*Progress in science comes when experiment contradicts theory. – Richard Feynman*

One of the tenets of modern portfolio theory is that you cannot generally beat the market after transaction costs. Yet academic researchers have shown that momentum consistently beats the market. Other factors besides momentum have also cast doubt on the efficacy of the efficient market hypothesis.

There is one way though that academics can still hold on to the efficient market hypothesis. It is to show that academic research on anomalies does not hold up in the real world after accounting for transaction costs.

Chen, Stanzl & Watanabe (2002) were the first to explore the price impact of large-scale factor investing. They concluded that the maximal fund sizes for factor-based anomalies, especially momentum, to remain profitable are small. Lesmond, Shill & Zhou (2003), Korajczyk & Sadka (2004), Fisher, Shah & Titman (2015), Novy-Marx & Velikov (2015), Beck, Hsu, Kalesnik & Kostka (2016) all came to similar conclusions.

Fund sponsors who jumped on the factor bandwagon were not happy to see these results. 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.

Frazzini, Israel & Moskowitz (2014) work for AQR. They analyzed 16 years of proprietary data ending in 2013. They showed scalable results over this period.

Ratcliffe, Miranda & Ang (2016) work for Black Rock. They also contend there is enough capacity for scalable results managing factor-based funds using their high frequency trading market data.

Some argue that trading costs are not an issue by pointing to similar performance between momentum based funds and the momentum indices these funds track. The problem with that argument is the indices themselves may suffer from the prior impact of trading costs on the stocks that make up those indices. Chow, Li, Pickard & Garg (2017) show that market impact costs can come from trading at temporarily inpacted prices during index rebalances. This means market impact costs are hidden and cannot be seen in a direct comparison between fund performance and index performance.

The main drawback of all these studies, whether academic or industry based, is that they depend on assumptions about future transaction costs and market liquidity. Assessing implementation costs using any transaction cost models may be incomplete or misguided. No one can say with any degree of certainty what the future will bring. Ratcliffe et al. acknowledge this when they say, “The exercise we conduct in this paper is hypothetical and involves several unrealistic assumptions.” This is undoubtedly true of most, if not all, of these studies.

**Real World Results**

It is not uncommon for academic finance theories to not hold up well in the real world. The capital asset pricing model (CAPM) is a good example of that. In past blog posts here, here, and here, we highlight some factor research using actual fund results. One study we cite by Loughran & Hough (2006) compares the past performance of value versus growth funds. After examining mutual fund performance from 1965 to 2001, they concluded that superior long-run performance from value is an “illusion.” It is important to look at factor performance across all funds since many use momentum or value implicitely even though they are not charaterized as factor funds.

A study by Arnott, Kalesnik & Wu (2017) applied two-stage Fama-MacBeth regression to the last quarter-century of mutual fund returns. They show the real-world return for the value and market factors to be half or worse than theoretical factor returns. On a real-time basis, the momentum factor provided no benefit whatever.

**New Study**

Two Duke professors, Patton & Weller (2017), recently came out with a study of real versus theoretical performance of momentum, value, and size factors called “What You See Is Not What You Get: The Costs of Trading Market Anomalies.”

The authors start with a two-stage Fama-MacBeth regression applied to 7320 U.S. domestic mutual funds from January 1970 to December 2016. In the first stage they determine the estimated factor loadings for each fund. In the second stage, they regress the excess returns of all funds against the estimated factor loadings to get the factor premia earned by each fund. They then compare these to the theoretical factor returns.

**Implementation Costs**

Their approach differs from the Arnott et al. one by focusing more explicitly on implementation costs. They make improvements in the way Fama-Macbeth regression is used. From 1970 through 2016, the authors find that annual implementation costs range from 2.2% to 8.5% for momentum strategies. This makes momentum profits inaccessible to typical asset managers, according to the authors.

For value, the authors come up with annual implementation costs of 2.6% to 5%. They report overall that “after accounting for implementation costs, typical mutual funds earn low returns to value and no returns to momentum.”

Implementation costs for both value and momentum are stationary throughout this period. The authors say industry inflows offset declines in bid-ask spreads and commissions.

In addition to Fama-MacBeth regression, the authors use a second approach called matched pairs analysis. Here they directly compare the compensation for stocks to mutual funds with similar characteristics. They sort stocks into quintiles and match them up with three mutual funds closest to them in factor beta. This is a more direct approach than Fama-MacBeth regression.

Their Fama-Macbeth approach shows that implementation costs erode almost all the return to value and momentum strategies of mutual funds. But there is little impact on market and size strategies. Matched pairs analysis shows comparable performance attrition for value and momentum strategies. But it also shows high costs to trading small stock portfolios.

In summary, the authors say the implementation gap is large and statistically significant for all the factors they examine. None of the factor strategies earn returns after real-world costs during the 1970 to 2016 period.

**Implications**

I wrote my first momentum paper in 2011. It was called “Optimal Momentum: A Global Cross Asset Approach.” I looked at momentum applied to stocks, industries, investment styles, and geographic equity markets. I found that momentum worked best when used with geographically diversified stock indices.

In 2015, Geczy & Samonov (2015) applied momentum to U.S. stocks, global sectors, country equity indices, government bonds, currencies, and commodities. Looking at the past 215 years of data, they came to the same conclusion as I did. Momentum works best when applied to geographically diversified stock indices. Neither my study nor Geczy & Samonov’s study took into account implementation costs, which could have made our equity index results even stronger compared to stocks.

The growth of factor- based investing has been explosive and is expected to continue.

Continued growth in factor-based investing could aggravate the scalability issue associated with high implementation costs.