Tradable Risk Factors for Institutional and Retail Investors

Abstract

We construct tradable risk factors using combinations of large and liquid mutual funds (long leg) and ETFs (exchange-traded funds) (long and short legs), based on their holdings, for both retail and institutional investors. Exploiting a novel dataset, our tradable factors take into account ETF shorting costs. Assessing the performance of our tradable factors against standard “on-paper” factors, we uncover an implementation shortfall of 2–4 percent annually. Shorting fees and transaction costs contribute to 58 percent of the performance differential between tradable and “on-paper” factors, assigning a non-trivial role to the opportunity cost of not trading the exact “on-paper” portfolio.

1. Introduction

Over the last decade, smart beta, also known as factor investing, has become a fundamental theme in the asset management industry. Many providers have started offering mutual funds and exchange-traded funds (ETFs) whose objective is to mimic the strategies underlying the risk-factors discovered in academic research, such as value (Fama and French 1992, 2006) or momentum (Jegadeesh and Titman 1993).

However, whether factor risk premia can be earned in practice and what kind of benchmarks retail and institutional investors should employ to evaluate the performance of portfolio managers remain open questions. An effective benchmark should offer attainable payoffs through trading, be accessible in real-time to both retail and institutional investors, and reflect the characteristics associated with the underlying risk (e.g., book-to-market for the value premium). Unfortunately, aside from the market factor, tradable benchmarks for standard risk factors are currently nonexistent.

In this article, we fill the void in the literature and propose tradable long–short risk factors to be used as benchmarks by both retail and institutional investors. Our analysis is informative about several fundamental, and yet unanswered, research questions. How can institutional and retail investors trade “on-paper” risk factors? Do these investors differ in their ability to implement factor strategies? What is the “opportunity cost”—defined as the potential benefits lost when traders alter their trading patterns to reduce transaction costs—associated with anomaly portfolios proposed in the asset pricing literature? Additionally, our tradable factor benchmarks could be used by investors to evaluate fund managers.

A few recent studies have attempted to quantify real-world implementation costs for academic “on-paper” risk factors using individual stocks. These papers use proprietary trading data to study trading costs for a single investment firm (e.g., Frazzini, Israel, and Moskowitz 2015), market-wide trading data such as NYSE Trade and Quote (TAQ) to estimate the trading costs of individual stocks selected by dynamic factor strategies (e.g., Detzel, Novy-Marx, and Velikov 2023), or directly estimate factor implementation costs based on cross-sectional Fama–MacBeth specifications augmented with mutual fund returns (Patton and Weller 2020).

We tackle the implementation of tradable risk factors using a novel and conceptually different approach. Instead of individual stocks, we use fund holdings to create portfolios of smart beta mutual funds and ETFs that are most exposed to the characteristic associated with the underlying theoretical risk factor. Our methodology is general and can be used to construct tradable benchmarks for any risk factor based on a given “sortable” characteristic (e.g., book-to-market). Importantly, the short leg of our tradable factors only includes ETFs and accounts for shorting fees in constructing the factor returns.¹ Hence, our long–short factors (e.g., HML_trad) explicitly account for real-world shorting costs of ETFs and, thus, are tradable by both institutional and retail investors in real-time. Moreover, in our analysis, we use only large and liquid smart beta funds to consider the capacity of factor strategies, since inflows affect the scalability of any strategy.² Overall, our tradable long–short factors serve as potential benchmarks, providing insights into the trading and opportunity costs of factor investing.

We present two key findings. First, the comparison between tradable benchmarks and standard “on-paper” factors reveals a performance gap, termed the implementation shortfall (Perold 1988). The performance of tradable size, value, momentum, profitability, and investment benchmarks in comparison to their respective “on-paper” proxies is 2–4 percent lower (annually) for both investor types. The return series exhibit low correlation, evident in low R² and substantial tracking errors. Although the implementation shortfall is generally similar for retail and institutional investors across most factors, we observe that the tradable size factor (SMB_trad) exhibits a stronger alignment with its “on-paper” counterpart for institutional investors, while it is the momentum factor (MOM_trad) of retail investors that more closely tracks its corresponding “on-paper” factor.

Second, we uncover the sources contributing to the inability of capturing the risk premia associated with the “on-paper” factors. The implementation shortfall encompasses both trading costs and opportunity costs. The latter involves, e.g., adjustment to trading patterns for minimizing transaction costs in practical scenarios. We proceed by quantifying the portion of the implementation shortfall specifically attributed to transaction and shorting costs, assigning the remaining performance differential to the opportunity costs incurred by not trading the exact “on-paper” portfolio.³

Considering shorting costs is crucial, as the (annualized) financing cost of the short leg, constructed using large and liquid ETFs, constitutes a significant portion—ranging from 18 to 41 percent—of tradable factor alphas. Most importantly, shorting illiquid, hard-to-borrow stocks, included in the short leg of many “on-paper” factors, is often infeasible. Several stocks have limited float and hence cannot be easily borrowed, and/or have extremely high shorting fees. In contrast, our analysis demonstrates that, across factors and over time, our tradable portfolios have, on average, lower shorting costs than those implied by “on-paper” factors (c.f., Section 5.1). This highlights that ETFs are financial instruments suitable for implementing the short legs of factor strategies.⁴ After accounting for the observed shorting fees of the “on-paper” factors, we can explain approximately 32 percent of the implementation shortfall across various strategies and investors. Using the value premium as an example, the alpha between our tradable HML_trad and the Fama–French HML goes from –2.9 to –1.88 percent for institutional investors.

Accounting for transaction costs is equally important. “On-paper” academic factors typically include numerous stocks in both the long and short legs, often resulting in substantial turnover. Our tradable factors are constructed using mutual funds and ETFs, which internalize the costs of trading individual stocks. When we put the tradable and “on-paper” factors on equal footing in terms of transaction costs, we are able to explain ∼29 percent of the implementation shortfall across strategies and investors. We also find that, together, shorting fees and transaction costs contribute to 58 percent of the performance differential between tradable and “on-paper” factor, assigning a non-trivial role to the opportunity cost of not trading the exact “on-paper” portfolio.

Finally, we examine separately the performance of each leg of our tradable factors. Our findings reveal that a substantial portion of the performance gap arises from investors struggling to attain appropriate exposure to the short legs of profitability (RMW) and investment (CMA) factors when trading ETFs. In contrast, the long leg of our tradable factors tracks well the long leg of the corresponding “on-paper” factors, with exceptions noted for the long leg of SMB implemented by retail investors and the long leg of MOM implemented by institutions.

Our contributions to the existing literature are both methodological and in terms of data. To the best of our knowledge, our article is the first to construct tradable risk factors using funds while explicitly accounting for shorting fees in their short legs. This requirement is of paramount importance to obtain tradable versions of the “on-paper” risk factors that can be used as valid benchmarks. Leveraging a unique dataset with daily ETF shorting costs, we calculate the financing costs of the short leg of our tradable factors, and incorporate them into the construction of long–short tradable factor returns. The shorting costs implied by a portfolio of ETFs constructed to proxy for the factors’ short legs range, on average, from 0.56 percent per year (SMB), to ∼0.70 percent per year for HML, MOM, RMW, and CMA. This is between 18 and 41 percent of the tradable factor alphas, a nontrivial amount. More importantly, we show that ETFs not only exhibit a larger short interest than most individual stocks, but are also cheaper to short-sell than hundreds of individual stocks included in the short legs of the “on-paper” factors. Hence, from this point of view, our methodology delivers an improvement with respect to using individual stocks in terms of cost-minimization and feasibility. Our article is also the first to construct tradable benchmarks for both retail and institutional investors. Empirically, we demonstrate that these two investor types have access to distinct investment opportunity sets. Specifically, institutional investors are better positioned to access the size premium, while retail investors outperform institutions in capturing the momentum premium.

Our article is most closely related to Patton and Weller (2020) and Berk and van Binsbergen (2015). Differently from Patton and Weller (2020), who estimate the implementation costs of standard “on-paper” factors, we construct tradable factors using both mutual funds and ETFs. Additionally, we offer estimates of their implementation shortfall and elucidate the separate contributions of implementation and opportunity costs to the total shortfall. Berk and van Binsbergen (2015) discuss the pitfalls of interpreting academic (risk) factors as investment opportunities, and employ Vanguard index funds to define the tradable benchmark of a given fund. Rather than constructing a fund-specific benchmark, we build factor-specific benchmarks that are tradable by investors. Relatedly, Cremers, Petajisto, and Zitzewitz (2012) propose creating size and value factors based on the commonly used benchmark indices (e.g., by replacing SMB and HML with the differences between the Russell 2000 and S&P 500, and the Russell 3000 Value and Growth indices, respectively) while Hunter et al. (2014) augment the standard Carhart four-factor model with an active peer benchmark “tradable” factor. Although the use of indices is intuitively appealing, this alternative has two main limitations. First, it cannot construct index-based factors for styles/anomalies not tracked by an index (e.g., profitability). Second, it fails to account for the capacity of factor strategies, as benchmark indices like the Russell 2000 are not inherently tradable—they can only be traded synthetically through futures contracts or funds. Differently from all these papers, our methodology can be applied to construct any “on-paper” factor, accounting for its capacity.

Our tradable factors are complementary to the standard “on-paper” factors, not mutually exclusive. As discussed in Berk and van Binsbergen (2015, p. 8), “on-paper” factors cannot be interpreted as valid benchmark portfolios, but could still be used as valid risk models for investors. In other words, while in some settings “on-paper” proxies of risk factors are a suitable choice, in other contexts, tradable factor benchmarks should be preferred. Two examples of this include evaluating portfolio managers and assessing the performance of trading strategies. This point is also emphasized by Gârleanu, Panageas, and Yu (2019), who argue that without considering the (shorting and leverage) constraints faced by an investor, risk-adjusted style evaluation is not a well-defined concept, and alphas cannot detect outperformance under these circumstances. Our article constructs tradable benchmarks for both retail and institutional investors that account for these frictions.

