Asset Allocation for the Short- and Long-Term

Transcription

1 Asset Allocation for the Short- and Long-Term Executive Summary This white paper explores challenges that International Forum of Sovereign Wealth Funds (IFSWF) members face as they balance short- and long-term investment objectives and proposes specific frameworks that may be useful in this endeavour. The investment landscape has evolved significantly in recent years and SWFs have contended with an ever-expanding array of investment opportunities in both public and private markets. In response, many are re-evaluating the methods they employ to construct portfolios and measure and manage portfolio risk. This paper also addresses the organizational challenges related to acquiring and maintaining the human talent that SWFs need to achieve their objectives. Our approach to this study was multifaceted and consisted of three distinct avenues of research. Specifically: I. We undertook an extensive review of the academic literature related to asset allocation challenges and solutions. II. III. We spoke to a leading researcher in the area of portfolio construction and risk management techniques. We surveyed a broad group of IFSWF members regarding the challenges that SWFs face and the ways that they address these challenges. Our goal throughout is to provide findings that are both descriptive, to enhance understanding of the issues involved, and prescriptive, to propose frameworks and solutions that may be helpful. The main body of this paper which synthesizes inputs from parts I, II, and III as outlined above presents our comprehensive findings. At the highest level, our key conclusions are as follows: In the years since the global financial crisis of , monetary policies across the globe have entered unfamiliar territory, interest rates have reached historic lows (some are even negative), return expectations have International Forum of Sovereign Wealth Funds 1

2 declined, market volatility has increased, and a variety of new investment styles have emerged. These changes have forced investors, SWFs among them, to adapt their thinking and reconsider traditional approaches to allocating investments and managing risks. At the same time, SWFs have become an important and rapidly growing investor class and now comprise one of the world s largest institutional asset pools. As SWFs have risen in prominence they have found themselves on the front lines of the portfolio management challenges of this new era. As they formulate investment strategies, it is critical for SWFs to adhere to their core investment beliefs and employ methods that make the best use of available information to meet their specific objectives. This paper is divided into seven sections, each of which explores challenges and solutions related to a particular area of portfolio management. In section 1, we present a discussion with Mark Kritzman, Senior Lecturer in Finance at the MIT Sloan School of Business. As both a practitioner and leading asset allocation and risk management researcher, Mark has deep expertise in portfolio and risk management methods. In this discussion, he shares his insights regarding the portfolio management challenges faced by SWFs. This section summarizes many of the key issues that we cover in greater detail in later sections. In section 2, we discuss challenges associated with defining the opportunity set. The first step in determining an optimal asset allocation is to identify suitable investments that may provide risk and/or return benefits to a portfolio. We consider three separate frameworks that could help an SWF determine whether a particular asset class or investment should be considered for inclusion. Section 3 explores different approaches to forming future beliefs about asset class return, risk, and diversification properties. SWFs face many challenges in investing for the long term, including being subject to short-term evaluations and managing risk in exploiting tactical opportunities. We discuss the significance of the investment horizon in determining the properties of asset classes as well as its impact on the evaluation of investment managers. We also explore the concept of risk regimes and how this framework can improve estimates of risk exposure. Finally, we review complexities that SWFs should consider when evaluating alternative asset classes, including accounting for performance fees, appraisal-based valuations, and liquidity. Section 4 presents portfolio construction approaches that take short- and long-term investment horizons into account. We consider portfolio construction methods that include different aversions to short- and long-term risk. We show how to incorporate risk regime information into both strategic and tactical allocation decisions. We also consider the implications of different investor preferences for example, distinguishing between upside and downside risk and describe frameworks that can help investors account for these preferences. Finally, we introduce the notion of asset class stability and discuss how it can be used to produce portfolios with more stable risk characteristics over time. Section 5 looks at techniques for measuring, evaluating, and communicating portfolio risk. SWFs must communicate their investment decisions and the risks associated with those decisions to a wide array of stakeholders that include governance bodies as well as the public. Managing stakeholder expectations International Forum of Sovereign Wealth Funds 2

