Tag Archives: ETFs

Replicating Fundamental Indexing with Factor Tilts

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:

Chart of the absolute and relative returns of PowerShares FTSE RAFI US 1000 Portfolio (PRF) and a replicating Market and Sector Factor tilt portfolio

Replicating fundamental indexing with Market and Sector Factor tilts: absolute performance

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):

Chart of the absolute and relative returns of PowerShares FTSE RAFI US 1000 Portfolio (PRF), a replicating Market and Sector Factor tilt portfolio, and SPDR S&P 500 ETF (SPY)

Replicating fundamental indexing with Market and Sector Factor tilts: relative performance

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:

Chart of the absolute and relative returns of PowerShares FTSE RAFI US 1000 Portfolio (PRF) and a replicating Market, Sector, and Style Factor tilt portfolio

Replicating fundamental indexing with Market, Sector, and Style Factor tilts: absolute performance

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:

Chart of the absolute and relative returns of PowerShares FTSE RAFI US 1000 Portfolio (PRF), a replicating Market, Sector and Style Factor tilt portfolio, and SPDR S&P 500 ETF (SPY)

Replicating fundamental indexing with Market, Sector, and Style Factor tilts: relative performance

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.
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What Fraction of International Smart Beta is Dumb Beta?

Though many smart beta ETFs do provide valuable exposures, others mainly re-shuffle familiar dumb beta factors. Our earlier article showed that traditional, or dumb, Market and Sector Betas account for over 92% of monthly return variance for most U.S. equity smart beta ETFs. This article extends the analysis to international smart beta ETFs.

It turns out that international smart beta ETFs are even more heavily dominated by dumb beta factors than their U.S. counterparts. Consequently, rigorous quantitative analysis is even more critical when deploying smart beta strategies internationally. With capable analytics, investors and allocators can detect unnecessarily complex and expensive re-packaging of dumb international factors as smart beta, identify products that do provide unique exposures, and control for unintended international dumb factor exposures.

Measuring the Influence of Dumb Beta Factors on International Smart Beta ETFs

We started with approximately 800 smart beta ETFs. Since our focus was on the broad international equity strategies, we removed portfolios with over 90% invested in U.S. equities and portfolios dominated by a single sector. We also removed portfolios for which returns estimated from historical positions did not reconcile closely with actual returns. We were left with 125 broad international equity smart beta ETFs, covering all the popular international smart beta strategies.

For each ETF, we estimated monthly positions and then used these positions to calculate portfolio factor exposures to traditional (dumb beta) factors such as global Regions (regional equity markets) and Sectors.  These ex-ante dumb factor exposures provided us with replicating portfolios composed solely of traditional dumb beta factors. For each international smart beta ETF, we compared replicating portfolio returns to actual returns over the past 10 years, or over the ETF history, whichever was shorter.

The correlation between replicating dumb factor portfolio returns and actual ETF returns quantifies the influence of dumb beta factors on international smart beta ETFs. The higher a correlation, the more similar an ETF is to a portfolio of traditional, simple, and dumb systematic risk factors.

The Influence of Region Beta on International Smart Beta ETFs

Our simplest test used a single systematic risk factor for each security – Region (Region Market Beta). Region Beta measures exposure to one of 10 broad regional equity markets (e.g., North America, Developing Asia). These are the dumbest traditional international factors and also the cheapest to invest in. Since Market Beta is the dominant factor behind portfolio performance, even a very simple model measuring exposures to regional equity markets with robust statistical techniques delivered 0.95 mean and 0.96 median correlations between replicating dumb factor portfolio returns and actual monthly returns for international smart beta ETFs:

Chart of the correlations between returns of replicating portfolios constructed using Region Factors and actual historical returns for over international smart beta equity ETFs

International Smart Beta Equity ETFs: Correlation between replicating Region Factor portfolio returns and actual monthly returns

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.6577  0.9390  0.9645  0.9461  0.9818  0.9975

In short: For most broad international smart beta ETFs, Region Market Betas account for at least 93% (0.9645²) of monthly return variance.

