Beta (Exposure)

Definition

beta coefficient can measure the volatility of an individual stock compared to the systematic risk of the entire market, a market sector, or style. In statistical terms, beta represents the slope of the line through a regression of data points. In finance, each of these data points represents an individual stock’s returns against those of the market (or sector) as a whole.

Beta effectively describes the activity of a security’s returns as it responds to swings in the market. A security’s beta is calculated by dividing the product of the covariance of the security’s returns and the market’s returns by the variance of the market’s returns over a specified period.

A portfolio’s market beta is the dollar-weighted sum of individual security market betas.

Beta and exposure, though expressed differently, mean the same thing.

A market beta of 1.0 implies a 100% exposure to the market. A market beta of 2.0 implies a 200% exposure to the market.

Examples

If a fund with a benchmark with market beta of 1.0 has a consistent market beta of 0.8, the fund will underperform by 2.0% when the market is up 10% and outperform by 2.0% when the market is down 10%, absent any impact from security selection.

If a fund has a consistent tech sector beta of 1.5 when its benchmark’s tech beta is 1.0, that fund will outperform by 2.0% if the tech sector outperforms the market by 4.0%

Since market and sector betas other than 1.0 can be obtained passively, performance due to consistent beta differences from the benchmark is not part of active contribution.

Factor Risk Models Built for Allocators find Statistical Evidence of Skill and Improve Risk Management

New factor risk models, built for allocators with passively-investable factors, distinguish between performance due to security selection and that due to unintended passively-available market exposures* that differ from those of the benchmark.

 

The difference with conventional factor risk models from Barra and others is that all of our factors are investable as passive ETFs.

From an allocator’s perspective, passively investable factors are a game-changer.

 

Passive factor risk models offer robust decomposition of incremental performance into:

  • Passive return: consistent passive exposures that differ from the benchmark (performance available without active fees)
  • Timing return: changes in passive exposures  (part of active contribution, whether or not intentional)
  • Security selection return (worth paying for)

 

Properly isolating return due to security selection proves to be a breakthrough. We can prove:

  • Past performance is, for the first time, predictive.
  • One-third of active managers take too little active risk to ever compensate for fees — even with skill.
  • Unintended exposures that endanger performance can be cheaply offset.

 

Detect managers with statistical evidence of skill likely to persist

Managers in the top security-selection skill decile are twice as likely to outperform in the subsequent three years. Managers in the bottom skill decile are more than twice as likely to underperform.

 

Ensure active managers are taking sufficient security-selection risk to justify active fees

Skill by itself is insufficient. Managers must also take enough security-selection risk to overcome fees.

One-third of active equity mutual funds, and roughly half of fund assets, appear to be closet-indexing, taking too little active risk to overcome active fees, even with top-decile skill.

We require managers with statistical evidence of security-selection skill who also take sufficient security-selection risk.

 

Know when a manager change is appropriate (and when it is not)

Portfolio performance evaluation is useful only if it can lead to actionable insights. Unfortunately, conventional performance measurement has little to no value, and it is almost never actionable.

 

It’s well known that past returns are not positive predictors of future returns. In fact, with conventional performance measurement, managers in the top quartile in one period are more likely to be in the bottom quartile the next than to remain in the top.

The problem is that the impact of randomness (which, it turns out, is primarily mean-reverting market exposures that differ from the benchmark) overwhelms any return due to security- selection skill—too much noise to detect a signal. Passive factor risk models distinguish between return due to randomness and return due solely to security selection, isolating the signal from the noise.

Performance evaluation is, for the first time, actionable.

 

Improve allocations among managers

Asset owners can avoid unintentionally reinforcing passive bets or offsetting active bets among individual managers, offset unintended risk exposures (i.e., risk without expected return), avoid closet indexing the overall portfolio, and better assess how individual managers contribute to aggregate portfolio exposures.

Managers with complementary risk exposures can be combined to reduce risk relative to the benchmark while retaining the security-selection risk worth paying for.

 

Model Validation

Though mathematically complex, equity risk models are easily tested. Just as we don’t need to understand Google Maps’ time-to-arrival algorithm if we observe that we consistently arrive at the predicted time, we evaluate the accuracy of an equity risk model by comparing returns predicted by past factor exposures to subsequent portfolio performance: We measure factor exposures using end-of-month holdings and predict the following month’s return as a function of index returns.

The correlation between predicted and actual returns measures a model’s accuracy. The higher the correlation, the more effective a model is at hedging, stress testing, and scenario analysis, as well as evaluating investment risk and skill.

Our risk models are highly predictive and deliver over 0.97 median correlation between predicted ex-ante and reported ex-post portfolio returns for both U.S. and Global Equity mutual funds (see: testing predictions of equity risk models and testing global equity risk models).

