As highlighted in our Fairholme analysis, concentrated stock bets often lead to concentrated sector bets and both contribute to the fund’s performance. It’s easy to run for the exit after experiencing losses like this but, as always, one should first do a quantitative analysis to understand where the losses are coming from. If one finds significant sector overweighting in an otherwise solid fund, investors may consider offsetting such sector bets with other investments that will help the overall portfolio achieve sector allocations that are close to the benchmark. Thus, if one believes that the manager’s stock selection ability is still there, the heavy exposure to financials in Fairholme could be offset by adding a fund with negligible financials exposure or eliminated by hedging the exposure with a short-financials ETF such as ProShares SEF.

There also exists a “stock-picker fund” that tasks itself with performing such risk management for investors. American Funds Growth Fund of America (GFA) is a multi-strategy domestic equity fund run by several management teams each implementing its own unique investment strategy. Their portfolios are then blended into the fund which is diversified by design. American Funds indicates that, since the product’s launch in 1973, it has outperformed the S&P by 3% a year. The combination of risk management, stock selection ability and exceptional long-term performance previously attracted huge AUM and GFA consistently maintained the status of the largest US equity fund for over six years. Additionally, as of late last year, it was the most popular fund in the enormous U.S. 401k market according to a study done by Brightscope in the October 3rd, 2010 issue of Investment News.

As of September 2011, however, the fund has lost its spot as the largest mutual fund with deep withdrawals. Morningstar indicates that the fund now has $137 billion in assets. In the face of an industry wide flow to passive products, a recent Bloomberg article questions the ability of such a large, focused stock selection fund to outperform in the current market environment. The previously cited Investment News article also indicates that many advisors feel that the fund’s size prevents it from being nimble enough to replicate its past performance.

Given the enormous interest in this fund, we felt compelled to provide some quick insights into the fund’s recent performance since returns-based style analysis (RBSA) is perfectly suited for such a task (as it does not require daily positions on the hundreds of stocks in the portfolio). We performed our analysis with MPI’s Stylus Pro software using Class A shares (AGTHX) 2011 daily NAVs through Oct 14th from Lipper/ThomsonReuters. Note the fund’s losses in Aug-Sep in the chart below, albeit partially offset by Oct gains thus far. It’s not yet clear, though, what portion is due to systematic market conditions.

The first step is to look at the performance relative to S&P 500 Index. The picture is a bit sharper as both months show significant underperformance vs. the index.

We then performed RBSA using daily returns of the S&P 500 sectors and MSCI AC World ex US Index to better assess the fund’s daily exposures. As always, please note that we are not determining what the actual holdings were but, using only return streams, indentifying the mix of indices that best replicates the performance of the actual fund. A high level of diversification (the fund held over 400 positions per latest SEC filing) results in the analysis having a very high R-squared of 99.5%, which makes such an analysis very credible. Note that the exposures are very stable in the chart below – in line with the fund’s low turnover. Some notable observations:

• Significant exposure to foreign equities, and
• Very recent increase in cash exposure.

We would like to again stress that the results of style analysis are not equivalent to actual fund holdings, although they could be very close. For example, AGTHX has 16% in foreign stock holdings as of June according to the company’s website while our analysis shows exposure to MSCI AC World x US index at around 10%. The differences could be attributed, for instance, to ADRs spread between S&P500 sectors or foreign stocks that behave more like U.S. equity. One should keep in mind that exposures derived through RBSA could prove to be more valuable than holdings information as they represent how fund positions are being viewed by market participants. And while the list of holdings represents simply a snapshot of accounting data, exposures mimicking the funds behavior represent market’s assessment of these holdings: it could happen that a fund’s positions behave closer to sectors that are different than the sectors they’re being assigned to.

One could also view the allocations above as a replication portfolio that mimics the fund’s performance. We call the performance of such a portfolio, a mix of passive indices, a fund’s Style Return, which could be achieved by simply investing in sector indices such as ETFs. In RBSA, the difference between the fund’s return and its Style Return is often called Selection Return, which could be viewed as a proxy for the fund’s stock selection ability. It is important to note that the Selection Return derived from RBSA is purely quantitative and may be due to other factors that are not associated with stock picking – especially in low R-squared cases. A high level of R-squared, by definition, leaves little room for variability in selection, which is confirmed in the figure below. Selection represents a fraction of the total return volatility – which was noted in the Bloomberg article.