Our article is also related to Detzel, Novy-Marx, and Velikov (2023), who focus on the transaction costs involved in replicating the risk factors using individual stocks. Differently from their work, we instead provide time series of tradable factor returns for both retail and institutional investors using publicly available investment funds. While transaction costs are important when trading hundreds of stocks, and severely impact the real-world factor performance, we show that accounting for transaction costs does not make “on-paper” factors tradable in general. The reason is that many of the stocks in the short-leg of the factors not only are not easily shortable, but many of them are also illiquid.⁵ As an example, 93.2 percent of the stocks included in the short leg of RMW during 2017 had an average dollar daily trading volume of less than $50 million, making any sizable trading position not easily implemented, and, as a consequence, “on-paper” factors only adjusted for transaction costs still not tradable in practice. As we show in the article, using ETFs and factoring in their shorting costs represents instead a feasible way to implement the short legs of factors.

Our work is complementary to the literature documenting the impact of short selling constraints on stock and fund returns (e.g., Figlewski 1981; Jones and Lamont 2002; Almazan et al. 2004; Cohen, Diether, and Malloy 2007; Engelberg, Reed, and Ringgenberg 2018; Drechsler and Drechsler 2021; Muravyev, Pearson, and Pollet 2023). Whereas these papers focus on the shorting costs of individual stocks, we exploit a novel dataset to account for the borrowing costs of ETFs when constructing tradable risk factors. Karmaziene and Sokolovski (2021) and Li and Zhu (2022) provide evidence that ETFs can be used to circumvent short-selling constraints at the individual stock level. Similarly to our paper, Brightman, Li, and Liu (2015), Ben-David et al. (2022), and Huang, Song, and Xiang (2023) also study smart-beta ETFs and their performances, while Brown, Davies, and Ringgenberg (2021) and Box et al. (2021) focus on ETF mispricings. Our article is also related to Lewellen (2011), who finds that institutions as a whole closely mimic the market portfolio. Conversely, our article aims to identify a subset of funds that significantly deviate from the market by tilting toward characteristics underlying academic risk factors, for example, profitability.

Our analysis shows that the performance of tradable factors is often different from that implied by “on-paper” risk factors. In addition to transaction and shorting costs, another factor contributing to this performance gap is the challenge investors face in obtaining significant exposure to the short legs of factors, such as momentum and profitability. This becomes evident when examining the characteristic scores of the tradable factor legs, which markedly differ from those implied by the “on-paper” factors. Patton and Weller (2020) show that the short leg of the “on-paper” factors is what makes them hard to trade in practice. However, while in the work of Patton and Weller (2020) the limitation stems from the mutual funds’ shorting constraints of individual stocks, this is not a concern in our setting, since all ETFs in our synthetic portfolios are highly liquid and can be easily sold short. The issue, in our case, is related to the structure of the fund industry: there is a scarcity of funds investing in “losers,” “weak profitability,” and “aggressive” stocks, which are required to implement a tradable version of “on-paper” factors. This also explains why the performance of the “on-paper” SMB factor is close to our tradable counterparts, since several large-cap ETFs do exist.

More broadly, the fact that the space of tradable risk factors is quite different from that typically described by multi-factor asset pricing models has implications for evaluating fund managers’ skill (i.e., alpha) and, more generally, the performance of trading strategies. This raises the question of whether portfolio managers should be evaluated against benchmarks that represent the truly achievable returns of a risk factor rather than against those implied by “on-paper” factors (Gârleanu, Panageas, and Yu 2019). In other words, their alpha should be estimated with respect to what institutional and retail investors could have achieved by trading themselves in a publicly available, liquid combination of smart beta funds.⁶ Hence, our tradable factors, which combine large and liquid smart beta funds, could be applied as potential, valid benchmarks to evaluate the performances of mutual fund managers or stock anomalies.

Our article proceeds as follows. Section 2 describes the data and presents descriptive statistics on the smart beta industry. Section 3 details the construction process of our tradable risk factors. Section 4 quantifies the implementation shortfall between tradable and “on-paper” factors, while Section 5 estimates the proportion attributable to shorting and trading costs. Section 6 concludes.

2. Data

We use monthly data on the universe of the US equity mutual funds, ETFs, and individual US stocks from January 2007 to December 2019. This is the longest possible sample, since very few large ETFs exist before 2007. We merge data from several sources to obtain our final dataset of monthly tradable factor returns. Fund returns and fees, assets under management (AUM), and quarterly fund holdings are from the CRSP Mutual Fund dataset, which also includes data on ETFs. We use the CRSP flag to identify institutional/retail mutual funds, as in Etula et al. (2019) and Cooper Halling, and Yang (2021). On the other hand, ETFs can be traded by both institutional and retail investors. Individual stock characteristics are from Compustat.

We obtain daily data on ETFs’ shorting fees from S3 Partners and individual stocks’ shorting costs from Markit.⁷ The shorting fee data are very detailed, and include, among other variables, a bid, an ask, and a last rate for each ETF. The bid rate is the average cost prime brokers are paying to beneficial owners for borrowing ETF shares, while the ask rate denotes the average fee that existing shorts are paying to borrow the ETF shares. We calculate the monthly shorting costs by averaging the daily shorting fees within each month. Data on ETF short interest are obtained from the CRSP MF database.

Risk factors in our study are proxied using the corresponding “on-paper” Fama–French risk factors, namely the market factor (MKT-Rf), value factor (HML), size factor (SMB), profitability factor (RMW), investment factor (CMA), and momentum factor (MOM). We choose these factors because of their central role in the literature on mutual fund performance evaluation and asset pricing anomalies, and their tracking by smart beta funds.⁸

Mutual fund returns are calculated from CRSP as the change in net asset value, including reinvested dividends from one period to the next. Mutual fund returns in the main analysis of the article are net of all fees except for front and rear loads. These loads are usually one-time charges and are often insignificant for equity funds, particularly for large funds such as those examined in our study. This approach aligns with our goal of constructing synthetic, tradable factors that represent the true implementation cost (Perold 1988; Pedersen 2015) of factor investing for retail and institutional investors. In other words, the returns of our tradable risk factors should be what investors actually earn (before taxes).⁹

Following the literature (e.g., Patton and Weller 2020), for funds with multiple share classes, we eliminate the duplicated funds and compute the fund-level variables by aggregating across the different share classes.¹⁰

To be consistent with the assets used to construct the “on-paper” risk factors (e.g., stocks of the US companies), we restrict our main sample to mutual funds and ETFs whose mandate is to invest in US equities. We also require each fund to have at least 12 months of returns, and AUM greater than $1 billion (in real terms as of 2019).

The choice of a $1 billion fund size cutoff is consistent with our goal of creating risk factors tradable by both institutional and retail investors.¹¹ Moreover, small funds are more likely to invest in illiquid securities given their size, hence their strategies might not be as scalable as those available to larger funds. It is important to note that no fund of funds is left in our final dataset, as they cannot be easily traded. Supplementary Appendix B describes in detail the data cleaning and merger procedures used to obtain our final dataset.

2.1 Descriptive statistics

Table 1 reports the descriptive statistics of our final sample. We split the sample into two sub-periods (2007–2012 and 2013–2019) to highlight the role that smart beta investing played following the Global Financial Crisis. We also split the funds into those available to retail investors (Panel A) and institutional investors (Panel B).

Table 1.

Descriptive statistics.

Notes: This table reports summary statistics of our final fund sample: mutual funds + ETFs (columns 1 and 2), and ETFs only (columns 3 and 4). The first (second) column in each set reports results from 2007 to 2012 (2013–2019). All funds have AUM greater than $1 billion. Monthly data from January 2007 to December 2019.

Panel A: Retail investors
	MF + ETF		ETF
	2007–2012	2013–2019	2007–2012	2013–2019
Number of funds	707	850	87	227
Average AUM ($ millions)	5,690	8,154	7,030	10,453
Median AUM ($ millions)	2,435	2,524	3,454	3,598
Median fund age	8.1	9.8	5.5	5.1
Median number of holdings	101	103	326	232
Median return over S&P500 p.a. (%)	−0.10	−0.57	0.20	−0.46
Median FF5-factor α p.a. (%)	−0.23	−0.76	0.03	−0.13

Panel B: Institutional investors
	MF + ETF		ETF
	2007–2012	2013–2019	2007–2012	2013–2019
Number of funds	462	801	87	227
Average AUM ($ millions)	4,798	7,378	7,030	10,453
Median AUM ($ millions)	2,047	2,500	3,454	3,598
Median fund age	4.3	6	5.5	5.1
Median number of holdings	149	123	326	232
Median return over S&P500 p.a. (%)	−0.20	−0.55	0.20	−0.46
Median FF5-factor α p.a. (%)	−0.19	−0.51	0.03	−0.13

The total number of unique funds increases steadily over time. Institutional investors have 801 mutual funds and ETFs available in the second half relative to 462 in the first half, an increase of 73 percent. The increase for funds available to retail investors is a moderate 20 percent.

The size distribution exhibits a notable right-skew, with the average fund size in the latest sample at ∼$8.1 billion (median $2.5 billion) for retail investors and slightly smaller for institutional investors.

The average ETF in the most recent sample is very large compared to the average mutual fund ($10.4 billion versus $7 billion); this is consistent with the large ETF inflows observed over the last decade. The median age of mutual funds and ETFs in the most recent sample period is around 9.8 (6) years for retail (institutional) investors, and only 5.1 years for ETFs. The median number of stocks held by mutual funds is slightly greater than 100, whereas ETFs, during the most recent sample period, typically hold 232 stocks. This suggests that large mutual funds tend to selectively choose their holdings, while ETFs are more diversified. Looking at the returns of mutual funds and ETFs, we note that the median retail (institutional) fund has underperformed the S&P 500 in both halves of our sample, by 10bps (20 bps) per year and 57bps (55bps), respectively. Overall, the median five-factor alphas are negative for both retail and institutional investors.¹²

Our focus is on equity “smart beta” funds. For exposition clarity, in this section, we classify funds into smart beta strategies based on their names and describe their time series properties. Focusing on smart beta fund names allows us to show the growing importance of factor investing in the asset management industry, at least from a marketing perspective. However, as we discuss in Supplementary Appendix A.4, classifying funds by name is not optimal since many funds are not consistently tracking the factor leg mentioned in their names (Cooper, Gulen, and Rau 2005; Chen, Cohen, and Gurun 2021).

The top panel of figure 1 shows the growth in the smart beta industry over time. As of the fourth quarter of 2019, smart beta equity mutual funds and ETFs command more than $5 trillion in total AUM. This represents about 50 percent of the total AUM of equity mutual funds and ETFs, with the relative importance of smart beta funds steadily increasing over the last decade.