The Influence of Region and Sector Betas on International Smart Beta ETFs

We next tested a two-factor model that added Sector Factors. Each security belongs to one of 10 broad sectors (e.g., Energy, Technology). Region and Sector Betas, estimated with robust methods, delivered 0.96 mean and 0.97 median correlations between replicating dumb factor portfolio returns and actual monthly returns for international smart beta ETFs:

Chart of the correlations between returns of replicating portfolios constructed using Region and Sector Factors and actual historical returns for over international smart beta equity ETFs

International Smart Beta Equity ETFs: Correlation between replicating Region and Sector Factor portfolio returns and actual monthly returns

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.7017  0.9526  0.9722  0.9578  0.9849  0.9941

In short: For most broad international equity smart beta ETFs, Regional Market and Sector Betas account for over 94% (0.9722²) of monthly return variance. Put differently, only less than 6% of the variance is not attributable to simple Region and Sector factors.

International Smart Beta Variance and International Dumb Beta Variance

Rather than measure correlations between replicating dumb beta portfolio returns and actual ETF returns, we can instead measure the fraction of variance unexplained by dumb beta exposures. The Dumb Beta Variance (in red below) is the distribution of ETFs’ variances due to their dumb beta Region and Sector exposures. The Smart Beta Variance (in blue below) is the distribution of ETFs’ variances unrelated to their dumb beta exposures:

Chart of the percentage of variance explained by traditional, non-smart, or dumb beta Region and Sector Factors and the percentage of variance unexplained by these factors for international smart beta equity ETFs

International Equity Smart Beta ETFs: Percentage of variance explained and unexplained by Region and Sector dumb beta exposures

Percentage of international equity smart beta ETFs’ variances due to dumb beta exposures:

 Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
49.24   90.74   94.52   91.95   97.00   98.83  

Percentage of international equity smart beta ETFs’ variances unrelated to dumb beta exposures:

 Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
1.174   3.004   5.484   8.052   9.258  50.760 

Note that market timing of dumb beta exposures can generate an active return. This return is still due to traditional dumb factor exposures, but it adds value through smart variation in such exposures. Market timing is a relatively small source of return for most international smart beta ETFs and is beyond the scope of this article.

Our analysis excludes Value/Growth and Size Factors, which are decades old and considered dumb beta by some. If one expands the list of dumb beta factors, smart beta variance shrinks further.

Conclusions

  • Traditional, or dumb, Region and Sector Betas account for over 94% of variance for most international smart beta ETFs.
  • Smart beta, unexplained by the traditional Region and Sector Betas, accounts for under 6% of variance for most international smart beta ETFs.
  • With proper analytics, investors and allocators can guard against elaborate re-packaging of dumb international beta as smart beta and spot the products that actually do provide international smart beta exposures.
  • Investors and allocators can monitor and manage unintended dumb factor exposures of international smart beta portfolios.
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.
 
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What Fraction of Smart Beta is Dumb Beta?

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:

Chart of the correlations between predicted returns constructed using a single-factor statistical equity risk model and actual historical returns for over 200 U.S. smart beta equity ETFs

U.S. Smart Beta Equity ETFs: Correlation between a single-factor statistical equity risk model’s predictions and actual monthly returns

  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:

Chart of the correlations between predicted returns constructed using a two-factor statistical equity risk model and actual historical returns for over 200 U.S. smart beta equity ETFs

U.S. Smart Beta Equity ETFs: Correlation between a two-factor statistical equity risk model’s predictions and actual monthly returns

  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:

Chart of the percentage of variance explained by traditional, non-smart, or dumb beta factors Market and Sectors and the percentage of variance unexplained by these factors for over 200 U.S. smart beta equity ETFs

U.S. Smart Beta Equity ETFs: Percentage of Variance Explained and Unexplained by Dumb Beta Factors

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 © 2012-2016AlphaBetaWorks, a division of Alpha Beta Analytics, LLC. All rights reserved.
Content may not be republished without express written consent.
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Returns-Based Style Analysis – Overfitting and Collinearity

Plagued by overfitting and collinearity, returns-based style analysis frequently fails, confusing noise with portfolio risk.

