Active Share: The Parts Are Worth More Than The Whole

Active Share: The Parts Are Worth More Than The Whole Active Management Georgios Costa Georgiou Director, Performance & Portfolio Risk Much like technological innovation, alpha is largely the outcome of a combinatorial process 1 bringing together previous technologies, or alpha and beta, in ways not seen before. For innovation, that combinatorial process is well documented by patents. In patent law, it is not the new device itself that is patented but rather the nuts and bolts making it work. In this sense, the parts are worth more than the whole. Recombined, they may very well propel further innovation. There are good reasons to extend this analogy to active equity management, and more specifically to the concept of Active Share. Understand Christian Franzen Global Head of Performance & Portfolio Risk Active Share is a spare measure of how much an equity portfolio s composition differs from that of its benchmark index. The number crunching is simple. Take all the securities included in an equity portfolio and compare them with all those in the benchmark. For each security, compute the difference between the benchmark percentage weight and the portfolio percentage weight. Then, turn all the differences into positive numbers, sum them up, and divide that sum by two. We end up with a figure between zero and 100 % 2, which is increasingly referenced by investors when selecting managers for the active portion of their equity allocation. Mathematically, Active Share is equal to the sum of its parts, neither more nor less. However, research on Active Share seems to imply that the whole is greater than the sum of its parts in terms of being a good predictor of alpha rather than simply a measure of portfolio activity. Cremers and Petajisto (2009) 3 were probably the first to test this concept empirically using a large sample of US mutual funds. They showed that the funds with the highest Active Share had a positive historical correlation with consistent, above-benchmark returns (alpha). 1 Youn, H., Bettencourt, L. M. A., Strumsky, D., and Lobo, J. 2014. Invention as a Combinatorial Process: Evidence from U. S. Patents. Accessed on 1 December 2014 at: http://arxiv.org/abs/1406.2938. 2 Zero means the portfolio is an exact replica of the benchmark, while 100 % indicates that they share no common securities. This range applies to long-only portfolios, whereas those holding short positions can reach an Active Share greater than 100 %. 3 Cremers, M., and Petajisto, A. 2009. How Active is Your Fund Manager? A New Measure that Predicts Performance. The Review of Financial Studies 22 (9): 3329 3365. Understand. Act.

That consistent alpha was found to be larger than the alpha generated by non-index funds with the lowest Active Share, even on a net-of-fee basis. Several subsequent studies have broadly corroborated these statistics for both US and non-us funds. There is also some evidence that higher Active Share may translate into more downside risk and wider dispersion of returns, as well as higher tracking error depending on market volatility levels and investment style 4. These findings look fairly persuasive at first reading. The bulk of the research has controlled for a number of factors that could have otherwise led to a spurious correlation between Active Share and alpha. However, there may be additional confounding variables lurking in the background especially given the high level of data aggregation required to extract generalizations from decades-long time series, covering thousands of funds. We know, for instance, that Active Share levels can be significantly skewed by the properties of the benchmark selected. Take the S&P SmallCap 600 and the Russell 2000. The difference in number of constituents alone may bias Active Share toward higher figures for funds measured against the latter market index. Capitalization-weighting is also key. Several singlecountry emerging market indices are weighted very steeply, with the top ten constituents sometimes accounting for more than half of the index, as is the case with the MSCI China Index. This can create an obstacle to higher Active Share, compared to less top-heavy indices. On balance, most would agree that the relationship between Active Share and performance is nonlinear, with several other variables coming into play. A prime example is tracking error, itself a non-linear function of the active decisions made by the portfolio manager, market volatility and the correlation of returns. Active Share in its original construction should, at best, be used to evaluate whether an equity manager selected for an active mandate is truly active, and whether the benchmark chosen makes sense. Meanwhile, the data mining exercise involved in the early research on Active Share offers some clues about where the sweet spots of active management can be found 5. Tinker, Tailor, Soldier, Sailor Where do we go from here? We think investors can benefit from a more micro-analytic approach to Active Share when assessing portfolio performance and risk within the most active portion of the fund universe spectrum. Previous studies have, indeed, highlighted some typical sources of high Active Share, such as smaller-cap stock selection in large cap funds. However, this says little about why that benchmark deviation or investment strategy drift came about in the