Figure 1.

Smart beta equity mutual funds and ETFs. The top panel plots the AUM of smart beta funds, while the bottom panel plots the AUM of mutual funds and ETFs available to institutional and retail investors. Funds are labeled as smart beta if their name contains words related to factor investing (e.g., momentum and value). Every year, the sum of the bars in the bottom panel is larger than the corresponding ones in the top panel because ETFs are available to both retail and institutional investors. The sample period is from 2007 to 2019 and it includes funds with AUM greater than $50 millions.

The recent growth in factor investing is largely due to ETFs. These funds have become a popular instrument to passively invest in equities and risk factors. Over the last decade, the number of ETFs has skyrocketed, with a large fraction of them (supposedly) tracking risk factors. In 2018, for example, around 50 percent of all ETFs with more than $1 billion AUM were smart beta.

Some examples of large smart-beta, factor ETFs included in our sample are the iShares Edge MSCI USA Quality Factor ETF (QUAL, $19.6 billion AUM), the iShares Edge MSCI USA Momentum Factor ETF (MTUM, $14.4 billion AUM), the iShares Edge MSCI USA Value Factor ETF (VLUE, $10.5 billion AUM), and the Goldman Sachs ActiveBeta U.S. Large Cap Equity ETF (GSLC, $11.7 billion AUM).¹³ To further highlight the importance of ETFs in the competitive asset management industry, the U.S. Securities and Exchange Commission (SEC) recently relaxed the requirements for launching ETFs by lowering the barriers to entry.¹⁴

The bottom panel of figure 1 illustrates the total AUM of institutional and retail funds investing in smart beta strategies, providing insights into the significance of factor investing for both investor types. The share of institutional AUM relative to the total smart beta assets has increased over time from 25 percent to around 50 percent. This trend underscores the increasing relevance of smart beta strategies for institutional investors over the past decade.

In summary, factor strategies have gained prominence for both institutional and retail investors, to the point of being coined the “new kings of Wall Street” in 2019.¹⁵

3 Constructing tradable risk factors

3.1 Fund holdings and characteristic scores

Following Leippold and Ruegg (2019) and Lettau, Ludvigson, and Manoel (2021), we categorize funds based on their holdings. For each fund, we construct factor scores, indicating its exposure to various factors. To obtain these scores, we proceed as follows. Every period t, we obtain a factor score $s_{i,f,t}$ for each security $i=1,2,\dots ,N$⁠, on each characteristic (e.g., book-to-market) underlying the factor $f\in \{\mathit{HML},\mathit{SMB},\mathit{MOM},\mathit{RMW},\mathit{CMA}\}$⁠. We normalize each characteristic score from minus one (signifying a growth stock) to plus one (indicating a value stock). We denote with S_t the time-varying factor score matrix. We aggregate these scores at the fund level as follows:

$$X_{m,t}={\omega }_{m,t}\times S_t,$$

(1)

where ${\omega }_{m,t}$ is the weight of the individual stock in fund m at time t. Economically, $X_{m,t}$ is the relative “strength” of the fund with respect to each factor. This methodology is informative about what factors the funds are exposed to, including multi-factor funds¹⁶ (e.g., if the book-to-market and momentum fund scores are both large and similar, our methodology will categorize the fund as “value-momentum”).

In figure 2, we present the time series of the characteristic scores for two funds, the Vanguard Growth Index Fund (top panel) and iShares Russell 2000 Value ETF (bottom panel). We chose these funds because they have a long time series and they enter our tradable factors at some point in time. Several comments are in order. First, the book-to-market score is higher for the iShares Russell 2000 Value but less extreme (in absolute value) than that of the Vanguard Growth Index Fund. This result is consistent with Lettau, Ludvigson, and Manoel (2021), who document that, despite a large number of “value” funds, very few have high book-to-market ratios. Second, funds are not neutral to characteristics that are absent from their name; for example, the Vanguard Growth Index Fund features a high exposure to profitability.¹⁷ Third, the scores are quite stable over time for both funds, suggesting that our tradable factors will experience minimal turnover (see Supplementary Appendix A.9).

Figure 2.

Time series of the characteristic scores for two funds in our sample. The top panel plots the time series of the characteristic scores for the Vanguard Growth Index fund which is classified as “Large-Growth” according to Morningstar. The bottom panel plots the time series of the characteristic scores for the iShares Russell 2000 Value ETF which is classified as “Small-Value” according to Morningstar.

3.2 Tradable risk factors

We now describe our method for developing tradable long–short factors intended as benchmarks for both retail and institutional investors, with a focus on the timing of the data. The construction of a tradable value factor serves as an illustrative example throughout.

First, we observe that there are two levels for the characteristic score: stock- and fund-level. At the stock-level, we follow closely Fama–French for the definition of stock characteristics. As an example, when constructing the book-to-market of a stock in June of year t, we use its book-equity as of last fiscal year ending in t − 1, and market equity as of end of December of t − 1. In other words, as in Fama–French, the characteristic score of an individual stock changes only once a year, that is, in June.¹⁸

At the fund level, each month (due to our monthly portfolio formation frequency), we calculate cross-sectionally standardized characteristic scores, for each firm characteristic of all available stocks.¹⁹ Lastly, for each given fund, we use its holdings to construct the value-weighted fund characteristic scores (equation (1)).

Note that, despite the fact that the Fama–French characteristic score of an individual stock changes only once a year, for example, in June for book-to-market, the characteristic scores of each fund changes more frequently since fund holdings can be reported at higher frequency.

In constructing the value-weighted (standardized) fund characteristic scores, we use the most recent fund holdings available in real time. The reporting date of the holdings is always within 60 days from the end of the fiscal quarter as per SEC rules.²⁰ We always use the latest holdings available in real-time in the CRSP Mutual Fund Holdings dataset (variable: REPORT_DT). As a clarifying example, if we construct our tradable risk factors at the end of May 2019, we use the latest available fund holdings, published before the end of May 2019, perhaps in April or March 2019.

Lastly, at the end of each month t and for each characteristic, we rank funds using their fund-level scores. Then, for each characteristic, we construct the tradable long leg of the risk factor by equally weighting the top ten mutual funds and ETFs. We form the short leg by equally weighting the cheapest ten ETFs among the twenty with the lowest score. Since the funds included in our tradable factors are large ($1 billion+), equally weighting funds ensures better diversification and tradability.²¹ We then hold the synthetic portfolio until the next rebalancing period (e.g., next month).

We implement the described procedure separately for the universe of funds available to institutional and retail investors. Analyzing factor strategies for different investor types poses challenges when using individual stocks, as these are theoretically tradable by both sets of investors (although institutional investors may have additional trading venues, e.g., OTC, dark pools). In our setting, instead, it is natural to investigate whether the set of trading strategies for institutional investors differs from that of retail investors.

Our decision to use a fixed number of funds, namely ten, in the construction of tradable risk factors strikes a balance between achieving a well-diversified portfolio and ensuring ease of tracking and monitoring for investors. Additionally, the characteristic scores of the twenty most exposed ETFs are highly similar, validating our criterion of selecting the ten cheapest funds out of twenty to effectively build the cheapest feasible short leg with maximal exposure to the characteristic. Further discussion about this choice is available in Supplementary Appendix A.6.

Note also that, had we chosen, for instance, the top 10 percent of all available funds, the number of funds would have varied over time and across styles due to the increasing number of funds in our sample (as observed in Table 1). In turn, this procedure would introduce varying levels of idiosyncratic risk to tradable factors, complicating comparisons across samples and specifications. Conversely, by fixing the number of funds, we ensure consistent testing of tradable factors across various samples and specifications.

As mentioned above, the short side of our tradable factors solely consists of ETFs because shorting mutual funds is not feasible, whereas short-selling liquid ETFs is comparatively straightforward. Note also that the shorting fee is deducted from the tradable long–short factor return since it is an additional cost incurred by investors. Lastly, including mutual funds in the long leg serves several important purposes. First, the number of ETFs at the beginning of our sample is limited. Second, during market distress periods like the Global Financial Crisis, “smart beta” mutual fund managers exhibit lower return volatility compared to a portfolio of ETFs with similar factor exposure.²² Additionally, not all brokerages used by retail investors might provide real-time access to the full universe of available ETFs. Lastly, mutual funds are older, on average in our sample, than ETFs, and might be perceived as safer by investors.

4. Empirical results

4.1 Summary statistics

In Table 2, we present summary statistics of the first and higher moments of both Fama–French and our tradable factors, across both investor types. The next section explores the performance of tradable and “on-paper” factors, emphasizing their first moment, as is customary in the literature. Here, our emphasis is on the similarity in performances based on higher-order statistics.

Table 2.

Moments of tradable factors.

Notes: This table reports monthly summary statistics of the Fama–French factors together with those of our tradable factors. Panel A reports the results for the on-paper Fama–French factors, which do not account for either transaction or shorting costs, while Panel B (Panel C) reports the results for tradable factors available to retail (institutional) investors, which account for both. The bottom half of each panel shows, for each factor, its net exposure to the various characteristics, by calculating separately for the long and short legs of each factor the characteristic score with respect to size, book-to-market, momentum, profitability, and investment, and reporting the ratio of the long and short leg scores. Monthly data (annualized), sample period from January 2007 to December 2019.