Skeptical?  We’re happy to provide passive ETF-replicating portfolios for any of your managers, and you can validate our models’ accuracy for yourself by comparing predicted ex-ante with reported ex-post portfolio returns.

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Test Drive

Why not take a look at an analysis of one or two of your managers?  We have all historical holdings data preloaded, so there’s nothing required on your part; just reply below with a couple of fund names or email michele@peeranalytics.com.

 

 

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* Exposures to market, sector, size, value, and interest rates (global models add region, country, and currency exposures) are the dollar-weighted sum of individual security market betas, sector betas, etc.

 

Exposure (beta) examples:

If a fund with a benchmark with market beta of 1.0 has a consistent market beta of 0.8, the fund will underperform by 2.0% when the market is up 10% and outperform by 2.0% when the market is down 10%, absent any impact from security selection.

If a fund has a consistent tech sector beta of 1.5 when its benchmark’s tech beta is 1.0, that fund will outperform by 2.0% if the tech sector outperforms the market by 4.0%

Since market and sector betas other than 1.0 can be obtained passively, performance due to consistent beta differences from the benchmark is not part of active contribution.

A Peer Company Risk Modeling Approach to Asset Allocation

How much downside can your business tolerate?

Asset allocation, the most important decision any investor makes, explaining more than 90% of performance, is particularly complex for P&C and health insurers who must balance asset risk against underwriting risk, asset and premium leverage, and dividend policy.

Yet this most important decision rarely receives the attention it deserves.

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BACKGROUND

For endowments, foundations, and individual investors, quantifying the trade-off between short‐term investment risk and long‐term gain is relatively straightforward. The question is more involved for pension funds and insurance companies that aren’t concerned with asset volatility but rather with volatility of assets less liabilities (surplus) and the short‐term volatility of net income (insurers) or normal cost (pensions).

 

Property & casualty and health insurers, in particular, must consider the trade-off among asset risk, liability risk, pricing, and dividend policy decisions in the context of existing asset and liability leverage, ratings, and capital adequacy.

 

To quantify these trade-offs, most insurers use a Monte Carlo Simulation approach to model and consider all potential future financial statement results. This approach provides decision-makers a distribution of potential outcomes for any financial metric of interest (e.g., surplus, net income, RBC ratio, policyholder dividends, etc.) and evaluates trade-offs between expected and worst-case results.

 

While this DFA (also called ALM or ERM) modeling approach to determining asset-mix is a powerful tool, it has limitations, including capital market assumptions, potential model or user error, and lack of insight into short-term risk tolerance.

 

POTENTIAL DFA MODELING LIMITATIONS

 

  1. Capital Market Assumptions

All models are constrained by the validity of underlying assumptions, both explicit and implicit. The impact of explicit capital market and liability assumptions should be evaluated by varying assumptions to test the sensitivity of results. Models should be sufficiently transparent to allow users to identify any implicit assumptions. We believe that it is critical for users to evaluate the sensitivity of model results to changes in assumptions.

 

  1. Model error

Too many model providers seem to have gotten hung up creating overly complex models in an attempt to achieve results that are as close to perfection as possible. Perfection, unfortunately, is never possible with stochastic modeling. The validity of underlying assumptions constrains robust results for any model — and both capital market and liability assumptions are imperfect.

 

No investment professional would make the significant-figure mistake of carrying calculations to greater accuracy than the original data. Yet today’s DFA models too often try to deliver results with four or more significant figures based on underlying capital market and liability assumptions with only one!

The more serious concern is that this pursuit of model perfection comes at a substantial cost in terms of complexity, significantly increasing the opportunity for error: both model misspecification and user error.

There are multiple models currently available to insurers. Most suffer from the same limitations: They are complex for the sake of complexity, opaque, unnecessarily time-consuming to use, and invariably expensive. Perhaps the overly complicated models can command higher prices, but they don’t better serve the client.

A better approach offers the advantages of transparency and ease-of-use without any real sacrifice in the robustness of results.

 

 

  1. User error

We’ve seen multiple examples of user error over the years, but one of the worst is using geometric return assumptions when the model requires the arithmetic mean.

Since volatility drag is already part of a Monte Carlo analysis, the return assumption plugged into a Monte Carlo projection should actually be the higher arithmetic return and not the investment’s long-term compound average growth rate. Otherwise, the impact of volatility drag is effectively counted twice, which significantly understates long-term returns and overstates risk.

 

 

  1. Lack of insight into short-term risk tolerance

Finally, while DFA models are effective at quantifying the trade-off between expected and worst-case results, they do not address the critical question of how much short-term downside can be tolerated in pursuit of long-term growth.

