The Predictive Power of Information Ratios

Our earlier work showed that simple performance metrics, such as nominal returns and Sharpe Ratios, revert. Because of this reversion, above-average past performers tend to become below-average and vice versa. This reversion is primarily due to systematic (factor) noise. Consequently, metrics that remove factor effects from performance reveal persistent stock picking skill. Prompted by readers’ questions, we have investigated the predictive power of popular performance metrics. This article reviews the predictive power of information ratios. They offer a large improvement over simple nominal returns, naive alphas, and Sharpe ratios, but still fall short of the most predictive metrics. Over a 3-year window, the predictive power of information ratios for skill evaluation and manager selection is approximately half that of security selection distilled with a statistical equity risk model.

Measuring the Predictive Power of Information Ratios

We analyze portfolios of all institutions that have filed Forms 13F in the past 15 years. This survivorship-free portfolio dataset covers firms that have held as least $100 million in long U.S. assets. Approximately 5,000 portfolios had sufficiently long histories and low turnover to be analyzable.

To measure the persistence of performance metrics over time, we compare metrics measured in two 12-month periods separated by variable delay. One example is the 24-month delay that separates metrics for 1/31/2010-1/31/2011 and 1/31/2013-1/31/2014. A 24-month delay of 12-month metrics thus covers a 48-month time window. We use Spearman’s rank correlation coefficient to calculate statistically robust correlations.

Serial Correlation of Information Ratios

The information ratio is similar to the Sharpe ratio, but with a key upgrade: Sharpe ratio evaluates returns relative to the risk-free rate. Information ratio evaluates returns relative to a (presumably appropriate) benchmark. We use the S&P 500 Index as the benchmark, following a common practice. As a benchmark increasingly matches the factor exposures of a portfolio, information ratios converge to the standard score (z-score) of active returns estimated with a capable equity risk model. Due to the more effective handling of systematic risk, the predictive power of information ratios receives a boost.

The chart below shows correlation between 12-month Information Ratios calculated with lags of one to sixty months (1-60 month delay):

Chart of the predictive power of information ratios as measured by their autocorrelation (the correlation between Information Ratios for one 12-month period and a different 12-month period separated by a given lag) for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of Information Ratios

Delay (months) Serial Correlation
1 0.06
6 0.05
12 0.03
18 0.05
24 0.06
30 0.06
36 0.02
42 -0.02
48 -0.06
54 -0.04
60 0.02

Over the 3-year window, the serial correlation (autocorrelation) of Information Ratios is approximately half of the serial correlation of security selection returns provided in the following section. Unlike simple nominal returns and Sharpe ratios, information ratios do not suffer from short-term reversion.

Serial Correlation of Nominal Returns

For comparison, the following chart shows serial correlation of 12-month cumulative nominal returns calculated with 1-60 month lags. As we discussed in prior articles, these revert with an approximately 18-month cycle – so strong past nominal returns are actually predictive of poor short-term future nominal returns:

Chart of the correlation between returns for one 12-month period and a different 12-month period separated by a given lag for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of nominal returns

Delay (months) Serial Correlation
1 -0.14
6 -0.24
12 -0.33
18 -0.06
24 0.16
30 0.23
36 0.08
42 -0.26
48 -0.44
54 -0.23
60 0.13

Serial Correlation of Security Selection Returns

As we mentioned above, when a benchmark’s factor exposures match those of the portfolio, information ratio is equivalent to the standard score (z-score) of active returns estimated with a capable equity risk model. In practice, however, information ratio is typically calculated relative to a broad benchmark, such as the S&P 500 Index for equity portfolios. Consequently, one would expect the predictive power of information ratios to be lower than the predictive power of security selection returns, properly estimated. For comparison, we provide serial correlation of a security selection metric that uses an equity risk model to control for factor exposures.

To eliminate the disruptive factor effects responsible for performance reversion, the AlphaBetaWorks Performance Analytics Platform calculates each portfolio’s return from security selection net of factor effects. αReturn is the return a portfolio would have generated if all factor returns had been zero. The following chart shows correlation between 12-month cumulative αReturns calculated with 1-60 month lags:

Chart of the correlation between αReturns (risk-adjusted returns from security selection) for one 12-month period and a different 12-month period separated by a given lag for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of αReturns (risk-adjusted returns from security selection)

Delay (months) Serial Correlation
1 0.08
6 0.10
12 0.08
18 0.05
24 0.06
30 0.04
36 -0.02
42 -0.04
48 -0.05
54 -0.04
60 -0.02

The predictive power of αReturns, as measured by their serial correlation of 12-month performance metrics, is approximately twice that of information ratios over a 3-year window (12-month delay between 12-month performance metrics), but the two begin to converge after three years.

For all performance metrics, the above data is aggregate, spanning thousands of portfolios and return windows. Individual firms can overcome the averages; however, the exceptions require especially careful monitoring.

Summary

  • The predictive power of information ratios is significantly higher than that of nominal returns and Sharpe ratios.
  • As a benchmark converges to the factor exposures of a portfolio, information ratios converge to the standard score (z-score) of active returns estimated with a capable risk model.
  • Over a 3-year window, the predictive power of information ratios, as commonly calculated, is approximately half that of the security selection return calculated with a predictive equity risk model.
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.
U.S. Patents Pending
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The Predictive Power of Sharpe Ratios

Our earlier work showed that performance metrics dominated by market noise, such as simple nominal returns, revert. Because of this reversion, above-average performers of the past tend to become below-average performers and vice versa. Since the reversion is primarily due to systematic (factor) noise, metrics that control for factor exposures reveal persistent stock picking skill. Prompted by readers’ questions, this series of articles will measure the predictive power of popular performance metrics. We first consider the predictive power of Sharpe Ratios. For the universe of all institutional U.S. long equity portfolios, the use of Sharpe Ratios for skill evaluation and manager selection is almost as damaging as the use of simple nominal returns.

Measuring the Predictive Power of Sharpe Ratios

We analyze portfolios of all institutions that have filed Forms 13F in the past 15 years. This survivorship-free portfolio dataset covers firms that have held as least $100 million in long U.S. assets. Approximately 5,000 portfolios had sufficiently long histories, low turnover, and broad holdings to be analyzable.

To measure the decay of performance metrics over time, we compare metrics measured in two 12-month periods separated by variable delay. One example of 24-month delay is metrics for 1/31/2010-1/31/2011 and 1/31/2013-1/31/2014. We use Spearman’s rank correlation coefficient to calculate statistically robust correlations.

Serial Correlation of Sharpe Ratios

Sharpe Ratio is perhaps the most common performance metric. Since it does not directly control for systematic (factor) portfolio exposures, one would expect this approach to suffer from similar reversion as nominal returns. Indeed, tests reveal that Sharpe Ratios fail to isolate security selection performance: Sharpe Ratios of portfolios revert when factor regimes change. Thus, former leaders tend to become laggards, and former laggards tend to become leaders.