Returns-based style analysis (RBSA) is a common approach to investment risk analysis, performance attribution, and skill evaluation. Returns-based techniques perform regressions of returns over one or more historical periods to compute portfolio betas (exposures to systematic risk factors) and alphas (residual returns unexplained by systematic risk factors). The simplicity of the returns-based approach has made it popular, but it comes at a cost – RBSA fails for active portfolios. In addition, this approach is plagued by the statistical problems of overfitting and collinearity, frequently confusing noise with systematic portfolio risk. 

Returns-Based Style Analysis – Failures for Active Portfolios

In an earlier article we illustrated the flaws of returns-based style analysis when factor exposures vary, as is common for active funds:

  • Returns-based analysis typically yields flawed estimates of portfolio risk.
  • Returns-based analysis may not even accurately estimate average portfolio risk.
  • Errors will be most pronounced for the most active funds:
    • Skilled funds may be deemed unskilled.
    • Unskilled funds may be deemed skilled.

These are not the only flaws. We now turn to the subtler and equally critical issues – failures in the underlying regression analysis itself. We use a recent Morningstar article as an example.

iShares Core High Dividend ETF (HDV) – Returns-Based Style Analysis

A recent Seeking Alpha article provides an excellent illustration of problems created by overfitting and collinearity. In this article, Morningstar performed a returns-based style analysis of iShares Core High Dividend ETF (HDV).

Morningstar estimated the following factor exposures for HDV using the Carhart model:

Morningstar: Returns-Based Analysis of the iShares Core High Dividend ETF (HDV) Using the Carhart Model

iShares Core High Dividend ETF (HDV) – Estimated Factor Exposures Using the Carhart Model – Source: Morningstar

The Mkt-RF coefficient, or loading, is HDV’s estimated market beta. A beta value of 0.67 means that given a +1% change in the market HDV is expected to move by +0.67%, everything else held constant.

The article then performs RBSA using an enhanced Carhart + Quality Minus Junk (QMJ) model:

Morningstar: Returns-Based Analysis of iShares Core High Dividend ETF (HDV) Using the Carhart + Quality Minus Junk (QMJ) Model

iShares Core High Dividend ETF (HDV) – Estimated Factor Exposures Using the Carhart + Quality Minus Junk (QMJ) Model – Source: Morningstar

With the addition of the QMJ factor, the market beta estimate increased by a third from 0.67 to 0.90. Both estimates cannot be right. Perhaps the simplicity of the Carhart model is to blame and the more complex 5-factor RBSA is more accurate?

iShares Core High Dividend ETF (HDV) – Historical Factor Exposures

Instead of Morningstar’s RBSA approach, we analyzed HDV’s historical holdings using the AlphaBetaWorks’ U.S. Equity Risk Model. For each month, we estimated the U.S. Market exposures (betas) of individual positions and aggregated these into monthly estimates of portfolio beta:

Chart of the historical market exposure (beta) of iShares Core High Dividend ETF (HDV)

iShares Core High Dividend ETF (HDV) – Historical Market Exposure (Beta)

Over the past 4 years, HDV’s market beta varied in a narrow range between 0.50 and 0.62.

Both of the above returns-based analyses were off, but the simpler Carhart model did best. It turns out the simpler and a less sophisticated returns-based model is less vulnerable to the statistical problems of multicollinearity and overfitting. Notably, the only way to find out that returns-based style analysis failed was to perform the more advanced holdings-based analysis using a multi-factor risk model.