 

For example, a given increase in the equity allocation results in an expected incremental gain in surplus of $20 million, but also a five-percent probability of a surplus loss of $15 million. Whether this is a good exchange depends on the impact of a $15 million loss in surplus.

 

To add context, we suggest a DFA Peer Company Risk Analysis (incorporating the same stochastic modeling analysis of individual peer companies) to describe the client’s asset, liability, surplus, net income, and capital adequacy risk positions in context with those same risk positions of individual peer companies.

This perspective adds insight into how much short-term surplus loss clients can comfortably withstand while pursuing maximum surplus growth (or policyholder dividends) over time.

 

 

We believe:

DFA/ERM models should be user-friendly, transparent, easily vetted, available to clients with all assumptions challenged, tested, and fully disclosed.

All model assumptions should be explicit.

Models should be transparent and readily tested.

Clients should have access to all models that inform reports, analysis, and recommendations so that they may vet models for themselves, either with transparent models that can be readily understood, and sensitivity of assumptions tested as with DFA/ERM models or by testing ex-ante predictions against ex-post results as with factor risk models.

Surplus, net income, and capital adequacy risk postures should be considered relative to peer and competitor risk postures to provide insight into risk tolerance.

 

 

 

Please contact Garth Flint  gflint@beaconpointe.com if you’d like to see a sample DFA Peer Risk Analysis for your company.

Manager Selection: The Quixotic Search for Skill

Active skill exists …. but it is challenging to detect reliably and, even when present, decays over time.

 

The Problem:

The traditional approach to manager selection involves some combination of quantitative and qualitative analysis, but conventional quantitative methods have not been very effective, and qualitative insights without a rigorous study of their predictive effectiveness are inadequate.

The generic quantitative approaches of evaluating managers’ performance suffer from the overwhelming limitation that simplistic measures of past performance are not positive predictors. The reality is the reverse. Managers in the top quartile during one period are more likely to be in the bottom quartile the next than to remain in the top. Selecting managers based on a simple analysis of absolute or relative returns, no matter how well massaged, is a losing game.

Manager search analysts are also at a disadvantage when it comes to qualitative manager assessments in which analysts attempt to discover managers with relative skill by differentiating between the smart and the brilliant (whether people, philosophies, or stories). But there are more equity managers than equities, and managers have the advantage of telling a single story to dozens of consultants while, in contrast, search consultants, with limited time, must critique many dozens of different stories, all while laboring under the huge information gap into portfolio details. Investment managers, collectively, hold all power in qualitative interviews.

But what if you could isolate the part of performance that does indicate skill and is predictive?

And what if you could quantify all current risk exposures which reliably predict future return due to market effects?

Wouldn’t manager discussions, armed with that information, lead to meaningful qualitative assessments and improved performance?

 

 

The Solution:

New Equity Factor Risk Models, built specifically for oversight using a limited number of passively investable factors, accurately isolate performance due to market timing and security selection from the performance due to passive bets relative to the benchmark. This approach effectively eliminates the noise that has always overwhelmed any active skill signal. These models are highly predictive and easily validated by comparing ex-ante predictions with ex-post results.

Managers in the top security-selection skill decile in one period are twice as likely to outperform in the subsequent three years. Managers in the bottom skill decile are more than twice as likely to underperform.

Skill by itself, however, is insufficient. Managers must also take enough security-selection risk to overcome fees. One-third of active mutual funds, and half of fund assets, take too little active risk to overcome active fees, even with top-tier skill. We require managers with security-selection skill who also take sufficient security-selection risk.

Our manager search process begins by screening out those managers who take too little active risk relative to fees, as well as those that fail to show evidence of security selection skill, allowing us to focus deep qualitative assessments on a small subset (6-8 percent) of all managers.

Manager interviews incorporating equity factor risk data allow search analysts to focus discussions on the true drivers of performance and understand investment processes at levels never before imagined.

New equity factor risk models built for oversight are a game-changer in the search for active skill and put the power back in the hands of asset owners, where it belongs.

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If you’d like to see an analysis of a particular manager or portfolio, please email gflint@beaconpointe.com.

 

The Problem with Performance Evaluation

The Conventional Approach to Evaluating past performance does not tell us anything useful about the future.

 

Problem

Portfolio performance evaluation is useful only if it can lead to actionable insights.

The uncomfortable truth is that conventional performance measurement has little to no value, and it is almost never actionable. We all understand that past returns are not positive predictors of future returns. In fact, managers in the top quartile in one period are more likely to be in the bottom quartile the next than to remain in the top.

The reason past performance is not a positive predictor is that the impact of market randomness overwhelms any return due to security selection skill. Every active portfolio has systematic bets relative to the benchmark, typically unintentional, and common techniques cannot effectively distinguish return due to security selection from the return due to these passive differences.