The serial correlation (autocorrelation) of Sharpe Ratios is similar to the serial correlation of nominal returns in the next section. The following chart shows correlation between 12-month Sharpe Ratios calculated with lags of one to sixty months (1-60 month lag):

The predictive power of Sharpe Ratios: Chart of the correlation between Sharpe Ratios for one 12-month period and a different 12-month period separated by a given lag for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of Sharpe Ratios

Delay (months) Serial Correlation
1 -0.09
6 -0.20
12 -0.28
18 -0.06
24 0.12
30 0.15
36 -0.08
42 -0.40
48 -0.49
54 -0.24
60 0.12

Sharpe Ratios revert with an approximately 18-month cycle. Historical Sharpe Ratios thus have some predictive value, but a negative one. There is a narrow window at 2-3 year lag when past Sharpe Ratios are positively predictive of the future Sharpe Ratios. This is due to the approximately 18-month cycle of reversion.

Serial Correlation of Nominal Returns

For comparison, the following chart shows serial correlations between 12-month cumulative nominal returns calculated with 1-60 month lags. The relationship is similar to that of the Sharpe Ratios. Strong past (nominal) returns are predictive of poor short-term future returns:

Chart of the correlation between returns for one 12-month period and a different 12-month period separated by a given lag for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of nominal returns

Delay (months) Serial Correlation
1 -0.14
6 -0.24
12 -0.33
18 -0.06
24 0.16
30 0.23
36 0.08
42 -0.26
48 -0.44
54 -0.23
60 0.13

Serial Correlation of Security Selection Returns

For additional comparison, we provide serial correlation of a security selection metric that adjusts for factor exposures. To eliminate the disruptive factor effects responsible for performance reversion, the AlphaBetaWorks Performance Analytics Platform calculates each portfolio’s return from security selection net of factor effects. αReturn is the return a portfolio would have generated if all factor returns had been flat. Firms with above-average αReturns in one period are likely to maintain them, though with a decay. The following chart shows correlation between 12-month cumulative αReturns calculated with 1-60 month lags:

Chart of the correlation between αReturns (risk-adjusted returns from security selection) for one 12-month period and a different 12-month period separated by a given lag for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of αReturns (risk-adjusted returns from security selection)

Delay (months) Serial Correlation
1 0.08
6 0.10
12 0.08
18 0.05
24 0.06
30 0.04
36 -0.02
42 -0.04
48 -0.05
54 -0.04
60 -0.02

Though the above serial correlations of αReturn may appear low, they are amplified and compounded in practical portfolios of multiple funds. A hedged portfolio of the net consensus longs (relative overweights) of the top 5% long U.S. equity stock pickers delivered approximately 8% return independently of the market. The above data is aggregate. Specific outstanding disciplined firms can overcome performance reversion, but they are the exceptions that require careful monitoring.

Summary

  • Sharpe Ratios revert rapidly and are not significantly better predictors of future performance than nominal returns.
  • Once performance is controlled for systematic (factor) exposures, security selection returns persist for approximately 5 years.
  • Selection of superior future performers is possible, but it requires abandoning popular non-predictive metrics and spotting skill long before it is plainly visible and arbitraged away.
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.
U.S. Patents Pending
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Berkshire Hathaway’s Alpha Decay

Berkshire’s Recent Exposure and Performance Raise Questions

There is a good reason many investors consider Berkshire Hathaway the paragon of investment success. For over 20 years, Berkshire’s equity portfolio has outperformed the general market on a risk-adjusted basis. But, in the past two years Berkshire’s alpha has turned negative. We identify the principal culprit and provide evidence of style drift at Berkshire – either by Warren Buffett or one of his possible successors.

Berkshire Hathaway Security Selection Return

Below is a chart showing Berkshire’s long equity portfolio performance since 2006, during which time it gained 108%. Many investors and guru-followers will dig no further. But simplistic analysis produces dangerous conclusions. Much of Berkshire’s performance—and that of most stocks—can be attributed to systematic sources, or factors. Berkshire’s nominal performance is influenced by the Market, bond rates, and FX rates. Since factor returns revert, and nominal returns are a contrarian indicator of future performance, it is important to separate Berkshire’s factor performance from its stock-picking skill.

We use the AlphaBetaWorks Statistical Equity Risk Model to analyze Berkshire’s equity portfolio since 2006. The chart below shows Berkshire returns due to systematic (factor) and idiosyncratic (stock selection, alpha) components.

Chart of the Factor and Stock Selection Components of Berkshire Hathaway's Long Equity Portfolio Returns

Berkshire Hathaway Long Equity Portfolio Performance – Factor and Stock Selection Components

In the chart above, the black line represents Berkshire’s long equity portfolio total return. Within this, the gray line is performance due to factors, and the blue area reflects Berkshire’s positive returns from stock selection, or αReturn. Since “alpha” and security selection performance are widely and often inconsistently used, AlphaBetaWorks defines a rigorous metric of security selection performance as αReturn, which is performance net of all factor effects, or the return a portfolio would have generated if markets were flat.

From 2006 to 2013 Berkshire’s return from stock selection alone was +29.9%. But in 2014 Berkshire’s αReturn started to decline (thinning blue area). Between 2014 and 2015, Berkshire’s return from stock selection was -16.3%.

Whereas the chart above depicts Berkshire αReturn including factor returns, the chart below depicts Berkshire’s ten-year αReturn in isolation.

Chart of the cumulative Return from Stock Selection (αReturn) of Berkshire Hathaway

Berkshire Hathaway Return from Stock Selection (αReturn)

Berkshire’s αReturn began to decay in 2014. There is one principal sector responsible for this: Technology.

Berkshire Hathaway Technology Exposure

Berkshire made a significant bet in the technology sector in mid-2011 after having avoided it for a very long time:

Chart of the historical technology factor exposure of Berkshire Hathaway Long Equity portfolio

Berkshire Hathaway Long Equity Factor Exposure – Technology

From 2006 to 2011, Berkshire’s technology exposure was effectively zero. But starting in 2011 it went up dramatically.

Berkshire Hathaway Technology Security Selection

This bet has gone poorly. In fact, this sector is the principal contributor to Berkshire’s recent αReturn decay:

Chart of the cumulative Return from Stock Selection (αReturn) of Berkshire Hathaway technology portfolio

Berkshire Hathaway Return from Stock Selection (αReturn) – Technology Sector

Berkshire’s long equity portfolio suffered over a 12% loss from technology stock selection, peak-to-trough.

Style Drift, Succession Issues?