Panel A: Fama and French
	MKT	SMB	HML	MOM	RMW	CMA
$\overline{r}$	0.089	0.003	−0.032	0.007	0.033	−0.001
$\sigma (r)$	0.150	0.079	0.093	0.163	0.055	0.051
Skew(r)	−0.756	0.252	0.146	−2.633	0.089	0.332
Exc.Kurt(r)	1.612	−0.240	2.146	17.780	0.304	−0.247
Size		0.385	0.949	1.021	1.117	0.965
Book to market		1.040	5.489	0.930	0.773	1.234
Momentum		1.008	0.944	4.513	1.033	0.988
Profitability		0.668	0.809	1.061	4.702	0.950
Investment		0.899	0.852	1.004	1.085	0.203

Panel B: Retail investors
	SMBtrad	HMLtrad	MOMtrad	RMWtrad	CMAtrad
$\overline{r}$	−0.026	−0.044	−0.015	−0.003	−0.040
$\sigma (r)$	0.088	0.077	0.121	0.069	0.077
Skew(r)	0.304	0.282	−0.452	−0.361	0.237
Exc.Kurt(r)	0.701	0.295	0.988	−0.068	0.134
Size	0.610	0.904	0.972	1.224	0.995
book to market	1.391	2.528	0.769	0.577	1.424
Momentum	0.944	0.934	1.490	1.043	0.957
Profitability	0.764	0.808	1.003	1.439	1.000
Investment	0.993	0.874	1.105	0.962	0.651

Panel C: Institutional investors
	SMBtrad	HMLtrad	MOMtrad	RMWtrad	CMAtrad
$\overline{r}$	−0.015	−0.051	−0.027	−0.010	−0.037
$\sigma (r)$	0.094	0.080	0.110	0.073	0.075
Skew(r)	0.293	0.231	−0.151	−0.344	0.169
Exc.Kurt(r)	0.452	0.348	0.852	0.145	0.077
Size	0.616	0.886	0.999	1.234	1.013
Book to Market	1.392	2.533	0.763	0.587	1.472
Momentum	0.964	0.927	1.454	1.044	0.948
Profitability	0.765	0.801	1.026	1.429	0.998
Investment	0.992	0.868	1.094	0.954	0.670

The tradable SMB_trad and HML_trad factors exhibit similar volatility to their “on-paper” counterparts, while MOM_trad displays ∼40 percent lower volatility for both retail and institutional investors (see also figure 3). This difference is attributed to the well-known fact that the short leg of MOM is subject to momentum crashes (Daniel and Moskowitz 2016), which our MOM_trad avoids by sidestepping the 2009 crash. Additionally, tradable versions of SMB, HML, and MOM demonstrate thinner tails compared to their “on-paper” counterparts. For instance, MOM has an excess kurtosis of 17.78, while our tradable factor has an excess kurtosis that is a fraction of that (0.99 and 0.85 for retail and institutional investors, respectively), indicating substantially lower tail risk for our tradable momentum factors.

Figure 3.

Cumulative returns of the tradable factors and the “on-paper” Fama–French factors. The figure shows in each panel three cumulative return series: the Fama–French long–short factor, and both the retail (orange line, circles) and institutional (blue line, triangles) tradable long–short factors. Monthly data, sample period from January 2007 to December 2019.

Moving on, we investigate the exposure of Fama–French factors and our tradable factors to characteristics beyond those used in the sorting procedure (cross-exposures). The bottom part of all three panels in Table 2 presents, for each factor, the ratio of the scores of the long and short legs with respect to five characteristics (size, book to market, momentum, profitability, and investment). Taking the exposure of SMB to book-to-market as an example, we first take the Small leg and calculate its book-to-market score based on the stocks included in the portfolio, obtaining a number between zero and one. We repeat the same analysis for the Big leg. We then take the ratio of the book-to-market score of Small (long leg) and Big (short leg). The resulting number can be interpreted as the net exposure of the SMB (long–short) factor to the book-to-market characteristic.

Notably, the cross-exposures of our synthetic factors closely resemble those of the Fama–French factors, except for the tradable SMB’s exposure to the book-to-market characteristic. The fact that the cross-exposures are often close to one implies that the long and short legs of our tradable factors are similarly exposed to that characteristic, for example, close to neutral. For example, the score of the tradable HML (institutional) on past returns is 0.927, comparable to the 0.944 attained by the Fama–French HML factor, indicating that the long and short legs of HML_trad and HML_FF contain stocks with similar momentum exposure. This result underscores that the presence of multifactor funds in our sample does not pose an issue, as our methodology generates tradable portfolios with exposures to other factors of similar magnitude to those of the “on-paper” portfolios, often close to neutral.

4.2 Long–short tradable versus On-paper factors: the implementation shortfall

To investigate the relationship between our tradable risk factors and their respective “on-paper” versions, we run the following monthly regression:

$$re{t}_{\mathit{tra}{d}_{LS},t}=\alpha +\beta re{t}_{F{F}_{LS},t}+{\epsilon }_t,$$

(2)

where $re{t}_{F{F}_{LS},t}$ and $re{t}_{\mathit{tra}{d}_{LS},t}$ denote the monthly returns of the long–short “on-paper” (Fama–French) factor, and its tradable counterpart, respectively.

Table 3 reports the results.²³ Panel A shows the estimates using the universe of funds available to retail investors, while Panel B shows the results using funds available to institutional investors. We emphasize that our tradable factors and “on-paper” factors complement each other. In fact, as discussed in Berk and van Binsbergen (2015, p. 8), “on-paper” factors cannot be interpreted as valid benchmark portfolios, but could still be used as valid risk models for investors. Our article addresses this need by providing tradable benchmarks.²⁴

Table 3.

Tradable risk factors performance versus “on-paper” factors.

Notes: This table reports the performance of long–short tradable factors from the regressions

$$re{t}_{\mathit{tra}{d}_{LS},t}=\alpha +\beta re{t}_{F{F}_{LS},t}+{\epsilon }_t$$

accounting for ETF shorting costs. Panel A (Panel B) reports results for retail (institutional) investors using mutual funds and ETFs on the long leg, and ETFs on the short leg. The tests on the coefficients are H₀: ${\alpha }_i=0$ and H₀: ${\beta }_i=1$⁠. ΔSR is the Sharpe ratio test of the bootstrapped difference ΔSR = SR(on paper) − SR(tradable) of Ledoit and Wolf (2008). $\sigma (\Delta r)$ = $\sigma (r_{\mathit{onpaper}}-r_{\mathit{trad}})$ is the tracking error in percentage. Newey-West standard errors. Monthly data, sample period from January 2007 to December 2019. *P < .1; **P < .05; ***P < .01.

Panel A: Retail investors
	α (% p.a.)	β	R2	ΔSR	$\sigma (\Delta r)$ (%)
SMBtrad	−2.95**	1.00	0.80	0.34***	1.15
t-stat	[−2.48]
HMLtrad	−2.55**	0.59***	0.51	0.24	1.90
t-stat	[−2.07]
MOMtrad	−1.79	0.46***	0.38	0.17	3.75
t-stat	[−0.66]
RMWtrad	−2.59*	0.72***	0.32	0.64**	1.70
t-stat	[−1.82]
CMAtrad	−3.81***	1.14	0.56	0.49**	1.50
t-stat	[−2.81]

Panel B: Institutional investors
	α (% p.a.)	β	R2	ΔSR	$\sigma (\Delta r)$ (%)
SMBtrad	−1.81	1.08*	0.83	0.20*	1.14
t-stat	[−1.37]
HMLtrad	−2.92**	0.70***	0.66	0.30*	1.56
t-stat	[−2.41]
MOMtrad	−2.98	0.38***	0.32	0.29	3.91
t-stat	[−1.07]
RMWtrad	−3.45**	0.74***	0.30	0.74**	1.80
t-stat	[−2.30]
CMAtrad	−3.56***	1.08	0.54	0.47**	1.47
t-stat	[−2.68]

Across panels, we observe negative and economically large alphas (annualized) for all tradable risk factors. In the context of retail investors (Panel A), the failure of SMB stands out. Indeed, since shorting large and liquid stocks is relatively easy, one would expect SMB_trad to have a similar performance to SMB_FF. This is confirmed by a large (in fact, the largest) R² of 80 percent, and the lowest tracking error (1.15 percent). Nonetheless, the alpha is a large and statistically significant −2.95 percent. Unlike SMB_trad, RMW_trad, CMA_trad, and to a lesser extent, HML_trad and MOM_trad have relatively low R² values, around 56 percent or less. Relatively speaking, MOM_trad has the closest performance to its “on-paper” counterpart, displaying both the smallest alpha (in absolute value) and the least Sharpe ratio difference relative to MOM_FF.²⁵

Turning to institutional investors (Panel B), we observe an improvement in the performance of SMB which yields a substantially smaller alpha. Also, the Sharpe ratio difference between “on-paper” and tradable SMB reduces from 0.34 to 0.20 when transitioning from Panel A to Panel B. HML displays an increase in R², from 51 percent (Panel A) to 66 percent (Panel B). However, this better tracking ability does not translate into superior performance as evidenced by the increase in the absolute value of alpha. Regarding RMW and CMA, both retail and institutional investors exhibit comparable tracking errors and wedges, whether measured by alphas or the difference in Sharpe ratios, in comparison to the “on-paper” factors.

In figure 3, we present the outcomes from Panels A and B of Table 3. The figure shows cumulative returns of the tradable factors (SMB_trad, HML_trad, MOM_trad, RMW_trad, and CMA_trad), for both retail and institutional investors, along with the cumulative returns of the corresponding “on-paper” Fama–French factor. The graphical evidence concurs with the regression results, indicating that: (1) neither retail nor institutional investors can effectively track the value, momentum, profitability, and investment “on-paper” factors; (2) institutional investors can reap the size premium better than retail investors, while retail investors have access to a momentum factor that is “closer” to the “on-paper” one. Importantly, since the short leg remains the same across investor types, the improvement for institutional investors in size and retail investors in momentum must stem from differences in the long leg, as confirmed in Section 5.4. In essence, our findings underscore the intricacies of harvesting the “on-paper” factor risk premia through trading.

To further understand the performance of retail and institutional tradable factors, figure 4 displays the characteristic scores of the individual legs for both the tradable and “on-paper” factors. We observe a large score difference between the tradable and “on-paper” factors, particularly for the long leg of SMB and for the short leg of RMW and MOM; instead, both legs of CMA are far from their respective “on-paper” factor-implied characteristic score. This analysis suggests a form of market incompleteness, resulting from investors not being able to achieve proper exposure to the short legs of MOM, RMW, and CMA when trading ETFs.²⁶

Figure 4.

Characteristic scores of the tradable factors. The figure plots the characteristic scores of the tradable factor legs (solid lines), for both retail and institutional investors, together with the Fama–French “on-paper” characteristic scores (dashed line). The long leg is plotted in blue (circles for retail investors and triangles for institutional investors), and the short leg in orange (squares using ETFs). The long leg of the tradable factor is constructed using both mutual funds and ETFs, while the short leg only using ETFs. Monthly data, sample period from January 2007 to December 2019.

