Factor investing, and the associated intellectual battles, have raged for decades in academic finance journals. However, now that factor investing has gone mainstream via ETFs, the debate has broader interest among the investing public. In this paper we discuss this key question: Do factor portfolios survive transaction costs?

Some investors question the very existence of factor premiums. We are sympathetic to this viewpoint given the noise around poor factor replication and the potential for data-mining (although we think they are wrong).

However, one thing is clear: it is hard to have a factor debate with those who fall in the “factors don’t exist” camp. So let’s move past this debate and discuss another debate among those investors who believe factors exist.

Factor Portfolios and Transaction Costs

Among those who believe in the potential of factor investing, there is debate around a simple question:

Do factor portfolios survive transaction costs?

Turns out this question does not have a simple answer.

Some commentators, such as our friend Gary Antonacci, highlight research which suggests that factor strategies have very limited capacity before transaction costs.

On the flip side, we have spotlighted research and we have constructed focused factor indexes, which argue that factor capacity, while not infinite, is certainly investable.(1)

Are we crazy to believe that factors have some investable capacity? Possibly, but the answer to this question will depend on who you ask.

For example, consider the momentum factor, where the estimated capacity ranges from $5B to over $300B — a wide range to say the least!(2)

In this piece, we’ll try and summarize the key research and ideas that will help readers ascertain the intellectual “truth.”(3)

The essay is broken into two core sections:

  1. Microstructure transaction cost analysis via high-frequency trading data
  2. Inferred transaction cost analysis via fund manager performance data

For the microstructure transaction cost analysis we examine multiple academic papers that attempt to model out trading costs, using TAQ data, which is the core dataset available for academic researchers via the WRDS. platform(4)

We also look at 2 papers that use live high-frequency transaction data from Blackrock and AQR. The conclusion from this research is that factor investing has limited capacity, but there is a substantial debate over the actual capacity levels.

The second attempt at tackling the question of how transaction costs affect factor portfolios is to look at the performance of live fund managers to back out, or infer, transaction cost estimates. These research papers examine trading costs via a two-pass Fama-Macbeth regression technique. The novel idea behind this approach is that one does not need to “model” trading costs and look at cumbersome high-frequency execution data, rather, via the Fama-Macbeth regression framework, one can learn the true transaction costs under various assumptions. This vein of research seeks to compare “realized factor premiums” to hypothetical factor premiums to determine the “net factor premium” received by actual fund managers. The conclusion from this research is one-sided: factor premiums are shaky at best, net of transaction costs. Below we perform an extended analysis of these research papers.

Where does this all lead us in our quest to answer the question: Do factor portfolios survive transaction costs?

Well, there are no definitive answers, but we come to the following conclusions:

  • Factors have capacity constraints.
  • One can learn little about transaction costs via two-pass regression procedures.

Let’s dig into the papers on trading costs.

A PDF version of this is available here.

Summary of Microstructure Transaction Cost Papers

So what does the research say about trading costs? As mentioned above, it depends on who you ask.

Results Using TAQ data (Dataset available to academic researchers)

First, there are a handful of studies done using trading-execution estimates from the NYSE Trade and Quote (TAQ) database (available for academic researchers via WRDS).

A few of these papers are listed below:

We have discussed the last paper on our website here. Here is the abstract of the paper:

We study the after-trading-cost performance of anomalies, and effectiveness of transaction cost mitigation techniques. Introducing a buy/hold spread, with more stringent requirements for establishing positions than for maintaining them, is the most effective cost mitigation technique. Most anomalies with turnover less than 50% per month generate significant net spreads when designed to mitigate transaction costs; few with higher turnover do. The extent to which new capital reduces strategy profitability is inversely related to turnover, and strategies based on size, value, and profitability have the greatest capacities to support new capital. Transaction costs always reduce strategy profitability.

All three papers above come to similar conclusions — trading costs reduce factor premiums, and momentum, the so-called “premier anomaly,” suffers the most from transaction costs, leaving it with a fairly low capacity and questionable after-frictional-cost performance.