Warren Buffett has long been very public about his avoidance of technology investments, citing reluctance to allocate capital to a business he cannot understand. So why was a manager with no record in, and known skepticism towards, the technology industry making large bets in it? In this light, the above data indicates worrying style drift. Perhaps this large technology sector bet was made by one of his likely successors, which raises an equally important question about manager succession and the style drift risk therein: does a new portfolio manager demonstrate security selection skill (positive αReturn) in general, and in the areas of growing allocation like technology? And what other changes should investors expect of new leadership?

Whether Berkshire’s recent negative αReturn is Buffett’s own error or commission or a byproduct of portfolio manager transition is beyond the scope of this piece. Our focus is identifying active return, its sources (factor timing, stock selection), and their predictive value. All of the above lead to improved performance. In Berkshire’s case, our approach has identified that an established star manager shifted focus to an area previously avoided (technology), and that this shift reduced stock selection performance. Whatever the reason, the results are troublesome. Their early warnings are critical to investors’ and managers’ performance.

Such analysis of risk and performance using holdings data and a predictive equity risk model provides indicators that enhance manager/fund selection and future performance. It can also highlight emerging issues, such as style drift.

Summary

  • After a long, positive run, Berkshire Hathaway’s stock selection returns (alpha) turned negative in 2014.
  • Berkshire’s allocation to the technology sector was the principal driver behind its recent negative alpha.
  • Whether by Buffett or someone new, style drift is a cause of Berkshire’s increased allocation to technology and the resulting negative alpha.
  • Even when investing in or alongside star managers, it is critical that investors and allocators rely on robust and predictive tools to detect early signs of style drift and stock selection decay.
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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Tests of Equity Market Hedging: U.S. Hedge Funds

Our earlier piece tested several equity market hedging techniques on U.S. equity mutual fund portfolios. We now extend the tests to U.S. hedge fund long equity portfolios. Since these are generally less diversified and more active than mutual funds, simplistic approaches that use a fixed 100% short (1 beta) or rely on returns-based style analysis (RBSA) fail even more dramatically for hedge funds. Yet, a robust statistical equity risk model applied to portfolio holdings remains close to the ideal of perfect hedging. A robust and well-tested technique is thus even more vital for managing hedge fund exposures.

Equity Market Hedging Techniques

We analyze approximately 600 hedge fund long U.S. equity portfolios that are tractable from regulatory filings. Note that roughly half of U.S. hedge fund portfolios are impossible to analyze accurately due to the quarterly data frequency and high turnover. Similarly to our earlier analysis of mutual fund portfolio hedging, we evaluate three approaches to calculating market hedge ratios:

  • Constant 100% market exposure (1 beta): This common ad-hoc approach used by portfolio managers and analytics vendors supposes that all portfolios have the same risk as a benchmark or a hedge.
  • Returns-based style analysis (RBSA): This statistical approach estimates portfolio factor exposures by regressing portfolio returns against factor returns.
  • Statistical equity risk model applied to portfolio holdings: A more statistically and algorithmically intensive technique estimates factor exposures of positions, essentially performing RBSA on individual stocks, and aggregates these to calculate portfolio factor exposures.

Our study spans 10 years. We calculate hedge ratios at the end of each month and use these to hedge portfolios during the following month. This produces a series of 10-year realized (ex-post) hedged portfolio returns. We further break these series into 12-month intervals and calculate their correlations to the Market. Low average market correlation and low dispersion of correlations indicates that a hedging technique effectively eliminates systematic market exposure of a typical portfolio.

Realized Market Correlations of Hedged Hedge Fund Portfolios

Realized Market Correlations of Random Return Series

A large return dataset, even when perfectly random, will contain some subsets with high market correlations. To control for this, we generate random return samples (observations) and calculate their market correlations. These results, attainable only with a perfect hedge, are the standard against which we evaluate equity market hedging techniques:

Chart of the correlations between 12-month random return series and 12-month returns of U.S. Equity Market, with sample size chosen to match the hedge fund dataset, used as a baseline for equity market hedging effectiveness.

Realized 12-month market correlations of random return series

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
-0.9374 -0.2157 -0.0001  0.0022  0.2173  0.9190

Realized Market Correlations of Portfolios Hedged using a 100% Market Short

As with mutual funds, the assumption that all hedge fund long equity portfolios’ market exposures are 100% (market betas are 1) is flawed:

Chart of the correlations between realized 12-month returns of U.S. Long Equity Hedge Fund Portfolios hedged using a 100% market short and 12-month returns of U.S. Equity Market, used to evaluate equity market hedging effectiveness of a fixed beta assumption.

U.S. Long Equity Hedge Fund Portfolios: Realized 12-month market correlations of portfolios hedged using a 100% market short

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-0.9999 -0.2131  0.0927  0.0578  0.3706  0.9789

A 100% hedge is too small for high-risk portfolios and too large for low-risk ones. Also as seen for mutual funds, some hedged low-exposure portfolios formed a fat tail of nearly -1 realized market correlations.

Realized Market Correlations of Portfolios Hedged using Returns-Based Analysis

Most RBSA assumes that portfolio factor exposures are constant over the regression window.  Some advanced techniques may allow for random variation in exposures over the window, yet even this relaxed assumption is flawed. Our earlier posts covered the problems that arise when RBSA fails to detect rapid changes in portfolio risk. It turns out that the months or years of delay before RBSA captures changes in factor exposures are especially damaging when analyzing hedge fund portfolios:

Chart of the correlations between realized 12-month returns of U.S. Long Equity Hedge Fund Portfolios hedged using returns-based style analysis and 12-month returns of U.S. Equity Market , used to evaluate equity market hedging effectiveness of a returns-based analysis.

U.S. Long Equity Hedge Fund Portfolios: Realized 12-month market correlations of portfolios hedged using returns-based style analysis

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
-0.9998 -0.3321 -0.0503 -0.0527  0.2311  0.9993

RBSA fails more severely for hedge funds than for mutual funds. In fact, RBSA has similar defect as a fixed 100% hedge for some low-exposure portfolios and produces a fat tail of nearly -1 market correlations. Hedge funds’ long equity portfolios can and do cut risk rapidly, so RBSA’s failure to detect these rapid exposure reductions is expected.

Realized Market Correlations of Portfolios Hedged using a Statistical Equity Risk Model

The AlphaBetaWorks Statistical Equity Risk Model continues to produce hedges close to the ideal:

Chart of the correlations between realized 12-month returns of U.S. Long Equity Hedge Fund Portfolios hedged using the AlphaBetaWorks Statistical Equity Risk Model applied to holdings and 12-month returns of U.S. Equity Market , used to evaluate equity market hedging effectiveness of the model.