first place. Does it produce intentional, repeatable alpha? Or just circumstantial beta outperformance? To answer these questions with confidence, Active Share should be made more sensitive to fund characteristics and the investment process. All the more so, if we expect the most active funds to exhibit greater heterogeneity in design than the least active ones. Additionally, it is not enough to focus on the distribution of portfolio metric correlations across funds using a snapshot of their holdings, usually at quarter-end. To properly relate active portfolio construction with alpha, it is necessary to analyse the evolution of Active Share within the portfolio, as well as its time-series dynamics with other metrics. What might that micro-analytic approach look like? Our own experience, based on the regular portfolio reviews we run with portfolio managers and Chief Investment Officers, suggests breaking down Active Share into its basic nuts and bolts. To increase Active Share in an equity portfolio, benchmarked against a fully-invested equity index, at least one of four parts needs to be engaged. We label the parts using a descriptive metaphor 6 for ease of reference: 1. Tinker: When a manager tinkers with, that is overweights or underweights, a benchmark security. 2. Tailor: When a manager tailor cuts a benchmark by zero-weighting a constituent security. 3. Soldier: When a manager buys an off-benchmark security, while at the same time soldiers on with the same fundamental factors characterizing the stocks found in the benchmark (e. g. country, sector, market cap, value / growth). In other words, the off-benchmark security does not directly expose the portfolio to an off-benchmark factor. 4. Sailor: When a manager buys an off-benchmark security, while at the same time sails off the fundamental factors found in the benchmark. That is, the off-benchmark security directly exposes the portfolio to an off-benchmark factor. 4 Morningstar. Active Share: What You Need to Know, May 2014, and How Active Are the Biggest Active Foreign Funds?, June 2014. 5 See Allianz GI publication, The Changing Nature of Equity Markets and the Need for More Active Management. 6 Here we borrow the title of the old English fortune-telling rhyme Tinker, Tailor, Soldier, Sailor. 2

These parts have been largely overlooked by previous studies. They can be derived by splitting a portfolio s holdings into four buckets according to the criteria set out above. There is a rather important caveat here in the differentiation between Soldier and Sailor. It will not always reflect all off-benchmark factor exposures, as some will be more readily observable at the single-security level (e. g. sector) than others (e. g. momentum). And it is clearly not meant to identify all portfolio factor bets over time, whether intentional or not, as these can involve combinations of securities spread across all four of our parts 7. Put simply, the Soldier-Sailor distinction is not a substitute for a good portfolio risk model. Its purpose is to help apply a reasonable litmus test for going off-benchmark: does it improve the portfolio s risk-return payoff? So what is the value of understanding the timevarying portfolio weights of the Tinker, Tailor, Soldier and Sailor approaches, as well as their performance and risk contribution? We think this framework offers a good approximation of the Fundamental Law of Active Management 8. The theory decomposes a portfolio s information ratio, as the measure of alpha for a given level of tracking error, into three variables: the Information Coefficient, multiplied by Breadth, multiplied by the Transfer Coefficient: 1. Information Coefficient: The correlation between a manager s alpha predictions, or informational advantage, on a portfolio holding and the actual alpha generated by that holding. 2. Breadth: The square root of the number of independent investment ideas or bets in the portfolio. Breadth may increase not just by adding more holdings, but also through more investment strategies, such as shorter-term trading of a small number of holdings. 3. Transfer Coefficient: The correlation between the optimal bets (those that can be backed by informational advantage) and the bets actually implemented in the portfolio. Low correlation here can result from investment restrictions or risk limits. Although this decomposition of the information ratio is theoretically sound, it is impractical. The typically proprietary data required to quantify the three variables is difficult to get hold of, short of reverse-engineering the portfolio construction process. Several attempts to derive measurable units of those variables have come at the expense of more mathematical complexity and oversimplifying assumptions about the investment process 9. One of those assumptions is that the Information Coefficient, Breadth and the Transfer Coefficient are always distinguishable. In reality, managers tend to focus their energy on a manageable number of executable investment ideas. A Tinker-Tailor-Soldier-Sailor decomposition of portfolio alpha and tracking error (see Figure 1) is a more practical approximation of manager foresight, breadth and investment constraints. The combined effect of these variables is effectively the manager s active management opportunity set. What Tinker- Tailor-Soldier-Sailor does is turn that opportunity set into an information set for exploring, and acting on, some elementary counterfactuals. 