TEACHERS RETIREMENT BOARD INVESTMENT COMMITTEE SUBJECT: 2012-13 Asset Liability Study Review of Normal versus ITEM NUMBER: 4 Representative Distributions CONSENT: ATTACHMENTS: 1 ACTION: DATE OF MEETING: February 7, 2013 / 30 mins. INFORMATION: X PRESENTERS: Allan Emkin and Neil Rue, PCA Christopher J. Ailman POLICY This item is covered by the Teachers Retirement Board Policy Manual, Section 1000, Page A-1: Investment Policy & Management Plan, (IPMP). HISTORY OF THE ITEM CalSTRS reviews our asset allocation targets once every three years through a full asset / liability (A/L) study. The 2012-13 study will transpire over several Investment Committee meetings and is expected to conclude at the July 2013 meeting. Tentative Agenda Plan for 2012-13 Asset-Liability Project Asset/Liability Topic(s) September November December January 2013 February April June July Investment Return Objectives, Investment Objectives and Philosophy Introduction of risk allocation across asset types Continued discussion of risk class allocation across asset types Risk Class Framework discussion continued Review of normal versus representative distributions Discuss and approve capital market assumptions, and asset class constraints. Approve decision factors. Presentation of CalSTRS A/L Model Interactive sensitivity analysis of objective / decision factors Approve factor weightings, select policy portfolio and set allowable ranges, adopt the strategic asset class targets into the Investment Policy & Management Plan PURPOSE OF THIS AGENDA ITEM The purpose of this step is to respond to three Investment Committee questions regarding the normal versus representative distributions used in the PCA risk framework modeling that was presented at the January 2013 meeting by Neil Rue of Pension Consulting Alliance (PCA), as INV35
Investment Committee Item 4 February 7, 2013 Page 2 well as including the upside impacts, and mapping the risk framework to the traditional asset class framework. BACKGROUND AND DISCUSSION During the Investment Committee discussion at the January meeting, a question was raised over the meaning of the past data used to estimate future returns. The specific reference from the January agenda item is noted below: Optimizations are examined under two versions of risk: (i) the traditional standard deviation (total volatility) measure and (ii) a downside risk measure. Under the assumption of normal (i.e., symmetric) distributions, both measures would produce the same optimal portfolios, but the world is far from normal. In fact, over the course of this asset-liability study, PCA has not relied on the normal distribution assumption. Instead, PCA s assumptions reflect the actual behavior of each investment class (assetbased or risk-based) overlaid with forward-looking long-term views about the expected return-and-risk tradeoffs of each class. PCA then applies simulation procedures to project expected class and portfolio behavior as well as determine optimal portfolios given certain return/risk criteria. For this specific presentation, PCA determines optimal portfolios using the return-and-risk characteristics of CalSTRS current policy portfolio as the baseline reference point. At this presentation, PCA will present two sets of optimizations: (i) those presented at the January meeting that relied upon PCA s 2012 forward-looking time series return and risk assumptions for each component/class overlaid by preserving each class s (or component s) historical time series return behavior and (ii) those utilizing PCA s 2012 forward-looking capital market assumptions for each component under a traditional mean-variance framework (i.e., expected returns, risks, and correlations, where all components/classes are assumed to exhibit traditional normal distributions that are IID i.e., independent and identically distributed). The Investment Committee can then compare the results of the respective optimizations to determine whether the differences between the two strategic class frameworks presented in January (asset classes vs. risk classes) are influenced by the type of assumptions being applied. Under (i), optimal portfolios were found utilizing a bootstrapping (simulation) methodology that samples from modeled time series. Under (ii), optimal portfolios are determined utilizing the traditional mean-variance/covariance modeling approach. This effort is very valuable because a critical part of any asset / Liability study is estimating the future behavior of asset returns. Since we don t know what returns will be like over the next 10 to 20 years, we look to the past behavior of asset prices and make and adjustment to the current starting point of time INV36 Applicable Historical Data Thanks to the ground breaking work of the Ibbotson Sinquefield s 1981 study and the work of University of Chicago and Professor Jeremy Siegel of Yale University, we now have a return history of U.S. stocks stretching back to the 1860s. The history of other asset classes is shorter due to changes in regulations or the life of the asset class. For example, while we have fixed
Investment Committee Item 4 February 7, 2013 Page 3 income returns back to the 1800s (typically a specific bond and not a bond market) it is often recommended to rely only on bond market data since 1974, when the U.S. ended the adopted Bretton Woods system and moved off the gold standard allowing the U.S. dollar and in turn interest rates to fluctuate more dramatically. Other components/classes, such as real estate, private equity, and infrastructure have even more limited histories, many of which do not have data prior to the 1970s. Normal Distributions vs. True (or Representative) Distributions Today, it is widely recognized among the practitioner community that the utilization of the normal distribution to describe investment behavior, while incredibly elegant for modeling purposes, is insufficient to grasp the reality of investment behavior. Even Harry Markowitz, in his foundational Modern Portfolio Theory paper, sought to focus on a loss measure to proxy risk. 1 He opted to use the standard deviation (total volatility) measure as a proxy for risk because it lended itself nicely to the computational capacity at the time (the 1950s) and its statistical properties and relationship to the average of a dataset allows for intuitive interpretation of modeling outcomes. However, as computing power has increased and global investment markets volatility has become more erratic, practitioners have opted to utilize new metrics and procedures for determining optimal portfolios. One of the first modifications to take place is to develop models that do not rely strictly on the normal distribution assumption. The debate over normal versus actual is best seen in diagrams of the distribution. A normal distribution is often referred to by its shape as a bell curve However, when one charts U.S. stock market annual returns since the 1860s (over 150 years), you see a very uneven pattern as displayed on the following page: 1 INV37 Markowitz, Harry, Portfolio Selection: Efficient Diversification of Investments, Chapter 9, Wiley Press, 1959.