The trick is to separate performance due to security selection from performance due to passive systematic exposures (e.g., market, sector, and size betas) that differ from the benchmark.

Brinson attribution and Active Share – common techniques of risk and performance analytics software – attempt to distinguish active return (Brinson) and risk (Active Share) from their passive counterparts. Unfortunately, both approaches implicitly assume that individual securities all have identical systematic exposures, including identical market and sector betas.

In fact, betas vary significantly. For example, as of 12/31/2019, U.S. market betas ranged from -1.4 to 4.6 and U.S. sector betas ranged from -4.1 to 5.7.

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The wide variation in market and sector betas is one of the fatal flaws with Brinson attribution and Active Share. Failure to consider individual security betas prevents these methods from being effective. If they were effective, they would prove predictive.

Consider your own performance reports. Is there any data metric that, if it were different, would trigger an action?

 

Solution

New factor risk models, which model individual securities using a handful of (cheaply and passively investable) risk factors, accurately distinguish between return due to security selection and return due to passive factor betas. The result is a persistent metric of security selection performance. Skill exists, can be identified, and is persistent. But it does not last forever. This decay of skill makes it even more imperative to identify skilled managers quickly and reliably.

 

We hire managers with statistical evidence of skill who take sufficient security-selection risk to overcome fees and combine them to mitigate unintentional market exposures. We then monitor them continually, looking for reasons to make changes.

  • Does performance indicate that our confidence level in a manager’s skill has fallen below 90%?
  • Has active risk declined below the active fee threshold?
  • Have passive exposures started changing too much to be effectively offset?
  • Is the manager becoming overcapitalized?
  • Has the manager’s contribution to aggregate portfolio risk changed?

None of the above reasons to take action can be detected without robust factor risk models designed specifically for manager and portfolio oversight.

If you’d like to see an analysis of any particular manager or portfolio, please email a couple of fund names to gflint@beaconpointe.com

 

How ESG Overlays Can Lead to Unintended Market Bets

ESG constraints can create unintentional systematic exposures within equity portfolios.
Once identified and measured, these exposures are easily managed.

Over the past decade, many insurers have incorporated Environmental, Social, and Governance (ESG) investment strategies into their portfolios, either by creating separate ESG mandates or by incorporating ESG constraints across the entire portfolio.

These developments raise the vital question of how ESG criteria alter the risk profiles and the factor exposures of portfolios.

To help address this question, we used the ABW – Peer Analytics U.S. Equity Statistical Risk Model, which was built for oversight using only investable factors. Using the model, we compared an ESG constrained S&P 500 Index portfolio with its unconstrained counterpart.

Using FTSE-Russell ESG ratings for S&P 500 Index constituents, we created a sample ESG constrained index fund by excluding companies with ESG ratings below 2.6 from the index benchmark. This constraint excluded 23% of the market capitalization of the index.

In this simple example, ESG constraints changed the risk profile of the portfolio and added 1.7% volatility (tracking error) relative to the unconstrained benchmark.

 

However, 76% of relative risk in this example is due to relative exposures to market factors. These may be offset with inexpensive passive investment vehicles such as index funds, ETFs, futures, and swaps.

In fact, 72% of relative factor risk in our sample portfolio is due to only three factors: Market, Consumer Discretionary, and Communication Services sectors.

We’ve seen how ESG constraints can significantly alter the risk profile and passive factor exposures of portfolios. One option is to adjust the benchmark – this leaves the unanswered question of whether performance is sacrificed. Instead, insurers who have adopted, or are considering, ESG guidelines would be well-served by multi-factor risk models, built with investable factors. Such models can identify and offset the unintended market bets, thus avoiding style drift and potential underperformance.

We would be more than happy to provide a complimentary review of your portfolio. Please reach out to Garth Flint for additional information or any questions.

See here to learn more about Beacon Pointe Services for Insurers.

How ESG Overlays Can Lead to Unintended Market Bets

ESG constraints can create unintentional systematic exposures within equity portfolios. Once identified and measured, these exposures are easily managed.

 

Over the past decade, many insurers have incorporated Environmental, Social, and Governance (ESG) considerations into their portfolios, either by creating separate ESG mandates or by incorporating ESG constraints across their entire portfolios.

These developments raise the vital question of how ESG criteria alter the risk profiles and the factor exposures of portfolios.

To help address this question, we used the ABW – Peer Analytics U.S. Equity Statistical Risk Model, which was built for oversight and uses investable factors only. Using the model, we compared an ESG constrained S&P 500 Index portfolio with its unconstrained counterpart.