7 Even cash, which conceptually should be included in the Sailor part here, can operate as a factor bet under certain market conditions. 8 Clarke R., de Silva, H., and Thorley, S. 2006. The Fundamental Law of Active Portfolio Management. Journal of Investment Management 4 (3): 54 72. 9 Clarke R., de Silva, H., and Thorley, S. 2006. The Fundamental Law of Active Portfolio Management. Journal of Investment Management 4 (3): 54 72. Figure 1*. Decomposition of alpha (cumulative) & tracking error Basis points 900 800 700 600 500 400 300 200 100 0 100 200 300 400 500 4Q11 1Q12 2Q12 3Q12 4Q12 1Q13 2Q13 3Q13 4Q13 1Q14 2Q14 3Q14 Tinker alpha Tinker tracking error Tailor alpha Tailor tracking error Soldier alpha Soldier tracking error Sailor alpha** Sailor tracking error * Example equity portfolio benchmarked against EURO STOXX 50 Index. ** Includes cash positions. Source: Allianz Global Investors 3

Tinker What would risk-adjusted returns look like if the manager had been more benchmark-aware when pairing beta with alpha? Provided the right benchmark is chosen, the opportunity set embedded in a market index can be quite rewarding. That is, to some degree, a function of pairwise correlations between a benchmark s constituents. The lower those correlations are, as a result of less indiscriminate risk-on / risk-off trading, the more potential to demonstrate stock-picking and fundamental analysis skills through a more benchmark-aware strategy. Additionally, stock correlations broken down by sub-index country and sector views are a good gauge for the relative value of successful factor-driven bets. As correlations do not always reflect the level of idiosyncrasy in stocklevel performance, it is important to complement that view with the dispersion of realized returns. Against this backdrop, overweight and underweight decisions provide a more direct informational link between activeness and alpha than fund-level Active Share. This is supported by evidence from a study of US equity funds covering the period 1980 to 2008, which shows that benchmark overweights consistently contributed superior riskadjusted performance relative to underweights 10. The same goes for top, best-idea overweights and underweights, particularly for stocks which have higher idiosyncratic volatilities, low research analyst coverage, and which attract fewer investors. The correlation between overweights and superior alpha remains robust even when stripping out trading on earnings momentum and demand pressure (i. e. managers continuing to plough into previous overweights). These findings are in line with the notion that high Active Share funds exploit their asymmetric informational advantage, which is not fully incorporated in security prices. There is a compelling logic for expecting a return premium from overweights relative to underweights. Assuming active managers foresight of losers in a benchmark is just as good as their ability to pick outperforming stocks, then their portfolio should be made up of as many equallysized underweight positions as overweight positions. However, the shorting restrictions on most long-only funds lead to an asymmetry that can delimit Breadth and the Transfer Coefficient. The same can be said for a very broad benchmark acting as a constraint on research coverage, which can increase the number of residual, passive underweights. Aggregate Active Share figures tell us nothing about how a manager tackles this asymmetry in the portfolio construction process. Understanding the Tinker component of Active Share can tell us a whole lot more. Tailor Would actively zero-weighting benchmark losers enhance alpha? Consider the basic math of drawdown recovery: all other things being equal, a portfolio that loses 50 % in value would need to generate a return of 100 % to just get back even with its benchmark. That hurdle rate gets compounded for funds that also need to distribute income on a regular basis. In some cases, poor returns might not be anywhere near as significant as a loss coinciding with the income distribution phase; the so-called sequencing of returns risk. This explains why many investors have asymmetric preferences over gains and losses, and why they look for outperformance both when their benchmark is rising (upside capture ratio) and falling (downside capture ratio). It is important to understand the downside risk mitigation built into Active Share, as it may lead to significant differences in long-term returns. Small cap is a notable example of how actively avoiding benchmark constituents can have a material impact on alpha. Take the S&P SmallCap 600 which, unlike the Russell 2000, applies a profitability tailoring to its constituent securities. To be eligible for the S&P SmallCap 600, a company must have been profitable for the previous four quarters. In contrast, unprofitable companies have historically accounted for about a quarter of the Russell 2000. Since its launch in 1994, the S&P SmallCap 600 has outperformed the Russell 2000 in 12 out of 19 years. The Tailor component of Active Share sheds light on how alpha can be generated through loss-avoidance levers, such as a focus on quality. Soldier How about increasing the breadth of independent stock bets through a broader off-benchmark opportunity set? A higher dispersion of returns across benchmarks would be a strong signal to that effect even more so, if the wider difference between winners and losers is driven by more company-specific characteristics as opposed to an emphasis on a handful of risk factors. Such market conditions help further diversify individual stock positions, while in parallel soldiering on with the benchmark s geographic, sectoral or style focus. This approach can pay off if the benchmark reflects the manager s informational advantage as it 10 Jiang, H., Verbeek, M., and Wang, Y. 2014. Information Content When Mutual Funds Deviate from Benchmarks. Management Science 60 (8): 2038 2053. 4

