**Transaction Costs of Factor-Investing Strategies (2019)***Feifei Li, Tzee-Man Chow, Alex Pickard, Yadwinder Garg*

Financial Analysts Journal 75(2), 47-61, URL

I already did a post on transaction costs some time ago, but this week’s AGNOSTIC Paper has a slightly different focus. The authors develop a transaction cost model and use it to estimate the *capacity* of the major factors. There are many ways to define capacity in more detail, but the general idea is quite simple. It is the amount of money you can invest in a profitable strategy before you move prices too much and lose your advantage. Unfortunately, what theoretically sounds simple and intuitive is quite difficult to estimate in practice…

Before we continue, a brief note. This paper is not necessarily the go-to reference for research on equity transaction costs. At least in my perception, the “Trading Costs” paper from Frazzini et al. (2018) received somewhat more attention. I still picked this one as it includes an overview of the literature including Frazzini et al. (2018) and is somewhat more practical.

Everything that follows is only my summary of the original paper. So unless indicated otherwise, all tables and charts belong to the authors of the paper and I am just quoting them. The authors deserve full credit for creating this material, so please always cite the original source.

## Setup and Idea

Over the last weeks, I may have convinced you that factors are at least not entirely stupid. But of course, even the best strategies are worthless if you cannot implement them at reasonable costs. Given that factor strategies typically rely on large diversified portfolios, trading costs are obviously an important issue. If factors don’t survive real-world trading costs, the whole literature wouldn’t be more than an interesting intellectual pastime without any practical application. Fortunately, this is not the case. Many studies (including this week’s paper) find that the major factor premiums remain sizable after costs. And of course, many well-known asset managers like AQR, Research Affiliates, or Robeco wouldn’t exist without profitable factors…

So transaction costs don’t change the story. A more interesting (and difficult) question is therefore *how much* money we can throw at a profitable factor strategy before it stops working. Critics of factor investing sometimes bring the capacity-story and argue that even profitable factors are unattractive if too many investors sit on the same trade. This became known as *crowding*. Unfortunately (for factor investors), this is one of the hardest arguments to counter because it is generally true. The side-effect of pursuing a profitable strategy is that with each additional dollar, it becomes less attractive as you move the price in the desired direction. Factors are no different.

The only way to address this is to look at the data and develop an estimate for each factor’s capacity to check if we are already reached the limit. That’s where this week’s paper comes in. Before we continue, however, one further note. At least as I understand it, all of the following estimates are *bottom-up*. What I mean by that is the research takes the perspective of an asset manager and asks *“How much money can I put in this strategy before it becomes too costly to implement?”* This is not necessarily the same as the *top-down* perspective which asks what fraction of actively managed assets can be factor strategies.

## Data and Methodology

The authors estimate a trading cost model from data on rebalancing transactions of several factor-index funds in equity markets. For this purpose, they analyze almost 50,000 trades with a total volume of $56.6B between 2009 and 2016. I will not go into detail about this model here but interested readers find a lot of details and statistics in the paper.

For the application of their model, the authors use data from CRSP and Compustat to construct backtests for the most important factors and group them into Value, Income, Low-Volatility, Quality, Momentum, and a Multi-Factor combination.

## Important Results and Takeaways

### Implementation costs depend on tilt, turnover, and execution speed

Arguably, those first results are from the category of stating the obvious but it is still nice to see the relations in a formalized model. The authors show that the cost of strategies intuitively depend on three variables: tilt, turnover, and the speed of execution.

*Tilt* measures how much an active strategy deviates from the passive benchmark. This is important because a passive market-cap weighted portfolio, due to its self-rebalancing character, is the cheapest strategy in terms of trading costs.

The next variable is *turnover*. All else equal, a strategy that requires more trading faces higher implementation costs (who would have thought that?). The authors also introduce the concept of *turnover concentration* which is another determinant for trading costs. Strategies with high turnover concentration (Momentum, for example) require a lot of trading in relatively few stocks. Suppose you have two portfolios which both have a turnover of 20%. In the first one, you trade the 20% in only 5 stocks. In the second, you spread it across 100. Despite identical turnover in aggregate, the first one will most likely be more costly because the trading is concentrated in a few names.