Here is Table 7 of the Novy-Marx and Velikov paper:


The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Note, that the capacity of momentum is only $5.81B, which is a relatively small amount of capital in a global equity market with a multi-trillion dollar notional value.

Results Using Practitioner Transaction Data

While the 3 papers mentioned above are in general agreement when it comes to limited capacity constraints on various factor strategies (especially with respect to momentum), there are two papers, that find strikingly different results. The key difference between these papers and the prior three papers discussed is related to the data source deployed.

The first paper is, “Capacity of Smart Beta Strategies: A Transaction Cost Perspective,” by Ratcliffe, Miranda, and Ang (2017), researchers connected to Blackrock (We discuss this paper here). This paper, using a proprietary transaction model and leverages high-frequency data compiled from Blackrock’s live trading transactions. The key finding is that there is a much larger capacity for momentum (and the other factor approaches) than what previous research had described.

Below are the capacity estimates assuming different premium levels and trading over 1-day.

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

The capacity is estimated anywhere between $27B and $65B for momentum, which is almost a magnitude larger than the estimates from the prior papers.

But what if we allow the factor manager to trade into the positions over multiple days?

A multi-day trading and execution cycle is both reasonable and fairly typical for large asset managers.

The capacity estimates for this multi-day approach are posted below:

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

In a multi-day transaction cost model, the momentum factor strategy has a greatly expanded capacity limit that dwarfs the ~$5B capacity constraint from the original academic research on the subject.

Clearly, small differences in transaction costs models, and/or the underlying data fed into these models, can make a large difference for capacity estimates.

For another take from a practitioner-associated research piece, we can look at the analysis from, “Trading Costs of Asset Pricing Anomalies,” by Frazzini, Israel, and Moskowitz (2015) (the researchers are associated with asset manager AQR). This paper uses proprietary transaction data to estimate the transaction costs of trading factor-style stocks (value, momentum, etc.) (We dig into the paper in detail here).

The abstract of the paper is as follows:

Using over a trillion dollars of live trading data from a large institutional money manager across 21 developed equity markets over a 16-year period, we measure the real-world transactions costs and price impact function facing an arbitrageur and apply them to trading strategies based on empirical asset pricing anomalies. We find that actual trading costs are an order of magnitude smaller than previous studies suggest. In addition, we show that small portfolio changes to reduce transactions costs can increase the net returns and break-even capacities of these strategies substantially, with little tracking error. Use of live trading data from a real arbitrageur and portfolios designed to address trading costs give a vastly different portrayal of implementation costs than previous studies suggest. We conclude that the main capital market anomalies – size, value, and momentum – are robust, implementable, and sizeable in the face of transactions costs.

A key table from the paper highlights the capacity of the long/short momentum factor:

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

This paper finds the long-short momentum capacity to be $56.16B, which is magnitudes higher than the academic papers utilizing the TAQ dataset.

Who’s Right? The Ivory Tower Academics or the Conflicted Practitioners?

Research from AQR and Blackrock researchers uses real-world trading costs to assess trading costs on factor-investing styles. These authors find that capacity levels for the momentum factor are 10x higher than the estimates presented by the academic researchers before them.

Who are we to believe?

On one hand, the academics don’t have factor products to push into the market; on the other hand, the practitioners have actual transaction data that better reflects the real-world. Or as Gary Antonacci puts it:

…Like what happens when drug companies have academics do trials of their products, fund sponsors had their own researchers look at the capacity of factor-based strategies.

AQR provides a clever experiment to zero in on the ground truth, despite doing research that has a potential conflict of interest.