Examining HML, we note a gradual convergence of the characteristic scores of both tradable legs to those of the “on-paper” factors over time. We also observe that the robust tradable leg of RMW approaches that of the “on-paper” Fama–French legs toward the end of our sample. The overall tilting of funds toward highly profitable, growth firms may be driven by their positive performance in the later part of the sample, but it is also consistent with more funds abiding by a responsible investing mandate and buying green stocks, which happen to be growth stocks (Pástor, Stambaugh, and Taylor 2022).

In conclusion, our findings underscore a substantial performance gap between tradable risk factors, constructed using large and liquid mutual funds and ETFs, and the commonly used “on-paper” factors. Adopting the terminology of Perold (1988) and Pedersen (2015), we refer to this gap as the implementation shortfall (IS). This shortfall encompasses both trading costs (TC) and the opportunity cost (OC) incurred by, for example, adjusting trading patterns to minimize transaction costs in practical scenarios.²⁷ In formula, we define the IS as:

$$\text{IS}=\text{TC}+\text{OC}$$

In the next section, we quantify the portion of the implementation shortfall attributed to TC and infer the opportunity cost of not trading the exact “on-paper” portfolio as the difference, OC = IS-TC.

5. Drivers of the implementation shortfall

5.1 Shorting costs

The costs incurred in borrowing the securities to construct the short leg of the factors constitute a friction that may affect the implementation shortfall.²⁸ Consequently, we start our analysis by contrasting the shorting costs of our tradable factors with those linked to “on-paper” factors. If the shorting fees of the tradable factors prove to be lower than those of on-paper factors, factoring in this cost has the potential to mitigate the implementation shortfall between the two.

5.1.1 Tradable vs on-paper shorting costs

Figure 5 plots the financing costs incurred by our tradable factors. The time-variation in the series is evident. The shorting fee rises over time, peaking around 2016, and persistently declines until the end of 2019. The time-series average annualized financing cost for our Big leg is 0.56 percent, while for the Growth, Down, Weak, and Aggressive legs the shorting cost is close to 0.70 percent per year. These costs are a large fraction of the tradable factor alphas, between 18 and 41 percent. Importantly, the median shorting fee of all ETFs in our final sample is 1.6 percent over the last 5 years, while its volatility is 3.8 percent, implying that the ETFs used in our tradable short legs have much lower shorting fees than the median ETF.

Figure 5.

Financing cost of the tradable factors. The figure shows the shorting fees of the short legs of our tradable risk factors over time. The short leg only includes ETFs, hence it is the same for retail and institutional investors. Monthly data, sample period from January 2007 to December 2019.

Next, figure 6 plots the shorting costs of our synthetic short factor legs along with those associated with the “on-paper” Fama–French short factor legs. It is clear that, except for the Big leg, our synthetic short legs are not only tradable, but also less expensive by, on average, 0.84, 1.02, 0.90, and 0.53 percent for Growth, Down, Weak and Aggressive, respectively.²⁹

Figure 6.

Comparison between the shorting costs of our tradable and “on-paper” factors. The figure shows the shorting fees of the short legs of our tradable risk factors and the Fama–French factors, over time. The short leg of our synthetic factors is composed only of ETFs, so it is the same for retail and institutional investors. Monthly data, sample period from January 2007 to December 2019.

Two remarks are in order. First, figure 6 illustrates the “theoretical” (observed) shorting fee of the “on-paper” factors based on the available data. This is because not every stock included in the short leg of the “on-paper” factors has accessible shorting data quotes. On average, the coverage across factors in 2019 is ∼88 percent. On the other hand, the shorting fees and short interest of large ETFs are always available, even during periods of market turmoil.³⁰

Second, many of the stocks included in the short leg of the “on-paper” factors cannot be shorted in large amounts because their supply is very thin. In fact, Supplementary Appendix figure A.1 shows that the short interest of the tradable short legs is usually larger than that implied by the stock holdings of the Fama–French factor legs. Hence, the “true” (unobserved) shorting fees of the “on-paper” factors is likely to be much larger because of market impact if those stocks were to be shorted in practice. On the other hand, our approach utilizes large and liquid ETFs to reduce the market impact caused by a thin supply of individual stocks.

5.1.2 Shorting costs and implementation shortfall

In Table 3, we deduct shorting fees from tradable factors but not from the Fama–French factors, following the standard practice in the literature. Moreover, figure 6 points to tradable factors having lower shorting fees than on-paper factors. Thus, shorting costs could potentially help explain the implementation shortfall between the tradable and “on-paper” factors.

To quantify this effect, Table 4 presents the results from regressing our tradable factors on the Fama–French factors that take into account the shorting fees of the underlying stocks. Notably, there is a substantial decrease in the implementation shortfall of momentum for retail investors (alpha decreases by 43 percent in absolute value, from –1.79 to –1.01 percent) and of HML for institutions (alpha decreases by 35 percent in absolute value, from a significant –2.92 to –1.88 percent).

Table 4.

Tradable risk factors performance versus “on-paper” factors adjusted for shorting costs.

Notes: This table reports the performance of long–short tradable factors from the regressions.

$$r_{\mathit{tra}{d}_{LS},t}=\alpha +\beta r_{F{F}_{LS-sc},t}+{\epsilon }_t.$$

where the Fama and French “on-paper” risk factors have been adjusted by the shorting cost (denoted sc) of the underlying stocks (from Markit). Investors use mutual funds and ETFs on the long leg, and ETFs on the short leg. The tests on the coefficients are H₀: ${\alpha }_i=0$ and H₀: ${\beta }_i=1$⁠. ΔSR is the Sharpe ratio test of the bootstrapped difference ΔSR = SR(on paper) − SR(tradable) of Ledoit and Wolf (2008). $\sigma (\Delta r)$ = $\sigma (r_{FF}-r_{\mathit{trad}})$ is the tracking error in percentage. Newey-West standard errors. Monthly data, sample period from January 2007 to December 2019. *P < .1; **P < .05; ***P < .01.

Panel A: Retail investors
	α (% p.a.)	β	R2	ΔSR	$\sigma (\Delta r)$ (%)
SMBtrad	−2.52**	1.00	0.80	0.28**	1.15
t-stat	[−2.11]
HMLtrad	−1.67	0.59***	0.51	0.08	1.89
t-stat	[−1.32]
MOMtrad	−1.01	0.46***	0.38	0.06	3.75
t-stat	[−0.39]
RMWtrad	−1.47	0.71***	0.31	0.35	1.70
t-stat	[−1.00]
CMAtrad	−2.48*	1.14	0.56	0.26	1.49
t-stat	[−1.80]

Panel B: Institutional investors
	α (% p.a.)	β	R2	ΔSR	$\sigma (\Delta r)$ (%)
SMBtrad	−1.33	1.08	0.83	0.14	1.14
t-stat	[−1.01]
HMLtrad	−1.88	0.70***	0.66	0.14	1.56
t-stat	[−1.53]
MOMtrad	−2.32	0.38***	0.32	0.18	3.92
t-stat	[−0.86]
RMWtrad	−2.29	0.74***	0.30	0.45*	1.80
t-stat	[−1.51]
CMAtrad	−2.29*	1.08	0.54	0.24	1.47
t-stat	[−1.69]

Figure 7 provides a graphical summary of Tables 3 and 4. The top panels display results for retail investors, while the lower panels depict findings for institutional investors. The left (right) panels display the alphas (and Sharpe ratios’ difference) from the two regressions (of tradable factors on standard Fama–French factors, or on Fama–French factors adjusted for shorting fees). We observe that the squared symbols corresponding to “on-paper” factors, net of shorting fees, exhibit a closer proximity to zero compared to the filled circles associated with standard Fama–French factors. In other words, accounting for shorting fees in the Fama–French factors narrows the implementation shortfall (measured by either alphas or Sharpe ratios’ difference). At the same time, we emphasize that the performance gap is still economically large (with an alpha of −1.9 percent for institutional investors in the case of HML, for example).

Figure 7.

Performance gap between tradable factors and the Fama–French “on-paper” factors with and without shorting costs. The left panels of the figure show the α (e.g., the return of the tradable factor adjusted for exposure to the corresponding Fama–French “on-paper” factor), while the right panels plot the Sharpe ratio difference ΔSR$=S{R}_{\mathit{bench}}-S{R}_{\mathit{trad}}$⁠. Filled circles represent standard Fama–French” on-paper” factors, while diamonds denote Fama–French “on-paper” factors adjusted for shorting costs. The sample period is from January 2007 to December 2019.

5.2 Transaction costs

We proceed to investigate whether trading costs could explain the implementation shortfall between our tradable factors and the “on-paper” factors.³¹ Indeed, “on-paper” factor portfolios comprise hundreds of stocks, have large turnover and, thus, incur substantial trading costs.³² However, while our tradable factors already incorporate the trading costs of individual securities owned by the funds, with realized fund returns implicitly reflecting these costs, the “on-paper” factors in Table 3 do not account for these trading costs.

To quantify the effect of trading costs on the IS, Table 5 presents the results from regressing our tradable factors on the Fama–French factors that take into account transaction costs. Specifically, to compute trading costs for the Fama and French on-paper factor leg f, we follow Novy-Marx and Velikov (2016) and Detzel, Novy-Marx, and Velikov (2023) and calculate:

$$T{C}_t^f=\sum _{i=1}^N|w_{i,t}-{\tilde{w}}_{i,t-}|·c_{i,t}$$

(3)

where $w_{i,t}$ is the weight of stock i in the factor portfolio at time t, ${\tilde{w}}_{i,t-}=\hspace{0.17em}{w}_{i,t-1}·(1+r_{i,t})$⁠, is the weight of stock i at time t before rebalancing, and $c_{i,t}$ is the one-way transaction cost of stock i at time t. To measure trading costs $c_{i,t}$⁠, we use the effective bid–ask spread estimator from Hasbrouck (2009).³³ The net-of-costs long return on f is

$$f_t^{L,\mathit{net}}=f_t^{L,\mathit{gross}}-T{C}_t^{f^L}$$

and the corresponding short return is:

$$f_t^{S,\mathit{net}}=f_t^{S,\mathit{gross}}-T{C}_t^{f^S}$$

where $f_t^{·,\mathit{gross}}$ denotes the return ignoring costs. Note that, as we already discussed, the fund returns already account for trading costs, and hence we sidestep the problem of estimating trading costs of individual stocks directly (e.g., Novy-Marx and Velikov 2016) or requiring access to proprietary data (e.g., Frazzini, Israel, and Moskowitz 2015).