U.S. Long Equity Hedge Fund Portfolios: Realized 12-month market correlations of portfolios hedged using a statistical equity risk model applied to holdings

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
-0.9913 -0.2683 -0.0304 -0.0273  0.2085  0.9252

The edge comes from the analysis of individual positions that responds rapidly to portfolio changes and the robust regression methods that are resilient to outliers. The result is superior analysis of individual funds.

Whereas tests using hedge fund long equity portfolios accentuate the flaws of simple hedging and returns-based analysis, the AlphaBetaWorks Statistical Equity Risk Model remains close to the baseline of a perfect hedge. Thus, it is even more vital that portfolio managers and investors who analyze or manage hedge fund equity risk rely on robust models and thoroughly tested methods.

Summary

  • Random portfolio returns that would be produced by a perfect hedge are the standard to which equity market hedging techniques can be compared.
  • Simplistic hedging that assumes 1 beta for all hedge fund long equity portfolios over-hedges some and under-hedges others, resulting in hedged portfolios with net short and net long realized exposures, respectively.
  • Returns-based style analysis (RBSA) is especially dangerous for hedge funds, as it overlooks rapidly changing exposures and fails similarly to the fixed hedge approach.
  • Analysis of holdings using a robust and predictive Statistical Equity Risk Model produces close to perfect equity market hedges and is especially critical for managing hedge fund equity risk.
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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Tests of Equity Market Hedging: U.S. Mutual Funds

Equity market hedging techniques can be complex and their effectiveness hard to assess. In this piece we evaluate the effectiveness of several market hedging techniques by comparing them to the (idealized and unattainable) perfect market hedge. Specifically, we compare realized market correlations of hedged U.S. equity mutual fund portfolios to market correlations of random return series. Random return series are the ideal that would have been produced by perfect hedging of portfolios satisfying the random walk hypothesis. Whereas hedges that use a fixed 1 beta and hedges that use returns-based style analysis (RBSA) are flawed, a statistical equity risk model applied to portfolio holdings is close to the ideal.

Equity Market Hedging Techniques

We analyze approximately 3,000 non-index U.S. Equity Mutual Funds over 10 years. These provide a broad sample of the real-world long equity portfolios that investors may attempt to hedge. We evaluate the effectiveness of three techniques for calculating hedge ratios:

  • Assuming constant 100% market exposure (1 beta): Absent deeper statistical analysis, it is common to assume that all portfolios have the same market risk, equal to that of the broad benchmarks.
  • Using returns-based style analysis (RBSA): RBSA is a popular technique that attempts to estimate portfolio factor exposures by regressing portfolio returns against factor returns.
  • Applying a statistical equity risk model to portfolio holdings: This technique essentially performs RBSA on the individual portfolio holdings and aggregates the results.

For each fund and for each month of history we calculate market exposure at the end of the month and then use this estimated (ex-ante) exposure to hedge the fund during the following month. We then analyze realized (ex-post) 12-month hedged portfolio returns and calculate their correlations to the Market. The lower this correlation, the more effective a hedging technique is at eliminating systematic market exposure of a typical U.S. equity mutual fund portfolio.

Realized Market Correlations of Hedged U.S. Mutual Fund Portfolios

Realized Market Correlations of Random Return Series

An effective hedging technique should produce zero mean and median market correlations of hedged portfolio returns. Yet, if sufficiently large, even a set of perfectly random 12-month return series will contain some with large market correlations. Since our study covers over 200,000 12-month samples (observations), some market correlations are close to 1 by mere chance. To account for this and to create a baseline for comparisons, we calculated market correlations for random return series with a Monte Carlo simulation. These results, attainable only with a perfect hedge, are the baseline against which we evaluate equity market hedging techniques:

Chart of the correlations between 12-month random return series and 12-month returns of U.S. Equity Market

Realized 12-month market correlations of random return series

    Min.    1st Qu.     Median       Mean    3rd Qu.       Max.
  -0.9243    -0.2162     0.0001    -0.0006     0.2146     0.9409

Realized Market Correlations of Portfolios Hedged using a 100% Market Short

A naive assumption that market exposures of all portfolios are 100% (market betas of all portfolios are 1) is obviously wrong:

Chart of the correlations between realized 12-month returns of U.S. Equity Mutual Fund portfolios hedged using a 100% market short and 12-month returns of U.S. Equity Market

U.S. Equity Mutual Funds: Realized 12-month market correlations of portfolios hedged using a 100% market short

    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
  -0.9956  -0.2927   0.0469   0.0148   0.3527   0.9958

This approach over-hedges some portfolios and under-hedges others. There is a group of low-exposure portfolios for which a fixed 100% market short is too large. These produce a fat tail of negative market correlations of nearly -1 for some hedged portfolios. There is also a group of portfolios for which a fixed 100% market hedge is too small.

Realized Market Correlations of Portfolios Hedged using Returns-Based Analysis

Returns-based style analysis with multiple factors suffers from known issues of overfitting and collinearity. Less well-known are the problems that arise from RBSA’s assumption that exposures are constant over the regression window. In practice, portfolio exposures vary over time and can change rapidly as positions change. RBSA will capture these changes months or even years later once they influence portfolio returns, if at all.

RBSA thus fails similarly to the fixed hedging above, if less dramatically: hedges are too large in some cases and too small in others. The exposure estimates are also apparently biased, since they produce hedges that are too large and market correlations that are negative, on average:

Chart of the correlations between realized 12-month returns of U.S. Equity Mutual Fund portfolios hedged using returns-based style analysis and 12-month returns of U.S. Equity Market

U.S. Equity Mutual Funds: Realized 12-month market correlations of portfolios hedged using returns-based style analysis

    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
  -0.9946  -0.3229  -0.0518  -0.0459   0.2274   0.9762

Realized Market Correlations of Portfolios Hedged using a Statistical Equity Risk Model

The AlphaBetaWorks Statistical Equity Risk Model produces hedges close to the ideal:

Chart of the correlations between realized 12-month returns of U.S. Equity Mutual Fund portfolios hedged using a statistical equity risk model applied to holdings and 12-month returns of U.S. Equity Market

U.S. Equity Mutual Funds: Realized 12-month market correlations of portfolios hedged using a statistical equity risk model applied to holdings

    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
  -0.9565  -0.2230   0.0184   0.0214   0.2669   0.9755

The model estimates security market exposures using robust regression methods to control for outliers. Though robust techniques perform well for most portfolios, they appear to produce hedge ratios that are too low for some high-beta portfolios. This leads to small positive mean and median market correlations of hedged portfolio returns and to the higher probability of positive market correlations compared to random portfolios.

Aside from this under-hedging of a small fraction of portfolios, application of the AlphBetaWorks Statistical Equity risk model to fund holdings comes closest to perfect equity market hedging. Portfolio managers and investors who rely on robust risk models and hedging techniques can thus nearly perfectly hedge the market risk of a typical equity portfolio.