To identify which approach is more akin to reality, the AQR researchers conduct a “what-if” analysis using their transaction cost estimation approach versus the approaches of researchers using TAQ data to assess the estimated transaction costs associated with the implementation of the S&P 500 index portfolio.  The image below highlights that the academic models/data are likely misspecified. Using the approach of the original academic researchers (with TAQ data) suggests that the annual trading costs for the SP500 would be 0.63%, while the data from AQR suggests trading costs are 0.06%. We can compare this AQR estimate to the known transaction costs from Vanguard (0.12% per the paper) and iShares (0.07% per the paper) associated with actually implementing portfolios that track the S&P 500.

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

The analysis from AQR using live transaction data (and by extension, Blackrock) seems to paint a much clearer picture of reality, despite being conflicted. Unless the academic researchers can reconcile why it is so expensive to buy beta, when in fact, we know it is relatively cheap, the conflicted practitioner-associated researchers seem to be winning the argument that factor strategies have greater capacity than prior research has identified.

Transaction Cost Research Summary

In the end, a summary of the papers above highlights the following fact–depending on the model/data one chooses, the conclusion regarding factor capacity can vary wildly.

(5)

Perhaps measuring transaction costs via microstructure data is an example of trying too hard?

What if there were a way to measure trading costs without a model?

This novel idea was first proposed by Research Affiliates (RAFI), and we dig into the idea below.

Ditch the High-Frequency Data and Measure Trading Costs Via Performance?

Earlier this year, the Research Affiliates team (Rob Arnott, Vitali Kalesnik, and Lilian Wu) came out with a provocatively titled paper, “The Incredible Shrinking Factor Return” (“RAFI paper”). The researchers came up with a novel approach to identify if investors can exploit factors after transaction costs. Their solution to the puzzle is to bypass transaction cost analysis and simply review live portfolio results. The authors utilize a two-stage regression, also known as a Fama-MacBeth regression on live, net-of-fee returns of mutual funds over the 1991-2016 time period.

How does a two-stage regression propose to identify transaction costs?

If funds are efficiently capturing factor premiums, the estimated factor premia from the two-stage regression approach should approximately equal the premiums to the hypothetical research factors (e.g., SMB, HML, MOM, etc.) in a zero transaction cost world. Any spread between realized premia and paper-portfolio premia arguably reflects unobservable transaction costs incurred by live fund managers…in theory…

Here is the idea in more detail: In the first-stage regression, for each fund, regress the net-of-fee returns (excess of RF rate) against the standard factor models (market, SMB, HML, MOM). After this stage, for each fund, one will have the “estimated beta loadings” on each of the factors. Then, in the second stage regression, across all months, regress the net-of-fee returns (excess of RF rate) for all funds against the estimated beta loadings from the first stage for each fund. The “beta estimates” from the second stage regression represent the factor premium earned for each factor for a particular month. Averaging across time, one comes up with the factor premia achieved by all mutual funds over time. These premia estimates are then compared to the paper portfolio returns to the factors, such as the Market, SMB (size), HML (Value) and MOM (Momentum) factors.

What Does the RAFI Paper Find?

Table 2 in the paper shows the following–paper portfolios for the market (Mkt-RF), Size, Value, and Momentum factors earned 8.2%, 2.6%, 3.6%, and 5.7%, respectively. Meanwhile, the real-world mutual fund portfolios earned 4.1%, 3.3%, 2.2%, and 0.4%, respectively! So in real-world portfolios, the premia earned (as measured in the two-stage regressions) is reduced by 4.1% for the market portfolio, 1.4% for the HML portfolio (and is not significant in the real-world) and 5.3% for the MOM portfolio. According to the tests, real-world portfolio managers deliver a lot less of the factor premia than the paper portfolios…and this includes the generic market factor. Weird, to say the least.

The difference between hypothetical and “realized” factor premia is staggering for long-term investors.  For example, the compounding of $100 in the paper MOM portfolio increases to $247, while the real-world premia compounds from $100 to only $110! The figures in the paper drive home the author’s point: using two-stage regression premia estimates, real-world portfolios wildly underperform the paper factor portfolios.

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

After a series of robustness tests, the results are the same–the real-world portfolios deliver lower factor premia than the paper portfolios.