Table 5.

Tradable risk factors performance versus “on-paper” factors adjusted for transaction costs.

Notes: This table reports the performance of long–short tradable factors from the regressions.

$$r_{\mathit{tra}{d}_{LS},t}=\alpha +\beta r_{F{F}_{LS-tc},t}+{\epsilon }_t.$$

accounting for the transaction costs (denoted tc) of the Fama and French “on-paper” factors as in Detzel et al. (2023). Panel A (Panel B) reports results for retail (institutional) investors using mutual funds and ETFs on the long leg, and ETFs on the short leg. The tests on the coefficients are H₀: ${\alpha }_i=0$ and H₀: ${\beta }_i=1$⁠. ΔSR is the Sharpe ratio test of the bootstrapped difference ΔSR = SR(on paper) − SR(tradable) of Ledoit and Wolf (2008). $\sigma (\Delta r)$ = $\sigma (r_{FF}-r_{\mathit{trad}})$ is the tracking error in percentage. Newey-West standard errors. Monthly data, sample period from January 2007 to December 2019. *P < .1; **P < .05; ***P < .01.

Panel A: Retail investors
	α (% p.a.)	β	R2	ΔSR	$\sigma (\Delta \mathit{r})$ (%)
SMBtrad	−2.08*	1.00	0.80	0.23	1.14
t-stat	[−1.82]
HMLtrad	−1.93	0.59***	0.52	0.13	1.88
t-stat	[−1.58]
MOMtrad	−1.20	0.45***	0.38	0.09	3.77
t-stat	[−0.45]
RMWtrad	−1.87	0.71***	0.31	0.45	1.70
t-stat	[−1.28]
CMAtrad	−2.69*	1.14	0.56	0.29	1.50
t-stat	[−1.94]

Panel B: Institutional investors
	α (% p.a.)	β	R2	ΔSR	$\sigma (\Delta \mathit{r})$ (%)
SMBtrad	−0.86	1.09*	0.83	0.09	1.13
t-stat	[−0.68]
HMLtrad	−2.20*	0.71***	0.67	0.19	1.55
t-stat	[−1.81]
MOMtrad	−2.48	0.38***	0.32	0.21	3.93
t-stat	[−0.92]
RMWtrad	−2.71*	0.75***	0.31	0.56*	1.79
t-stat	[−1.83]
CMAtrad	−2.49*	1.09	0.54	0.27	1.47
t-stat	[−1.88]

Table 5 shows that accounting for the “on-paper” portfolio-level trading costs reduces the performance gap. Specifically, focusing on HML, we see that the alpha goes from −2.55 percent (see Table 3, Panel A) to −1.93 percent for retail investors, and from −2.92 percent (see Table 3, Panel B) to −2.20 percent for institutions.

Comparing these results to those reported in Table 4, we observe that the implementation shortfall is reduced more when one accounts for shorting costs relative to when one accounts for trading costs. For example, focusing on institutional investors, the alphas for HML and MOM are, respectively, 36 and 22 percent smaller (in absolute value) when we account for shorting costs, versus 25 and 17 percent smaller when we account for trading costs. The sole exception is SMB, in which case trading costs matter more. Focusing again on institutional investors, accounting for shorting fees reduces the alpha by 27 percent, whereas trading costs lower the SMB performance gap by 52 percent.

5.3 Transaction and shorting costs

A natural question at this point is: to what extent can accounting for both shorting and transaction costs collectively narrow the differential in performance between tradable and Fama–French factors? To this end, we regress our tradable factor returns on Fama–French factors net of costs and accounting for shorting fees. The results are displayed in Table 6. Relative to the benchmark case reported in Table 3, accounting for implementation costs (shorting fees and transaction costs) reduces the differential gap for SMB, HML, and MOM respectively, by 44, 59, and 77 percent for retail investors, and by 79, 60, and 39 percent for institutional investors. Perhaps not surprisingly, we find the effects of shorting fees and trading costs to be additive. Examining the particular implementation of factors by retail and institutional investors, we find that both can replicate Fama–French HML after accounting for implementation costs, for example, for institutional investors, the HML alpha is −1.15 percent in Table 6 relative to the large and significant −2.92 percent in Table 3. We also observe interesting differences between retail and institutional investors. For example, whereas institutional investors seem to be able to replicate SMB but not MOM, the opposite can be said for retail investors. Indeed, the SMB Sharpe ratio difference is 0.03 (relative to the large and significant 0.2 in Table 3) for institutional investors but still economically large at 0.17 for retail investors. On the other hand, the MOM Sharpe ratio difference is −0.02 (relative to the large value of 0.17 in Table 3) for retail but still economically large at 0.11 for institutional investors.

Table 6.

Tradable risk factors performance versus “on-paper” factors adjusted for both shorting and transaction costs.

Notes: This table reports the performance of long–short tradable factors from the regressions.

$$r_{\mathit{tra}{d}_{LS},t}=\alpha +\beta r_{F{F}_{LS-tc-sc},t}+{\epsilon }_t$$

accounting for both the transaction costs (denoted tc) of the Fama and French factors as in Detzel et al. (2023), and the shorting costs (denoted sc). Panel A (Panel B) reports results for retail (institutional) investors using mutual funds and ETFs on the long leg, and ETFs on the short leg. The tests on the coefficients are H₀: ${\alpha }_i=0$ and H₀: ${\beta }_i=1$⁠. ΔSR is the Sharpe ratio test of the bootstrapped difference ΔSR = SR(on paper) - SR(tradable) of Ledoit and Wolf (2008). $\sigma (\Delta r)$ = $\sigma (r_{FF}-r_{\mathit{trad}})$ is the tracking error in percentage. Newey-West standard errors. Monthly data, sample period from January 2007 to December 2019. *P < .1; **P < .05; ***P < .01.

Panel A: Retail investors
	α (% p.a.)	β	R2	ΔSR	$\sigma (\Delta \mathit{r})$ (%)
SMB trad	−1.64	1.00	0.80	0.17	1.14
t-stat	[−1.43]
HMLtrad	−1.05	0.59***	0.52	−0.03	1.88
t-stat	[−0.83]
MOMtrad	−0.42	0.45***	0.38	−0.02	3.77
t-stat	[−0.16]
RMWtrad	−0.76	0.71***	0.31	0.17	1.71
t-stat	[−0.50]
CMAtrad	−1.35	1.14	0.56	0.06	1.49
t-stat	[−0.98]

Panel B: Institutional investors
	α (% p.a.)	β	R2	ΔSR	$\sigma (\Delta \mathit{r})$ (%)
SMBtrad	−0.38	1.09*	0.83	0.03	1.13
t-stat	[−0.30]
HMLtrad	−1.15	0.71***	0.67	0.03	1.54
t-stat	[−0.94]
MOMtrad	−1.83	0.38***	0.32	0.11	3.94
t-stat	[−0.70]
RMWtrad	−1.55	0.74***	0.30	0.27	1.80
t-stat	[−1.01]
CMAtrad	−1.21	1.09	0.54	0.04	1.47
t-stat	[−0.89]

Figure 8 summarizes in graphical form the takeaways of the analysis done so far. Interestingly, we can interpret the remaining alphas between our tradable (funds-based) factors and the Fama–French factors net of “shorting costs” and trading costs as an opportunity cost (Perold 1988; Pedersen 2015) of not trading the exact on-paper portfolio due to additional considerations (e.g., the fact many stocks in the short leg of the “on-paper” factors are illiquid and hard to trade in large amounts).³⁴ By using funds, we take all these additional frictions embedded in the “on-paper” factors into account, since funds internalize the trading of individual securities.

Figure 8.

Performance gap between tradable and Fama–French “on-paper” factors considering the impact of trading and shorting costs. The left panels of the figure show the α (e.g., the return of the tradable factor adjusted for exposure to the corresponding Fama–French “on-paper” factor), while the right panels plot the Sharpe ratio difference ΔSR$=S{R}_{\mathit{bench}}-S{R}_{\mathit{trad}}$⁠. Filled circles signify standard Fama–French “on-paper” factors, diamonds and crosses indicate Fama–French “on-paper” factors adjusted for shorting and transaction costs, respectively, while filled diamonds represent Fama–French “on-paper” factors adjusted for both trading and shorting costs. The sample period is from January 2007 to December 2019.

The fact that trading costs and shorting costs, together, reduce substantially the gap is crucial. Our funds-based approach considers both these costs, and the influence of the short legs of our tradable factors on the differential performance is a direct result of this consideration. Next, we zoom into the short leg of the factor.

5.4 Dissecting the long and short legs of the factors

In this section, we analyze the long and short legs of the factors separately.

We start by investigating the role of the long leg in explaining the performance differential between the tradable and “on-paper” factors. Figure 9 plots, for each factor characteristic (rows), the long legs of retail and institutional investors constructed using both mutual funds and ETFs (left panels), and a long leg constructed using only ETFs (right panels). Since ETFs are available to both types of investors, the distinction between retail and institutional investors is now irrelevant.

Figure 9.

Cumulative returns of the tradable and “on-paper” Fama–French long legs. The left panels of the figure show the cumulative returns of the long legs for retail and institutional investor, while the right panels show the long leg of the factors constructed only using ETFs. Monthly data, sample period from January 2007 to December 2019.

Several interesting facts emerge from figure 9. First, the tradable Small and Value legs align well with the Fama–French benchmarks. When comparing institutional and retail investors, we note that the small and value legs of institutional investors track the respective on-paper factor legs better than those of retail investors. Second, for Winners, we observe that our tradable leg tracks well until 2016, but underperforms relative to the “on-paper” factor leg thereafter. This result holds for both types of investors, and for the two investment universes (MFs and ETFs versus ETFs only). Hence, the differential performance between the tradable MOM and the Fama–French one is likely deriving not only from the short leg (in particular during 2009) but also from the long leg post-2016. Third, comparing the right and left columns, we conclude that mutual funds are important to mimic the “on-paper” Small factor leg. This evidence speaks to the large literature documenting that (some) mutual fund managers have skill (Pástor and Stambaugh 2002; Kacperczyk, Sialm, and Zheng 2005; Kosowski et al. 2006; Kacperczyk and Seru 2007; Cremers and Petajisto 2009; Koijen 2014; Kacperczyk, Van Nieuwerburgh, and Veldkamp 2014, 2016). In contrast, using only ETFs allows one to track the long leg of the profitability factor better than when including mutual funds as well. This is interesting since, by construction, the characteristic score obtained by using mutual funds and ETFs is more extreme than that obtained by using only ETFs. The additional discretionality of mutual fund managers with respect to ETFs may account for the performance wedge between the two, leading to lower returns for investors.