Using FTSE-Russell ESG ratings for S&P 500 Index constituents, we created a sample ESG constrained index fund by excluding companies with ESG ratings below 2.6 from the index benchmark. This constraint excluded 23% of the market capitalization of the index.

In this simple example, ESG constraints changed the risk profile of the portfolio and added 1.7% volatility (tracking error) relative to the unconstrained benchmark.

However, 76% of relative risk in this example is due to relative exposures to market factors. These may be offset with cheap passive investment vehicles such as index funds, ETFs, futures, and swaps.

In fact, 72% of relative factor risk in our sample portfolio is due to only three factors: market, Consumer Discretionary, and Communication Services sectors.

 

We’ve seen how ESG constraints can significantly alter the risk profile and passive factor exposures of portfolios, including their market risk. One option is to adjust the benchmark – this leaves unanswered the question of whether performance is sacrificed.

Instead, insurers who’ve adopted, or are considering, ESG guidelines would be well-served by multi-factor risk models, built with investable factors. Such models can identify and offset the unintended market bets, thus avoiding style drift and potential underperformance.

 

We would be more than happy to provide a complimentary review of your portfolio. Please contact Dave Newsom for additional information or any questions.

Testing Active Share

The Predictive Power of Active Share

Active Share is a popular metric that purports to measure portfolio activity. Though Active Share’s fragility and ease of manipulation are increasingly well-understood, there has been no research on its predictive power. This paper quantifies the predictive power of Active Share and finds that, though Active Share is a statistically significant predictor of the performance difference between portfolio and benchmark (there is a relationship between Active Share and how active a fund is relative to a given benchmark), it is a weak one. The relationship explains only about 5% of the variation in activity across U.S. equity mutual funds. The predictive power of Active Share is a small fraction of that achieved with robust and predictive equity risk models.

The Breakdown of Active Share

Active Share — the absolute percentage difference between portfolio and benchmark holdings – is a common metric of fund activity. The flaws of this measure are evident from some simple examples:

  • If a fund with S&P 500 benchmark buys SPXL (S&P 500 Bull 3x ETF), it becomes more passive and more similar to its benchmark, yet its Active Share increases.
  • If a fund uses the S&P 500 as its benchmark but indexes Russell 2000, it is passive, yet its Active Share is 100%.
  • If a fund differs from a benchmark by a single 5% position with 20% residual (idiosyncratic, stock-specific) volatility, and another fund differs from the benchmark by a single 10% position with 5% residual volatility, the second fund is less active, yet it has a higher Active Share.
  • If a fund holds a secondary listing of a benchmark holding that tracks the primary holding exactly, it becomes no more active, yet its Active Share increases.

Given the flows above, the evidence that Active Share funds that outperform may merely index higher-risk benchmarks is unsurprising.

Measuring Active Management

A common defense is that these criticisms are pathological or esoteric, and unrepresentative of the actual portfolios. Such defense asserts that Active Share measures active management of real-world portfolios.

Astonishingly, we have not seen a single paper assess whether Active Share has any effectiveness in doing what it is supposed to do – identify which funds are more and which are less active. This paper provides such an assessment.

We consider two metrics of fund activity: Tracking Error and monthly active returns (measured as Mean Absolute Difference between portfolio and benchmark returns). Both these metrics measure how different the portfolios are in practice. Whether Active Share measures actual fund activity depends on whether it can differentiate among more and less active funds.

The study dataset comprises portfolio histories of approximately 3,000 U.S. equity mutual funds that are analyzable from regulatory filings. The funds all had 2-10 years of history. Our study uses the bootstrapping statistical technique – we select 10,000 samples and perform the following steps for each sample:

  • Select a random fund F and a random date D.
  • Calculate Active Share of F to the S&P 500 ETF (SPY) at D.
  • Keep only those samples with Active Share between 0 and 0.75. This filter ensures that SPY may be an appropriate benchmark, and excludes small- and mid-capitalization funds that share no holdings with SPY. Such funds would all collapse into a single point with Active Share of 100, impairing statistical analysis.
  • Measure the activity of F for the following 12 months (period D to D + 12 months). We determine how active a fund is relative to a benchmark by quantifying how similar its performance is to that of the benchmark.

After the above steps, we have 10,000 observations of fund activity as estimated by Active Share versus the funds’ actual activity for the subsequent 12 months.

The Predictive Power of Active Share for U.S. Equity Mutual Funds

The following results quantify the predictive power of Active Share to differentiate among more and less active U.S. equity mutual funds. For perspective, we also include results on the predictive power of robust equity risk models. These results illustrate the relative weakness of Active Share as a measure of fund activity. They also indicate that, far from mitigating legal risk by reliance upon a claimed “best practice,” the use of Active Share to detect closet indexing may instead create legal risk.