But what is the source of the slippage?

The paper gives two suggestions — (1) trading costs and (2) manager skill. Both can have an effect.

The paper ends with this concluding remark (last paragraph of the paper):(6)

We find that fund managers experience significant shortfalls in their ability to capture factor returns compared to theoretical paper portfolios. In particular, the shortfall is quite strong for the market and value factors, where the return delivered to the end-investor is halved or worse. For the momentum factor the end-investor seems to have enjoyed no benefit whatsoever from fund momentum loadings nor any penalty for funds that have an anti-momentum bias. We suspect the lion’s share of the shortfall is due to trading costs, a topic we may explore in a future article. Factor returns are inherently uncertain, whereas some drivers of slippage, such as costs or returns, which are not captured by the short side of the paper portfolio are a lot more predictable. If these predictable factors are responsible for the slippage, we are likely to see a similar magnitude of slippage in the future.

One thing is clear — using the two-stage regression premia estimation approach, one finds that real-world portfolios deliver lower premia than the paper factor portfolios.

But wait, there’s more…

Following up on the RAFI paper, there is a new working paper by Andrew Patton and Brian Weller, titled, “What You See Is Not What You Get: The Costs of Trading Market Anomalies.” This paper is a more formal academic research paper that builds upon the limited, albeit concise, discussions in the RAFI paper. For example, the RAFI paper attempts to explain why the 4.2 percentage point gap between the realized factor premia and the market factor portfolio is reasonable because of measurement issues, whereas the other factor gaps are not measurement related, but associated with implementation costs. The explanations, while interesting, lack depth. Patton and Weller fix these issues and make it clear that the RAFI paper’s empirical approach tells us little about implementation costs:

[The RAFI paper]…sheds little light on implementation costs because realized factor slopes and factor returns may have very different means…

Here is the full abstract of the Patton and Weller paper (10/31/17 version):

Is there a gap between the profitability of a trading strategy “on paper” and that which can be achieved in practice? We answer this question by developing two new techniques to measure the real-world implementation costs of financial market anomalies. The first method extends Fama-MacBeth regressions to compare the on-paper returns to factor exposures with those achieved by mutual funds. The second method estimates average return differences between stocks and mutual funds matched on risk characteristics. Unlike existing approaches, these techniques deliver estimates of implementation costs without estimating parametric microstructure models from trading data or explicitly specifying factor trading strategies. After accounting for implementation costs, typical mutual funds earn low returns to value and no returns to momentum.

To summarize, the authors come to the same conclusion as RAFI, but via a more rigorous route. Patton and Weller essentially claim that factor investing doesn’t work after transaction costs.

Let’s dig deeper into their results.

The paper examines the returns to both mutual funds and paper portfolios over a longer time period than the RAFI paper (1970-2016).

Below is an image from the paper highlighting the number of mutual funds in the sample each month from 1970-2016.

Source: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3034796 (accessed 11/17/17)

The image above splits the sample into before and after 1993, to account for the Jegadeesh and Titman (1993) momentum finding.

As mentioned above, the paper uses a similar methodology as the RAFI paper, with two-stage regressions. However, the paper adds an additional wrinkle–they compare the second-stage premia estimates of the mutual fund sample to the second-stage premia estimates of “paper portfolios.” This testing environment allows them to compare second-stage premia estimates on live portfolios to second-stage estimates on paper portfolios, thus eliminating the worry that the second-stage premia estimate procedure itself may be driving the results from the RAFI paper. See the appendix for a detailed explanation on this subject.(7)

The paper portfolios examined are mainly from Ken French’s website.