Summary

  • The effectiveness of equity market hedging techniques can be assessed by comparing hedged portfolio returns to random portfolio returns that would be produced by a perfect hedge.
  • Simplistic hedging that assumes 1 beta for all portfolios fails, most spectacularly for low-risk portfolios.
  • Returns-based style analysis (RBSA) both over-hedges and under-hedges, likely due to its failure to capture rapidly changing exposures.
  • Analysis of fund holdings using a Statistical Equity Risk Model comes closest to perfect equity market hedging.
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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The Persistence of Negative Investment Performance

And why Poor Nominal Returns are a Reason to Hire Rather than Fire a Manager

Our earlier pieces discussed how nominal investment performance reverts. Since returns are dominated by systematic risk factors (primarily the Market), they are subject to reversal when investment regimes change. In the simplest terms, high risk funds do well in bull markets, and low risk funds do well in bear markets, irrespectively of stock picking skill. When the tide turns, so does the funds’ relative performance. The persistence of stock picking skill becomes evident once systematic effects are removed.

This piece focuses on the persistence of negative investment performance. Negative investment performance exacerbates the losses due to simplistic performance metrics and sharpens the edge of predictive skill analytics: Negative nominal returns revert more sharply than overall nominal returns; negative security selection returns persist longer.

Measuring Persistence of Investment Performance

As our prior performance persistence work, this study analyzes portfolios of all institutions that have filed Form 13F during the past 15 years. This survivorship-free portfolio database covers thousands of firms that have held at least $100 million in U.S. long assets during this period.

The relationship between performance metrics of a portfolio calculated at different points in time captures their persistence. To measure the persistence of nominal returns, we analyze nominal returns during two 12-month periods separated by variable delay. For example, analysis of 24-month delay includes periods 1/31/2010-1/31/2011 and 1/31/2013-1/31/2014. We use the Spearman’s rank correlation coefficient to calculate statistically robust correlations between metrics. Technically speaking, we are studying the metrics’ serial correlation or autocorrelation.

The Persistence of Investment Performance

The following charts of autocorrelation have been updated with data through 5/31/2016 and remain virtually unchanged from our earlier work on the decay of stock picking skill.

Serial Correlation of Nominal Returns

Portfolios with above-average nominal returns for prior 12 months tend to underperform for approximately the following two years; similarly, those with below average nominal returns tend to then outperform:

Chart of the persistence of stock picking performance as measured by the correlation between returns for one 12-month period and a different 12-month period separated by a given lag for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of nominal returns

Delay (months) Serial Correlation
1 -0.11
6 -0.26
12 -0.36
18 -0.09
24 0.15
30 0.22
36 0.08
42 -0.26
48 -0.42
54 -0.22
60 0.17

Serial Correlation of Security Selection Returns

To eliminate the disruptive factor effects responsible for the above reversion, the AlphaBetaWorks Performance Analytics Platform calculates return from security selection after controlling for the factor exposures. The resulting metric, αReturn, is the return a portfolio would have generated if all factor returns had been flat. Above-average and below-average 12-month αReturns tend to persist for approximately four years:

Chart of the persistence of stock picking performance as measured by the correlation between <span style=

Delay (months) Serial Correlation
1 0.08
6 0.10
12 0.08
18 0.05
24 0.05
30 0.04
36 -0.01
42 -0.03
48 -0.04
54 -0.03
60 -0.01

The Persistence of Negative Investment Performance

The autocorrelation of overall nominal returns and αReturns captures the persistence of both negative and positive investment performance, but positive and negative metrics need not have similar persistence. In fact, the problems with nominal returns and simplistic performance metrics derived from them are accentuated when the nominal returns are negative.

Serial Correlation of Negative Nominal Returns

Negative 12-month nominal returns revert even more rapidly and more strongly than overall returns. Rank correlation coefficient for 12-month nominal returns separated by 6 months is approximately -0.5 for negative nominal returns and -0.2 for overall nominal returns. Poor recent nominal returns are a reason to hire rather than fire a manager, at least in the short term (the subsequent 12-18 months):

Chart of the persistence of negative investment performance as measured by the correlation between negative returns for one 12-month period and a different 12-month period separated by a given lag for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of negative nominal returns

Delay (months) Serial Correlation
1 -0.57
6 -0.23
12 -0.01
18 -0.14
24 0.52
30 0.18
36 -0.27
42 -0.27
48 -0.24
54 -0.12
60 0.07

Serial Correlation of Negative Security Selection Returns

This reversion is not present for αReturns. Negative αReturns have similar autocorrelation for the first few years and decay more slowly than overall αReturns:

Chart of the persistence of negative investment performance as measured by the correlation between negative αReturns (risk-adjusted returns from security selection) for one 12-month period and a different 12-month period separated by a given lag for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of αReturns (risk-adjusted returns from security selection)

Delay (months) Serial Correlation
1 0.08
6 0.09
12 0.08
18 0.08
24 0.08
30 0.06
36 0.03
42 0.03
48 0.02
54 0.01
60 0.00

The decay in security selection performance is typically due to such things as talent turnover, style drift, management distraction, and asset growth. Since these are more likely to affect the top-performing funds, negative αReturn remains predictive for longer. The above data is aggregate and specific firms can and do overcome the average fate. Though the above serial correlations may appear low, they are amplified and compounded in portfolios of multiple funds.

Cheerful consensus is usually a recipe for mediocrity, whether investing in a stock or in a fund. Fear and panic in the face of nominal underperformance are more dangerous still. Just as it pays to be a contrarian stock picker, it pays to be a contrarian fund investor or allocator.

Summary

  • Nominal returns and related simplistic metrics of investment skill revert rapidly.
  • Negative nominal returns revert more strongly than overall nominal returns.
  • Negative security selection performance persists longer than overall security selection performance.
  • When negative investment performance is merely nominal, it is a contrarian indicator.
  • When negative investment performance is due to poor security selection net of factor effects, it is a persistent and predictive indicator.
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.
U.S. Patents Pending
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The Decay of Stock Picking Skill

Our earlier work showed that nominal returns and related simplistic performance metrics are dominated by market noise and hence revert. The reversion means that yesterday’s best-performing managers tend to be tomorrow’s worst. Yet, once distilled from systematic noise, stock picking skill is evident. This piece measures the decay of stock picking performance over time and identifies the historical window most predictive of future performance. We demonstrate that superior manager selection requires spotting skill well before the crowd arbitrages it away.

