Using Regime-Based Analysis to Develop a Resilient Glide Path

LEADERSHIP SERIES Using Regime-Based Analysis to Develop a Resilient Glide Path Being aware of extended and cyclical market environments can help inform the ongoing development and evaluation of a glide path. Key Takeaways The financial markets have historically featured distinctive extended time periods (i.e., states ) and shorter cyclical market environments (i.e., regimes ) that have influenced the risk and return characteristics of asset classes. For any long-term investment strategy, such as a target date fund, understanding the impact of states and regimes and the transitions between different market environments can provide insights that inform the ongoing development of a glide path, the major driver of a target date strategy s return and risk over time. Authors Srinivas Maloor, PhD Senior Research Analyst, Target Date Strategies, Global Asset Brett Sumsion, CFA Portfolio Manager, Target Date Strategies, Global Asset Brian Leite, CFA, CEBS Head of Consultant Relations, Fidelity Institutional Asset Management Glide path construction is an active decision by the investment manager; glide paths vary because they are based on each provider s assessment of the important elements that influence outcomes, including capital market views, demographic research, and risk management. Fidelity uses proprietary machine learning and artificial-intelligence based frameworks to deconstruct historical financial market environments. This research helps provide investors in our target date strategy with a portfolio that seeks to be resilient to different market environments, and flexible enough to evolve with the dynamic nature of the markets.

Introduction Target date strategies have become the primary retirement investment vehicle for a large percentage of defined contribution workplace retirement plans. Eighty-seven percent of all defined contribution plans offer a target date strategy as the default investment option. 1 Target date strategies represent the sole investment option for nearly half of all plan participants, and two-thirds of millennials. 2 At Fidelity, our view is that the glide path, the time-varying asset allocation of a target date strategy, is an important investment driver as to whether a retirement saver achieves his or her target retirement outcome. Given this importance, plan sponsors, participants, advisors, and consultants should evaluate the research, resources, and approach that goes into the ongoing development and evaluation of any target date provider s glide path. Glide paths are an active decision based on the views of an investment provider. As a result, glide paths for target date strategies vary in the marketplace. Quite often, glide path discussions are focused on simplistic representations of the portfolios, such as the level of equities at different points in an investor s time horizon. In our view, equity exposure at a point in time is one of many factors to consider when evaluating a long-term asset allocation approach (see Fidelity Leadership Series paper Selecting a Target Date Glide Path: A Framework for Active Decisions ). This paper illustrates how Fidelity Investments uses modern artificial intelligence and machine learning tools to deconstruct the history of the financial markets for the purpose of understanding the patterns of different market environments and their corresponding influences on asset pricing. Generally, glide paths are designed to manage the risks associated with volatility in capital markets and asset classes during certain market climates, while striving to achieve a high level of performance that provides income throughout retirement. EXHIBIT 1: Target date strategies built for diversification using long-term averages as a starting point may be suboptimal, failing to recognize that long-term history is comprised of a series of extended periods (i.e., states ) when asset class behaviors and interrelationships differ markedly from what the averages would suggest. Rolling Returns and Long-Term Averages for Major Asset Classes Illustrative Efficient Portfolio Based on Long-Term Asset Returns Rolling 20-Year Real Returns (Monthly Data) 16% 12% 8% 4% 0% 4% U.S. Equity Investment- Grade Bonds Short-Term Investments 1947 1951 1955 1959 1963 1967 1971 1975 1979 1983 1987 1991 1995 1999 2003 2007 2011 2015 2016 Long-Term Average 6.9% 2.4% 0.6% Monthly data: Sep. 1927 to Apr. 2016. Past performance is no guarantee of future results. See pages 11-12 for methodology/index definitions. Source: Bloomberg Finance L.P., Fidelity Investments as of Apr. 30, 2016. Return 8% 6% 4% 2% 0% 0% 2% 4% 6% 8% 10% 12% 14% 16% Risk (annualized standard deviation) Bonds U.S. 35% Equity Long-Term 39% Average Portfolio at Retirement Non-U.S. Equity 26% Illustrative Efficient Long-Term Average Portfolio at Retirement assumes a retirement age of 65. See pages 11-12 for efficient frontier and index definitions. Source: Fidelity Investments, as of Aug. 1, 2017. 2

