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138 AN ANALYSIS OF THE EXPENSE RATIO PRICING OF SMB, HML, AND UMD EXPOSURE IN U.S. EQUITY MUTUAL FUNDS FALL 2016

SEAN GROVER

is an investment strategist at Buckingham Asset Management, LLC, in St. Louis, [email protected]

JARED KIZER

is the chief investment officer at Buckingham Asset Management, LLC, in St. Louis, [email protected]

An Analysis of the Expense Ratio Pricing of SMB, HML, and UMD Exposure in U.S. Equity Mutual FundsSEAN GROVER AND JARED KIZER

The expense ratio price of U.S. market equity exposure is near zero. Vanguard U.S. Total Stock Market Index Fund (ticker:

VTSAX) charges an expense ratio of just 5 basis points (bps). The Fama–French [1993] three- and the Carhart [1997] four-factor model regression coefficient estimates for the fund are nearly 1.00 on equity market beta and zero on all other factors; thus, the Van-guard fund’s expense ratio is a pure measure of the price of U.S. equity market beta in the U.S. mutual fund marketplace.

Apart from market equity (MKT), the expense ratio price of exposure to other factors like size (SMB), value (HML), and momentum (UMD) is less clear, despite the multidecade explosion in the number of mutual funds and exchange-traded funds (ETFs) explicitly seeking to provide exposure to these and other factors ( Jegadeesh and Titman [1993]). One source of confusion is that funds with similar titles, such as “small-cap,” can provide materi-ally different factor exposure; consequently, it is difficult to compare expense ratios between funds. Understanding the relative pricing of funds requires a quantitative assessment of each fund’s expense ratio relative to the factor exposures that it provides.

In our literature review process, we were not able to identify any published research that has quantified the portion of mutual fund and ETF expense ratios that can be attributed to

factor exposures like SMB, HML, and UMD. Existing expense ratio literature typically examines a connection between expense ratio and fund performance (Garyn-Tal [2013]). We think the expense ratio price of factor exposure is an intriguing topic to explore, given the quantity of empirical research dedi-cated to the exploration of the SMB, HML, and UMD premiums in U.S., international, and emerging markets, and the large number of funds seeking to capture these return pre-miums. Thus, our study provides an impor-tant link between the academic research and the implementation at the practitioner level.

Assuming that positive exposures to factors will provide excess return, improved portfolio eff iciency, or both, on a forward-looking basis, one might expect an attribution of general fund expense ratios to show the following ordering from the least expensive to the most expensive sources of return:

1. General equity market exposure; expo-sure to MKT

2. Exposure to relatively seasoned factors like SMB, HML, and UMD

3. Exposure to newer factors like profit-ability and investment (Fama and French [2015]; Hou, Xue, and Zhang [2015])

4. Pure alpha.

From a practitioner’s standpoint, cate-gory 1 refers to the broadest and most easily

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THE JOURNAL OF PORTFOLIO MANAGEMENT 139FALL 2016

accessible form of equity exposure, which makes it the cheapest. Category 2 refers to factor exposures that are widely known to the marketplace as a result of academic and practitioner research and that are expected to gen-erate positive, forward-looking excess returns, relative to MKT. We argue that factors in category 3 should generally be more expensive than those in category 2 (and 1) because some time may need to pass before multiple fund companies compete against each other to provide exposure to these factors with low-cost fund offerings. Factors that are not broadly known and are not explained by other factors fall into category 4. Strategies that capture such factors should command relatively high expense ratios if they can deliver long-term positive alpha. The equilibrium arguments in support of this ordering include the following:

1. Scarcity of supply relative to MKT—for example, not everyone can tilt toward small-company stocks

2. Higher level of manager expertise needed to imple-ment strategy

3. Low correlation of the strategy to MKT

For point 2, factor-oriented tilts generate higher turnover than market-cap-weighted equity exposure; consequently, investment managers implementing such strategies must have an efficient portfolio management and trading structure in place to preserve the factor premiums on a net-of-transactions costs basis (Novy-Marx and Velikov [2016]). For point 3, to the extent that the factor tilts allow investors to build more mean–variance efficient portfolios on a net-of-all-costs basis, fund investors may be willing to pay higher expense ratios compared to the cost of owning a market-cap weighted strategy.

For SMB, HML, and UMD in the U.S. equity fund marketplace, we find that investors are paying more than 5 bps for one unit of exposure, where a unit of factor exposure means a coeff icient loading equal to one in the factor model regression. For the sample of long-only U.S. equity funds with 60 months of return history ending January 2015, we find that investors are paying 11.9, 27.0, and 72.5 bps for unit exposure to SMB, HML, and UMD, respectively. All results are statistically significant.