We still do not have a good explanation for the Aug-Sep underperformance vs. S&P 500, however, and it does not seem like selection accounts for the gap. At this point, it is worth looking at various sector and style bets of the fund vs. the benchmark. We present such an analysis in the figure below where overexposure to certain sectors is shown above X-axis while under-exposure is shown below the X-axis. The fund behaves as if it is overexposed to Consumer Discretionary, Materials and Foreign stocks while being under-exposed to Industrials and Consumer Staples. Also, note the increased cash exposure not present in the index.

Next, we quantify the monthly impact of sector bets on the fund’s performance relative to the benchmark. Timing Return – driven by differences in sector exposures between the fund and the benchmark – is part of the total excess return vs. the benchmark. Please note that the Timing Return in our RBSA does not necessarily insinuate swings in allocations or true “market timing” (AGTHX has been a relatively style consistent fund), it is simply showing the performance attributed to differences in exposure between the Style Return and Benchmark Return. From this returns-based analysis, it appears that both August and September returns were primarily driven by such exposure differentials.

Also, overall monthly volatility of the fund’s Timing Return this year is much higher than that of the Selection Return. In the current market environment, sector bets should be examined more closely than individual stock bets as the impact of the over- and under-exposure of sectors can be quantified. In the figure below we show both positive and negative contributions to AGTHX performance from the exposure differentials observed in our analysis of the fund’s NAVs. It is easy to see that the positive and negative Aug-Sep sector contributions almost cancel each other out, with the notable exception of the foreign stock contribution (including Emerging Markets), Consumer and, especially, Materials sector. Indeed, the fund’s underperformance during these months appears to be largely driven by its exposure to these sectors.

As always, our analysis is purely based on returns and does not reflect actual holdings, but it does provide meaningful insight for investors and advisors. The results of such a short-term analysis do not necessarily lead one to judge AGTHX conclusively though. Certainly, the fund has enjoyed a pretty amazing run over the past 39 years. However, those looking for evidence that the fund’s large size has hurt its ability to pick stocks will not find anything here to dismiss that suspicion. On the contrary, most of the fund’s recent returns can be attributed to its overall asset allocation and sector exposures in our returns-based analysis. Indeed, the fund has underperformed its “Style” or tracking portfolio (the mix of passive indices that best explain its performance) over this period. Much of the fund’s recent sector exposures appear to have contributed to its underperformance against the S&P 500 and returns-based Selection Return has been generally negative over this short period. The better take-away might be that the S&P 500 is not really the most appropriate benchmark to judge AGTHX’s performance. It is difficult to assess the value of a growth-oriented equity product with overseas exposure against the S&P 500 – which is why many prefer to use a blended “style” benchmark to determine a manager’s value. Growth Fund of America has been a very stable fund from a returns-based style perspective – perfect for long-term, strategic investors like 401k participants seeking predictability and, ideally, some alpha. One might conclude from this very short-term analysis, however, that the real value here is not as a “stock picking”, alpha-focused fund but as a consistent active component of a strategic portfolio. Viewed from that perspective though, the recent flows to ETFs and other passive investments become pretty understandable.

Jeff Schwartz contributed to this article

We were interested to know whether there were any investment style changes that resulted in the fund’s recent good performance. Following our previous research paper (“Uncovering the Dynamics of Carmignac Patrimoine”), we ran an updated analysis of the fund using MPI’s proprietary Dynamic Style Analysis (DSA) model in our MPI Stylus Pro software. In figure below we show the fund’s exposures (in excess of the benchmark) vs. its performance relative to the benchmark (“Excess” dots).

According to the chart above, the fund continues to invest in gold (S&P GSCI Gold), fixed income (U.S. 3M LIBOR) and buys put contracts (short position in CBOE S&P 500 PutWrite) as a hedging tool. In the first half of the year these defensive positions resulted in significant underperformance against the benchmark; however, the same exposures staged a dramatic comeback for Carmignac Patrimoine in the recent months.