Measuring the Decay of Stock Picking Skill

This study analyzes portfolios of all institutions that have filed Form 13F. This is the broadest and most representative survivorship-free portfolio database covering thousands of firms that hold at least $100 million or more in U.S. long assets. Approximately 5,000 firms had sufficiently long histories, low turnover, and broad portfolios suitable for skill evaluation.

To measure the decay of stock picking performance over time, we compare metrics measured in two 12-month periods separated by variable delay. One example of 24-month delay is metrics for 1/31/2010-1/31/2011 and 1/31/2013-1/31/2014. We use Spearman’s rank correlation coefficient to calculate statistically robust correlations.

Serial Correlation of Nominal Returns

The following chart shows serial correlation (autocorrelation) between 12-month cumulative nominal returns calculated with lags of one to sixty months (1-60 month lag). The relationship is generally negative. This illustrates that strong past (nominal) returns are predictive of future returns, albeit poor in the short-term:

Chart of the decay of stock picking performance as measured by the correlation between returns for one 12-month period and a different 12-month period separated by a given lag for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of nominal returns

Delay (months) Serial Correlation
1 -0.11
6 -0.26
12 -0.36
18 -0.09
24 0.15
30 0.22
36 0.08
42 -0.26
48 -0.42
54 -0.22
60 0.17

There is a narrow window at 2-3 year lag when past returns are predictive of the future results. This appears to be due to the approximately 18-month cycle of reversion in 12-month nominal performance.

Serial Correlation of Naive Alphas

It is common to measure alpha simply as outperformance relative to a benchmark. We will call this approach “naive alpha.” Since it ignores portfolio risk, this approach does not eliminate systematic (factor) effects and fails to isolate security selection performance: The top nominal performers who took the most systematic risk in a bullish regime remain the top performers after a benchmark return is subtracted. When regimes change, these former leaders tend to become the laggards, and vice versa.

Indeed, the serial correlation of naive alphas is similar to the serial correlation of nominal returns. The following chart shows correlation between 12-month cumulative naive alphas calculated with 1-60 month lags:

Chart of the decay of stock picking performance as measured by the correlation between naïve alphas (returns over S&P 500) for one 12-month period and a different 12-month period separated by a given lag for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of naive alphas (returns relative to the S&P 500 index)

Delay (months) Serial Correlation
1 0.00
6 -0.02
12 -0.02
18 0.03
24 0.04
30 0.05
36 0.01
42 -0.02
48 -0.05
54 -0.02
60 0.04

Serial Correlation of Security Selection Returns

To eliminate the disruptive factor effects responsible for performance reversion, the AlphaBetaWorks Performance Analytics Platform calculates each portfolio’s return from security selection net of factor effects. αReturn is the return a portfolio would have generated if all factor returns had been flat.

Firms with above-average αReturns in one period are likely to maintain them in the other, but with decay. The following chart shows correlation between 12-month cumulative αReturns calculated with 1-60 month lags:

Chart of the decay of stock picking performance as measured by the correlation between αReturns (risk-adjusted returns from security selection) for one 12-month period and a different 12-month period separated by a given lag for all U.S. equity 13F portfolios

13F Equity Portfolios: Serial correlation of αReturns (risk-adjusted returns from security selection)

Delay (months) Serial Correlation
1 0.08
6 0.10
12 0.08
18 0.05
24 0.05
30 0.04
36 -0.01
42 -0.03
48 -0.04
54 -0.03
60 -0.01

Though the above serial correlations of αReturn may appear low, they are amplified and compounded in practical portfolios of multiple funds. A hedged portfolio of the net consensus longs (relative overweights) of the top 5% long U.S. equity stock pickers delivered approximately 8% return independently of the market.

For approximately 3 years, strong security selection performance, as measured by the 12-month αReturn, is predictive of the future 12-month results. Returns due to security selection thus persist for approximately 5 years. This means that as little as 12 month of consistently positive αReturns are a positive indicator for the following four years. Skilled stock pickers can be spotted years before their skill is plainly visible and broadly exploited.

The decay in security selection performance is typically due to the following sources: talent turnover, style drift, management distraction, and asset growth. It is not a coincidence that the conventional requirement for large institutional allocation is 3-5 year track record.

The above data is aggregate. Specific outstanding disciplined firms can overcome this reversion, but they are the exceptions that require careful monitoring. Spotting skilled managers before their skill is visible to all is a sounder path to superior selection. In this respect, investing with managers is very similar to investing in stocks. Manager skill is arbitraged away – analytical advantage over the crowd is key. Cheerful consensus is usually a recipe for mediocrity whether investing in a stock or in a fund.

Summary

  • Nominal returns and related simplistic metrics of investment skill revert rapidly.
  • Security selection returns persist for approximately 5 years.
  • Selection of superior future performers is possible, but it requires spotting skill long before it is plainly visible and arbitraged away.
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.
U.S. Patents Pending.
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Top Stock Pickers’ Exposure to Valeant

In Early – Out Just in Time

Our recent article established that a portfolio of skilled stock pickers’ ideas generates consistent alpha.  This brief analyzes what the AlphaBetaWorks Expert Aggregate had to say about one controversial name, Valeant Pharmaceuticals (VRX).  In short, the smart money was in early and left almost a year before Valeant’s recent headaches.

Performance of the Top U.S. Stock Pickers

Since genuine investment skill persists, top U.S. stock pickers tend to generate persistently positive returns from security selection (idiosyncratic, residual returns). This strong performance derives from the top stock pickers’ individual positions. Their consensus exposures thus cut through the fog of panic and confusion, such as that surrounding VRX.

We track institutional ownership of Valeant by the AlphaBetaWorks Expert Aggregate (ABW Expert Aggregate). The ABW Expert Aggregate is sourced from all institutions that have filed Form 13F.

Nominal returns and related simplistic metrics of investment skill (Sharpe Ratio, Win/Loss Ratio, etc.) are dominated by systematic factors and thus revert. So for an accurate assessment of manager skill, we must eliminate the systematic effects and estimate residual performance due to stock picking. The AlphaBetaWorks Performance Analytics Platform calculates each portfolio’s return from security selection – αReturn. αReturn is the performance a portfolio would have generated if all factor returns had been flat. Each month we identify the five percent of 13F-filers with the most consistently positive αReturns over the prior 36 months. This expert panel of the top stock pickers typically consists of 100-150 firms.