3 can be critical to maintaining confidence in both investment decisions and expected outcomes through good times and bad. Most risk metrics focus implicitly on risk at the end of a specific investment horizon. However, in practice, stakeholders are also keenly interested in understanding the losses that might occur along the way. We explore the distinction between end-of-horizon and within-horizon risk and discuss its practical relevance. Section 6 provides an overview of the Reference Portfolio approach to portfolio management. It then addresses how the methods presented in this paper can be complementary to the use of reference portfolios. It expands on this notion by proposing the use of active risk budgets as a method of constraining active decisions and managing risk. Section 7 presents the key findings from a survey of SWFs intended to provide insights into areas of interest and trends in investment preferences. In this section, we also discuss how SWFs align their organizational structures to meet their objectives. The views and interpretations expressed herein are those of the authors and do not necessarily reflect the views of the IFSWF or of State Street Corporation. International Forum of Sovereign Wealth Funds 3

4 Table of Contents Executive Summary... 1 Table of Contents... 4 Contributors... 6 About the International Forum of Sovereign Wealth Funds (IFSWF)... 6 IFSWF Subcommittee Acknowledgements Discussion with Mark Kritzman from the MIT Sloan School of Management Defining and Selecting Asset Classes Defining Asset Classes Asset Class Criteria for Portfolio Inclusion Estimating Asset Class Risk, Returns, and Correlations Return Risk, Co-movement, Risk Regimes, and the Investment Horizon Considerations for Alternative Assets Portfolio Construction for the Short- and Long-term Multi-Risk Optimization: Balancing Short- and Long-Horizon Risks Risk Regimes and Conditioned Covariance Risk Regimes and Tactical Shifts Investor Utility Preferences Stability-Adjusted Portfolio Optimization Evaluating Portfolio Risk Risk and the Investment Horizon Risk Regimes and Stress Testing Reference Portfolios Survey Results: The Experience of Sovereign Wealth Funds Current Fund Asset Allocations The Evolution of Fund Allocations International Forum of Sovereign Wealth Funds 4

5 Private Markets Fund Organization Appendix IFSWF Member Survey References Legal Disclaimers International Forum of Sovereign Wealth Funds 5

6 Contributors About the International Forum of Sovereign Wealth Funds (IFSWF) The International Forum of Sovereign Wealth Funds (IFSWF) is a global network of sovereign wealth funds (SWFs) established in 2009 to enhance collaboration, promote a deeper understanding of SWF activity, and raise the industry standard for best practice and governance. IFSWF Subcommittee 2 Subcommittee 2 (SC2) is an integral part of the IFSWF and has been established to provide a consultative forum that can effectively address and discuss matters relating to investment and risk for international sovereign wealth funds. Every year, through the efforts of its members and its research partners, SC2 prepares research papers on topics of interest to the SWFs. The topics are typically selected a year in advance by the members. SC2 s scope includes: facilitating co-operation between SWFs in initiating, developing, and monitoring good practices in investment and risk management; assisting in the development, review and distribution of investment and risk management practices, procedures and policies; and monitoring developments in the fields of investment and risk management. Subcommittee 2 Members: Italy CDP Equity (Lead) Alaska (USA) Alaska Permanent Fund Corporation Alberta (Canada) Alberta Finance Australia Future Fund Korea Korea Investment Corporation Kuwait Kuwait Investment Authority Morocco Ithmar Capital New Zealand New Zealand Superannuation Fund Oman State General Reserve Fund Palestine Palestine Investment Fund International Forum of Sovereign Wealth Funds 6

7 Acknowledgements Research for this whitepaper was conducted by a working group within IFSWF Subcommittee 2 including CDP Equity SpA (lead), the Korea Investment Corporation, and State Street, the IFSWF s official research partner. This paper was written by Kenneth Blay, Vice President of State Street, Roberto Marsella, Head of Business Development at Cdp Equity S.p.A., Roberto Baggiano, Senior Associate at Cdp Equity S.p.A., Rhee Keehong, Deputy CIO and Head of Private Markets at Korea Investment Corporation, and Will Kinlaw, Senior Vice President of State Street. The working group is also grateful to Mark Kritzman Founding Partner of State Street Associates, CEO of Windham Capital Management, and faculty member at the MIT Sloan School of Management for for sharing his insights with us. In compiling this document, we have drawn extensively from previously published papers coauthored by staff members and academic partners of State Street Associates. In some cases, we have included direct excerpts. Finally, we thank the IFSWF Secretariat for its invaluable support, assistance, and input as we undertook this study, the IFSWF members that contributed their time in completing the member survey and sharing valuable information about their asset allocations, and Bayasgalan Rentsendorj, Senior Membership Manager at the IFSWF along with Roberto Marsella, Head of Business Development at Cdp Equity S.p.A., for their tireless efforts in coordinating membership participation in SC2 studies and work programmes. International Forum of Sovereign Wealth Funds 7

