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## Abstract

Using a transaction cost model and an assumption for the smart beta premium observed in data, the authors estimate the capacity of a particular implementation of momentum, quality, value, size, minimum volatility, and a multifactor combination. For a given trading horizon, they can find the fund size at which the transaction costs from flows into these strategies negate the smart beta premium. For a one-day trading horizon, momentum is the strategy with the smallest assets under management (AUM) capacity of $65 billion, and size is the largest with an AUM capacity of $5 trillion. At five days, momentum and size capacity rise to $320 billion and over $10 trillion, respectively.

Flows into smart beta strategies have significantly increased in recent years. As of April 6, 2016, Morgan Stanley reports that since 2010, the total assets under management (AUM) for the U.S. Smart Beta exchange-traded funds (ETFs) market have grown at a rate of 30% per year, to $225 billion (Cyprys [2016]). This implementation of factor investing is long only, fully transparent, and can be traded directly on public exchanges. BlackRock forecasts that this category of ETFs might reach $1 trillion by 2020, representing projected organic growth rates of 18% in the United States and 21% in Europe (BusinessWire [2016]).

Although academics have studied these risk premiums for decades, the ability of individual investors to directly access these investment styles through ETFs is relatively recent.^{1} A natural question, given the growing popularity of these strategies, is what is their capacity and is the trend sustainable? At what level of AUM do these historically observed premiums attenuate? These questions are especially relevant given that the vast majority of a large academic literature studying these style premiums has done so without taking transaction costs into consideration.^{2}

We study the capacity, in terms of AUM, of smart beta strategies—momentum, quality, size, value, and minimum volatility. We also study a strategy combining the first four of these factors.^{3} All of these smart beta strategies can be implemented with transparent, third-party indexes (in our case, MSCI) and directly traded as ETFs.^{4} (For a more detailed description, please see the Appendix.) This makes our study different from those by Garleanu and Pedersen [2013] and Landier, Simon, and Thesmar [2015], who derived optimal weights for a proprietary trading strategy taking into account transaction costs. Our factor strategies—both the predictive variables used to construct the strategy and their portfolio weights—are publicly known.

We base our analysis on a transaction cost model developed by BlackRock, Inc. that is used on a daily basis by different investment teams. It is not our intention to develop a new transaction cost model—we use a state-of-the-art model that is integral to the research, execution, and portfolio management of a large asset manager involving hundreds of billions of dollars every year; our contribution is to apply that transaction cost framework to address the important question of factor capacity for factor ETF instruments. In line with a sizeable microstructure literature building on work by Glosten and Harris [1988] and Hasbrouck [2009], the transaction cost model includes both fixed cost and nonlinear market impact components. The parameters of the model are updated on a daily basis, based on trading executed by BlackRock across all of its portfolios—not just the trading data of securities within the smart beta strategies. For example, BlackRock traded over $340 billion in U.S. equities during January to March 2016, an indication of the amount of data that is used to calibrate the model. Thus, the transaction cost model gives an estimation that a large asset manager would face in executing trades in ETF securities.

We define *capacity* as the breakeven hypothetical AUM at which the associated turnover transaction costs exactly offset the historically observed style premium.^{5} Because this calculation is sensitive to the assumption of the magnitude of the premium, we present results varying the premiums. A key variable that determines smart beta capacity is the turnover of the factor, and we assume recent rebalancing trends are a good representation of the expected turnover going forward.

The exercise we conduct in this article is hypothetical and involves several unrealistic assumptions. We assume that all trading takes place in a given interval: over one day and over a longer horizon of five days. We assume that market structure characteristics of the factor vehicles, like turnover (measured as two-way, annualized), and of the market itself, like no entry and exit of stocks in these strategies, are held fixed as the flows come in. We gauge capacity only by the transaction costs incurred by the rebalancing activity as the inflows increase the AUM of the strategy and so ignore the funding costs of those flows (which could come from other stocks or asset classes). We are not saying the transaction cost estimates are definitive measures of the capacity of smart beta strategies—but they are informative in that they measure an important real-world friction that reduces returns earned by investors.