In addition, we include two other related analyses. We examine expense ratio pricing by fund company and find that fund companies differ in how they price

the factor exposures their funds provide. We also study portfolio-level expense ratio pricing for portfolios with matching coeff icient exposures to SMB and HML. Interestingly, we find that portfolio-level expense ratios vary widely for portfolios that have had identical his-torical exposures to SMB and HML.

In the next section, we outline the data sources and methodology used to arrive at our universe of funds for the 60-month sample. The following section out-lines the methodology we used to estimate the expense ratio prices of SMB, HML, and UMD. The last section reviews our key results.

DATA SOURCES AND FUND-SELECTION METHODOLOGY

Our initial universe of mutual funds and ETFs included all U.S. equity funds managed by Blackrock iShares, Dimensional Fund Advisors (DFA), SPDR State Street Global Advisors, and Vanguard that were listed in the Morningstar Office dataset as of March 2015.1 We intentionally limited our analyses to these four fund companies because each has numerous low-cost funds designed specifically to capture the SMB and HML pre-miums. Conversely, we excluded the relatively high-cost funds that actively pursue alpha. In addition to requiring 60 months of returns history ending January 2015, we also excluded the following:

1. Funds with less than 90% of assets allocated to U.S. equities as of the most recently reported portfolio-holdings date

2. Sector-oriented funds3. Actively managed funds (which only applied to

some Vanguard funds)4. Funds with an inception date later than the begin-

ning date of our sample2

For the final universe of funds, we also obtained fund assets under management (AUM) measured by fund net assets per share class in billions of dollars and prospectus expense ratio. We also note that our datasets contain some return histories that correspond to dif-ferent share classes of the same fund. Although strategy is implemented at a fund level, expense ratio is imple-mented at a share class level. Because we wish to capture all funds that fit our parameters, we include the different share classes.


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The MKT, SMB, HML, and UMD monthly factor premiums we use in the first regression specification are the research factors per Ken French’s data library. The particular version of HML we use is formed using two-by-three sorts on market capitalization and book/price, respectively.

ANALYSIS METHODOLOGY

We attempt to explain a fund’s expense ratio with respect to the factor exposure the fund provides. If we take the estimated factor model loadings as a proxy for the true factor exposures, we can then develop a pricing model for expense ratio. This leads us to a two-stage regression procedure.

In stage one, we regress each fund’s monthly returns history less the one-month T-bill rate on two different factor model specif ications. The first factor model is the Fama–French three-factor model consisting of MKT, SMB, and HML. The second factor model is the Carhart four-factor model, which is composed of the three Fama–French factors plus a momentum factor, UMD. Parameters in both factor model specifications are estimated using ordinary least squares and include a constant (alpha) term. The regression equation associ-ated with the Fama–French three-factor model is then

− = α + β + β

+ β + ε ,

FundFF RF S+ β MBSS

HMLMM

it t iαFF iMKT

t iβ+ βSMBMt

iHMLMM

t i+ ε t (1)

and the regression equation associated with the Carhart four-factor model ref lects the addition of the UMD factor:

− = α + β + β

+ β + β + ε .

FundFF RF S+ β MBSS

HMLMM UMD

it t iαFF iMKT

t iβ+ βSMBMt

iHMLMM

t i+ βUMDMMt i+ ε t (2)

Fundit denotes the period t arithmetic return of fund i = 1, …, m; RFt denotes the period t one-month T-bill rate; β β β,βi

MKTiSMBMM

iHMLMM and βi

UMDMM denote the fund-specific loadings on MKTt, SMBt, HMLt, and UMDt of period t return premiums; and εit is a zero-mean residual. From this regression routine, we save the estimated factor loadings across all m funds for both respective factor models.

The second stage of our analysis begins by first calculating a new measure of expense ratio. We define

our measure to be a fund’s prospectus expense ratio less the expense ratio required to gain a unit of exposure to MKT scaled by the fund’s estimated MKT loading. We price a unit of exposure to MKT at 5 bps because that is the expense ratio of Vanguard Total Stock Market Index Fund, which has a factor loading of nearly one on MKT and nearly zero on all other factors. We take this as the market price of gaining one unit of MKT exposure. Thus, fund i’s expense ratio net of the cost of the MKT exposure it provides is defined as

= − × β5 ˆNetExpenseRatio

Prospes ctusExpx enseRatio bps

i

i i× β5bps MKT (3)

NetExpenseRatio is a measure of the portion of the expense ratio associated with factor attributes of the fund after accounting for MKT exposure (as well as other attributes such as a fund’s AUM). It is a measure of the expense ratio an investor is paying in excess of the cost of general equity market exposure.