Returns-Based Style Analysis (RBSA) Approach

- Upon review of the strategy of a number of funds, a theme emerged: a large number claimed that they sought an absolute performance over time, regardless of the movement of the market by hedging their bets using derivatives or taking long/short positions. For this reason, we used a modified RBSA model to allow for sensing hedging.

- In terms of style and capitalization average exposure over the past 12 months, the funds in the universe cover the entire equity style space:

Selection of Top/Bottom Groups of Funds

- Based on the universe of 797 funds, we calculate the total annualized performance over the last 52 weeks and rank the funds from the best to the worst performers. Using the top 5% (39 funds) and bottom 5% (25 funds) we create equally weighted, daily rebalanced portfolios in order to understand why, on average, one group performed better than the other in terms of style exposures.

Analysis Highlights

- As evidenced by the chart, the top 5% outperforms its peers, benchmark, and the bottom 5%. Over the period of analysis, the top 5% return is approximately 15% on top of MSCI Europe, while the bottom 5% return is 15% below MSCI Europe.

- The style map and asset loadings give us some insight into how the top and bottom performers differ:

- The average style exposures suggest that the top 5% (in average) had over-weighted exposures to small value and large growth, whereas the bottom 5% had a significant large value bias. The negative exposure to MSCI Europe suggests that hedging decisions were made.

- As expected, the diversification effects of blending a large number of funds together in an equally-weighted portfolio results in very high explanatory power of the analysis with R-squared values in the 90s. As a group, the top 5% group displays strong selection and timing skill whereas the bottom 5% group displays the opposite. Both, selection and timing returns represent components of excess benchmark performance.

Rolling Risk/Return Analysis: Consistent Behaviours

- Over the period of analysis, one can see that the top (bottom) 5% consistently outperformed (underperformed) the benchmark on a 12-week rolling return basis. This over (under) performance account to the 14.82% (-14.86%) return in excess over (under) the benchmark during this period.

- Both portfolios display less risk than the benchmark, as defined by the 12-month rolling standard deviation. For the majority of the period, the top 5% has a higher risk than the bottom 5%, which once again confirms the adage that the higher the risk, the higher the return.

- On a risk-adjusted basis, the top 5% portfolio clearly dominates, providing a higher return per unit of risk than the benchmark and the bottom 5%.

UNIVERSE ASSUMPTIONS

• Database provider: Lipper, a Thomson Reuters Company
• Registered for sale countries: Austria, France, Germany, Italy, Netherlands, Offshore, Spain, Sweden, Switzerland, and the UK
• Filters: Primary share class, at least 1 year of performance history, Lipper Global Category: Equity Europe, Assets Under Management of at least EUR 10 Million
• Number of funds analyzed: 797
• Date interval: Last 52 weeks ending on July 30^th 2010
• Currency: Euro
• Analysis Frequency: Weekly (with compounded daily data)
• Cash proxy (Risk Free Rate): EONIA Index
• Benchmark: MSCI Europe
• Style factors: MSCI Europe Large Value, Large Growth, Mid Value, Mid Growth, Small Value, and Small Growth. MSCI Europe as a generic hedging instrument.
• Analysis performed with mpi Stylus Pro™

UNIVERSE DEFINITIONS

Style Return: Return of the Best Fit Portfolio for the Manager Series, where the holdings of the portfolio are the Style Indices.

Selection Return: Calculated as the Manager’s Return subtracted by the Style Return. This is an indication of the Manager’s Selection or Stock Picking abilities.

Timing Return: Calculated as the Manager’s Style Return subtracted by the Benchmark’s Style Return. This indicates whether the Manager’s decisions, to over or under weight the style holdings, as compared to the benchmark, added to the portfolio’s return or not.

Style R Squared (R2): Measure of the model’s power in describing the Manager’s past behaviour in terms of style. The higher the Style R Squared value, the better the model’s explanatory power.

Predicted Style R Squared (PR2): Measure of the model’s power in predicting the Manager’s future behaviour in terms of style. The higher the Predicted Style R Squared value, the better the model’s predictive power.

Style Map: Graphic representation of the results of the Style Analysis. The series being analyzed are mapped unto a Cartesian plane, in which the X and Y axis represent exposures to different Styles and Sizes.