As expected, the strategy with the smallest capacity is momentum—the style factor with the highest turnover. Momentum has an estimated breakeven AUM of $65 billion for a one-day trading horizon. At this horizon, we find that the breakeven AUM for size is the largest, at approximately $5 trillion, followed by minimum volatility, which is above $1 trillion. However, if trading is allowed to occur over five days, which is common for larger trades, the capacity of momentum increases from $65 billion to $324 billion. Finally, the combination of value, size, momentum, and quality factors has an estimated breakeven AUM of $316 billion and $1.6 trillion over trading horizons of one and five days, respectively. In reality, it is likely that many aspects of the markets—including the composition of the stocks in the factor strategies themselves—will change before flows of this magnitude are realized. What is important is the large size of these numbers, rather than the absolute numbers themselves, which indicates that transaction costs have to be very large to have a significant effect in reducing returns to investors in smart beta strategies. Put another way, capacity considerations in smart beta are likely to come from economic sources other than trading costs.

## TRANSACTION COST APPROACH TO CAPACITY

To measure the capacity of smart beta strategies from a transaction cost perspective, we require a transaction cost model, which includes the estimated turnover of the factor strategy, and an estimate of the smart beta premium. We then compute, using the transaction cost model, the critical level for the particular fund at which the trading costs (fixed costs and market impact) associated with turnover offset the smart beta premium.

### Transaction Cost Model

We use BlackRock’s proprietary transaction cost (*t*-cost) model (Mayston [2012]), which has two components: a fixed cost component, *FC*, and a market impact component, *MI*. The total transaction cost, *TC*, is the sum of the two components:

The fixed component in the *t*-cost model includes fixed commissions (which are specific to each country), variable commissions (specific to each stock and a particular time), taxes (specific to each country), bid–ask spreads (specific to each country and capitalization), overnight price movements from the previous close to next day’s open, and slippage from open to snap price at the time of execution.

The market impact component proportionally increases in the size of the trade. This component incorporates the size of the trade relative to the stock’s average daily volume and the volatility of the stock that is being traded. Intuitively, stocks with higher volatility generally have higher market impact, and vice versa. Furthermore, when market volatility increases, the market impact component also increases. The function for market impact, as a percentage of trade size, is concave and asymptotically linearly increasing.

The *t*-cost model gives estimates of transaction costs for every stock traded by BlackRock. We estimate the transaction costs of multiple stock trades as the weighted sum of each constituent trade. This approach is used on a daily basis by multiple investment teams in BlackRock that require estimates of trading costs as part of their investment process. The expected alpha after transaction costs is a key ingredient in portfolio construction, and as such, BlackRock has a dedicated trading research team to keep transaction cost models current and accurate.

The model’s parameter estimates, which use data such as average daily volume and stock volatility, are updated daily. For our estimates of capacity, we use parameters as of June 14, 2016, unless specified otherwise. The functional form of the market impact component, for different trade sizes and time executions, can be found in the Appendix.

### Example: Cost of Trading Apple

To illustrate, we use the transaction cost model to estimate the cost of trading Apple, Inc. stock for different trade size and trading time horizons. As shown in Exhibit 1, Panel A, the transaction cost function is concave, and the market impact component is a nonproportionally increasing function of the trade size, consistent with the existing literature (see, e.g., Frazzini, Israel, and Moskowitz [2012]). Trading $100 million of Apple stock over one day costs approximately $120,000, or 12 bps, with 10 bps attributed to market impact. However, trading $1,000 million would cost approximately 32 bps, with a much larger 30 bps of estimated market impact ($3 million, roughly 30 times the market impact cost of a one-tenth-sized trade).

Portfolio managers have the flexibility of trading over longer time horizons to reduce the market impact of their trades, at the cost of higher tracking error versus a theoretical frictionless portfolio implementation.^{6} Exhibit 1, Panel B, shows the estimated total transaction costs for Apple, Inc. stock as we increase the trading time horizon. Trading $100 million of Apple stock over five days costs approximately $61,600, or roughly 50% less than what it costs if the trading is done over one day. Trading $1,000 million over five days would cost $1.5 million (in comparison with $3.2 million if the trading is done over one day). Extending the trading horizon can reduce transaction costs significantly; therefore, we expect the estimated capacity of smart beta strategies to increase with longer horizons.