Overall, figure 9 shows that the long leg of our tradable HML, RMW, CMA, and SMB (for institutions) tracks well the long leg of the respective “on-paper” factors. Thus, we turn to the short legs, and its role in the results presented in Table 3.

Figure 10 compares the cumulative performance of the short legs of our tradable and Fama–French factors.³⁵ Both series abstract from any transaction or financing costs. We observe that the cumulative return differential is substantial, particularly for the short leg of RMW and CMA, and to a lesser extent, HML. This arises from the inclusion of stocks in the short legs of “on-paper” factors that (i) display extreme exposure to the underlying factor characteristic (see figure 4) and (ii) are not traded in practice, as revealed by fund holdings.

Figure 10.

Cumulative returns of the tradable and “on-paper” Fama–French short legs. The figure shows in each panel two cumulative return series, the Fama–French short leg and the tradable short leg of each factor. Monthly data, sample period from January 2007 to December 2019.

Overall, this evidence indicates significant opportunity costs, especially for the short legs of the factors. In other words, funds deviate from trading the exact “on-paper” portfolio implied by the short legs of RMW and CMW.

5.4.1 The role of the short leg: additional analysis

The stocks held in the short leg of the “on-paper” factors do not accurately represent what can be practically shorted in the real world, e.g., through funds. This is because the theoretical short leg does not factor in considerations such as trading costs, shorting costs, capacity, and other relevant aspects. This can be seen by the differential characteristic scores of the short legs of the tradable vs “on-paper” factors shown in figure 4.

To provide further evidence, we devise a formal test to link the performance gap between the returns of the Fama–French “on-paper” factors and our tradable counterpart to the difference in their characteristic scores. Specifically, Supplementary Appendix Table A.1 reports the results of the following cross-sectional regression

$$\left|{\widehat{\alpha }}_{i,t}\right|={\gamma }_0+{\gamma }_1·\Delta \mathit{CHA}{R}_{i,t}+{\gamma }_2{D}_{\mathit{short}}+{\gamma }_3\Delta \mathit{CHA}{R}_{i,t}\times D_{\mathit{short}}+{\epsilon }_{i,t}$$

(4)

where ${\widehat{\alpha }}_{i,t}$ is the monthly (annualized, in absolute value) alpha obtained from the daily regression $r_{i,t,\mathit{trad}}-r_{f,t}={\alpha }_i+{\beta }_i(r_{i,t,FF}-r_{f,t})+{\epsilon }_{i,t}$⁠, where i refers to the legs $\in \{\mathit{SMALL},\mathit{BIG},\dots ,$  $\mathit{AGGRESSIVE}\}$⁠, D_short is a dummy variable equal to one if it is a short leg, and zero otherwise, and $\Delta \mathit{CHA}{R}_{i,t}=|\mathit{CHA}{R}_{FF,i,t}-\mathit{CHA}{R}_{\mathit{trad},i,t}|$ is the absolute difference between the characteristic scores of our tradable and the “on-paper” factor legs in any given month t. Note that the results in columns (1)–(3) of Supplementary Appendix Table A.1 are obtained using long and short legs together for both retail and institutional investors.

Column (1) shows a positive γ₁ of 3.11, suggesting that the larger the difference in characteristic score between our tradable leg and the respective “on-paper” one, the larger the performance gap (measured by alpha) between the two in a given month.³⁶ The specification in column (2) shows that γ₂ coefficient is positive and statistically significant at the 1 percent level, implying that the performance gap tends to be larger for the short legs.

Most importantly, Column (3) reveals a notably large and statistically significant γ₃. This indicates that, the disparity in characteristic scores has a more substantial impact on alpha for the short legs. These results align with the notion that the differential performance between the tradable and “on-paper” factors is primarily driven by the short legs, given the significantly larger difference in characteristic scores for the short legs (see figure 4).

The analysis in Supplementary Appendix Table A.1 pools together the performance gap of the different styles. To provide further evidence on the relationship between performance differential and characteristic scores for each specific leg, we follow the empirical asset pricing literature starting from Fama and French (1992), and use funds to build decile portfolios sorted on the various characteristics (book-to-market, size, etc.). We then look at the average returns of these fund portfolios relative to the “benchmark”, that is the “on-paper” Fama–French factor relevant leg.

Figure 11 shows the results.³⁷ The left panels compare the tradable deciles against the short leg of the “on-paper” factors, while the right panels use the “on-paper” long legs as the benchmark. If the tradable (by using funds) bottom deciles for book-to-market, momentum, profitability, and top deciles for size and investment, end up close to the red dotted line, it indicates that the performance of our synthetic legs is close to that of the “on-paper” leg (i.e., the alpha is small).

Figure 11.

Tradable portfolio alpha relative to the Fama and French factor portfolio. Each month, all available funds are sorted into 10 EW decile tradable portfolios of funds based upon their VW characteristic score: me, beme, ret${}_{12–1}$⁠, profitability, and investment. The returns of each tradable fund-decile portfolio is regressed on the Fama and French factor portfolio, $r_{\mathit{decile}}-r_f={\alpha }_{\mathit{decile}}+{\beta }_{\mathit{decile}}(r_{FF}-r_f)+{\epsilon }_{\mathit{decile}}$⁠, where r_FF is either the long or short-leg of that factor. The sample period is from January 2007 to December 2019.

The red squares in the left panels highlight that the distance between the tradable and the benchmark is significantly larger for the short legs, particularly for MOM, RMW, and CMA.³⁸ The red squares in the right panels show instead that, for these factors, the replication of the long leg is good, consistent with our analysis in Section 5.4.

5.5 Capacity

Taking transaction and shorting costs into account does not render “on-paper” factors generally tradable. Many stocks in the short leg of factors exhibit relatively low liquidity and pose challenges for shorting. For instance, during 2017, 93.2 percent of the stocks in the short leg of RMW during 2017 had an average daily trading volume of less than $50 million. This makes implementing substantial trading positions potentially difficult.³⁹

To assess whether large investors with billions in AUM can effectively earn factor risk premia such as HML, it is crucial to analyze the capacity constraints of smart beta strategies. This involves understanding how much capital can flow into smart beta strategies through funds without distorting market prices. Employing large and liquid ETFs is a critical step to implement the short legs of factors while addressing capacity constraints. However, in Supplementary Appendix A.9, we delve more deeply into the capacity of smart beta strategies and attempt to estimate it using Blackrock’s proprietary transaction cost model (Ratcliffe, Miranda, and Ang 2017). Our exploration suggests that, in general, considering price impact—the most significant component of the transaction cost function—is unlikely to be the limiting factor for our synthetic factors.

6. Conclusion

Factor investing, or “smart beta,” has become one of the most important investment topics over the last decade, as evidenced by the amount of AUM flowing toward these strategies, and the proliferation of funds tracking risk factors discovered in academic studies (“on-paper” factors). While the recent literature highlights challenges in replicating “on-paper” factors using individual stocks due to trading costs, our article takes a novel approach by examining the tradability of these factors using portfolios of stocks, specifically mutual funds and ETFs. This approach offers several advantages. First, in terms of transaction costs, trading a small number of funds is cheaper than trading hundreds of stocks included in “on-paper” academic factors. Second, and most importantly, shorting illiquid, hard-to-borrow stocks, included in the short leg of the “on-paper” factors, is often infeasible. Using ETFs in the short leg of the tradable factors mitigates this problem, since ETFs have typically low shorting fees and higher short interest compared to individual stocks.

We construct synthetic, tradable factors using a combination of smart beta mutual funds and ETFs with maximal exposure to the underlying characteristic. Mindful of the fact that mutual funds cannot be shorted, all our results are obtained by only using ETFs in the short leg of the factors. Most importantly, and a key contribution of this article, we exploit a novel dataset to properly account for ETF-level shorting fees in order to construct truly tradable risk factors. These factors mimic the frictions and costs faced by real-world investors, which our analysis shows to be non-trivial. Specifically, our findings reveal a 2–5 percent annual performance difference, measured by alphas, between tradable and “on-paper” factors.

Following the terminology of Perold (1988) and Pedersen (2015), we term the performance gap between tradable risk factors constructed using mutual funds and ETFs and the commonly used “on-paper” factors the implementation shortfall. The shortfall includes both trading costs and opportunity costs incurred by adjusting trading patterns to minimize transaction costs in practical scenarios. Our analysis shows that accounting for trading costs (shorting fees and transaction costs) reduces the differential gap for SMB, HML, and MOM respectively, by 44, 59, and 77 percent for retail investors, and by 79, 60, 39, and 36 percent for institutional investors. Interestingly, we can interpret the remaining alphas between our tradable (funds-based) factors and the Fama–French factors net of “shorting costs” and trading costs as an opportunity cost (Perold 1988; Pedersen 2015) of not trading the exact on-paper portfolio due to additional considerations (e.g., the fact many stocks in the short leg of the “on-paper” factors are illiquid and hard to trade in large amounts). By using funds, we take into account all these additional frictions embedded in the “on-paper” factors, since funds internalize the trading of individual securities, offering a comprehensive perspective.

Further analysis shows that investors are not able to get exposure to the short legs of RMW, CMA and, to a lesser extent, HML, when trading liquid financial instruments such as ETFs. This implies that the feasible set of strategies available to both retail and institutional investors may be smaller than previously thought.

In assessing the performance of fund managers or trading strategies, investors face the challenge of selecting suitable benchmarks. Two key requirements must be met: (1) it should be feasible to replicate the benchmark’s payoff through trading and (2) the benchmarks must be accessible in real-time to all market participants. Unfortunately, except for the market factor, tradable benchmarks do not exist for the standard risk factors. This article’s key contribution is the introduction of such benchmarks. Our analysis bears implications for portfolio manager evaluation (e.g., Berk and van Binsbergen 2015; Gerakos, Linnainmaa, and Morse 2021) and cross-sectional return anomalies. Future work will leverage our tradable factors to offer further insights into these areas.