USING REGIME-BASED ANALYSIS TO BUILD A RESILIENT GLIDE PATH Awareness of distinctive market environments is important to glide path design Target date strategies are constructed to provide diversification among risks and asset classes throughout one s life cycle. Asset allocation can be influenced by the long-term past performance of financial assets, and investment managers often use historical averages as a guide or starting point when constructing a portfolio (Exhibit 1). The left chart in Exhibit 1 illustrates how 20-year inflation-adjusted returns for stocks, bonds, and short-term investments have varied significantly over time. The right chart in Exhibit 1 illustrates an efficient frontier a curved line that represents a series of portfolios (i.e., maximum return for a given level of volatility) based on the historical return averages for major asset classes. The pie chart shown in Exhibit 1 illustrates a representative portfolio based on historical average returns for a hypothetical investor at a target retirement age of 65, presuming a targeted volatility of 9% annualized. 3 This approach fails to recognize that long-term history includes a series of extended periods when asset class behaviors and interrelationships differ markedly from what the historical averages would suggest. These periods, or states, are distinct from one another, shift over time, and can be driven by a number of forces, such as macroeconomic changes, labor markets, and geopolitical events. Being aware of how the secular states, and how the corresponding returns, volatilities, and correlations among various assets in different states can alter the outcome of a portfolio is important when developing and evaluating a glide path. Our framework of market environment analysis incorporates a look back at history the various states and cyclical regimes and its impact on asset pricing. Deconstructing history: Four secular states correspond to different return and volatility characteristics for various assets Using modern artificial intelligence and machine learning tools, 4 our research has identified four distinctive EXHIBIT 2: The history of the financial markets can be categorized into four distinctive states, each of which has often lasted for multiple years. Probability of Four Historical Market Environments (1952-2016) Market Environment Probability (%) 100% 80% 60% 40% 20% Growth (17% of the time) Strong returns for stocks Strong growth Benign inflation Moderately negative correlation between stocks and bonds Stagflation (17% of the time) Expansion (52% of the time) Relatively sluggish growth Low inflation Moderately good for bonds Recovery periods post-wwii, 1957, 2000, 2008 Stress (14% of the time) 0% 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 High inflation Low U.S. Treasury returns Deflationary/recession Market volatility [1987 U.S. stock market decline, 1998 Russian financial crisis (Long-Term Capital Mgt.), 2008-2009 subprime credit crisis] Duration percentages of four historical market environments from Jan. 1, 1952 to Dec. 31, 2016. Research uses Fidelity s Hidden Markov Model (HMM) with Gaussian Mixtures framework (part of Fidelity s proprietary artificial intelligence and machine learning methodology to identify data-driven market regimes), which assumes there are four structural states or market environments that are more consistent, given historical realized asset class returns data. This framework was used to develop this concept further to apply to our target date strategies. Please see Appendix for a detailed view of this work and analysis. Source: Fidelity Investments, as of Aug 1, 2017. 3

structural states that have taken place in the history of the financial markets, which we categorize for classification purposes as Growth, Expansion, Stagflationary, and Stress (see The Application of Machine Learning, Artificial Intelligence, and Hidden Markov Models, Appendix, page 8). Each of these categorized states corresponds to distinct risk and return characteristics for the major asset classes (i.e., U.S. stocks, foreign stocks, U.S. investmentgrade bonds, and U.S. short-term investments). For example, historical periods that featured high returns for stocks, low returns for investment-grade bonds, and benign inflation are categorized as a Growth state. Conversely, periods featuring deflation, recession, low stock returns, and above-average bond returns are categorized as a Stress state (Exhibit 2). Our