Statistical Problems with Returns-Based Analysis

Multicollinearity

Collinearity (Multicollinearity) occurs when risk factors used in returns-based analysis are highly correlated with each other. For instance, small-cap stocks tend to have higher beta than large-cap stocks, so the performance of small-cap stocks relative to large-cap stocks is correlated to the market.

Erratic changes in the factor exposures for various time periods, or when new risk factors are added, are signs of collinearity. These erratic changes make it difficult to pin down factor exposures and are signs of deeper problems:

A principal danger of such data redundancy is that of overfitting in regression analysis models.
-Wikipedia

Overfitting

Overfitting is a consequence of redundant data or model over-complexity. These are common for returns-based analyses which usually attempt to explain a limited number of return observations with a larger number of correlated variable observations.

An overfitted returns-based model may appear to describe data very well. But the fit is misleading – the exposures may be describing noise and will change dramatically under minor changes to data or factors. A high R squared from returns-based models may be a sign of trouble, rather than a reassurance.

As we have seen with the HDV example above, exposures estimated by RBSA may bear little relationship to portfolio risk. Therefore, all dependent risk and skill data will be flawed.

Conclusions

  • When a manager does not vary exposures to the market, sector, and macroeconomic factors, returns-based style analysis (RBSA) using a parsimonious model can be effective.
  • When a manager varies bets, RBSA typically yields flawed estimates of portfolio risk.
  • Even when exposures do not vary, returns-based style analysis is vulnerable to multicollinearity and overfitting:
    • The model may capture noise, rather than the underlying factor exposures.
    • Factor exposures may vary erratically among estimates.
    • Estimates of portfolio risk will be flawed.
    • Skilled funds may be deemed unskilled.
    • Unskilled funds may be deemed skilled.
  • Holdings-based analysis using a robust multi-factor risk model is superior for quantifying fund risk and performance.
The information herein is not represented or warranted to be accurate, correct, complete or timely.
Past performance is no guarantee of future results.
Copyright © 2012-2015, AlphaBetaWorks, a division of Alpha Beta Analytics, LLC. All rights reserved.
Content may not be republished without express written consent.
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When “Smart Beta” is Simply High Beta

WisdomTree Mid Cap Earnings Fund (EZM) vs. PowerShares Dynamic Large Cap Value Portfolio (PWV)

Many “smart beta” funds are merely high-beta, delivering no value over traditional index funds. On the other hand, some smart beta strategies are indeed exceptional and worth their fees.

Most analyses of enhanced index funds and smart beta strategies lack a rigorous approach to risk evaluation and performance attribution. Consequently, risky and mediocre funds are mislabeled as excellent, while conservative and exceptional funds are wrongly considered mediocre. Investors relying on simplistic analyses may end up with mediocre funds, hidden risks, and subpar performance.

The Not-So-Smart Beta

Some smart beta funds deliver consistent outperformance with high liquidity and low tracking error. Others merely deliver high market beta or high exposures to other common risk factors. Analyses of these funds’ performance are usually simplistic, failing to differentiate between the two groups.

Enhanced indexing and smart beta strategies are usually more active than the underlying indices. This can cause their risk to vary dramatically over time. For instance, a fund’s market beta can vary by 40-50% over a few years. This variation makes it difficult to determine whether a particular strategy is smart or merely risky. When a market correction arrives, risky funds suffer outsized losses.

Many estimate the beta of a fund by fitting its returns to the market or a benchmark using a regression, a technique known as returns-based style analysis. This is a flawed approach, which fails to accurately estimate the risk of active strategies. We discussed the flaws of returns-based style analysis in earlier articles.

A robust approach to estimating a fund’s historical risk and risk-adjusted performance is to evaluate its holdings over time. At each period, the risk of individual holdings is aggregated to estimate the risk of the fund. This is AlphaBetaWorks’ approach, implemented in our Performance Analytics Platform. Our analysis reveals that many “smart beta” funds are merely high-beta. These funds deliver no value over traditional index funds. On the other hand, some smart beta strategies are indeed exceptional and worth the fees they charge.

