The proliferation of smart beta strategies has raised questions about the relationship between the core risk factors that have formed the foundation of quantitative investment analysis for decades and the growing factor zoo of strategies. Whereas some state that “smart beta is the vehicle to deliver factor investing” others argue that “factor tilts are not smart ‘smart beta’”. A central question is how well dumb beta factors such as Market, Sectors/Industries, and Style (Value/Growth, Big/Small) can replicate the zoo’s residents. The answers drive risk modeling, performance evaluation, and portfolio construction. This article studies replicating fundamental indexing with factor tilts over the past ten years and illustrates how well it has worked. We will discuss the other popular smart beta strategies in subsequent articles.

In this 10-year replication example, the reality falls between the extreme viewpoints above:

• Factor tilts replicate virtually all (>96%) of the absolute variance.
• In a typical market environment, factor tilts replicate most (60-75%) of the relative variance. In fact, in this environment, fundamental indexing is substantially replicated with sector rotation. Indeed, most U.S. and international smart beta strategies are largely instances of sector rotation.
• In periods of stress, factor tilts fail to replicate the relative variance.
• The difference in returns between the target and replicating portfolios is statistically insignificant.
• The relative return of the target and replicating portfolios does not follow a random walk – fundamental indexing goes through periods of outperformance and underperformance relative to the replicating portfolio.

We illustrate and quantify the systematic performance that is attainable, and the residual performance that is unattainable, when replicating fundamental indexing with a portfolio of atomic and liquid factor tilts. The replication uses only the rudimentary factors that most commercial equity risk models implement: Market, Sectors, and optionally Style. We also show the environments when replication is more or less successful. It is up to the user to determine whether a given tracking error is adequate for a given application.

Prior Research on Replication

When assumptions and idiosyncrasies of a factor replication exercise are not made explicit, confusion can arise. Any test replicating smart beta with dumb factor tilts is a joint test of the following components:

• The equity risk model and the optimizer used to create replicating factor tilt portfolios,
• The securities used to implement replicating portfolios,
• The portfolio constraints.

Failure of replication based on a flawed model or flawed factors (such as the simple three Fama-French factors suffering from multicollinearity) merely shows the replication process to be flawed; it does not prove the replication impossible.

Replicating Smart Beta Strategies with Dumb Factor Tilts

This article considers fundamental indexing as implemented by the PowerShares FTSE RAFI US 1000 Portfolio (PRF).

We constructed quarterly replicating portfolios using PRF’s position filings. We lagged positions by two months and risk model data by one month to account for filing and processing delays. For example, pre-1/31/2017 PRF positions and 2/28/2017 AlphaBetaWorks U.S. Equity Risk Model were used to construct the 3/31/2017 portfolio, which was next rebalanced on 6/30/2017. The optimizer aimed to minimize estimated future tracking error of the replicating portfolio to PRF, subject to portfolio constraints. Results were unaffected by changes in rebalance delay of a few months.

We attempted to use the simplest replication methodology that is practical and sound. Results vary depending on the security universe, the equity risk model, the optimizer, and the portfolio parameters.

Replicating Fundamental Indexing with Market and Sector Factor Tilts

Market and Sector Factor portfolios were constructed using a Market ETF and nine top-level sector ETFS:

SPY	SPDR S&P 500 ETF Trust
XLY	Consumer Discretionary Select Sector SPDR Fund
XLP	Consumer Staples Select Sector SPDR Fund
XLE	Energy Select Sector SPDR Fund
XLF	Financial Select Sector SPDR Fund
XLV	Health Care Select Sector SPDR Fund
XLI	Industrial Select Sector SPDR Fund
XLB	Materials Select Sector SPDR Fund
XLK	Technology Select Sector SPDR Fund
XLU	Utilities Select Sector SPDR Fund

Position constraint for Sector ETFs was 0 to +100%, and for SPY -100% to +100%. Negative Market weight is necessary to target Market exposures that are not attainable by a long-only portfolio of Sector ETFs. Advanced sector indices, such as the NYSE Pure Exposure Indices, avoid this problem and enable long-only replicating portfolios targeting any combination of exposures.