### Estimation of Smart Beta Premiums

We estimate the beta premium using historical monthly returns provided by MSCI up to March 31, 2016. To remove the market exposure of these long-only indexes and capture the pure style premium, we run the following regression:

2where *Y _{t}* is the return of the MSCI factor index;

*X*is the return of the market, as proxied by the return of the MSCI USA Index; and

_{t}*r*

_{f}is the risk-free rate, as proxied by the effective federal fund rate.

Given that the MSCI smart beta indexes rebalance every six months, we work with the historically observed six-month premium:

3Exhibit 2 reports the summary statistics and the premiums used in our capacity analysis. We show the index starting date, annualized mean return, standard deviation, estimated beta to MSCI USA, and the estimated premium. The exhibit also shows the market capitalization, average daily volume (ADV) of underlying constituents, and the number of constituents in the index. Over our sample period, the minimum volatility style has the highest long-term premium, followed by size. These high premiums are partly driven by the low betas of these strategies, which are 0.73 and 0.90 for minimum volatility and size, respectively. Value has the lowest premium, at 0.70%. The combination of factors, with a premium of 3.40%, has performed better than the individual factors. A caveat is that we are using different sample periods for these comparisons.

### Estimates of Smart Beta Capacity

With the transaction cost model and estimated smart beta premiums, we proceed with estimating capacity. Our estimate of capacity is implicitly defined using the following equation:

4where *TC* is the transaction cost function given in Equation (1), *AUM*_{c} is the critical AUM level that we are looking for—the estimate of capacity, *TO* is the turnover of the strategy, *T* is the trade time horizon, and *SBP* is the estimated smart beta premium for a particular strategy.

We can interpret Equation (4) as follows: The money spent to trade the smart beta strategy on the left-hand side is equal to the returns earned by that strategy on the right-hand side. The breakeven AUM is defined so that as flows to the strategy increase, the incurred transaction costs exactly match the smart beta premium, which is normalized appropriately for the strategy’s turnover. For example, for a smart beta strategy with a premium of 1% and turnover of 20%, the critical AUM would be $2 trillion if trading $400 billion over one day incurs costs of 5%. That is, the smart beta premium of 1% is eliminated with an AUM of a $2 trillion portfolio.

The expected turnover rate of the smart beta strategy is an important input. All else equal, higher turnover implies lower capacity as a direct consequence of increased trading activity and trading costs. In fact, turnover enters explicitly in Equation (4).

We compute capacity for the smart beta strategies using the constituents of the smart beta indexes as of June 14, 2016. Note that the smart beta index constituents do change, as do the transaction costs, but we expect that our estimates will be approximately the same for other dates because the parent universe consists of generally large, liquid stocks.

## EMPIRICAL RESULTS

Using the previously described *t*-cost model and smart-beta premiums, we estimate capacity for each of the five smart beta strategies, as well as the multifactor combination. We analyze the impact of trading over different trade time horizons, as well as alternative scenarios on market volatility, turnover, and trading volume. We present more detailed results on momentum because we that find it is the strategy with the smallest capacity among the analyzed factors.

### Trading over a One-Day Horizon

We report estimated breakeven fund sizes for each smart beta index in Exhibit 3. Overall, our results indicate that that the smart beta premiums of value, momentum, minimum volatility, quality, size, and the multifactor combination are highly robust and implementable at very large scale.

Taking as a reference realized turnover rates over the last year and assuming a premium equal to the one observed in data, all the strategies, except for momentum, have capacities of several hundred billion dollars. For the case of momentum, our results indicate an estimated capacity of $65 billion. Interestingly, the size factor has the highest capacity among all the factors analyzed ($5 trillion) because among the factors considered, size has the largest market capitalization and underlying average daily trading volume as well as the largest number of constituents. Furthermore, turnover for size is lowest among the indexes considered here. Consequently, size has the largest capacity to absorb capital inflows.

Because the size strategy has the lowest turnover, it consequently has the smallest trading activity, with low transaction costs and high capacity. For some securities, this would mean a breakeven AUM allocation that is actually larger than the current market capitalization of these companies (for context, the market cap of the index, as of September 14, 2016, is approximately $21 trillion). The actual numbers should not be interpreted literally: The fact that they are so large indicates that the capacity is substantial, and it is unlikely that transaction costs are the limiting consideration for factor capacity.