Finally, the *number of days* to execute trades obviously also matters. If you stretch your trading over 5 days it is most likely cheaper than if you do it an hour. Of course, there is a trade-off between “expensive fast execution” and “cheap waiting”. You save implementation costs but in the meantime, you run a higher tracking error to the rebalanced portfolio you actually want to have.

### Capacities of factors for a maximum cost of 0.5% per year

The following table shows the estimated implementation costs and capacities for factor index funds in the US. As a benchmark, the authors calculate *Market Impact Costs* under the assumption of $10B assets under management. For *Capacity (US$ billions)* they show the assets above which the market impact costs rise above 0.5% per year (see columns).

The results are very interesting and consistent with some of individual factors’ characteristics that I mentioned over the last weeks. *Momentum* is the most turnover-intense strategy and therefore already reaches 0.5% implementation costs at a capacity of “just” $2B. The “slow” Value strategy, in contrast, reaches this threshold only at a capacity of $290B. Low-Volatility factors are somewhere in between and have capacities reaching from $2.6B to $107.8B. Quality factors also fall within this range and come with capacities in the double-digit billions. Finally, combining the strategies into a Multi-Factor portfolio reduces turnover and tilt, and thus leads to lower costs and higher capacities.

You may correctly observe and argue that the actual assets in factor strategies easily exceed those capacities. How can this be? Well, as I mentioned before, the authors calculate capacities with a cost threshold of 0.5% per year. But this is just an arbitrary threshold to make the results comparable. You can still invest whatever amount you like in those factors if you are willing to tolerate higher costs. In fact, even the authors sample funds have already invested about $36B in momentum which comes with estimated costs of 2%. This is obviously a lot, but as long as implementation costs are smaller than the pre-cost Momentum premium, you still have a profitable factor. And this is all that counts.

Finally, the authors briefly comment on results for equity markets of developed and emerging countries. Those are not available in the paper but in an online appendix for those who need specific numbers. For developed equity markets, the results are very similar which is (in my opinion) not too surprising. By contrast, capacities are generally lower in emerging markets. This is again not too surprising as less-developed markets tend to come with more frictions and higher costs.

### There is not yet a consensus on factor capacities

Interestingly, the authors arrive at quite different results than other papers. Given that the paper is published in a peer-reviewed journal and that the authors work at a reputable asset manager (Research Affiliates), I trust the methodology and data. In fact, the authors are well-aware of their deviations from earlier studies and therefore put their results into context.

The following table summarizes the current state of the literature and I really find it interesting that the papers arrive at such different conclusions in some points. For example, the introductory mentioned Frazzini et al. (2018) find a US momentum capacity of $159B which is much higher than the $2B in this week’s paper. This is just one example, but my personal takeaway from this chart is that we have not yet found a consensus on implementation costs and capacities of factors.^{[1]}A lot of research and insights in this area are most likely proprietary. Efficient implementation is the real challenge of systematic investing, so asset managers are usually silent about the techniques they are using…

## Conclusions and Further Ideas

What do we make from the results? Unfortunately, I think it is hard (if not impossible) to nail down any specific numbers. However, I think we can still use the results on capacity to roughly assess the current state of the factor investing world. Despite different estimates, the literature definitely suggests that we shouldn’t expect factor investing to become much larger than something between $1T $1.5T (with the exception of Value and Size).

Those are giant numbers, but this limited capacity differentiates systematic factor investing from the traditional fundamental managers. As we see at the example of Warren Buffett, it is absolutely possible to run a $200B equity portfolio with a concentrated low-turnover buy-and-hold stock-picking strategy. The opportunity set is small at this stage, but it remains possible.

This is not the case with factor investing which require large diversified portfolios and frequent trading. Implementation costs and capacities are therefore much more important in this area. Given how wide the estimates currently are, I would bet that this is going to be an active research area over the next years…

- AgPa #56: The Equity Risk Premium of Small Businesses
- AgPa #55: Backtests in the Age of Machine Learning
- AgPa #54: Transitory Inflation
- AgPa #53: Investing in Interesting Times

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