Fundamental Indexing vs. Market and Sector Tilts: Absolute Performance

The following chart plots cumulative and relative returns for the fundamental indexing portfolio and the replicating Market and Sector Factor portfolio:

R-squared       0.9615
Correlation     0.9805
Tracking Error  3.50%

We performed a t-test on the difference in monthly log returns to determine whether they are statistically different from zero:

t = -0.3439
p-value = 0.7315
95 percent confidence interval = (-0.1976, 0.1391)
sample estimate mean = -0.0293

We also performed a Ljung-Box Test on the difference in monthly log returns to determine whether it is a random walk (specifically, whether there are non-0 autocorrelations of the time series):

X-squared = 6.0837
p-value = 0.0136

Though the mean difference in log returns is not statistically different from 0, relative performance is not a random walk. The relative returns of PRF and the replicating portfolio are autocorrelated, as is evident in the chart above.

Fundamental Indexing vs. Market and Sector Tilts: Relative Performance

The following chart plots cumulative and relative returns for the fundamental indexing portfolio, the replicating Market and Sector Factor portfolio, and the SPDR S&P 500 ETF (SPY):

R-squared       0.4929
Correlation     0.7020
Tracking Error  3.50%

Performance difference mostly comes from a few months during the 2008-2009 crisis when residual variance spikes. The replicating portfolio first sharply outperforms and then sharply underperforms. In a calmer environment post-2009, the fit is much closer:

R-squared       0.6124
Correlation     0.7825
Tracking Error  1.75%

Replicating Fundamental Indexing with Market, Sector, and Style Factor Tilts

Market, Sector, and Style Factor tilt portfolios add a Growth/Value ETF pair and a Small-Cap ETF to capture the additional Style Factor exposures:

IWF	iShares Russell 1000 Growth ETF
IWD	iShares Russell 1000 Value ETF
IWM	iShares Russell 2000 ETF

Fundamental Indexing vs. Market, Sector, and Style Tilts: Absolute Performance

The following chart plots cumulative and relative returns for a fundamental indexing portfolio and the replicating Market, Sector, and Style Factor portfolio:

R-squared       0.9619
Correlation     0.9807
Tracking Error  3.61%

The t-test results are similar to those of the Market and Sector replicating portfolio:

t = -0.0062504
p-value = 0.995
95 percent confidence interval = (-0.1802, 0.1791)
sample estimate mean = -0.0006

The Ljung-Box test results are also similar:

X-squared = 6.1228
p-value = 0.0134

Fundamental Indexing vs. Market, Sector, and Style Tilts: Relative Performance

The following chart plots cumulative and relative returns for the fundamental indexing portfolio, the replicating Market, Sector, and Style Factor portfolio, and SPY:

Over the entire 10-year history, the style factors do not materially change the quality of replication:

R-squared       0.4794
Correlation     0.6924
Tracking Error  3.61%

Post-2009, the style factors do improve the fit:

R-squared        0.7501
Correlation      0.8661
Tracking Error   1.44%

Conclusions

• Whether the tracking error of replication is acceptable depends on the application.
• Though fully replicating fundamental indexing without any residual tracking error is impossible, even simple Market and Sector factor tilts replicate over 96% of the absolute variance for the fundamental indexing portfolio over the past ten years.
• In a normal market environment, factor tilts replicate most (60-75%) of the relative variance for the fundamental indexing portfolio.
• In periods of market stress, the tracking error of the replicating portfolio relative to the target is substantial.
• The difference in returns between the target and replicating portfolios is statistically insignificant, but it does not follow a random walk and exhibits cycles.

The information herein is not represented or warranted to be accurate, correct, complete or timely.
Past performance is no guarantee of future results.
Copyright © 2012-2017, AlphaBetaWorks, a division of Alpha Beta Analytics, LLC. All rights reserved.
Content may not be republished without express written consent.

Our earlier articles discussed how some smart beta strategies turn out to be merely high beta strategies, and how others actively time the market, requiring careful monitoring. We also showed that the returns of popular factor ETFs such as Momentum and Quality are mostly attributable to exposures to traditional Market and Sector Factors. We now quantify the influence of traditional factors, or dumb beta, on all broad U.S. equity smart beta ETFs.