Exhibit 3 also reports capacity results if we assume that the smart beta premium going forward is just 50% of the historical one. We find that the capacity of the most constrained strategy, momentum, is $27 billion, followed by quality, value, minimum volatility, and size, with $130, $153, $657, and $2,477 billion, respectively. This robustness exercise alleviates some concern about capacity in a potential setting in which the smart beta premiums themselves decrease.

The capacity numbers in Exhibits 2 and 3 are calculated for MSCI smart beta indexes that are long only, and that index construction results in particular levels of active risks. In Exhibit 4, we report capacity in terms of unit-geared (long–short with $1 per side) strategies over a one-day horizon, which expresses capacity AUM in terms of active risk. To determine these numbers, we look at the smart beta strategy as the market-cap portfolio (MSCI USA) plus a long–short overlay and then rescale this overlay to have 100% notional long and 100% notional short exposure. Thus, Exhibit 4 can be used to convert capacity to any level of gearing of active risk. In particular, a 130/30 multifactor fund has a capacity of $900 billion. Exhibit 4 also reports the AUM capacity in dollar terms versus the market-cap-weighted portfolio (the tracking error of MSCI strategies is estimated using a BlackRock proprietary risk model). The multifactor index has an estimated tracking error of roughly 3%. If this changed to 2%, capacity would increase to $474 billion from $316 billion.

An important robustness exercise for capacity estimates is to examine different turnover rates, which we do in Exhibit 5. (Note that in some smart beta strategies, like minimum volatility, the MSCI index construction imposes a maximum bound on turnover.) We hold the premiums at the baseline case, as in Exhibit 3. In Exhibit 5, we observe that estimated capacity is highly sensitive to turnover—which is not surprising, given its effect on trading costs. On average, starting from the baseline turnover rates, a 10% decrease in turnover increases capacity by approximately 60%, and the largest impact occurs in the strategies with the lowest turnover, like size. Furthermore, we also observe that as turnover decreases, the sensitivity of capacity to turnover is higher. Intuitively, if turnover doubles, not only do we need to pay higher market impact in every stock we trade, but the transaction cost as a percentage of the amount traded needed to eliminate the smart-beta premium decreases by half (given that the amount traded is doubled).

Exhibit 6 reports estimated capacity as a function of the smart beta premium, holding constant turnover equal to realized turnover over the last year for each index, rounded to the nearest 5%. The capacities for the 100% and 50% premium case are the same as those reported in Exhibit 3. As we increase the premium estimates from 50% to 100% and 150% of the historically observed premium for minimum volatility in Exhibit 6, the capacity estimates move from $657 billion to $1,353 billion and $2,049 billion, respectively. The estimated capacity is approximately linear, which makes sense given that turnover is fixed and trading costs are an asymptotically, linearly increasing function.

It is worth noting, and based on Exhibits 5 and 6, that capacity estimates are more sensitive to the assumption of the expected turnover rate than the expected premium. This is driven by the important nonlinear effect of turnover versus a smaller linear effect of the expected premium in the *t*-cost model.^{7}

### Trading over a Five-Day Horizon

In Exhibit 7, we re-estimate capacity assuming that the trading is done over a horizon of five days instead of one day.^{8} The five-day horizon is typical when implementing larger, capacity-constrained strategies and when doing so is beneficial to investors. In fact, passive funds that track certain markets, like certain single-country, frontier, or emerging market funds, do actually trade over longer time horizons when necessary. Typically, those horizons can vary from one to five days or longer (some allow up to 30 days) depending on the trade size and the market liquidity at a specific point in time.^{9}

Exhibit 7 shows that increasing the horizon from one day to five days results in substantial increases in capacity. Momentum, the strategy with the smallest capacity, reaches a breakeven size of $324 billion at a five-day trading horizon, compared to $65 billion for a one-day horizon (see Exhibit 3). With a five-day horizon, capacity is estimated to be significantly above $1 trillion for all the other styles. In particular, the multifactor strategy reaches a capacity of approximately $1.6 trillion, significantly higher than the estimated $316 billion if trading occurs over one day. Significantly decreased market impact costs drive these substantial increases in capacity: As the time horizon increases, market impact costs rapidly shrink, and this is the major component of total *t*-costs.

