SSgA CAPITAL INSIGHTS viewpoints Part of State Street s Vision thought leadership series A Stratified Sampling Approach to Generating Fixed Income Beta PHOTO by Mathias Marta Senior Investment Manager, Fixed Income Beta Solutions the case with strictly model-driven approaches such as optimization. Although the two approaches share common elements: they are both quantitative, systematic and systems driven, there are also core differences that investors should take into consideration. State Street Global Advisors conducted an analysis comparing two portfolios using each approach. In this article, we highlight both the similarities and differences and also discuss the potential for different outcomes from each approach. Optimization Fully replicating the most common fixed income indexes is neither practical nor necessary to generate high quality beta performance. Indexes such as the US and Global Aggregates track thousands of bonds across several sectors in varying maturities, yields, credit qualities and liquidity features, which makes full replication inefficient, time consuming and costly. Beta managers can, however, construct portfolios with the characteristics and returns of these and many broad market indexes while delivering the desired risk and return elements to investors without fully replicating them. There are two alternative approaches to full replication. They are, stratified sampling and optimization. Both methodologies attempt to create portfolios that provide exposure to the desired risk level with limited tracking error. We believe stratified sampling, which breaks broad indexes into smaller, more manageable risk buckets, provides a distinct advantage over optimization as it delivers on tracking error while keeping a watchful eye on changing liquidity conditions and transaction costs. Experienced portfolio managers can add further value through stratified sampling because the approach allows flexibility when trading or liquidity conditions change, which is not In mathematics, computer science or economics, optimization refers to choosing the best element from a set of available alternatives. By maximizing or minimizing a real function, optimization strives to find the best available values of this function given a defined domain. In portfolio management, optimization is a portfolio construction methodology where benchmark constituents are categorized into risk factors that a model resolves in order to generate an optimal portfolio. The process relies on two steps: First, the overall fund s risk assessment will review pre-defined or historical analytics Second, the calibration model where the portfolio manager can build up objectives and constraints functions Risk criteria used in an optimization model include currency, yield curve, duration, sector, credit, issuer and liquidity. Optimization is also often associated with minimizing tracking error, more specifically ex-ante tracking error which is defined as the funds expected return deviation against the benchmark at one standard deviation level.
Stratified Sampling Stratified sampling is based on stratifying or dividing an index into manageable risk elements (also called buckets). The multiple dimensions of risk within a bond portfolio are commonly defined as follows: currency, yield curve, duration, sector, credit, issuer and liquidity. Portfolios using stratified sampling follow tolerance guidelines to ensure broad representation of the index on multiple levels and to deliver performance within a tight level of tracking error. SSgA has pioneered stratified sampling methods to match a benchmark s defining characteristics, even in the most volatile of environments. In our experience, stratified sampling is the most efficient fixed income index management technique for constructing broad index portfolios when full replication is not an option. This investment process relies on two steps: Screening the universe using a broad set of analytics Building a portfolio to reflect the index as closely as possible across multiple dimensions with a focus on minimizing transaction costs and maintaining pools of liquidity Using a stratified sampling approach, tracking error can be minimized with disciplined exposure guidelines based on duration, credit quality, seasonality, currency and optionality, which is a process further enhanced by input from experienced portfolio managers who maintain discretion to react to current market events. Portfolio Comparison To compare stratified sampling and optimization approaches, SSgA s Fixed Income team carried out a global research project involving portfolio managers from the Boston, London and Paris investment centres. We created two $100 million portfolios to track a US dollar denominated corporate bond index. Subsequently, we conducted similar analysis with smaller portfolios. In order to create an optimal parallel test of portfolio construction techniques, our research focused on integrating optimizer results within a stratified sampling approach, creating rules that are based on SSgA s tolerance-based risk management rules. Simply running an unconstrained portfolio optimization to minimize tracking error could yield dramatic sector over/under weightings. Optimizer constraints were based on SSgA s internal investment guidelines in order to establish a framework where the two approaches could be compared. Constraints focused on risk mitigation objectives including: interest rates, currency, curve and spread risk. More granular conditions including conditional issuer limits based on rating and sector contribution to durations were also used. The analysis was based on ex-post tracking error for 2007 because it involved both spread tightening and widening during the year. During the beginning of the period, the final phase of a rally in corporate bond market was playing out, marked by low volatility and tight credit spread levels. During the second part of the year there is sharp sell-off in risky assets in advance of the upcoming credit crunch. Due to the elevated levels of volatility during the crisis, transaction costs doubled from 40bps to 80bps. (See Chart 1). Chart 1: US Corporate Strategy Performance & Turnover Comparison NB: These are Model Returns based on SSgA Fixed Income internal guidelines. (bps) (%) 0.10 20.00 0.08 15.00 0.06 10.00 0.04 0.02 5.00 0.00 0.00-0.02-5.00-0.04-10.00-0.06-0.08-15.00-0.10-20.00 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 Performance difference vs index (Stratified) Performance difference vs index (Optimised) Sources: SSgA Monthly turnover (Stratified) Right-hand Side Monthly turnover (Optimised) Right-hand