Here is a description of the portfolios from the paper:

Our Fama-MacBeth tests of Section IV combine mutual fund data with common test portfolios. Because our factor set includes value (HML), size (SMB), and momentum (UMD), our baseline analysis uses the Fama-French 25 size-value double-sorted portfolios plus 25 size-beta portfolios, 25 size-prior return portfolios, and 25 size-Amihud illiquidity portfolios to ensure adequate dispersion in loadings to identify risk premia in the cross section. We supplement this set of test assets with an expanded cross section following the recommendation of Lewellen, Nagel, and Shanken (2010). In our larger portfolio set, we also include 49 industry portfolios, 25 size-operating profitability portfolios, 25 size-investment portfolios, 10 beta-sorted portfolios, 10 market capitalization-sorted portfolios, 10 book equity to market equity ratio sorted portfolios, 10 Amihud illiquidity-sorted portfolios, 10 operating profitability-sorted portfolios, and 10 investment-sorted portfolios for a total of 269 portfolios.

In total, the authors examine the returns to either 100 paper portfolios, or 269 paper portfolios, as described above.

Table II of the paper yields the main result, and is shown below:


The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

A quick description of the Table above–Panel A examines equal-weight paper portfolios, while Panel B examines value-weight paper portfolios. Within the panels, the first section examines the difference between the paper portfolios (second section) and the mutual fund sample (third panel). Examining Panel B (VW paper portfolios), we see that over the entire time period (1970-2016), the mutual fund sample delivered a market premium of 6.93%, which is similar to the paper portfolios (6.62% and 6.78%) — the difference between the two is small and statistically insignificant. Now examining the factor investing portfolios, we see that the mutual fund sample’s premia were 2.84% for HML, 1.47% for SMB, and 1.86% for UMD (Momentum), with only Value being marginally significant. Compare this to the paper portfolios, which deliver premia of either 7.06% or 5.46% to HML and 9.23% or 9.14% to UMD which are highly significant (note — SMB is not significant for the paper portfolios). Thus, the difference between the premia for the mutual funds and the paper portfolios for HML and UMD is large and significant–meaning the value and momentum factor premia are not being captured in live mutual funds, compared to paper portfolios.(8)

This analysis is interesting and corroborates the core thesis from the RAFI paper: real-world implementation costs erode the value and momentum factors.

Are the Results Subject to Debate?

Let’s summarize what we’ve covered thus far (a lot of material — congrats on making it this far!):

  • Researchers have looked at high-frequency trading data and came to the conclusion that transaction costs matter, but the range of possibilities is huge.
  • RAFI presents a new approach to identifying implementation costs and finds that fund managers can’t capture factor premiums
  • Patton and Weller conduct a more robust investigation of the RAFI concept and identify that fund managers can’t capture factor premiums.

Should factor investors give up? Not exactly.

The paper covered in the appendix by Ang et al. dives into some statistical issues regarding stocks and portfolios in two-stage regressions. This analysis brings into question many of the findings in the RAFI paper, however, the Patton and Weller paper (“PW” paper) is able to bypass these issues by comparing the premia from paper portfolios to the premia from real-world portfolios.

We dig into the weeds of the Patton and Weller analysis by introducing two realities of the fund marketplace:

  1. We assume some fund managers are closet-indexing.
  2. We assume some fund managers shift factor exposures over time.

What happens when we analyze these scenarios? For example, let’s “suspend belief” for a minute and pretend we live in a world where there might be a lot of closet-indexer mutual fund managers who value their careers more than their performance. Moreover, what happens if we assume there are these mythical creatures called, “stock-pickers,” and their real-world portfolios shift factor exposures?(9)

Below, we examine what happens to estimated factor premiums when a hypothetical portfolio manager, 1) closet indexes or 2) “shifts around” their factor exposures over time.

For these tests we examine 175 paper portfolios–these portfolios have no transaction costs at all–purely hypothetical. All portfolios are value-weighted. Specifically, the 175 portfolios are made up of the 25 size and B/M portfolios, the 25 size and momentum (12_2) portfolios, the 25 size and investment portfolios, the 25 size and operating profitability portfolios, the 25 operating profitability and investment portfolios, the 25 B/M and investment portfolios, and the 25 B/M and operating profitability portfolios. These portfolios were chosen to match factor portfolios used within the Fama and French 5-factor model.(10)

The factor returns are taken from Ken French’s website for the following 6 factors: Mkt_Rf, SMB, HML, MOM, CMA, RMW.