Investment Committee Item 4 February 7, 2013 Page 4 Fitted to a distribution, one can see annual U.S. equity returns do not fit a normal bell shaped pattern. The left tail is much longer and both tails are fatter (kurtosis) than implied by a normal distribution, plus there are lumps (more occurrences than assumed under a normal bell curve) above and below the median return. 30 25 20 15 10 5 0-40 -35-30 -25-20 -15-10 -5 0 5 10 15 20 25 30 35 40 45 50 INV38
Investment Committee Item 4 February 7, 2013 Page 5 When faced with estimating the future distribution of investment returns, PCA decided to use the actual behavior of the past 40 years back to 1970 rather than a normal smooth distribution pattern. As a result, under a simulation-based optimization approach, real-world behaviors such as fat tails, autocorrelation (trending), asymmetry, unstable and fluctuating correlations, etc. are all allowed to occur. As described by Allan Emkin of PCA, at the January meeting, we experienced two 100 year floods in an eight year period, so we have to change the model. In the prior graph, the bear markets of 2001 and 2008 land at the far left hand tail. In statistical terms, these were viewed at three to four standard deviation events (meaning that if one assumes a normal distribution, then such events should only occur once every 750 years). That raises the question of whether if the distribution pattern has actually changed in this highly dynamic global investment environment or if we are being overly influenced by recent events. Either way, it is it clear that there is more kurtosis, fatter tails, than previously expected. The following is a chart of U.S. Equity returns from 1970 to 2012. The following graph on the next page displays that time period into a distribution pattern for comparison. While the median return is slightly higher than the 150 year history, the left tail has more kurtosis (i.e. it stretches farther to the left), exhibiting the higher downside risk of the past decade. INV39
Investment Committee Item 4 February 7, 2013 Page 6 Upside Outcomes Included with Downside Outcomes Another topic that arose at the January meeting was the observation that as downside negative returns are reduced, then in turn would not upside positive results be reduced. PCA will incorporate equivalent outcomes in their updated analytics of the optimized portfolios. Mapping the Two Frameworks (Asset Classes vs. Risk Classes) One of the last questions raised at the January meeting centered on mapping from the Asset based framework, we currently use, to the Risk Framework that PCA presented. At the meeting PCA presented a pie chart comparing the current CalSTRS asset allocation to an optimized allocation that would reduce the downside deviation. In the graphs below, we show the typical CalSTRS asset classes and the PCA optimization color coding the sub assets back to their traditional asset class structure. Traditional CalSTRS asset chart Same asset allocation broken into the current sub asset slices. Using the same colors to depict the asset classes; this chart shows the PCA optimization for low volatility. INV40
Investment Committee Item 4 February 7, 2013 Page 7 The following chart shows the PCA unconstrained optimization for downside deviation. This optimization allocates assets to sub-classes that CalSTRS is currently being researched or testing in the Innovation team, which includes hedge funds, commodities, agriculture, and oil and gas. INV41
Investment Committee Item 4 February 7, 2013 Page 8 Another way to look at the difference is in a table format, the diagram below, shows the current asset structure on the vertical axis and the proposed framework section on the horizontal axis. Global Equity U.S. EQUITY NON U.S. EQUITY PRIVATE EQUITY FIXED INCOME CREDIT HIGH YIELD INTEREST RATES MBS U.S. T-BONDS LONG US TREASURIES BANK LOANS PRIVATE EQUITY PRIVATE EQUITY REAL ESTATE CORE REAL ESTATE VALUE ADDED REAL ESTATE OPPORTUNISTIC REAL ESTATE CORE REAL ESTATE INFLATION TIPS TIPS INFRASTRUCTURE OVER-LAY HEDGE FUNDS COMMODITIES HEDGE FUNDS COMMODITIES COMMODITIES CASH CASH Sub-sectors not in the CalSTRS current structure: convertibles, agriculture, and oil and gas. SUMMARY After responding to the questions raised by the Risk Framework, the next step in the Asset / Liability study will be to review and adopt Capital Market Assumptions (CapM) or assumptions about future investment returns over the next ten years and the correlation and risk of those asset classes. In addition, we will need to approve constraints of minimums and maximums for each asset class. To facilitate the discussion at the April meeting and provide a comparison, staff retained Gray & Co., a leading minority consulting firm, to survey all the leading investment consulting firms and large asset owners. While predicting the future is extremely challenging, we attempt to incorporate consensus -driven inputs into our models to optimize the allocation. No matter what we adopt there will be critics on all sides; we will endeavor to make our best efforts and ensure our expectations are fiduciary sound compared to other similar peers. INV42
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