Footnotes

1

Institutional and retail investors cannot short-sell mutual funds, but they can take short positions in large, liquid ETFs. For our article, it is irrelevant whether mutual funds or ETFs can engage in short-selling activities, since the constraint is on the investors in mutual funds/ETFs, not on the funds themselves.

2

Since transaction costs increase with fund size, most trading strategies have limited capacity (see Pástor, Stambaugh, and Taylor 2015). In our main analysis, we use the standard measure of transaction costs without explicitly accounting for their dependency on size. However, in Supplementary Appendix A.9, we decompose transaction costs into fixed and variable price impact components and attempt to quantify the capacity of tradable factors in our setting.

3

Starting with Perold (1988), the notion of implementation shortfall is understood as the cost of not being able to trade a paper portfolio due to difficulties in acquiring the desired securities in the requested quantities. Our approach replicates the on-paper portfolio with traded funds rather than trading the underlying securities directly (for reasons explained in Section 5). Thus, we gauge the opportunity costs indirectly through actual mutual fund performance. This approach—which is similar to Kacperczyk, Sialm, and Zheng’s (2008) attempt to measure the impact of unobserved fund managers’ trading actions—aligns with the implementation shortfall concept by accounting for the practical constraints faced by fund managers in the real world.

4

Consistent with this analysis, Evans et al. (2021) find that ETFs constitute 10 percent of the US equity market capitalization but make up over 20 percent of the aggregate short interest.

5

Several recent papers have highlighted the importance of short-sale constraints for cross-sectional asset pricing phenomena, both theoretically and empirically (see, e.g., Stambaugh, Yu, and Yuan 2012; Gârleanu, Panageas, and Yu 2019).

6

This is especially true, given the several spurious anomalies discovered in the literature (e.g., Harvey, Liu, and Zhu 2016).

7

Prior studies of shorting fees have used datasets obtained from an individual participating institution in the stock loan market (e.g. D’Avolio 2002; Geczy, Musto, and Reed 2002; Cohen, Diether, and Malloy 2007) or individual stock lending fees from Markit (e.g. Engelberg, Reed, and Ringgenberg 2018; Drechsler and Drechsler 2021). In addition to Markit, we have access to S3 data which has a more comprehensive and detailed coverage of ETFs.

8

In Supplementary Appendix A.2, we construct tradable versions of the ROE factor of Hou, Xue, and Zhang (2015), and the quality-minus-junk factor of Asness, Frazzini, and Pedersen (2019). We also considered including additional risk factors, such as the idiosyncratic volatility factor of Ang et al. (2006), and the betting-against-beta factor of Frazzini and Pedersen (2014). However, fund names and prospectuses indicate that very few funds, if any, are marketing themselves as tracking these factors. Thus, we exclude these factors from the analysis.

9

Using gross fund returns would only imply a positive shift in the mean returns of the tradable factors, equal to the difference in the expense ratio between the long (MF+ETFs) and short (ETFs) legs, but the tracking ability would be unchanged. See Supplementary Appendix A.3 for additional discussion.

10

To aggregate returns within a fund group, we calculate the total net asset weighted returns.

11

Morningstar defines small-cap funds as funds that primarily invest in stocks with market capitalization under $1 billion (Savov, 2014). Moreover, Brown, Davies, and Ringgenberg (2021) limit their sample to ETFs with at least $50 million in assets to mitigate the impact of illiquidity and possible non-synchronous prices due to infrequent trading. See also Elton, Gruber, and Blake (1996, 2001) for a discussion on the biases induced by funds with a low value of AUM.

12

The only exception is the 0.03 percent alpha for ETFs before 2013, although it is not statistically different from zero.

13

AUM as of January 2021.

14

See US regulator overhauls requirements for launching ETFs (Financial Times, September 26, 2019).

15

Index Funds Are the New Kings of Wall Street, WSJ September 2019.

16

According to an FTSE Russell survey done in 2019, multi-factor strategies are becoming the most popular among institutional investors globally. Multi-factor products captured 11 percent of new net flows into Europe-domiciled funds in 2019, compared to just 2 percent in 2015, according to BlackRock.

17

Novy-Marx (2013) shows that profitable firms tend to be growth firms, in the sense of having low book-to-market.

18

As a robustness check, Supplementary Appendix A.2.1 constructs the factors using “live” data.

19

A stock might disappear from the equity universe through events like a merger or a delisting.

20

https://www.sec.gov/divisions/investment/guidance/secg-investment-company-reporting-modernization-rules

21

Equal-weighting of the funds in the portfolio implies mechanical rebalancing every month. Supplementary Appendix A.5 reports similar results using value-weighted tradable factors.

22

During the Global Financial Crisis, the Value leg constructed using only ETFs has a 30 percent higher volatility than the retail Value leg constructed using both mutual funds and ETFs.

23

Supplementary Appendix Table A.2 reports the same analysis at the daily frequency.

24

The literature has traditionally assessed long-only managers using long–short “on-paper” factors. A crucial initial move towards a fair evaluation involves confirming whether a long–short portfolio is replicable. Otherwise, the concept of relative performance, or “alpha,” becomes ambiguous and lacks a clear definition. This is what we address in our article. The natural subsequent step is to benchmark the mutual fund manager against long-only benchmarks rather than long–short ones. We thank an anonymous referee for this observation.

25

To investigate differences in Sharpe ratios, we implement the robust Sharpe ratio test of Ledoit and Wolf (2008), which relies on the block-resampling suggested by Lahiri (2003). In our sample, HML_FF has negative returns and hence Sharpe ratio. We use Sharpe ratio differences even in this case primarily to determine if, after equalizing volatility, there is a significant difference in average returns between on-paper and tradable investments.

26

A potential concern with our approach is that there are no ETFs tracking stocks that are “losers” or with low profitability, that is, those stocks that end up in the short leg of MOM and RMW. In Supplementary Appendix A.7, we propose an alternative approach to construct a tradable long–short version of RMW and MOM by using mutual funds and ETFs in the long leg (as in our benchmark case), and a market ETF in the short leg to hedge market risk only. Overall, the performance of these alternative versions of MOM and RMW improves in terms of alpha, worsens in terms of overall R² and beta, and displays mixed results in terms of tracking errors.

27

In contrast to Pedersen (2015), who adopts TC to refer to transaction costs, our use of TC extends beyond transaction costs like bid–ask spreads to include expenses linked to funding short positions.

28

With few exceptions (Drechsler and Drechsler 2021; Muravyev, Pearson, and Pollet 2023), little attention has been devoted to the effect of short-sale costs for anomalies.

29

The shorting fees of individual stocks are from Markit (variable: IndicativeFee).

30

Li and Zhu (2022), Evans et al. (2021), and Ben-David, Franzoni, and Moussawi (2018) have documented that short-selling ETFs is relatively easier, since it is always possible to create new ETF shares to be shorted (e.g., naked shorting). As an example, during the recent meme-stocks turmoil of January 2021, while shorting GameStop might have been infeasible, given a shorting fee of more than 30 percent, it was still possible to short-sell ETFs owning GameStop shares. Quoting an extract from Novick et al. (2017), “ETFs have functioned well in times of stressed markets, with ETF shares being at least as liquid as underlying portfolio assets and serving as an important vehicle of price discovery.”

31

It is worth noting that while there is also a transaction cost associated with trading funds, this cost is generally negligible, often zero, especially for retail investors, as exemplified by Fidelity.

32

A few recent papers have documented the effects of trading costs on the return performance of “on-paper” risk factors (Patton and Weller 2020; Detzel, Novy-Marx, and Velikov 2023). Detzel, Novy-Marx, and Velikov (2023) estimate trading costs for standard factors ranging between 0.36 percent (SMB) to 5.64 percent (MOM) per year.

33

This procedure has been used by a growing literature. See, for example, Detzel and Strauss (2018), Barroso and Detzel (2021), and Chen and Velikov (2023). We kindly thank Andrew Chen for sharing the updated trading costs data with us.

34

Supplementary Appendix A.8 eliminates alternative drivers, such as lending activities and timing behavior of funds (Savov 2014), as contributors to the implementation shortfall.

35

We plot the cumulative performance of the short legs. If the tradable short legs outperform the “on-paper” leg, the tradable long-short portfolio will consequently underperform the “on-paper” factor.

36

The estimate is not statistically significant due to an omitted variable bias, as can be seen in Column (2) where the coefficient becomes significant and the R² substantially increases.

37

As expected, the relationship between characteristics and returns exists, not only at the individual stock level, a backbone finding in the asset pricing literature, but even at the fund level, suggesting that the well-known return spreads at the individual stock level carry over at the fund level.

38

The red rectangle approximates the type of funds included in our tradable factor. For instance, in the early part of the sample, we have around fifty ETFs, but we select ten on each leg, representing the top/bottom 20 percent of funds. In the later part of the sample, our tradable factors are closer to the top/bottom 10 percent of funds, instead.

39

The median market cap among the stocks with less than $50mn daily trading volume is $151 million.

Supplementary material

Supplementary material is available at Review of Finance online.

Acknowledgments

An earlier version of this article has been circulated under the title “Smart Beta Made Smart: Synthetic Risk Factors for Retail and Institutional Investors.” We are grateful to Jules van Binsbergen, Adam Farago (discussant), Christopher Hrdlicka (discussant), Kris Jacobs, Minsoo Kim (discussant), Juhani Linnainmaa, Dong Lou, Stavros Panageas, Per Strömberg, Allan Timmermann, and Sheridan Titman for many valuable suggestions on our article. We also received helpful comments from conference and seminar participants at the MFA 2022, BI-SHoF Conference 2021, Geneva Institute of Wealth Management, Eastern Finance Conference 2021, NFA Conference 2021, NFN Young Scholar Conference 2020, Chapman University, King’s College, Maastricht University, Stockholm School of Economics, Tilburg University, University of California, Berkeley, University of Houston, and Warwick Business School. The article received the 2021 Award from the Geneva Institute for Wealth Management and the 2020 ICPM Award Honourable Mention. R.S. acknowledges generous support from the Jan Wallanders and Tom Hedelius foundation.

Funding

Riccardo Sabbatucci acknowledges generous support from the Jan Wallanders and Tom Hedelius foundation.

Data availability

All data utilized in the article’s empirical analyses are available to the public through the sources referenced. Although most of these sources are subscription-based, any researcher can acquire the necessary data by paying or subscribing to the respective services.