A hedged portfolio that combines the top U.S. stock pickers’ net consensus longs (relative overweights) – lagged 2 months to account for filing delay (the ABW Expert Aggregate) – delivers consistent positive returns as illustrated below:

Chart of the cumulative return of the Market (Russell 3000) and the cumulative return of the hedged portfolio that combines the to 5% U.S. long stock pickers net consensus long (relative overweight) exposures

Cumulative Hedged Portfolio Return: Top U.S. Stock Pickers’ Net Consensus Longs

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
ABW Expert Aggregate 4.56 14.43 12.74 5.95 -1.25 15.35 2.20 2.24 15.47 8.81 13.16 1.70
iShares Russell 3000 ETF 9.04 15.65 4.57 -37.16 28.21 16.81 0.78 16.43 32.97 12.41 0.34 -5.72
ABW Expert Aggregate iShares Russell 3000 ETF
Annualized Return 8.36 6.40
Annualized Standard Deviation 5.25 15.50
Annualized Sharpe Ratio (Rf=0%) 1.59 0.41

Top Stock Pickers’ Exposure to Valeant Pharmaceuticals (VRX)

The positive idiosyncratic returns of the ABW Expert Aggregate come from its individual positions: Its longs (experts’ relative overweights) tend to generate positive future αReturns. Its shorts (experts’ relative underweights) tend to generate negative future αReturns. The ABW Expert Aggregate thus measures the top stock pickers’ positioning which is predictive of the stocks’ future performance.

The top panel on the following chart shows the performance of VRX. Nominal returns are in black and cumulative residual returns (αReturns) are in blue. αReturn is the performance VRX would have generated if all systematic factor returns had been flat. The bottom panel shows exposure to VRX within the ABW Expert Aggregate:

Chart of the cumulative αReturn (residual return) of Valeant Pharmaceuticals (VRX) and exposure to VRX within the hedged portfolio that combines the to 5% U.S. long stock pickers net consensus long (relative overweight) exposures

VRX: Cumulative αReturns and Exposure within the ABW Expert Aggregate

Top stock pickers had negligible exposure to VRX until 2011. In early-2011 smart-money exposure to VRX grew rapidly, peaking between 2012 and 2014. Throughout 2014, as the shares appreciated, the top U.S. stock pickers sharply cut their exposure to VRX.

The panic hit a year after the top stock pickers dramatically cut their exposure. By 2015 smart-money exposure to VRX was a mixed signal as it tracked the stock’s volatility. Ironically, this is when VRX became one of the most crowded hedge fund bets. Though VRX had a history of smart-money ownership, this vote of confidence was withdrawn by 2015. Future stock-specific returns to VRX, as predicted by the ABW Expert Aggregate, increased rapidly in 2011 and dropped rapidly by 2015.

Investors, allocators, and fund-followers, armed with our analytics, would have taken note. Those looking for the smart money to back their long or short views of VRX must now look elsewhere.

Conclusions

  • Top stock pickers’ ownership is predictive of future stock performance, since their net consensus longs (relative overweights) tend to generate positive future αReturns and net consensus shorts (relative underweights) tend to generate negative future αReturns.
  • Valeant Pharmaceuticals (VRX) was a large overweight of the top stock pickers between 2011 and 2014, but these positions were mostly liquidated by 2015.
  • Top stock pickers’ current ownership of VRX is not a predictive indicator, but their rapid liquidation in 2014 was a visible warning.
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.
U.S. Patents Pending.
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Testing Equity Risk Models: REIT Portfolios

Equity risk models can be complex and hard to interpret. Moreover, differences in financial reporting and transparency across markets, sectors, and companies can lead to inaccurate predictions and counter-intuitive exposures for common fundamental models. These problems are especially severe for sector-focused portfolios. For instance, generic fundamental models may use a single broad Leverage Factor to explain the profoundly different impacts of financial leverage on the risk of Airlines, REITs, and Oil Producers, with mixed results at best. Yet, when properly constructed with robust methods, statistical equity risk models that capture the relevant and intuitive sector-specific risk factors are highly predictive. We illustrate this predictive accuracy with a study of 1,000 REIT portfolios.

Real Estate Investment Trust (REIT) Portfolio Sample

We used Vanguard REIT Index Fund (VNQ) to define the Real Estate Investment Trust (REIT) Market Universe. To test equity risk models on realistic REIT portfolios, we constructed 1,000 random portfolios from VNQ. Each portfolio contained 20 equal-weighted positions and spanned 10 years. These random subsets of the REIT Universe should be representative of a typical REIT portfolio based on VNQ’s holdings with a 5% average position size.

Testing Predictive Power of Equity Risk Models

We follow the approach of our earlier studies of risk model accuracy. To evaluate the predictive accuracy of an equity risk model, we compare returns predicted by past factor exposures to the subsequent portfolio performance: We calculate factor exposures using holdings at the end of each month and predict the following month’s returns using these ex-ante factor exposures and ex-post factor 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 skill.

Testing Statistical Equity Risk Model with High-level Sectors

The default AlphaBetaWorks U.S. Equity Statistical Risk Model uses 10 high-level Sector Factors in addition to Market, Style (Value/Growth and Size) and a few Macroeconomic Factors (Bonds, Oil, Currency, etc.). Though these high-level factors are sufficient to predict accurately the performance of most mutual fund portfolios and most long equity hedge fund portfolios, they do not adequately capture the sector-specific systematic risk of REITs with their broad Finance Factor. In short, our model’s “standard setting” does not provide a fine enough focus for these instruments. For half of the REIT portfolios tested, the model delivers less than 0.80 correlation between predicted and actual monthly returns:

Chart of the correlations between predicted returns constructed using a multi-factor statistical equity risk model and actual historical returns for 1,000 20-position REIT portfolios constructed from the holdings of Vanguard REIT Index Fund (VNQ)

U.S. REIT Portfolios: Correlation between predictions and actual monthly returns for a statistical equity risk model with high-level sectors

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
0.7052  0.7821  0.8038  0.8021  0.8250  0.8823

Testing Statistical Equity Risk Model with Granular Sectors

For REITs, a more focused model is necessary. Fortunately, we offer such refined models for more accurate results. The 10 high-level sectors of the default AlphaBetaWorks U.S. Equity Statistical Risk Model can be sub-divided into more granular sectors to handle portfolios that are restricted to a narrow market subset. The AlphaBetaWorks Granular Sector Model that includes the REIT Sector Factor is far more effective in this case. For most REIT portfolios tested, the model delivered 0.94 or higher correlation between predicted and actual monthly returns:

Chart of the correlations between predicted returns constructed using a multi-factor statistical equity risk model with granular sectors and actual historical returns for 1,000 20-position REIT portfolios constructed from the holdings of Vanguard REIT Index Fund (VNQ)

U.S. REIT Portfolios: Correlation between predictions and actual monthly returns for a statistical equity risk model with granular sectors

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
0.7886  0.9202  0.9385  0.9324  0.9507  0.9766

Even for the 25% REIT portfolios it handled the worst, the model still achieved 0.79-0.92 correlation between predicted and actual returns.