should. Research on managers who prefer investing in companies geographically close to them, when that implies an informational advantage, has shown that local holdings tend to outperform more distant investments 11. Proximity to Silicon Valley, for investing in technology companies, is a case in point. One important thing to watch out for here is the standard deviation between the portfolio and benchmark factor exposures. A manager s stockspecific informational advantage, based on cash-flow fundamentals for example, may over time introduce unintended systematic risk into the portfolio through business cycle shocks. A disciplined, single-strategy approach to increasing Active Share is vulnerable to small differences in market conditions each time an off-benchmark holding is added. These differences can sometimes yield random-looking risk-return characteristics when factor risk is not managed more actively, since doing so could offset the desired exposure to stock-specific fundamentals. Understanding the Soldier component of Active Share, combined with a good risk model that mitigates any blind spots in portfolio construction, can help manage this complexity. Sailor Could a manager have generated higher alpha by constructing a more unconstrained portfolio, with sharper tilts away from the benchmark? Research on active management suggests that the growth of passive index investing and the shrinking pool of active investors should imply a much wider opportunity set of misplaced securities for active managers. However, the decline in noise-trader induced mispricing, due to the fall in individual stock ownership 12, might mean that the window of opportunity to capitalize on price discovery is getting narrower. Indeed, one recent large-scale study of actively-managed US equity mutual funds 13 documented that those trading more heavily delivered higher alpha. This trading-driven outperformance was weaker during periods of lower alpha dispersion across funds. Shorter-term trading is just one investment strategy among many for increasing the breadth of successful independent bets. A multi-strategy investment process usually involves a mix of bottom-up research on securities across multiple dimensions, as well as top-down capture of multiple risk premia (e. g. low volatility, value) 14. Therefore, trying to understand the Sailor component of Active Share through a plain benchmark comparison will inevitably fall short. Portfolio metrics should be inextricably linked to the time-series dynamics of the investment process, including any self-imposed portfolio limits and targets. A good example is off-benchmark holdings targeting an illiquidity premium in the market. If not managed actively enough, these time-varying alpha opportunities can suffer significant drawdowns due to aggregate liquidity shocks (liquidity beta) and other risk factors. The portfolio weights of Sailor securities, and their historical covariance with a worthwhile risk-return payoff, can demonstrate whether an appropriate premium is being harvested by going off-benchmark. Act When assessing a heterogeneous group of active equity managers, we think there are merits to sidestepping the debate on Active Share s predictive power. Aggregate Active Share figures are a good start, but only the tip of the iceberg. Investors can gain more actionable portfolio insights by recasting Active Share into its nuts and bolts, which we dub Tinker-Tailor-Soldier-Sailor. Understanding how these parts are used to express an investment idea, and whether that idea pays off, is one and the same. Only then can we be reasonably confident that active management is backed by informational advantage. The approach explored here also transforms Active Share into a more fungible concept that can potentially be extended to the Fixed Income, Multi Asset and Alternatives space where the relevant nuts and bolts might be nonadditive. Another reason why the parts are worth more than the whole. Imprint Allianz Global Investors GmbH Bockenheimer Landstr. 42 44 60323 Frankfurt am Main Global Capital Markets & Thematic Research Hans-Jörg Naumer (hjn), Ann-Katrin Petersen (akp), Stefan Scheurer (st) Data origin if not otherwise noted: Thomson Financial Datastream. Calendar date of data if not otherwise noted: January 2015 11 Coval, J. D., and Moskowitz, T. J. 2001. The Geography of Investment: Informed Trading and Asset Prices. Journal of Political Economy 109 (4): 811 841. 12 Stambaugh, R. F. Investment Noise and Trends. NBER Working Paper No. 20072. April 2014. 13 Pastor, L., Stambaugh, R. F., and Taylor, L. A. Do Funds Make More When They Trade More. NBER Working Paper No. 20700. November 2014. 14 See Allianz GI publication, Harvesting Risk Premium in Equity Investing. 5

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