market environment framework also reflects changes that have occurred over time, allowing us to understand the duration of each state and how different states have transitioned from one to another. In practice, recognizing these transitions is difficult, but understanding history helps to provide context. In addition, while states are more of a secular phenomenon, we recognize the existence of shorter-term or cyclical periods called regimes (Exhibit 3). Different regimes may occur within any particular secular state, and are state-dependent meaning the incidence of regime 1 in state 1 would be distinct from the incidence of regime 1 in another state, and so on. Identifying an appropriate asset allocation The efficient frontiers and corresponding efficient portfolios for each distinct state are substantially different from EXHIBIT 3: Our market environment research framework includes four distinctive structural states (S) and two different market regimes (R) that could take place within each state (left). Each state corresponds to historical asset characteristics (table, right). S1 S2 S3 S4 R1-S1 R2-S1 R1-S2 R2-S2 R1-S3 R2-S3 R1-S4 R2-S4 For illustrative purposes only. Source: Fidelity Investments, as of Aug. 1, 2017. STATE 1: GROWTH CORRELATIONS U.S. U.S. Avg. Sharpe U.S. Foreign Inv-Grade Short-Term Return Volatility Ratio Equities Equities Bonds Inv. U.S. Equities 20.9% 16.2% 1.29 1.00 0.70-0.02 0.11 Foreign Equities 14.8% 15.0% 0.99 0.70 1.00-0.06 0.12 U.S. Inv.-Grade Bonds 2.2% 4.4% 0.49-0.02-0.06 1.00 0.24 U.S. Short-Term Inv. 1.1% 1.0% 1.08 0.11 0.12 0.24 1.00 STATE 2: EXPANSION U.S. Equities 10.4% 10.8% 0.96 1.00 0.57 0.14 0.12 Foreign Equities 11.0% 11.9% 0.93 0.57 1.00 0.08 0.10 U.S. Inv.-Grade Bonds 1.8% 2.9% 0.62 0.14 0.08 1.00 0.42 U.S. Short-Term Inv. 1.0% 1.0% 0.92 0.12 0.10 0.42 1.00 STATE 3: STAGFLATION U.S. Equities 0.8% 12.9% 0.07 1.00 0.19 0.16 0.16 Foreign Equities 4.4% 12.1% 0.37 0.19 1.00 0.01 0.05 U.S. Inv.-Grade Bonds 0.6% 3.3% 0.18 0.16 0.01 1.00 0.26 U.S. Short-Term Inv. 1.1% 0.9% 1.20 0.16 0.05 0.26 1.00 STATE 4: STRESS U.S. Equities -8.8% 23.1% -0.38 1.00 0.71 0.18 0.11 Foreign Equities -10.0% 25.8% -0.39 0.71 1.00 0.16 0.12 U.S. Inv.-Grade Bonds 6.5% 7.0% 0.93 0.18 0.16 1.00 0.40 U.S. Short-Term Inv. 0.8% 1.7% 0.49 0.11 0.12 0.40 1.00 The weight of the color shading of each data point above (annualized and inflation-adjusted) is based on the relative set of data within each state. Average Return: Green shading reflects higher returns; red shading reflects relatively lower returns. Volatility (standard deviation): Lower volatility (green shading) is generally preferred over higher volatility (red shading). Correlations (returns data): Lower return correlation (green shading) is generally preferable over higher return correlation (red shading). Data from Jan. 1, 1952 to Dec. 31, 2016. Source: Bloomberg LP, Fidelity Investments, as of Aug 1, 2017. See index representation and labels in the Important Information section (pages 11-12). 4

USING REGIME-BASED ANALYSIS TO BUILD A RESILIENT GLIDE PATH each other and what would be appropriate based on the overall long-term average (Exhibit 4). Having an awareness of the current market state and one that could last several years is an important consideration when constructing and evaluating a portfolio with a long-term objective. Positioning a portfolio for one state, or for the long-term average, could lead to substandard outcomes if another state occurred for an extended period. For example, a hypothetical portfolio for an investor in a Stress state at a target retirement age of 65 could include 100% exposure to U.S. investment-grade bonds (Exhibit 4, Stress ). 5 Meanwhile, the allocation for the same investor in a Growth state could include more than 50% in equities (Exhibit 4, Growth ). Developing a glide path starting with a baseline neutral portfolio Another important consideration when analyzing the sequence, frequency, and duration of the states that we have experienced in the past is that this history represents one possible path the one that we have seen but is in practice one sample drawn from many possible paths. In other words, the future path may not mirror the past. Because we do not know how the future may unfold and what states or mix of states/regimes may exist, we believe that it is important to consider a neutral or baseline portfolio that is diversified across a combination of potential future paths. From our perspective, this neutral portfolio assumes no information or subjective views on the current or future market environment from a manager, and reflects an as- EXHIBIT 4: The optimal portfolio for each of our four secular states is quite different. Varied Optimal Portfolios for Hypothetical