### A Detailed Look at Momentum

Based on our analysis, momentum is the strategy with the smallest capacity; therefore, we proceed with a more detailed look at what is driving the top-line capacity of this strategy in Exhibit 8. For comparison, our baseline capacity estimate of momentum over one trading day is $65 billion assuming a premium of 2.05% in data (see Exhibit 2).

Assuming just a 1% premium and a one-day trading interval, we estimate that the capacity of momentum decreases to $25 billion. However, if we allow the trading time horizon to be extended to five days, capacity increases substantially to over $100 billion. Momentum capacity is sensitive to expected turnover rates, and slowing momentum by decreasing turnover can significantly increase estimated capacity. With a 2% momentum premium, if expected (two-way) annualized turnover decreases by 10% (from 180% to 170%) capacity increases by 13% from $63 billion to $71 billion. Exhibit 8 also examines momentum capacity with different levels of ADV traded in the marketplace. As expected, as trading volume increases, estimated capacity also increases. The increase is more significant when the premium is higher, as seen in the higher slopes of the capacity/ADV multiplier curves. Finally, Exhibit 8 also shows estimated capacity results for different levels of market volatility. If market volatility decreases by 10% (relative), assuming a premium of 2% and one-day trading interval, momentum capacity increases from $63 billion to approximately $71 billion.

## CONCLUSION

Smart beta strategies—momentum, quality, value, size, and minimum volatility strategies, and a multifactor combination of the first four—have been known historically to generate excess returns relative to market-capitalization-weighted indexes, at least since the 1990s. Investors are now able to directly trade these factor risk premiums with ETFs tracking transparent, third-party indexes. Although the current AUM in these strategies remains relatively small at $225 billion as of April 2016, this area of asset management is one of the fastest growing, with expected growth rates around 20%.

We estimate that capacity in smart beta strategies is large. We estimate capacity using a transaction cost model and an assumption for the smart beta premium. Flows into these strategies incur transaction costs: For a given trading horizon, we calculate the fund size at which the associated turnover transaction costs offset the smart beta premium historically observed in data. With a horizon of one day, we find that momentum is the strategy with the smallest capacity, at $65 billion, and size is the largest with a capacity of $5 trillion. Extending the trading horizon to five days increases capacity in momentum and size to $324 billion and over $10 trillion, respectively. A multifactor combination of momentum, quality, value, and size has an estimated capacity of $316 billion and $1.6 trillion at one- and five-day trading horizons, respectively. Our estimates of capacity are robust to market volatility, ADV traded in the market place, different assumptions on the expected smart beta premium, and expected turnover rates. Among these variables, changes in turnover rates have the largest impact on capacity estimates.

## APPENDIX

### MARKET IMPACT

The functional form for the market impact term of stock *i*, *MI _{i}*, in the

*t*-cost model (see Equation (1)), is given by

where *k*_{1} = 0.07; *k*_{2} = 0.04; *FV _{i}* is the amount traded in stock

*i*, in dollars;

*b*is unique to every stock and represents the sensibility of the market impact with respect to the market volatility (for every stock, this constant is proportional to estimated volatility); and

*ADV*

_{i}is the average daily volume (in dollars) of stock

*i*. This average daily volume is exponentially weighted.

The intuition behind the *t*-cost model is that the cost of a trade is higher if the size of the trade increases or the average daily volume of a particular stock is low, and vice versa. The *t*-cost model has a breakpoint when . That is, the model treats trades in a particular stock differently when the amount traded is higher than 40% of the average daily volume (large trades). In line with the literature, the market impact is concave, but for large trades, it is asymptotically linear, as shown in the following equation:

The units of the parameters are scaled such that they are consistent with expressing the estimated transaction cost in percentage points of the trade size. We assume that the market impact of a portfolio trade is the weighted average of the market impact of its stock constituents.