WisdomTree Mid Cap Earnings Fund (EZM) – Historical Risk

On the surface, the returns of the WisdomTree Mid Cap Earnings Fund (EZM) appear strong. The fund has dramatically outperformed its broad benchmark, the Russell Midcap Index (IWR):

Chart of the Cumulative Return of WisdomTree Mid Cap Earnings Fund (EZM) and of the Benchmark (IWR)

Cumulative Return of WisdomTree Mid Cap Earnings Fund (EZM) vs the Benchmark (IWR)

However, this is nominal outperformance, not risk-adjusted outperformance.

The main source of security risk and return is market risk, or beta. With this in mind, we analyzed the holdings of EZM and IWR during each historical period, calculated their holdings’ risk, and calculated the total risk of each fund. Not surprisingly, IWR’s beta has been stable, averaging 1.09 (109% of the risk of U.S. Market). Meanwhile, EZM’s beta has varied in a wide range, averaging 1.18 (118% of the risk of U.S. Market):

Chart of the historical beta of the WisdomTree Mid Cap Earnings Fund (EZM) compared to the historical beta of the Benchmark (IWR)

Historical Beta of WisdomTree Mid Cap Earnings Fund (EZM) vs the Benchmark (IWR)

EZM had higher returns, but it also consistently took more market risk. With greater risk comes greater volatility, and a down cycle will affect EZM more.

To determine its risk-adjusted return, we must compare the performance of EZM to the performance of a passive portfolio with the same factor exposures.  Below are EZM’s current and historical factor exposures:

Chart of the historical and current factor exposures of the WisdomTree Mid Cap Earnings Fund (EZM)

Historical Factor Exposures of WisdomTree Mid Cap Earnings Fund (EZM)

WisdomTree Mid Cap Earnings Fund (EZM) – Risk-Adjusted Performance

Instead of owning EZM, investors could have owned a passive portfolio with similar risk (a passive replicating portfolio). If EZM had profitably timed the market (varied its risk) or selected securities, it should have outperformed.

EZM’s risk-adjusted performance closely matches a passive replicating portfolio. Relative to its passive equivalent, EZM has generated negligible active return (abReturn in the following chart):

Chart of the historical passive and active returns of the WisdomTree Mid Cap Earnings Fund (EZM)

Historical Passive and Active Return of WisdomTree Mid Cap Earnings Fund (EZM)

PowerShares Dynamic Large Cap Value Portfolio (PWV) – Risk-Adjusted Performance

Let’s contrast the performance of EZM with the results of another smart beta option: PowerShares Dynamic Large Cap Value Portfolio (PWV).

PWV has also varied U.S. Market exposure by approximately 40%:

Chart of the historical and current factor exposures of the PowerShares Dynamic Large Cap Value Portfolio (PWV)

Historical Factor Exposures of PowerShares Dynamic Large Cap Value Portfolio (PWV)

PWV has consistently outperformed its passive replicating portfolio and produced strong active returns due to market timing and security selection:

Chart of the historical passive and active returns of the PowerShares Dynamic Large Cap Value Portfolio (PWV)

Historical Passive and Active Return of PowerShares Dynamic Large Cap Value Portfolio (PWV)

Conclusion

Performance evaluation tools lacking accurate insights into risk may rank the better-performing but riskier EZM ahead of PWV, which produced superior active returns. The accurate picture of their relative active performance emerges once both funds’ historical holdings are examined with a multi-factor risk model and their excess returns distilled.

Unsuspecting investors relying on simplistic analysis may conclude that a risky and mediocre fund is excellent while a conservative and exceptional fund is mediocre. At best, they will face higher-than-anticipated risks. At worst, they will get a nasty surprise when a correction comes.

The information herein is not represented or warranted to be accurate, correct, complete or timely.
Past performance is no guarantee of future results.
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