Investor at Retirement Based on Four Structural States Asset At Retirement Growth Expansion Stagflation Stress Long-Term Average Return 25% U.S. Equity Foreign Equity Bonds Short-Term 20% Growth 15% 10% 5% Stress Expansion Stagflation Long-Term Average 0% 0% 2% 4% 6% 8% 10% 12% 14% 16% Risk (annualized standard deviation) 18% Each curved line represents a series of optimal portfolios (mean variance efficient portfolios - see definition pages 11-12). Assumes a retirement age of 65. Research uses Fidelity s Hidden Markov Model (HMM) with Gaussian Mixtures framework (part of Fidelity s proprietary artificial intelligence and machine learning methodology to identify data-driven market regimes), which assumes there are four structural states or market environments, that are more consistent given historical realized asset class returns data. This framework was used to develop this concept further to apply to our target date strategies. Please see Important Information for a detailed view of this analysis. 5

set allocation that is resilient to the four structural states and transitions among the four states. 6 More specifically, rather than assuming, for example, that the future frequency of states will have a larger weighting to Expansion, as we have experienced historically in the United States, we may assign an equal likelihood (25% probability) of experiencing any of the four states going forward. In practice, if we were to determine an asset allocation for a hypothetical investor near retirement that was equally resilient to all four states, this may include a higher allocation to inflation-sensitive assets compared to a portfolio constructed based on historical averages (Exhibit 5). The reason: An increased exposure to inflation-sensitive assets helps make this hypothetical neutral portfolio more resilient to the potential for greater experience in Stagflationary states relative to what has occurred in history. In our view, a neutral or information-less portfolio would seek to have equal contributions to risk from its constituents, resulting in a higher allocation to fixed-income exposures. In summary, this neutral portfolio can be expected to provide a high level of diversification, resiliency, and efficiency in EXHIBIT 5: A hypothetical neutral portfolio that is intended to be risk/return efficient and resilient to the four states for an investor at retirement age 7 can serve as a starting point for a diversified portfolio with a long-term retirement objective. Neutral Portfolio Resilient to Four States The Neutral Portfolio Resilient to many market environments Optimizes diversification and efficiency Starting point for creating a long-term retirement strategy Long-Term Average Portfolio 65% Equity 35% Bonds Inflation- Protected 21% Neutral Portfolio at Retirement Bonds 61% For illustrative purposes only. Assumes a retirement age of 65. Equity 18% terms of seeking the highest possible risk-adjusted return across future paths (i.e., mix of state exposures). Modifying the neutral portfolio with an investment manager s capital market s views While the neutral portfolio may provide resiliency to the four major states in the future, there are other factors that a manager may consider when constructing and evaluating a glide path for a target date strategy. For example, the manager can apply forward-looking views of capital market relationships (including risk and return of asset classes) and make incremental adjustments to the neutral portfolio, thereby improving outcomes if the manager s views are correct. Factoring an investor s time horizon and investment objectives into glide path design An investor s time horizon, risk tolerance, and target retirement outcome can be considered for calibrating the appropriate level of volatility for investors of different ages. At Fidelity, we evaluate outcomes in the context of an income replacement objective meaning the rate of an investor s final preretirement salary that we believe an investor needs in order to maintain a comfortable income throughout retirement. Such decisions that influence a glide path are active in nature, and the trade-offs associated with risk, return, and other factors must be considered and balanced. For example, target date portfolio managers may select an asset allocation that is different from our neutral portfolio to meet a stated objective, such as income replacement. 8 The neutral portfolio in Exhibit 5 includes a high proportion of fixed-income assets, for example, and a larger weighting to equities might be warranted for a young investor with a long time horizon to capture the returns associated with the higher risk of equities. This, in turn, may help the investor to accumulate more assets toward the income replacement objective (see Exhibit 6). This increase in equity exposure comes with 6