Establishing some Baseline Results

First, we examine the factor premia estimates from the two-step regressions on the 175 paper portfolios. Regression results are shown across two time periods, 1970-2016 and 1993-2016 (similar to the Patton and Weller paper). The results are shown for 4 models commonly used–the market model (CAPM), the 3-factor model, the 4-factor model, and a 6-factor model (FF 5-factor plus momentum).

The results from the second-stage regressions are presented below:


The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

As found in the Patton and Weller paper, the paper portfolios achieve highly significant premia, in both time cycles.(11)

What happens if these paper portfolios are able to act more like real-world portfolio managers? Let’s examine what happens to the results when we allow closet-indexing into the sample.

Paper Portfolio Factor Premia with Closet-Indexers — statistical power degrades

One assumption being made in the comparison of real-world mutual funds to paper portfolios is that portfolios managers are taking pure bets on certain factors. What does that mean? Sometimes, a picture can be helpful. Below are images from our visual active share tool, which allows advisors to assess the characteristics or funds and even compare them to academic portfolios. This helps advisors/investors to understand the characteristics of the portfolio, as described here.

The first image below selects the academic high and low 12_2 momentum portfolios. The x-axis displays the percentile ranks of all firms in the universe on the 12_2 momentum characteristic, and the y-axis displays the percentile ranks of all firms on market capitalization. I also highlight 4 of the 25 paper portfolios used in the regressions analysis for illustrative purposes:

  1. Large, low momentum
  2. Large, high momentum
  3. Small(ME2), low momentum(12)
  4. Small (ME2), high momentum
Source: http://alphaarchitect.com/tools

So the above image designates what the factor paper portfolios should look like in practice.

The figure below adds the Vanguard Russell 1000 index (VONE), to highlight where most funds invest.

Source: http://alphaarchitect.com/tools

As one can see, the market-cap portfolio does not have a ton of overlap with the large-cap high and low momentum portfolios and has no overlap to the small-cap high and low momentum portfolios (which makes sense).

How do most mutual funds actually invest? Many fund managers maintain a low-tracking error relative to a broad index, meaning that the fund may “tilt” towards a factor, but probably won’t deviate too far from the market-cap weighted passive index portfolio. Some refer to this practice as closet-indexing. Closet-indexing behavior is not necessarily a bad thing (and can be considered a good thing in some cases), and we aren’t trying to create a debate on this subject, we are merely making a point that closet-indexing is a behavior exhibited by many fund managers in the marketplace.

But how does the introduction of closet-indexing potentially affect the results from two-step factor premia estimation procedures? (i.e., the technique used in the RAFI and Patton and Weller papers).

To examine this question we assume that the 175 paper factor portfolios in my tests are “transformed” into closet-indexers. We create this transformation by allowing the 175 paper factor portfolios to invest 80% in the market portfolio, and 20% in the factor portfolio. We then run the same tests from above on these 175 “closet-indexing” factor funds.

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

What do we find?

Well, the estimated premia are almost exactly the same, which is to be expected. However, interpreting the statistical significance of the results get trickier. The introduction of closet indexing lowers the statistical power of the tests and we notice that there is almost a complete loss of significance for the factor premia. A statistician would argue that the factor premia earned by these portfolios are not reliably different from zero.

What are the implications of this analysis? Well, interpreting the “statistically significance” of a factor premia is more challenging when there is a possibility that portfolios closet index. And by extension, if we relax the assumption that real-world mutual funds aren’t all disciplined factor quants following focused factor portfolios, interpreting “statistically insignificant” factor premia estimates doesn’t necessarily really tell us much about implementation costs.

Paper Portfolio Factor Premia with Factor Shifters — Factor Premia Shrink to Zero

In the analysis above we see that closet-indexing can cause estimates of factor premia to lose statistical significance, mechanically.