Asset Loadings: Weights of the Style Indices, as holdings, of the Style Portfolio, as calculated by mpi Stylus Pro.

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Markov Processes International, LLC (MPI) is a global provider of investment research and technology solutions. MPI’s analytical tools and methodologies are employed by the finest institutions and financial services organizations to enhance their investment research, reporting, data integration and content distribution. MPI offers the most advanced platform available to analyze hedge funds, mutual funds, portfolios and other investment products, as well as asset allocation and portfolio optimization tools.

MPI’s Stylus Pro software is utilized by alternative research groups, hedge fund of funds, family offices, institutional investors, consultants, private banks, asset managers, diversified financial services organizations as well as marketing, product development and IT departments around the world. MPI also offers solutions for investment advisors and private wealth professionals. For more information on past MPI research articles visit http://markovprocesses.com/company/research.htm

In our previous post below (referenced in a story from Jeff Sommer of The New York Times) we performed an analysis of the Laudus Rosenberg US Large Cap mutual fund (sub-advised by AXA Rosenberg) that indicated a significant change in the fund’s risk profile occurred as early as 2008. Our study showed a substantial increase in the daily tracking error of the fund to its benchmark – the Russell 1000 Index. The tracking error reached its peak in June 2009 and was several times higher than many of its quant Large Cap Core peers. So there was a symptom that could have alerted risk managers or investors to potential problems. Note that this symptom became apparent only on shorter-horizon (daily temperature charts) rather than two-year averages commonly used by many practitioners.

We then performed some quick diagnostics to understand the nature of the problem and to eliminate false alarms such as data issues or a specific stock bet. We found none of those but the fund’s daily beta was on a path of steep descent in 2009, another worrying symptom but no diagnosis yet.

To get a better understanding of the nature of the problem we will perform a full multi-factor, “metabolic panel”, of the fund’s daily returns-bases style analysis (RBSA). When performed with the right tools that can filter the daily noise, such an analysis could provide key insights and potential answers to specific questions. Through this daily returns-based analysis, we seek to learn more about attribution of the fund’s gains or losses: what bets were made, when were they made and for how long – and with what impact on both performance and risk? It is important to remember that this analysis does not look at actual holdings. Instead, our analysis seeks to understand a fund’s return behavior by comparing its daily returns to those of various passive indices.

Using daily fund NAVs we performed returns-based style analysis in MPI’s Stylus Pro software of Laudus Rosenberg US Large Cap funds against the S&P 500 sectors. The results of the analysis are presented in the charts below where color bands represent portfolio exposures to S&P sectors and cash (exposure to US Treasury bills).

The change in sector exposure at the end of 2008 is immediately apparent with some significant shifts both before and after. Exposure to Energy, Health Care and Consumer Staples changed in a profound way. The quality of this analysis is very high with R-squared being in the 99% range. Again, please note that the analysis was performed using only fund’s NAV and without use of any holdings information and such a result may not directly imply that the fund indeed had such sector position at the time. The best way to further identify possible bets is to plot the fund’s exposures over the S&P 500 index.

In the chart, the bands above the zero line denote sectors where the fund’s sector exposures are greater than those of the S&P 500 index and the ones lower than zero indicate sector exposures less than the index. In 2009, fund exposure differentials peaked in the 2nd QTR and then started slowly normalizing by the end of the year. Our returns-based analysis shows that the fund may have been significantly overexposed to Health Care (the lowest beta sector) and underexposed to some of the highest beta sectors such as Financials. The increased cash position (green color) may indicate that the fund selected more defensive (i.e. lower beta) stocks within sectors. All of these factors could have contributed to the fund having very low beta behavior in 2009, as identified in our previous post.

Incidentally, this period was characterized by what many referred to as a “dash for trash”. Lower quality stocks that were priced for an Armageddon scenario rebounded strongly when the cycle turned in the second quarter of 2009. Consequently, higher quality names, in general, underperformed these lower quality stocks resulting in the underperformance of many fundamental (both quantitative and non-quantitative) alpha strategies. The impact of this phenomenon on a fund’s performance depended on the extent to which these alpha bets were reined in by risk controls.