### TRANSACTION COSTS OVER LONGER HORIZONS

When a given trade is large relative to average daily volume, standard practice is that trading takes place not over one day but over a longer time horizon to reduce the market impact component of the total transaction cost. The transaction cost of a trade, assuming the trade is executed over *T* days, is given by the following equation:

Note that the transaction costs decrease over a longer horizon. In fact,

A-4## ENDNOTES

The views expressed here are those of the authors alone and not of BlackRock, Inc. We are grateful for helpful comments from Ben Golub, Ananth Madhavan, Daniel Mayston, Manish Mehta, Sara Shores, and Jack Reerink at BlackRock.

↵

^{1}Some seminal work was done by Fama and French [1993] for value and size and Jegadeesh and Titman [1993] for momentum, but the first references in academia to these factor premiums occur much earlier. A comprehensive summary is given by Ang [2014].↵

^{2}In contrast, a large microstructure literature, beginning with Glosten and Milgrom [1985], does show how prices are set in equilibrium to reflect trading costs and adverse selection.↵

^{3}Specifically, the MSCI Smart Beta Indices are defined by MSCI as follows. Momentum (USA Momentum Standard) measures the performance of U.S. large- and mid-capitalization stocks exhibiting relatively higher price momentum characteristics, while maintaining reasonably high trading liquidity, investment capacity, and moderate turnover. Quality (USA Quality Standard) measures the performance of U.S. large- and mid-capitalization stocks as identified through three fundamental variables: return on equity, earnings variability, and debt-to-equity. Value (USA Value Weighted Standard) measures the performance of U.S. large- and mid-capitalization stocks with value characteristics (book value to price, 12-month forward earnings to price, and dividend yield). Size (USA Risk Weighted Standard) measures the performance of U.S. large- and mid-capitalization stocks with a tilt toward the smaller, lower-risk stocks within that universe. Minimum Volatility (USA Minimum Volatility Standard) measures the performance of U.S. large- and mid-capitalization stocks that, in the aggregate, have lower volatility characteristics relative to the broader U.S. equity market. Diversified Multiple Factor (USA Diversified Multiple-Factor Standard) measures the performance of U.S. large- and mid-capitalization stocks and focuses on four proven drivers of return: financially healthy firms, stocks that are inexpensive, smaller companies, and trending stocks.↵

^{4}We acknowledge that there are active strategies that pursue similar investment objectives and these*indirect*effects might influence the capacity of direct investment in these factor ETFs. We deliberately focus on these strategies that are available to every investor through ETFs and with AUM that is easily measurable.↵

^{5}In this study, we do not consider other restrictions that may limit capacity, such as the maximum percentage ownership in a particular stock. We note that market capitalization and index composition are likely to change significantly before capacity estimates are reached. If we impose a maximum percent ownership constraint (e.g., the 95th percentile ownership of the constituent stocks is less than 10%) and assume that market capitalization is held constant, we estimate such a constraint to be binding at around $150 billion AUM for most strategies, except for size, which has a constraint of approximately $300 billion. On the other hand, we do not consider strategic trading that will reduce transaction costs relative to the calculations we present here.↵

^{6}Although we vary the time horizon, we do not consider dynamic strategic trading, which simultaneously varies both the horizon and quantity in response to other market participants’ trades (see Back, Cao, and Willard [2000]). On the one hand, this may lower the average cost of trading by taking advantage of time-varying high-liquidity, low-impact periods. On the other hand, this could increase transaction costs during certain periods when there are large numbers of informed traders. The*t*-cost model can still be applied in both cases because it predicts the cost of trading with characteristics measurable in all time periods; variables specifically measuring asymmetric information, in contrast, are usually not directly observable. Taking more realistic scenarios with longer trade horizons and optimized trading, the trading costs will be lower and capacity higher than the breakeven AUM stated here.↵

^{7}We found that ADV also has a smaller linear effect on estimated capacity. On average, if ADV increases by 10%, estimated capacity increases by 11%.↵

^{8}When estimating capacity under longer trading time horizons, we assume that the price impact of any trade fully reverses the next day.↵

^{9}Many ETFs are not constrained to trade over a specific time horizon; the ETF portfolio manager makes the decision based on the tracking error versus transaction cost trade-off of the particular fund. If AUM is near capacity levels, trading could be done not only over a longer time horizon but could be further optimized over trading sizes, frequencies, and venues.

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