The Predictive Power of Active Share to Forecast Future Tracking Error

Although Active Share is a statistically significant metric of fund activity, it is a weak one. Active Share predicts only about 5% of the variation in tracking error across mutual funds:

Active Share vs. Future Tracking Error

U.S. Equity Mutual Fund Portfolios: The Predictive Power of Active Share to Forecast Future Tracking Error

Residual standard error: 1.702 on 9998 degrees of freedom
Multiple R-squared:  0.05163,   Adjusted R-squared:  0.05154
F-statistic: 544.3 on 1 and 9998 DF,  p-value: < 2.2e-16

The distributions clearly suffer from heteroscedasticity, which can invalidate tests of statistical significance. To control for this, we also considered the relationship between the rankings of Active Share and future tracking errors. This alternative approach does not affect the results:

Active Share Rank vs. Future Tracking Error Rank

U.S. Equity Mutual Fund Portfolios: The Predictive Power of Active Share Rank to Forecast Future Tracking Error Rank

Residual standard error: 2811 on 9998 degrees of freedom
Multiple R-squared:  0.05226,   Adjusted R-squared:  0.05217
F-statistic: 551.3 on 1 and 9998 DF,  p-value: < 2.2e-16

 

The Predictive Power of Active Share to Forecast Future Active Returns

Active Share also predicts approximately 5% of the variation in monthly absolute active returns across mutual funds:

Active Share vs. Future Active Return

U.S. Equity Mutual Fund Portfolios: The Predictive Power of Active Share to Forecast Future Active Return

Residual standard error: 0.3986 on 9998 degrees of freedom
Multiple R-squared:  0.04999,   Adjusted R-squared:  0.04989
F-statistic: 526.1 on 1 and 9998 DF,  p-value: < 2.2e-16

The above results make a generous assumption that all relative returns are due to active management. In fact, much relative performance is attributable to passive differences between a portfolio and a benchmark. We will illustrate this complexity in our follow-up research.

The Predictive Power of Robust Equity Risk Models

To put the predictive power of Active Share into perspective, we compare it to the predictive power of tracking error as estimated by robust and predictive equity risk models. Instead of Active Share, we use AlphaBetaWorks’ default Statistical U.S. Equity Risk Model to forecast tracking error of a fund F at date D.

The Predictive Power of Equity Risk Models to Forecast Future Tracking Error

The equity risk model predicts approximately 38% of the variation in tracking error across mutual funds:

 

Risk Model Estimate vs. Future Tracking Error

U.S. Equity Mutual Fund Portfolios: The Predictive Power of Robust Equity Risk Models to Forecast Future Tracking Error

Residual standard error: 1.379 on 9998 degrees of freedom
Multiple R-squared: 0.3776, Adjusted R-squared: 0.3776
F-statistic: 6067 on 1 and 9998 DF, p-value: < 2.2e-16

As with Active Share above, heteroscedasticity does not affect the results. We see a similar relationship when we consider ranks instead of values:

Risk Model Estimate Rank vs. Future Tracking Error Rank

U.S. Equity Mutual Fund Portfolios: The Predictive Power of Robust Equity Risk Models to Forecast Future Tracking Error Rank

Residual standard error: 2278 on 9998 degrees of freedom
Multiple R-squared:  0.3773,    Adjusted R-squared:  0.3772
F-statistic:  6058 on 1 and 9998 DF,  p-value: < 2.2e-16

The Predictive Power of Equity Risk Models to Forecast Future Active Returns

The equity risk model predicts approximately 44% of the variation in monthly absolute active returns across mutual funds:

 

Risk Model Estimate vs. Future Active Return

U.S. Equity Mutual Fund Portfolios: The Predictive Power of Robust Equity Risk Models to Forecast Future Active Return

Residual standard error: 0.3068 on 9998 degrees of freedom
Multiple R-squared:  0.4375,    Adjusted R-squared:  0.4374
F-statistic:  7776 on 1 and 9998 DF,  p-value: < 2.2e-16

Conclusions

  • Active Share is a statistically significant metric of active management (there is a relationship between Active Share and how active a fund is relative to a given benchmark), but the predictive power of Active Share is very weak.
  • Active Share predicts approximately 5% of the variation in tracking error and active returns across U.S. equity mutual funds.
  • A robust and predictive equity risk model is roughly 7-9-times more effective than Active Share, predicting approximately 40% of the variation in tracking error and active returns across U.S. equity mutual funds.
  • In subsequent articles we will discuss the limitation of assuming a single index as the passive alternative, put the above predictive statistics into context, and quantify how likely Active Share is to identify closet indexers.