We collect NetExpenseRatio for all m funds into a single-column vector to be used in cross-sectional regressions as the dependent variable. We specify the second set of regressions in an attempt to describe Net-ExpenseRatioi as a function of each fund’s factor load-ings and AUM (billions of dollars). In other words, we price the expense ratio cost associated with gaining unit exposure to the factors described in stage one (excluding MKT).3 Along with the saved matrices of regression coefficients from stage one, we also include a constant term and control for each fund’s demeaned AUM. The Fama–French three-factor and Carhart four-factor specifications from stage one lead to two cross-sectional regression specifications here, respectively:

= γ + γ β + γ β

+ γ + η

NetExpenseRatio

AUMUU

iSMBMM

iSMB H+ γM MLH

iHMLMM

AUMUUi i+ η

ˆ ˆ0

(4)

= γ + γ β + γ β

+ γ β + γ + η

NetExpenseRatio

AUMU

iSMBMM

iSMB H+ γM MLH

iHMLMM

UMDMMiUMD A+ γM UM

i i+ η

ˆ ˆ

ˆ0

(5)

where β β βˆ ˆ , ˆ ,iMKT

iSMBMM

iHMLMM and β̂i

UMDMM are fund i’s estimated factor loadings from stage one and AUMi is fund i’s net assets per share class (measured in billions of dollars) less the sample average AUM. The estimated coeff i-cients on the factor loading independent variables from


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these regressions measure the average expense ratio cost, in basis points, associated with one unit of exposure to each factor, all else equal. The parameters of these two regressions are again estimated using ordinary least squares; but because this step uses generated regressors, heteroskedasticity in ηi is a concern. With this in mind, White’s [1980] corrected standard errors are used to conduct inference. We now discuss the results of our two-stage regression procedure.

RESULTS

The estimated factor loadings from the stage one regressions generally met our expectations; “small” and “value” funds showed positive loadings on these respec-tive factors, and there was variation in the magnitude of estimated loadings between similarly named funds from different companies.4 The stage two estimates seem to show that fund companies are indeed charging a positive expense ratio price for exposure to SMB, HML, and UMD and that these prices are a significant component of the NetExpenseRatio. Panels A and B of Exhibit 1 report the results from the stage two cross-sectional regressions.

The “coefficient” row reports the estimated price in basis points of each unit of factor exposure. For example, Panel B shows estimates for an intercept price of 8.8 bps, a unit price of SMB of 11.9 bps, a unit price of HML of 27.0 bps, and a unit price of UMD of 72.5 bps. Because the sign on the AUM coefficient is negative and statistically significant in all regressions (as one would expect), it can be interpreted as the estimated reduction in net expense ratio associated with each $1 billion in fund AUM above the sample average AUM.

The estimates of γ SMB, γ HML, and γ UMD all look reasonable, on a relative basis, and are statistically significant in every case. The intercept is positive and highly significant in all cases, possibly indicating that, on average, funds are charging more than 5 bps for one unit of MKT exposure. Adjusted R2 is relatively high in each regression, 28%–34%, indicating that estimated factor loadings explain a significant portion of the variation in the NetEx penseRatio variable.

We also estimated the stage two specif ications by fund company, because it is easy to argue that fund companies price factor exposures differently. Exhibit 2 reports these results.

These estimates reveal interesting differences across the fund companies. DFA appears to strongly price SMB (33.0 bps per unit of SMB in Panel B); iShares prices SMB moderately, whereas SPDR and Vanguard do not price it at all.5 DFA, iShares, and SPDR appear to price HML—and SPDR strongly so (71.8 bps per unit). SPDR and iShares appear to price UMD, while the DFA and Vanguard estimates are not distinguishable from zero. Interestingly, DFA and SPDR do not appear to price AUM. Compare this to Vanguard for which the AUM coefficient estimate is the only statistically significant estimate and adjusted R-squared is only 8%.

We also performed a portfolio construction exer-cise to examine portfolio-level expense ratios for port-folios with matching historical factor exposure. The study identifies all two- and three-fund portfolios that consist of funds from our sample and that satisfy various factor loading specif ications (loadings on both SMB and HML of 0.1, 0.2, and 0.3, respectively). All port-folios have a MKT loading of 1 and alpha is left as a free parameter.6 The results of this exercise are shown in Exhibit 3.

