal return using the Carhart (1997) four-factor model. For convenience, we label [lambda] as "Liquidity trading" and [delta] as "Discretionary trading" in the table. In Panel A, we assume a trade-to-flow ratio of 70% (c = 0.7) as our base specification but also consider alternative values of 100%, 40%, and 10% (c = 1, 0.4, or 0.1). Panel B assumes a trade-to-flow ratio of 70% (c = 0.7) and estimates the model during five distinct time periods. The coefficients are estimated using a monthly Fama-MacBeth regression. The t-statistics are derived from Newey-West standard errors with three lags and are presented in brackets below their respective coefficients. Panel A. Full Sample Variables c = 0.7 c=1.0 Liquidity trading -0.0059 (**) -0.0038 (**) [-2.46] [-2.17] Discretionary trading 0.0011 0.0011 [1.54] [1.54] Observations 125,034 125,034 [R.sup.2] 0.354 0.354 Variables c = 0.4 c=0.1 Liquidity trading -0.0112 (***) -0.0479 (***) [-2.73] [-2.97] Discretionary trading 0.0011 0.0011 [1.54] [1.54] Observations 125,034 125,034 [R.sup.2] 0.354 0.354 Panel B. Subperiods (c = 0.7) Variables 1997-1998 1999-2001 2002-2004 Liquidity trading -0.0037 -0.0038 -0.0112 (**) [-0.55] [-0.52] [-2.66] Discretionary trading 0.0040 (*) 0.0028 -0.0005 [1.89] [1.51] [-0.61] Observations 11,174 19,571 29,945 [R.sup.2] 0.383 0.313 0.331 Variables 2005-2007 2008-2009 Liquidity trading -0.0025 -0.0085 (**) [-1.15] [-2.34] Discretionary trading 0.0005 -0.0013 [0.75] [-0.94] Observations 39,198 25,146 [R.sup.2] 0.357 0.415 (***) Significant at the 0.01 level. (**) Significant at the 0.05 level. (*) Significant at the 0.10 level. Table III. How Does the Liquidity of a Mutual Fund's Equities Affect Liquidity Costs? This table presents results from estimating Equation (3): [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where D[V.sub.j,t] is the dummy variable for mutual fund j in month t and the remaining variables are as defined in Table II. The dummy variable takes on a value of one if fund j's average equity liquidity is among the lowest 20% in the sample at the beginning of month t, else zero. We test two different measures of liquidity. The first measure is the position-size weighted average Amihud (2002) liquidity of a fund's equity positions, and the second measure is the position-size weighted average bid-ask spread of a fund's equity positions. This estimation uses the subsample of funds for which we have Thomson Reuters and MFLINKS data and assumes a trade-to-flow ratio of 70% (c = 0.7). The base coefficients are reported in the Base columns, and the interaction coefficients are reported in the Interaction columns. The r-statistics are derived from Newey-West standard errors with three lags and are presented in brackets below their respective coefficients. Amihud Liquidity Variables Base Interaction Illiquid dummy 0.0013 [0.16] Liquidity trading -0.0015 -0.0129 (***) [-0.56] [-3.49] Discretionary trading 0.0008 0.0005 [1.19] [0.56] Observations 109,782 [R.sup.2] 0.392 Bid-Ask Spread Variables Base Interaction Illiquid dummy 0.0050 [0.68] Liquidity trading -0.0008 -0.0177 (***) [-0.29] [-4.13] Discretionary trading 0.0009 0.0003 [1.21] [0.26] Observations 109,782 [R.sup.2] 0.393 (***) Significant at the 0.01 level. Table IV. How Does the Concentration of a Mutual Fund's Portfolio Affect Liquidity Costs? This table presents results from estimating Equation (3): [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where D[V.sub.j,t] is the dummy variable for mutual fund j in month t and the remaining variables are as defined in Table II. The dummy variable takes on a value of one if fund j's equity portfolio concentration is among the highest 20% in the sample at the beginning of month t, else zero. We test two different measures of concentration. The first measure is the Herfindahl-Hirschman index (HHI) of the equity portfolio weights, and the second measure is the total weight given to the ten largest equity positions. This estimation uses the subsample of funds for which we have Thomson Reuters and MFLINKS data and assumes a trade-to-flow ratio of 70% (c = 0.7). The base coefficients are reported in the Base columns, and the interaction coefficients are reported in the Interaction columns. The t-statistics are derived from Newey-West standard errors with three lags and are presented in brackets below their respective coefficients. HHI Variables Base Interaction Concentrated dummy 0.0147 (***) [3.09] Liquidity trading -0.0027 -0.0101 (*) [-1.22] [-1.81] Discretionary trading 0.0011 (*) -0.0013 [1.81] [-1.06] Observations 109,782 [R.sup.2] 0.392 Top Ten Weight Variables Base Interaction Concentrated dummy 0.0177 (**) [2.46] Liquidity trading -0.0035 -0.0117 (*) [-1.49] [-1.76] Discretionary trading 0.0011 -0.0020 [1.60] [-0.98] Observations 109,782 [R.sup.2] 0.396 (***) Significant at the 0.01 level. (**) Significant at the 0.05 level. (*) Significant at the 0.10 level. Table V. How Do the Total Net Assets of a Mutual Fund Affect Liquidity Costs? This table presents results from estimating Equation (3): [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where D[V.sub.j,t] is the dummy variable for mutual fund j in month t and the remaining variables are as defined in Table II. The dummy variable takes on a value of one if fund j is among largest 20% of funds in the sample by total net assets at the beginning of month t, else zero. This estimation assumes a trade-to-flow ratio of 70% (c = 0.7). The base coefficients are reported in the Base columns, and the interaction coefficients are reported in the Interaction columns. The t-statistics are derived from Newey-West standard errors with three lags and are presented in brackets below their respective coefficients. Variables Base Interaction Large size dummy 0.0052 [1.60] Liquidity trading -0.0055 (**) -0.0108 (*) [-2.23] [-1.780] Discretionary trading 0.0012 (*) -0.0022 (**) [1.76] [-2.15] Observations 125,034 [R.sup.2] 0.378 (**) Significant at the 0.05 level. (*) Significant at the 0.10 level. Table VI. Characteristics of US Bond Mutual Funds This table presents summary statistics for our sample of US bond mutual funds. TNA is the total net assets reported in millions of dollars. Alpha is the monthly Fama-French (1993) five-factor bond model alpha reported as a percentage. Purchases and Sales are the annualized gross purchases and sales from the most recently available N-SAR filing. Both are measured over the six months prior to the filing and are scaled by TNA at the beginning of the reporting period. Inflow and Outflow are gross monthly inflows and outflows scaled by TNA at the beginning of the month. The sample covers 38,478 fund-months across 525 unique funds during the period 1997-2009. Variables Mean SD 25th Percentile TNA (millions of dollars) 790 2,067 81 Alpha (%) 0.06 0.15 0.03 Purchases (% of TNA) 141 128 58 Sales (% of TNA) 133 129 51 Inflow (% of TNA) 3.67 4.56 1.22 Outflow (% of TNA) 3.51 3.12 1.57 Variables 50th Percentile 75th Percentile TNA (millions of dollars) 204 627 Alpha (%) 0.08 0.13 Purchases (% of TNA) 106 182 Sales (% of TNA) 95 168 Inflow (% of TNA) 2.42 4.49 Outflow (% of TNA) 2.52 4.12 Table VII. Estimating Average Liquidity Costs for US Bond Mutual Funds This table presents results from estimating Equation (1): [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where A[R.sub.j,t] is the abnormal return for mutual fund j in month t, [??] is the liquidity-motivated trading for fund j in month t, and [??] is the discretionary trading for fund j in month t. In this instance, we estimate the model using a sample of US bond mutual funds. The abnormal return for fund j in month t is estimated using the Fama-French (1993) five-factor bond model. For convenience, we label [lambda] as "Liquidity trading" and [delta] as "Discretionary trading" in the table. This estimation assumes a trade-to-flow ratio of 40% (c = 0.4). The "Full sample" column estimates the model over the full time period, 1997-2009. The remaining columns estimate the model for five distinct time periods. The coefficients are estimated using a monthly Fama-MacBeth regression. The t-statistics are derived from Newey-West standard errors with three lags and are presented in brackets below their respective coefficients. Variables Full Sample 1997-1998 1999-2001 Liquidity trading -0.0043 (*) 0.0005 0.0006 [-1.87] [0.16] [0.29] Discretionary trading 0.0003 (*) 0.0002 0.0003 [1.73] [0.60] [1.04] Observations 38,478 4,139 8,766 [R.sup.2] 0.599 0.641 0.598 Variables 2002-2004 2005-2007 2008-2009 Liquidity trading -0.0030 -0.0024 -0.0215 (**) [-0.80] [-0.53] [-2.67] Discretionary trading 0.0000 -0.0000 0.0012 (*) [0.05] [-0.09] [1.72] Observations 10,066 9,807 5,700 [R.sup.2] 0.587 0.616 0.551 (**) Significant at the 0.05 level. (*) Significant at the 0.10 level.

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Author: | Fulkerson, Jon A.; Riley, Timothy B. |
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Publication: | Financial Management |

Date: | Jun 22, 2017 |

Words: | 9381 |

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