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The information herein is not represented or warranted to be accurate, correct, complete or timely.
Past performance is no guarantee of future results.
Copyright © 2012-2019, AlphaBetaWorks, a division of Alpha Beta Analytics, LLC. All rights reserved.
Content may not be republished without express written consent.

The Explanatory Power of Sectors and Style

Factor analysis is a popular and effective technique that explains and forecasts security returns. The factor models prevalent in academic circles (Fama-FrenchCarhart) tend to rely heavily on the size and value style factors. Meanwhile, effective industry models often attribute risk to sector and industry factors before style. Which approach is more effective? Though claims that style explains stock returns are common, they usually lack evidence – there is a paucity of research that compares the explanatory power of sectors and style.

This paper provides the missing data and analyzes the explanatory power of sectors and style for U.S. stocks. We find that, after controlling for the market exposure, sectors are slightly more effective than size and approximately four times more effective than value in explaining monthly returns.

Measuring the Explanatory Power of Sectors and Style for U.S. Stock Returns

  • We analyze the monthly returns of U.S. stocks over the 15-year interval 4/30/2004-4/30-2019. We start with approximately 6,000 stocks that pass minimum market capitalization and liquidity thresholds – a universe similar to the Russell 3000 Index.
  • For each month in the historical interval and each stock in the sample, we estimate the stock’s market beta.
  • We calculate (out-of-sample) market residuals (alphas) for a given month using the prior month’s market beta for each stock.
  • We restrict the analysis to stocks with at least five years of defined market residuals to have a significant sample. This final sample comprises approximately 3,600 stocks.
  • We construct sector, size, and value factors as follows:
    • The sector factors are cap-weighted portfolios of market residuals for the nine sectors equivalent to the top-level GICS sectors.
    • The size factor is long the cap-weighted portfolio of stocks in the top 25% and short stocks in the bottom 25%, as ranked by market capitalization.
    • The value factor is long the cap-weighted portfolio of stocks in the top 25% and short stocks in the bottom 25%, as ranked by Book/Price.

The results below are insensitive to the specific factor definition and hold across different sector and style portfolios.

  • For sector, size, and value factors, we regress stocks’ market residuals on the corresponding factor returns and measure each regression’s R². This measures the theoretical (in-sample) explanatory power of sectors and style.
  • We estimate factor exposures by robust regression. We fit models with iterated re-weighted least squares (IRLS). Observations are exponentially weighted with a half-life of approximately 36-months.

A Comparison of the Explanatory Power of Sectors and Style for U.S. Stock Returns

The chart below plots the distributions of  from the regressions of U.S. stocks’ market residuals against the sector, size, and value factors. The x-axis plots the intervals of regression R², and the y-axis plots the number of stocks in each interval. Since the distributions approximately follow a power law, we use a log y-axis:

Chart of the explanatory power of sectors, size, and value -- the distributions of the R² (the coefficient of determination) from regressions U.S. stocks’ Market residuals (alphas) on the Sector, Size, and Value Factors
U.S. Stocks: The Distributions of R² for the Regressions of U.S. Stock Market Residuals (Alphas) on the Sector, Size, and Value Factors

The distributions above illustrate the higher explanatory power of sectors compared to style: Whereas sector factors explain over 25% of the variance in market residuals for hundreds of stocks, style factors do so for only a small handful.

The chart below plots the mean R² values:

Chart of the explanatory power of market, sectors, size, and value -- mean R² (the mean coefficient of determination) from regressions U.S. stocks’ returns and Market residuals (alphas) on the Market, Sector, Size, and Value Factors
U.S. Stocks: Mean R² for the Regressions of U.S. Stock Returns and Market Residuals on the Various Factors

Reasons for Sectors’ Higher Explanatory Power

This higher explanatory power of sectors is unsurprising, given that commentary on style performance usually relies on sector factors: “Value underperformed because oil price crashed, and oil producer stocks, which are cheap, suffered.” On the other hand, even the most ideologically pure believer in the primacy of style would not make the statement: “Oil price crashed because oil producer stocks are cheap and value has recently underperformed.” Whereas sector factors can generally explain the reasons for style factor returns, style factors cannot explain the reasons for sector factor returns.

Since style factors capture systematic risk less effectively, portfolio construction from style building blocks can lead to significant unintended exposures. Studies of common smart beta strategies do indeed find such risks and significant market timing. On the other hand, sector and industry exposures offer superior control of systematic risk and more effective building blocks for portfolio construction.

In the sections that follow, we share the statistics on the explanatory power of the various factors.