And finally, let’s see what RBSA can tell us about fund liquidation. On May 2, the board of directors of Charles Schwab made a decision to liquidate four Laudus Rosenberg funds. The funds were immediately closed to new investors and the liquidation was scheduled for July 30th. The fund is still reporting daily NAVs which make it possible to understand how the liquidation is progressing in terms of the fund’s exposure to major sectors. The chart below, showing daily returns-based exposures of the US Large Cap fund , indicates that the fund is currently behaving as though it is about 65% cash with exposure to just a handful of other sectors.

Having such little exposure to the market over the past several weeks clearly boosted the fund’s performance for remaining investors! Again, we would like to make a disclaimer that this analysis is based only on the fund’s NAVs and may not reflect the fund’s actual positions.

With AXA Rosenberg’s recent admission of a 2009 coding error in its portfolio risk management programs during a year in which the firm’s equity mutual funds lagged their benchmarks by a large margin, the investment community must reflect on how we monitor investments. Specifically, investors (and their advisers) must ask if we have the right tools and protocols to identify unusual risk and performance patterns in a timely manner.

According to the company’s statement in an April 15th letter to investors, the error was discovered in June 2009 and fixed between September and mid-November. Because the “coding error” apparently impacted risk controls, we examined two basic risk measures that are routinely used by both fund managers and investors to evaluate and monitor investment products: Beta and Tracking Error. The chart below shows Beta of the Laudus Rosenberg US Large Capitalization Fund in 2009 with a sample of its peers computed using daily fund NAVs^[1].

The fund’s Beta appears to be very different from a sample of other quantitative large cap US equity funds^[2] –the Laudus Rosenberg fund had a sharp drop in market beta right from the start of 2009. It’s plausible that having a beta substantially below 1 during the market rally in March-June of 2009 may have impacted the fund’s performance. What’s intriguing is that another risk measure: the 3-month rolling tracking error to Russell 1000 (as shown in chart below) was unusually high throughout the entire 2009 and was several times higher than that of any of the other quant managers in the group.

Using daily data to monitor Laudus Rosenberg’s beta and tracking error, could we have raised a red flag in June 2009?

It is worth stressing that such an apparent aberration in the fund’s risk profile could be most clearly seen using daily data. Unfortunately, investors typically use monthly data even though daily returns are now easily available from data providers (e.g. Lipper), public sources (Yahoo, Google, etc.), funds and custodians. When using monthly data, a longer history needs to be used to have sufficient observations to estimate the regression. This longer history may cloud, or, as in the case of the Laudus Rosenberg fund, completely transform the picture. The chart below uses a rolling 24 month window to calculate the fund’s beta.

When used in more granular returns-based analysis (RBSA), daily fund NAVs could provide answers to specific questions about attribution of the fund’s gains or losses: what bets were made, when and for how long and with what impact on both performance and risk. Thus, in one of our recent research papers on Oppenheimer Core Bond Fund, we demonstrated the importance of daily data in analysis and monitoring leverage of complex fixed-income portfolios having derivative exposure.

Related links:
http://online.wsj.com/article/SB10001424052748704388304575202501743719416.html
http://www.pionline.com/article/20100419/PRINTSUB/304199980
http://www.pionline.com/article/20100518/DAILYREG/100519849
http://news.morningstar.com/articlenet/article.aspx?id=335669
http://online.wsj.com/article/BT-CO-20100510-714684.html

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1. The daily fund beta is calculated vs. Russell 1000 Index using rolling 66-day (approximately 3 calendar months) calculations. Russell 1000 is the stated benchmark of the Laudus fund.
2. Details on the other quant equity funds used in the study:
   1. The Vanguard Growth & Income fund is sub-advised by Mellon and uses the S&P 500 as a benchmark.
   2. The Russell US Quant Equity fund is a fund of quantitative funds and currently has 6 sub-advisers: Aronson + Johnson + Ortiz, Goldman Sachs Asset Management, INTECH, Jacobs Levy, Numeric and Russell Investment Management Company
   3. The Vanguard Structured Large-Cap Equity Fund (VSLIX) employs a quantitative strategy and is managed by the Vanguard Quantitative Equity Group. Benchmark: S&P 500 Index
   4. The Goldman Sachs Structured US Equity fund is managed by Goldman Sachs Asset Management and uses the S&P 500 as its benchmark.