Side Benchmark: Barclays Capital Intermediate Credit Corporate. The model portfolio performance shown was created by the Fixed Income Beta Solutions team. Barclays Point was used to calculate model performance. The model portfolio performance does not reflect actual trading and does not reflect the impact that material economic and market factors may have had on SSgA decision-making. The results shown were achieved by means of a mathematical formula. The model performance shown is not indicative of actual future performance, which could differ substantially. returns are not necessarily indicative of future performance, which could differ substantially. Exposures Both portfolios were broadly diversified across all sectors and quality levels, with durations within 0.10 years on an overall and partial duration basis. The portfolio constructed using stratified sampling was closer to neutral duration when compared to the benchmark on an overall and partial duration basis. This portfolio was more closely weighted on a credit quality and detailed sector level to minimize tracking error due to cyclical issues within these factors. The sampled portfolio is more broadly diversified on both an issue (644 vs. 593) and issuer (422 vs. 367) level, even though the optimizer conditions allowed for up to 700 positions. The increased diversification reduces the likelihood of an idiosyncratic event having a more significant impact on the portfolio than the index. 2
The optimizer constructed portfolio not only held fewer issuers, but held them in larger market value discrepancies than the index. This portfolio had exposure to 43 issuers that deviated from the benchmark by over 15 basis points on a market value basis, compared to 4 for the sampled portfolio. The optimized portfolio was heavily overweight to lower subordination debt early in the year, which exhibited significantly more volatility during the crisis. Performance and Tracking Error The performance of both portfolios was within 15 basis points annualized compared to the index, which is within one standard deviation for one year without taking into account transaction costs. Digging a little deeper, the performance deviations for the optimizer portfolio were on average, greater in size and the variances were more frequently greater than 1.5 basis points per month (8 months for the optimized portfolio vs. 5 months for the sampled portfolio). Key Observations: Over 12 months the annual tracking error starts to increase as soon as volatility spikes 12 month ex-post tracking error is 36% higher for the optimized portfolio compared to stratified sampling Monthly tracking error is higher for an optimization as confirmed by a higher standard deviation Monthly turnover is generally higher and increases in parallel with volatility in the market The increasing turnover during periods of high volatility is particularly concerning for the sustainability of the optimization based approach. Whereas the stratified sampling maintains a monthly turnover around 2 3%, this optimization output resulted in excess of 15%. During this period of high volatility, transaction costs averaged 80 bps; the high turnover would have a negative monthly return impact of up to 12bps. (See Chart 2). Chart 2: Generic 5Y Markit CDX North America Investment Grade Index (%) 100 90 80 70 60 50 40 30 20 10 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 2007 Generic 5Y Markit CDX North America Investment Grade Index Sources: SSgA, Markit, Barclays Capital, Citigroup Key Differences Optimization is backward looking as it relies on historical correlations and tracking error assumptions. Due to this constraint, the optimizer will not be able to take into account current market events during portfolio construction. This technique also relies on the full liquidity of the bonds that are selected and in the size that the model specifies. In fixed income, this assumption is often not valid, and there can be a need for substitution of bonds within issuers or sampling between issuers. Optimization requires calibrating a model as well as defining a set of constraints. SSgA has gone to great lengths to create a detailed set of constraints for a parallel test. Less sophisticated constraints can result in an outcome that may generate additional levels of idiosyncratic risk and elevated levels of tracking error. The optimizer is very rigid in analysis; there is no middle route but an all or nothing approach failing to fully capture the diverse needs of clients and market conditions. One key assumption for models is that historical correlations will continue to hold in the future. History has repeatedly shown that risk reducing correlations are most likely to break down in periods of high volatility. As a result, the ex-ante tracking error estimated as a result of optimization can significantly underestimate the active risk in the portfolio. Advantage to Stratified Sampling The key advantage to stratified sampling is the experience that a portfolio manager brings to the investment process. In stratified sampling, the portfolio manager plays a central role in striking a balance between the risks of exposure and transaction cost. Based on variables such as fund size and market liquidity, a portfolio manager can decide on the strategy and execution of how to minimize tracking error based on factors such as number of issuers, curve exposure, seasonality, etc. Transaction cost and turnover are minimized to avoid the drag on portfolio performance. Portfolio construction decisions based on historical risk correlations are inherently flawed. At the overall portfolio level, this approach may appear to mitigate systemic risks, but it can leave a portfolio exposed to idiosyncratic risk. For example, two automotive issuers operating in similar markets and with close rating profiles could be substituted with one another. The portfolio would still match the main risk characteristics of duration, quality, and sector exposure. But in case of market stress or a credit event, the portfolio may experience some unexpected level of tracking error volatility, as experienced during the financial crisis. 3