The Explanatory Power of Market for U.S. Stock Returns

The chart below plots the distribution of R² from the regressions of U.S. stocks’ returns against the Market factor. This step of the analysis allows us to control for market risk and to analyze the explanatory power specific to the other factors:

Chart of the explanatory power of Market -- the distributions of the R² (the coefficient of determination) from regressions U.S. stocks’ returns on the Market Factor
U.S. Stocks: The Distribution of R² for the Regressions of U.S. Stock Returns on the Market Factor
Min.    1st Qu.  Median    Mean    3rd Qu.    Max.
0.0000  0.1117   0.1770    0.1914  0.2563     0.6525

Market explains approximately 20% of the (in-sample) variance of stock returns. The tests below analyze the out-of-sample (investable) market residuals that this step produces.

The Explanatory Power of Sectors for U.S. Stock Returns

The chart below plots the distribution of R² from the regressions of U.S. stocks’ market residuals against sector factors:

Chart of the explanatory power of sectors -- the distributions of the R² (the coefficient of determination) from regressions U.S. stocks’ Market residuals (alphas) on the Sector Factors
U.S. Stocks: The Distribution of R² for the Regressions of U.S. Stock Market Residuals on Sector Factors
Min.    1st Qu.  Median    Mean    3rd Qu.    Max.
0.0000  0.0070   0.0267    0.0618  0.0767     0.6166

For most stocks, sectors explain 2.7% or more of return variance, after controlling for market risk. The average effectiveness is statistically much higher, since sectors explain a large fraction of return variance for some stocks (e.g., Energy sector for Exxon Mobil).

The Explanatory Power of Size for U.S. Stock Returns

The following chart plots the distribution of R² from the regressions of U.S. stocks’ market residuals against the Size factor:

Chart of the explanatory power of size -- the distributions of the R² (the coefficient of determination) from regressions U.S. stocks’ Market residuals (alphas) on the Size Factor
U.S. Stocks: The Distribution of R² for the Regressions of U.S. Stock Market Residuals on the Size Factor
Min.    1st Qu.  Median    Mean    3rd Qu.    Max.
0.0000  0.0089   0.0290    0.0415  0.0599     0.3366

These results support the popularity of the size factor in academic research. For most stocks, the size factor explains 2.9% or more of return variance, after controlling for market risk. Nevertheless, the average explanatory power of sectors is approximately 1.5 times greater.

The Explanatory Power of Value for U.S. Stock Returns

The following chart plots the distribution of R² from the regressions of U.S. stocks’ market residuals against the Value factor:

Chart of the explanatory power of value -- the distributions of the R² (the coefficient of determination) from regressions U.S. stocks’ Market residuals (alphas) on the Value Factor
U.S. Stocks: The Distribution of R² for the Regressions of U.S. Stock Market Residuals on the Value Factor
Min.    1st Qu.  Median    Mean    3rd Qu.    Max.
0.0000  0.0020   0.0092    0.0202  0.0251     0.3350

Contrary to its vogue in academic research, the explanatory power of Value is low, even in these in-sample results. The Value factor explains less than 1% of return variance, after controlling for market risk. Even for the 25% of stocks where the value factor has the greatest explanatory power, it only explains about 2.5% of return variance.

Notes on the Quantitative Methodology

This study controls for market risk before analyzing the explanatory power of sector and style factors. This two-step approach is necessary to avoid the multicollinearity problems that plague academic research into style factors. Since small and large companies typically have different market betas, and since cheap and expensive companies also typically have different market betas, the Fama-French and Carhart factors are collinear. Though this multicollinearity does not necessarily undermine the overall model, it does render individual factor betas and associated statistics meaningless.

We measured the in-sample explanatory power of various factors, similarly to typical academic research on the subject. These results are theoretical and do not represent practically attainable investment outcomes – they are the upper bound for out-of-sample explanatory power: This approach calculates factor exposures and residuals using a regression of stock returns on one or more factors. For instance, the regression of AAPL in the 4-factor Carhart model for 2010-2015 produces betas and alphas that are un-investable. To realize this alpha, one would need to know 2014 returns in order to effectively hedge AAPL in 2010. We use a similar approach in this study, and our analysis suffers from the same limitations – the results are in-sample.

Conclusions

  • Academic analysis favors factors with less explanatory power than industry’s real-world modeling.
  • The explanatory power of sectors is slightly higher than that of size, and approximately four times greater than that of value/growth.
  • Portfolio construction and manager allocation with sector, rather than style building blocks, provide greater control over systematic risk.
  • Risk models that seek to capture effectively systematic risk should account for sector or industry risk before style risk.
  • Sectors’ higher explanatory power holds across different industry classifications and style factor definitions.

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The information herein is not represented or warranted to be accurate, correct, complete or timely. Past performance is no guarantee of future results. Copyright © 2012-2019, AlphaBetaWorks, a division of Alpha Beta Analytics, LLC. All rights reserved. Content may not be republished without express written consent.