Let’s examine another angle on the analysis. What if portfolio managers switch between factors from month to month, i.e they are not 100% following a factor throughout time? And more importantly, how might this affect the interpretation of two-step factor premia estimation results?

We examine this question by simulating 875 paper “factor-switcher” portfolios.(13) To capture the idea of a “factor-switcher,” every month the portfolio manager randomly selects one of the 175 paper portfolio to invest in–this gives the managers the ability to switch their system (factor model) every month (which may represent an ad-hoc stock-picker).

The results of this analysis are shown below:

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

As can be seen above, factor-switching managers earn the small size premium and the market beta premium…and that’s about it. These hypothetical managers have little exposure to the other factors when they are allowed to randomly switch each month.

What are the implications? Once again, under the assumption of ZERO trading costs, factor premia estimates are insignificant when fund managers are able to factor switch over time.(14)

Why does this matter? If real-world portfolios factor shift, two-stage regression premia estimation techniques will low-ball factor premia earned by fund managers. In a factor-switcher world, one cannot interpret the “loss of factor premia” as an implementation cost, because this loss of premia may be observed simply because managers aren’t steely-eyed focused factor quant investors.

Interpreting the Results of Two-Step Factor Premia Estimates is Potentially Hazardous

The Patton and Weller paper is really interesting and we recommend that everyone check it out. These authors take on an immense challenge and do their best with the tools and data they are given. However, the extended analysis conducted above highlights that factor premia estimates from fancy statistical procedures are noisy and can be driven by many elements of the investing landscape that aren’t related to implementation costs. For example, by simply infusing the ideas of 1) closet-indexing and 2) factor-switching, frictionless paper factor portfolios generate negligible two-step factor premia estimates. And by extension, if real-world portfolios exhibit 1) closet-indexing or 2) factor-switch over time, they too will generate near zero factor premia estimates — even if we assume implementation costs are zero!

The reality is that trying to assess trading costs via indirect methods is fraught with challenges that are likely too steep to overcome. We have not even mentioned another realistic possibility–some managers over this time period were simply stock-pickers, not factor investors–these managers would simply add noise to the regressions, causing a difference between the paper portfolios and the real-world portfolios.(15)

The more direct approach associated with the analysis of live high-frequency trading data, although imperfect, is likely to give us better insights into the costs and potential scalability of various investment strategies. Of course, the challenge with this approach is getting access to more proprietary data from different institutional investors. Access to broader datasets would help researchers ascertain whether or not the scalability of factor investing is only accessible to a privileged few, or the broader professional investor landscape.

Summary on factor investing and transaction costs

We’ve highlighted the core research, and our additional analysis, associated with the following question:

Do factor portfolios survive transaction costs?

The key takeaways are as follows:

  1. Attempting to estimate factor trading costs can be difficult and depends on the data and assumptions employed. Institutional traders, such as AQR and Blackrock, clearly enjoy lower transaction costs than the average investor who buys at the ask and sells at the bid.
  2. A two-stage regression is a clever way to avoid the mess of delving into high-frequency, and often limited, transaction cost data. However, this methodology is fraught with interpretation issues. For example, one cannot simply compare two-stage factor premia estimates to factor portfolio returns and consider this a “transaction cost” estimate. Mechanically, two-stage factor premia estimates will be lower than factor portfolio returns (see reference 7 for full details)
  3. Two-stage factor premia estimation studies can be improved, but they face arguably insurmountable interpretation challenges. For example, the introduction of closet-indexing and factor-timing will mechanically degrade factor premia estimates in the face of zero transaction costs.(16)

“Great,” you might say, “what should I believe?”

Here are a few things:

  • Trading costs degrade performance.
  • Factor investing strategies have capacity constraints.
  • Higher turnover factors have lower capacity constraints than lower turnover factors.
  • Money doesn’t grow on trees. Excess returns are usually associated with some element of additional “risk.”

Thanks for reading–please let us know if you have any questions.

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