Stratified sampling allows for the flexibility to construct a portfolio to minimize tracking error using risk factors that are relevant historically and going forward. The portfolio manager has the discretion to react to current market events such as taking advantage of adding exposure to illiquid issuers in the primary market or evaluating idiosyncratic events. The portfolios can be adjusted to react to changing risk factors, such as when one factor begins to overshadow the other risks in the market. Using real time information to base investment decisions best minimizes risk when certain issuers or issues have low liquidity and high transaction costs. Two recent examples include Lehman Brothers in 2008 and Greek Sovereign Debt in 2010. An optimized portfolio could have created an overweight without regard to the market conditions. Specifically, in the case of the Greek crisis, SSgA portfolio managers employed a collective investment decision based on input from the global investment and analyst teams. In a region-specific index, a portfolio manager could have been prudent and maintained the market weight of Greece, for a broader index held exposure to liquid bonds to reduce additional volatility. The tracking error of the optimization portfolio overstates the performance because it does not take into account transaction cost. Based on the parallel test, the average turnover was almost 12% compared to the stratified portfolio of just over 1.25%. If transaction costs are assumed to average 50 basis points during the year, the optimized portfolio will face an additional drag of 5 basis points a month. During periods of high volatility, transaction costs are elevated during the periods of the highest turnover. While the model constraints can be calibrated to focus on other variables such as minimizing turnover, there may be effects to the overall tracking and risk profile. The optimization process can be iterative to adjust the level of priorities, but this could lead to a time consuming process to create and manage each constraint. Conversely, stratified sampling is a consistent approach that can be applied in every market environment for any Fixed Income Index. Conversly, stratified sampling is a consistent approach that can be applied in every market environment for any Fixed Income Index. However it requires a minimum fund s size which would not suit small portfolios. Optimization Can Help Small Portfolios When managing small portfolios, a traditional stratified sampling process may face some limitations. A small net asset value prevents the fund from holding a large and diversified number of securities. Consequently small portfolios would structurally hold less securities, be more concentrated and less diversified than bigger funds built with a stratified sampling process. In such a context, using an optimization approach can be useful in its ability to select a limited number of securities while seeking to mitigate the main sources of risk against the benchmark. This approach would mainly be used by active portfolio managers wishing to quickly replicate a beta exposure and focus time on generating alpha ideas that will be implemented in the portfolio. Smaller portfolios are often managed actively because of the difficulty to get a sufficiently diversified and tight exposure to the index. In that context, an optimizer can prove a very useful tool to rapidly build a portfolio that will be matching the main risk characteristics of this exposure. The extra active risk that are added with such an approach will be embedded in the overall risk budget and should be compensated by other active risks throughout the alpha generation process. Efficient Fixed Income Beta Exposure The multi-dimensional aspects of bonds and bond indexes pose a challenge for any investment approach, though full replication is near impossible due to many constraints, not to mention the potential for substantial transaction costs to rebalance every constituent in a portfolio for every cash flow event. Matching the characteristics of a bond index pose many challenges for beta managers, who seek to replicate risk factors such as issuer, sector, currency, rating, degree of subordination, optionality, yield, coupon, maturity, and duration. Investors seeking fixed Income beta exposure should consider the different approaches for how a manager seeks to achieve low tracking error. The clear choice for getting beta exposure is from a stratified sampling process that is, managed by experienced portfolio managers who can incorporate current market conditions and adapt to changing risk profiles to minimize tracking error. An investment process that has the flexibility to strike a balance between getting broad diversification exposures while minimizing transaction costs and managing changing liquidity conditions will create efficiencies, decrease risk and deliver tight tracking error for investors. 4
SSgA Capital Insights is an integrated thought leadership program designed to educate clients on timely investment and market topics. As part of State Street s Vision Thought Leadership series, the SSgA Capital Insights program gives clients access to the expertise and viewpoints of SSgA s thought leaders and investment talent via a variety of multimedia channels. Since 2006, State Street s Vision Series has been distilling our distinct research, perspective and opinions on key themes impacting institutional investors worldwide into publications for our customers around the world. This material is for your private information. The views expressed are the views of State Street Global Advisors only through the period ended March 31, 2011 and are subject to change based on market and other conditions. The information we provide does not constitute investment advice and it should not be relied on as such. It should not be considered a solicitation to buy or an offer to sell a security. It does not take into account any investor s particular investment objectives, strategies, tax status or investment horizon. We encourage you to consult your tax or financial advisor. All material has been obtained from sources believed to be reliable, but its accuracy is not guaranteed. There is no representation or warranty as to the current accuracy of, nor liability for, decisions based on such information. This document c ontains certain statements that may be deemed forwardlooking statements. These statements are based on certain assumptions and analyses made by SSgA in light of its experience and perception of historical trends, current conditions, expected future developments and other factors it believes appropriate in the circumstances. Past performance is not a guarantee of future results. Barclays Capital is a trademark of Barclays Capital, Inc. CITIGROUP is a registered trademark and service mark of Citigroup Inc. or its affiliates and is used and registered throughout the world. The Citigroup EMU Government Bond Index ( Index ) is owned and maintained by Citigroup Index LLC ( Citigroup ). 2011 State Street Corporation INST-1941 Exp. Date: 3/31/2012 5