Though many smart beta ETFs do provide valuable exposure to idiosyncratic factors, many others mostly re-shuffle exposures to basic dumb factors. To successfully use smart beta products, investors and allocators must apply rigorous quantitative analysis. With capable analytics, they can guard against elaborate (and often expensive) re-packaging of dumb beta as smart beta, identify smart beta products that time dumb beta factors effectively, and monitor smart beta allocations to control for unintended dumb factor exposures.

Measuring the Influence of Dumb Beta Factors on Smart Beta ETFs

We started with approximately 800 U.S. Smart Beta ETFs. Since our focus was on the broad U.S. equity strategies, we removed non-U.S. portfolios and sector portfolios. (Later articles will cover global equity portfolios.) We also removed portfolios for which returns estimated from historical positions did not reconcile closely to reported performance. We were left with 215 broad U.S. equity smart beta ETFs. This nearly complete sample contains all the popular smart beta strategies.

For each ETF, we estimated monthly positions and then used these positions to calculate portfolio factor exposures for traditional (dumb beta) factors such as Market and Sectors.  These ex-ante factor exposures can be used to predict or explain the following months’ returns.

The correlation between returns predicted by dumb beta factor exposures and actual returns quantifies the influence of dumb beta factors. The higher the correlation, the more similar a smart beta ETF is to a portfolio of traditional, simple, and dumb systematic risk factors.

The Influence of Market Beta on Smart Beta ETFs

Our simplest test used a single systematic risk factor – Market Beta. This is the dumbest traditional factor and also the cheapest to invest in. Since Market Beta is the dominant factor behind portfolio performance, even a very simple 1-factor model built with robust statistical methods delivered 0.92 mean and 0.94 median correlation between predicted and actual monthly returns for smart beta ETFs:

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.5622  0.8972  0.9393  0.9174  0.9693  0.9960

Put differently: For most broad U.S. equity smart beta ETFs, U.S. Market Beta accounts for over 88% of monthly return variance.

The Influence of Market and Sector Betas on Smart Beta ETFs

Since traditional sector/industry allocation is a staple of portfolio construction and risk management, we next tested a two-factor model that added a Sector Factor. Each security belongs to one of 10 broad sectors (e.g., Energy, Technology). Market and Sector Betas, estimated with robust methods, delivered 0.95 mean and 0.96 median correlation between predicted and actual monthly returns for smart beta ETFs:

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.5643  0.9320  0.9634  0.9452  0.9805  0.9974

Put differently: For most broad U.S. equity smart beta ETFs, U.S. Market and Sector Betas accounts for over 92% of monthly return variance.

Smart Beta Variance and Dumb Beta Variance

Rather than measuring the correlation between returns predicted by dumb beta exposures and actual returns, we can instead measure the fraction of variance unexplained by dumb beta exposures. This (in blue below) is the fraction of smart beta ETFs’ variance that is unrelated to dumb beta:

Percentage of Variance Explained by Dumb Beta Factors

Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
1.85   86.87   92.81   89.71   96.14   99.47 

Percentage of Variance Unexplained by Dumb Beta Factors

Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 .53    3.86    7.19   10.29   13.13   68.15

Note that some smart beta strategies do provide value by timing the dumb beta factors. This market timing can generate a positive active return, but it still consists of traditional dumb factor exposures and their variation. Market timing by smart beta ETFs is beyond the scope of this article.

The high explanatory power of dumb beta exposures above was achieved with a primitive model using Market and Sector Factors only. If one incorporates Value/Growth and Size factors that are decades old and considered dumb beta by some, smart beta variance shrinks further.

Conclusions

• Traditional, or dumb, Market and Sector Betas account for over 92% of variance for most U.S. equity smart beta ETFs.
• Smart beta, unexplained by the traditional Market and Sector Betas, accounts for under 8% of variance for most U.S. equity smart beta ETFs.
• With proper analytics, investors and allocators can guard against elaborate re-packaging of dumb beta as smart beta.
• With proper analytics, investors and allocators can monitor smart beta allocations to control for unintended dumb factor exposures.
• Equity risk models can adequately describe and predict the performance of most smart beta strategies with traditional dumb risk factors such as Market and Sectors.

The information herein is not represented or warranted to be accurate, correct, complete or timely.
Past performance is no guarantee of future results.
Copyright © 2012-2016, AlphaBetaWorks, a division of Alpha Beta Analytics, LLC. All rights reserved.
Content may not be republished without express written consent.