USING REGIME-BASED ANALYSIS TO BUILD A RESILIENT GLIDE PATH greater potential short-term risk or volatility, which may be a prudent trade-off given the investor s time horizon and risk tolerance. This is one example of the types of active decisions that require analysis and judgment. To conclude, each point along the glide path can be thought of as a combination of three portfolios with different objectives (Exhibit 6): A neutral portfolio, with an objective focused on portfolio efficiency, based on the potential mix of secular states that may occur in the future. An enhanced portfolio based on forward-looking views and conviction. A portfolio that is meant to represent an investor s time horizon and the strategy s desired retirement outcome. Final Thoughts: Identify a target date provider with a robust glide path framework We believe that research focused on market environment and regime-based analysis can provide helpful insight that can inform the ongoing development and evaluation of a glide path. In our glide path framework, this analysis complements other types of research that support the strategic allocation and glide path. This collective research helps provide investors in our target date strategy with a portfolio that seeks to be resilient to different market environments, and flexible enough to evolve with the dynamic nature of the markets (Exhibit 6). Given the importance of a glide path to an investor s retirement outcome, plan sponsors, participants, and advisors should evaluate target date managers on the basis of the research, resources, and thoughtfulness of approach that supports the glide path. EXHIBIT 6: Constructing a glide path should reflect an analysis of market environments and active decisions on behalf of a target date fund provider. Incorporating the Neutral Portfolio into the Glide Path to Equity 80% 25-Year-Old 65-Year-Old 85-Year-Old 60% Neutral Portfolio Forward-Looking Time Horizon and Retirement Outcomes Target Date Portfolio Composition Target Date Portfolio Composition Target Date Portfolio Composition 40% 20% Stocks Bonds Short-Term Investments Target Date Target Date Target Date 0% 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Age For illustrative purposes only. 7

Appendix: The Application of Machine Learning, Artificial Intelligence, and Hidden Markov Models Today, machine learning and artificial intelligence have come to play an integral role in many phases of the financial ecosystem, harnessing vast computational power and growth of data and providing investment professionals with access to highly sophisticated investment-decision-making resources. A common application of machine learning to financial data is in the study of financial time series data, where the time sequencing (or the temporal dimension of financial returns, for instance) is an important component. Markov chains (and models) have increasingly become a useful way of capturing the stochastic nature of many time series. For instance, the sequence of the four structural states described in this paper could be thought of as representing a four-state Markov chain. While Markov models have been used over the past few decades to train and recognize sequential data such as speech utterances, temperature variations, and biological sequences, they have more recently found wide applications in financial time series data. In a Markov model, each observation in the data sequence depends on previous elements in the sequence. Consider a system where there are a set of distinct states, S = {1, 2,...N}. At each discrete time step t, the system makes a move to one of the states according to a set of state transition probabilities in matrix A = [a ij ]. Let us denote the state at time t as s t. In many cases, the prediction of the next state and its associated observation only depends on the current state, meaning that the state transition probabilities do not depend on the whole history of the past process. This is called a first-order Markov process. This Markov property is described mathematically as: P(X t+1 = s k X 1,...,X t ) = P(X t+1 = s k X t ) are known so we can regard the state sequence as the output. The Markov model as described, while intuitive, has limited power in many applications. For instance, the structural states observed in financial time series, may not be directly visible and may indeed be latent. Therefore we extend it to a model with greater representation power, the Hidden Markov Model (HMM). 