Summary

  • Fundamental equity models often fail for sector-focused portfolios, such as REITs.
  • Statistical equity risk models with a few intuitive factors deliver accurate predictions for sector-focused portfolios, provided they are sufficiently robust and granular.
  • For most REIT portfolios tested, a robust statistical equity risk model with a REIT Sector Factor delivered over 0.94 correlation between predicted and actual monthly returns.
  • Greater model complexity offers diminishing returns: Even a perfect equity risk model would, at most, yield 0.06 higher correlation and explain 12% more ex-post monthly return variance.
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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Systematic Hedge Fund Volatility

Hedge fund replication, tracking, and analysis often focus on the individual positions and on the stock-specific risk they contribute. This overlooks the far more important return source – systematic hedge fund volatility. A statistical equity risk model that robustly captures exposures to the key systematic risk factors delivers 0.92 (92%) correlation between predicted and actual returns for most hedge fund long equity portfolios reported in regulatory filings. It follows that risk, performance, and crowding of these portfolios are overwhelmingly systematic. These systematic returns can be replicated and hedged with models built on investable factors and with passive investments that track these factors. Fixation on individual holdings and position overlap is misguided at best and dangerous at worst.

U.S. Hedge Fund Equity Portfolio Sample

Our analysis covers approximately 300 U.S. hedge fund long equity portfolios active over the past 15 years. We started with the universe of over 1,000 funds. First, we eliminated half that were not analyzable from regulatory filings (primarily because of high turnover). We then eliminated the portfolios that had less than five years of contiguous history or fewer than five equity positions during a period.

Our conclusions apply to most hedge fund long equity portfolios, though high turnover funds will require higher frequency of position data for predictive return forecasts. By extension, these findings also apply to long-biased hedge funds that derive most of their performance from their long portfolios. They apply to short books as well: our experience shows that short hedge fund books tend to be even more diversified and hence even more governed by their systematic exposures (possibly due to managers’ sensitivity to stock-specific risk). Finally, systematic volatility is even higher for funds of hedge funds due to their higher diversification.

Testing the Predictive Power of Equity Risk Models for Hedge Funds

To quantify the share of systematic hedge fund volatility, we need to test the ability of an equity risk model to predict future hedge fund returns. We followed the approach of our earlier studies of equity risk models’ predictive power:

  • Calculated factor exposures from the estimated holdings at the end of each month and the holdings’ factor exposures;
  • Predicted the following month’s returns using these ex-ante factor exposures and ex-post factor returns;
  • Compared returns predicted by past factor exposures to subsequent portfolio performance and evaluated the predictive accuracy of a model.

The correlation between predicted and actual returns measures a model’s accuracy and determines the fraction of systematic hedge fund volatility as defined by the model. The higher the correlation, the more effective a model is at hedging, stress testing, replication, and evaluating investment skill.

Systematic Hedge Fund Volatility within a Single-Factor Statistical Equity Risk Model

The simplest statistical equity risk model uses a single systematic risk factor – Market Beta. Since Market Beta is the dominant risk factor, even a simple model built with robust statistical methods delivers 0.87 mean and 0.90 median correlations between predicted and actual monthly returns:

Chart of the correlations between predicted returns constructed using a single-factor statistical equity risk model and actual historical returns for the equity portfolios of over 300 U.S. Hedge Fund Long Equity Portfolios

U.S. Hedge Fund Long Equity Portfolios: Correlation between a single-factor statistical equity risk model’s predictions and actual monthly returns

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.2924  0.8251  0.8978  0.8665  0.9420  0.9938

Within this model, 81% of hedge fund variance is systematic.

Systematic Hedge Fund Volatility within a Two-Factor Statistical Equity Risk Model

A two-factor model that adds Sector Risk Factors, estimated with robust methods, delivers 0.89 mean and 0.92 median correlations between predicted and actual monthly returns:

Chart of the correlations between predicted returns constructed using a two-factor statistical equity risk model and actual historical returns for the equity portfolios of over 300 U.S. Hedge Fund Long Equity Portfolios

U.S. Hedge Fund Long Equity Portfolios: Correlation between a two-factor statistical equity risk model’s predictions and actual monthly returns

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.5843  0.8584  0.9159  0.8946  0.9502  0.9957

Systematic Hedge Fund Volatility within a Multi-Factor Statistical Equity Risk Model

The standard AlphaBetaWorks U.S. Equity Statistical Risk Model extends the two-factor model with Style Factors (Value/Growth and Size) and Macroeconomic Factors (Bonds, Oil, Currency, etc.). This expanded model delivers 0.90 mean and 0.92 median correlations between predicted and actual monthly returns for U.S. hedge fund long equity portfolios:

Chart of the correlations between predicted returns constructed using a multi-factor statistical equity risk model and actual historical returns for the equity portfolios of over 300 U.S. Hedge Fund Long Equity Portfolios

U.S. Hedge Fund Long Equity Portfolios: Correlation between a multi-factor statistical equity risk model’s predictions and actual monthly returns

  Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.5055  0.8646  0.9204  0.9003  0.9554  0.9957

For the 25% of hedge fund portfolios it handles the worst, the model still achieves 0.51-0.86 correlation between predicted monthly returns and realized monthly returns.

Many of the outliers with low correlations hold substantial fixed income, exotic, and hybrid positions. To provide the most conservative assessment of the model’s predictive accuracy and the proportion of systematic risk, we did not alter the universe to exclude these outliers.

Unsurprisingly, given hedge funds’ aggressiveness, the model is less predictive for hedge funds than they are for mutual funds and insurance companies. Still, 85% of monthly return variance of most hedge fund long equity portfolios is systematic. And over 80% of that is due to a single factor. In other words, investors could replicate over 80% of this variance simply by replicating the hedge funds’ Market exposure.

Amazingly, much of the popular analysis of hedge fund risk and crowding ignores systemic factors and focuses solely on individual positions. This simplistic approach, even in the rare cases where it is done correctly, addresses only 15% of the risk that is residual, idiosyncratic, or stock-specific. Investors who rely on these simplistic approaches will make a variety of mistakes. For instance, they might wrongly conclude that two funds are differentiated because they have no positions in common. Yet, these two funds can have similar systematic factor exposures and thus high correlation; market hiccups will be magnified.

Conclusions

  • For most U.S. hedge fund long equity portfolios estimated from regulatory filings, a robust statistical equity risk model delivers over 0.92 correlation between predicted monthly returns and realized monthly returns.
  • 85% of the monthly return variance of hedge fund long equity portfolios is systematic, hence not attributable to individual stock bets.
  • Fixation on hedge funds’ stock-specific bets and crowding is misguided and dangerous, since this risk accounts for at most 15% of the portfolio variance for most hedge funds.
  • Investors who rely on simplistic approaches to hedge fund risk analysis may make a variety of mistakes, including missed crowding due to shared systematic factor exposures.
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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