We see that the mean portfolio expense ratio (where mean is the average expense ratio across all port-folios that satisfied the constraints) goes up as the port-folio tilt toward SMB and HML increases, which we expected in light of the stage two regression results. Arguably, the most interesting result is in the disper-sion of the expense ratio for portfolios with identical historical factor loading exposures—as much as 40 bps difference between the maximum and minimum in the three-fund, 0.3 loading case. These are wide ranges in expense ratio for portfolios that are providing fairly similar factor exposures. To be clear, however, we are

E X H I B I T 1Stage 2 Results


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not claiming that these portfolios are the same because we have not controlled for other factors (e.g., portfolios with identical SMB and HML exposures could have markedly different exposures to the profitability factor) or examined historical returns data across portfolios with identical SMB and HML factor loadings. We leave that to future work.

CONCLUSION

Given the growth of factor-based investment strat-egies and the concurrent multidecade growth in the availability of mutual funds and ETFs offering factor exposure, the fund pricing of these factor exposures is an interesting topic. Within the fund universe we examine, we find that fund expense ratio is strongly related to

E X H I B I T 2Stage 2 Results by Fund Family

E X H I B I T 3Portfolio Level Expense Ratios


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SMB, HML, and UMD exposures. Using 60 months of return history ending January 2015 and the Carhart four-factor model, we estimate that fund companies are charging 11.9 bps for one unit of SMB exposure, 27.0 bps for one unit of HML exposure, and 72.5 bps for one unit of UMD exposure. We find roughly similar results for SMB and HML when using the Fama–French three-factor model.

We conducted two additional studies on expense ratio pricing of factor exposure. First, we found that the expense ratio price of factor exposure appears to vary widely across the four fund companies in our sample. DFA and iShares appear to price SMB in their expense ratios. DFA, iShares, and SPDR appear to price HML in their expense ratios. And iShares and SPDR appear to price UMD in their expense ratios. There is no evi-dence that Vanguard prices any factor exposure in its fund expense ratios. Second, we found that portfolio-level expense ratios vary widely for portfolios with matching historical SMB and HML exposures. In the most extreme case—portfolios of three funds with 0.3 estimated factor loadings on both SMB and HML—we found a range of 40 bps between the expense ratios of the cheapest and the most expensive portfolios.

ENDNOTES

This analysis is for academic purposes only. The research, opinions, and data shared within this article are those of Mr. Kizer and Mr. Grover and do not directly ref lect those of Buckingham Asset Management, LLC.

1http://www.morningstar.com/.2Morningstar often provides returns for periods prior

to a fund’s inception date when the fund is a different share class of an existing fund. We wish to only include funds that have been live for our entire sample length.

3In this analysis, we used the expense ratio we observed as of March 2015 and not the actual expense ratio in effect over the period of the stage one regressions.

4We also examined longer returns histories and sub-samples within longer returns histories. We found no material differences in estimated fund factor model loadings across different samples and thus chose the 60-month sample because it provides sufficient stage one estimates while also increasing

the stage two sample size. Fund level and fund company level stage one regression results are available upon request.

5We caution that the Exhibit 2 results showing the SPDR fund family regressions rely on a small sample and appear to be driven in large part by a specific fund that sig-nificantly loads on UMD and is very expensive compared to other SPDR funds.

6A detailed description of the portfolio construction exercise is available upon request.

REFERENCES

Carhart, M. “On the Persistence in Mutual Fund Perfor-mance.” Journal of Finance, 52 (1997), pp. 57-82.

Fama, E., and K. French. “Common Risk Factors in the Returns on Bocks and Bonds.” Journal of Financial Economics, 33 (1993), pp. 2-56.

——. “A Five-Factor Asset Pricing Model.” Journal of Finan-cial Economics, 116 (2015), pp. 1-22.

Garyn-Tal, S. “Mutual Funds’ Performance, Expense Ratios, and Inf lows: Evidence and Implications for Policy.” The Journal of Index Investing, 4 (2013), pp. 12-21.

Hou, K., C. Xue, and L. Zhang. “Digesting Anomalies: An Investment Approach.” Review of Financial Studies, Vol. 28, No. 3 (2015), pp. 650-705.

Jegadeesh, N., and S. Titman. “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” Journal of Finance, 48 (1993), pp. 65-91.

Novy-Marx, R., and M. Velikov. “A Taxonomy of Anomalies and Their Trading Costs.” The Review of Financial Studies, 29 (2016), pp. 104-147.

White, H. “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heterskedasticity.” Econometrica, 48 (1980), pp. 818-838.

To order reprints of this article, please contact Dewey Palmieri at [email protected] or 212-224-3675.


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