9 In an HMM, one does not know anything about what generates the observation sequence. The number of states, the state transition probabilities, and from which state an observation is generated are unknown, and are all simultaneously estimated from data. Four states as described provided a robust mathematical (statistically significant) expression of the asset returns data. A Gaussian mixture distribution can represent state-conditional asset return distributions far better than a simple Gaussian. For instance, the two exhibits below show the histogram of a time series of returns. In the first panel below, the data is modeled Frequency 4 3 2 1 0 1 2 3 4 Simulated data For illustrative purposes only using randomly selected data. Frequency where X is a random variate representing state occupancy at any point in time, and the state transitions are recorded in the state transition probability matrix, A, as: [a ij ]= P(X t+1 = s j X t = s i ) and the probability of starting from a certain state, the initial state distribution, is mathematically described as: π i = P(X 1 = s i ) In a visible Markov model as above, the states from which the observations are produced and the probabilistic functions 4 3 2 1 0 1 2 3 4 Simulated data For illustrative purposes only using randomly selected data. 8

USING REGIME-BASED ANALYSIS TO BUILD A RESILIENT GLIDE PATH by a simple Gaussian, while in the second panel, the data is modeled by a mixture of two Gaussian distributions. The HMM process moves from state to state over time. When the process visits any state, it generates an asset return via a random draw from a (Gaussian mixture) distribution associated with that structural state. However, at any point, asset returns are generated from the same regime-based Gaussian mixture distribution, when that same (state-conditional) regime prevails. The possibility of interpreting the states, combined with the model s ability to reproduce stylized facts of financial returns (including volatility clustering and fat tails), is part of the reason that HMM states with Gaussian mixture regimes are particularly powerful. Our model has estimated that we have historically remained in State 1, approximately 17% of the time (see left table below). The state transition probability matrix (see right table below), represents the probabilities of transitioning from any state at time T to any other state at the next time step, i.e., at time T+1. For example, if at any point in time (say at time T), one is in State 1, the probability of staying in State 1 at the next time step (i.e., at time T+1, is 97.6%), while the probability of transitioning to State 2 in the next time step is 2.5%. HISTORICAL PROBABILITY OF EACH STATE Marginal Probability State 1 17.1% State 2 52.2% State 3 16.7% State 4 14.1% STATE TRANSITION MATRIX State 1 State 2 State 3 State 4 State 1 97.6% 2.5% 0.0% 0.0% State 2 0.0% 98.2% 0.7% 1.1% State 3 0.0% 0.0% 96.9% 3.1% State 4 8.6% 0.0% 0.0% 91.4% 9

Authors Srinivas Maloor, PhD l Senior Research Analyst Srinivas Maloor is a senior research analyst in the Global Asset (GAA) division of Fidelity Investments. He works with the target date portfolio management team, and leads the team s strategic asset allocation research and design. Additionally, he conducts investment research for multi-assetclass strategies investment decision-making in areas including active asset allocation, portfolio construction, and risk management. Mr. Maloor joined Fidelity in 2012 and has been part of the target date strategies team since then. Brett Sumsion, CFA l Portfolio Manager Brett Sumsion is a portfolio manager for Fidelity Investments. Mr. Sumsion currently co-manages several multi-asset-class portfolios, including target date strategies. He joined Fidelity in 2013. Brian Leite, CFA, CEBS l Head of FIAM Consultant Relations Brian Leite is the head of consultant relations for Fidelity Institutional Asset Management, Fidelity s distribution and client service organization dedicated to meeting the needs of consultants and institutional investors, such as defined benefit and defined contribution plans, endowments, and financial advisors. He joined Fidelity in 2000. Fidelity Thought Leadership Vice President Kevin Lavelle provided editorial direction. 10

USING REGIME-BASED ANALYSIS TO BUILD A RESILIENT GLIDE PATH Endnotes 1 Source: Fidelity investments recordkept data of 22,100 corporate DC plans and 14.5 million participants as of Dec. 31, 2016. 2 See endnote #1. 3 For illustrative purposes, we assumed 9% annualized volatility for an investor at a retirement age of 65. 4 See Appendix for more detail on the analytical approach behind our regime-based framework (i.e., Hidden Markov Models with Gaussian Mixtures). 5 See endnote #3. 6 Neutral portfolio: Diversification is typically an unconditional concept. An asset s ability to diversify a portfolio is a function of its volatility, and its correlation with the portfolio. If assets are held in equal-weight, high-volatility assets like stocks will overwhelm the diversifying properties of lower volatility assets like Treasury bonds. Our neutral or information-less portfolio, similar to risk parity portfolio construction, balances the contribution of the targeted risk premiums from different asset classes. However, balancing the risk contributions is not the only objective. Constructing a portfolio that achieves stable returns in various structural states and across different market regimes is the ultimate objective, wherein the portfolio risk/reward profile could be improved by owning assets that do not all move together. 7 See endnote #3. 8 No income replacement rate is guaranteed by any Fidelity target date portfolio. 9 A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition by Lawrence R. Rabiner, Proceedings of the IEEE, Vol. 77, No. 2, February 1989. Important Information Structural state/market environment analysis: Financial market behavior can change abruptly. Although some changes may be transitory, the new behavior often persists for several periods after a change. Such structural shifts lead to adjustments in asset pricing via changes in their means, volatilities, and serial correlation over time that may remain stable within that structural state, until markets transition to a different state. We have lived through only one sample of realized history. Embedded within this one window of history is a mix of different structural states (as well as state-conditional financial market regimes). The structural states could be thought of as referring to secular phenomena. However, within any such structural state, financial markets could transition between different regimes, which could be considered as cyclical trends that are reflected in asset pricing conditioned on the secular state. Markov chains (and models) have increasingly become a useful way of capturing the stochastic nature of many time series (the sequence of the four structural states as depicted, could be thought of as representing a four-state Markov chain). Markov models are used to train and recognize sequential data, such as speech utterances, temperature variations, biological sequences, and more recently, financial time series data. In a Markov model, each observation in the data sequence depends on previous elements in the sequence. A Hidden Markov Model (HMM) not only accommodates a Markov chain, but also considers the uncertainty in which state the system may be in at any given time. The word hidden in Hidden Markov Models means that market participants do not know with certainty which structural state the financial system may be in at any point in time, and has only some probabilistic insight on where it could be along the continuum of state transitions, given the observed behavior of (multi-class) asset returns. Hidden Markov processes have been widely employed for some time in many engineering applications, and their effectiveness has now been well recognized in modeling financial data. In an HMM, one does not know anything about what generates the observation sequence. The number of states, the state transition probabilities, and from which state an observation is generated are all unknown, and are all simultaneously estimated from data. Four states as described provided a robust mathematical expression (statistically significant) of the asset returns data. Representative asset class benchmark indices (Jan. 1952 Dec. 2016, monthly, real returns): U.S. equity: U.S. stock data is based on the value-weighted total return, obtained from CRSP, for all U.S. firms listed on the NYSE, AMEX, or NASDAQ (monthly). Foreign equity: MSCI World ex-usa Return Index (in U.S. dollars) from GFD. After 1970, MSCI EAFE Return Index (in U.S. dollars; monthly). U.S. investment-grade bonds: Bloomberg Barclays U.S. Aggregate Bond Index since 1976 and the 10-year U.S. Treasury Bond prior to that date (monthly). U.S. short-term Investments: 3-month U.S. Treasury Bill returns (GFD), entire time period (monthly). Risk/volatility represented by standard deviation, which quantifies the magnitude of variation from the average (mean or expected value). A low standard deviation indicates that the data tend to be very close to the mean, whereas a high standard deviation indicates that the data points are spread out over a large range of values. A higher standard deviation represents greater relative risk. Efficient frontier: the asset allocation of a series of portfolios reflecting the optimal mix of assets - those with the highest return for a given level of volatility (i.e., standard deviation). Rolling returns: the annualized average return for monthly rolling 20-year (240-month) periods. Real: inflation-adjusted returns using Consumer Price Index as deflator. The Consumer Price Index (CPI) is a monthly inflation indicator that measures the change in the cost of a fixed basket of products and services, including housing, electricity, food, and transportation. Standard deviation: A statistical measure of volatility, measuring how widely returns/prices are dispersed from the average price. Correlation reveals the strength of return relationships between investments. A perfect linear relationship is represented by a correlation of 1, while a perfect negative relationship has a correlation of -1. A correlation of 0 indicates no relationship between the investments. Correlation is a critical component to asset allocation and can be a useful way to measure the diversification of a combined plan portfolio. Sharpe ratio: compares portfolio returns above the risk-free rate relative to overall portfolio volatility. A higher Sharpe ratio implies better risk-adjusted returns. 11

Important Disclosures Unless otherwise disclosed to you, in providing this information, Fidelity is not undertaking to provide impartial investment advice, or to give advice in a fiduciary capacity, in connection with any investment or transaction described herein. Fiduciaries are solely responsible for exercising independent judgment in evaluating any transaction(s) and are assumed to be capable of evaluating investment risks independently, both in general and with regard to particular transactions and investment strategies. Fidelity has a financial interest in any transaction(s) that fiduciaries, and if applicable, their clients, may enter into involving Fidelity s products or services. Past performance is no guarantee of future results. Diversification and asset allocation do not ensure a profit or guarantee against a loss. Industry glide paths used in this article are illustrative, and comprise each of the four major asset classes: U.S. equities, foreign equities, investment-grade bonds, short-term investments. These four asset classes were used for consistency and ease of comparison; note that individual glide paths may incorporate additional asset classes that could lead to different results. While indexes can provide insight on how asset classes have performed during historical market cycles, they do not take into account key factors such as portfolio expenses or portfolio manager investment decisions, and should not be considered representative of how a portfolio has, or will, perform. Index performance included the reinvestment of dividends and interest income. Indexes are unmanaged. It is not possible to invest directly in an index. Target date funds are designed for investors expecting to retire around the year indicated in each fund s name. The funds are managed to gradually become more conservative over time as they approach the target date. The investment risk of each target date fund changes over time as the fund s asset allocation changes. They are subject to the volatility of the financial markets, including that of equity and fixed income investments in the U.S. and abroad, and may be subject to risks associated with investing in high-yield, small-cap, and foreign securities. Principal invested is not guaranteed at any time, including at or after the funds target dates. Target date portfolios are designed to help achieve the retirement objectives of a large percentage of individuals, but the stated objectives may not be entirely applicable to all investors due to varying individual circumstances, including retirement savings plan contribution limitations. No target date fund is considered a complete retirement program and there is no guarantee any single fund will provide sufficient retirement income at or through retirement. If receiving this piece through your relationship with Fidelity Institutional Asset Management (FIAM), this publication may be provided by Fidelity Investments Institutional Services Company, Inc., Fidelity Institutional Asset Management Trust Company, or FIAM LLC, depending on your relationship. If receiving this piece through your relationship with Fidelity Personal & Workplace Investing (PWI) or Fidelity Family Office Services (FFOS) this publication is provided through Fidelity Brokerage Services LLC, Member NYSE, SIPC. If receiving this piece through your relationship with Fidelity Clearing and Custody Solutions or Fidelity Capital Markets, this publication is for institutional investor or investment professional use only. Clearing, custody or other brokerage services are provided through National Financial Services LLC or Fidelity Brokerage Services LLC, Member NYSE, SIPC. 2017 FMR LLC. All rights reserved. 811824.1.0 12