8 1. Discussion with Mark Kritzman from the MIT Sloan School of Management For this section of our study, we present a summary of a discussion with Mark Kritzman who is a Senior Lecturer in Finance at the MIT Sloan School of Management and a leading researcher on asset allocation methods. He is also an expert on risk management and has developed many approaches for evaluating and addressing risk. Our conversation with Mark was an opportunity to draw from his insights on asset allocation for the short- and longterm with a focus on the unique challenges faced by sovereign wealth funds. He also addressed questions relevant to SWFs about risk management. Below, we present a summary of this discussion, which followed a question-and-answer style. Both the questions and answers have been edited for clarity. Q: The members of the IFSWF working group tasked with researching asset allocation for the short- and longterm has identified 5 key asset allocation challenges faced by SWFs: 1. Balancing the tension between long-term and short-term investment objectives 2. Dealing with uncertainty when constructing portfolios 3. Developing frameworks to incorporate alternative asset classes into the portfolio 4. Communicating with stakeholders 5. Optimizing the organizational structure Do you think we are missing anything here? Is there anything you would like to add? MK: Those are all good topics. Another topic that is of interest is the issue of estimation error. Whenever we build portfolios we need to estimate returns and risk. When we do that, we are, unfortunately, exposed to various sources of error. Q: That is an excellent point and a topic we should definitely cover. If you don t mind, perhaps we can begin with an initial step of the asset allocation process - defining and selecting asset classes. You have done some work in this area. Could you share any insights on what an asset class is, how you define an asset class, and how you might decide whether to incorporate an asset class in a portfolio or not? MK: That is a great question and I don t think many people have formally addressed it. There are three key criteria for distinguishing an asset class. The first is that is it should be something that raises the efficiency of the portfolio. To be more technical, it would raise the portfolio s expected utility. This means that it either raises the portfolio s expected return or it reduces the portfolio s risk. It should accomplish this without requiring investors to have skill in identifying superior managers. In other words, a passive exposure to the asset class should increase International Forum of Sovereign Wealth Funds 8

9 the expected utility of the portfolio. The second criterion is that the components within an asset class should be homogeneous. They should be similar. The reason for that is that if you combine components that are not very similar within an asset class, then you are imposing an unnecessary constraint on the asset allocation process. You are saying that I must hold these two components in the fixed weights that they appear within the asset class. If the components are very different from each other you should split that asset class into two separate asset classes and that will enable you to achieve a more efficient outcome. The third criterion for qualifying as an asset class is that it should be sufficiently large to absorb a meaningful fraction of one s portfolio. If you were to invest in an asset class that did not have adequate capacity you would drive up the cost of investment and reduce the portfolio s liquidity. That wouldn t be a very good outcome. There are a couple of categories of assets that are a bit tricky. For example, many investors consider hedge funds to be an asset class. I don t believe hedge funds are an asset class. Hedge funds invest in all different kinds of asset classes. So what we are really investing in is perceived manager skill. It is unlikely that you could invest in the average hedge fund without any ability to distinguish between a good fund and a bad fund and raise the portfolio s expected utility. Another possible asset class is private equity. Our research shows that the average private equity fund, measured on a risk-equivalent basis, has produced a premium relative to public. Therefore one should expect the average private equity fund to raise a portfolio s expected utility, without the benefit of selection skill. My inclination is to say that private equity is an asset class and hedge funds are not. Q: One question does come to mind with regard to SWFs investing in private equity. Given the size of some SWFs, could you provide any insights regarding how they might approach investing in private equity? It is likely that there isn t sufficient capacity in any particular fund to represent a meaningful allocation within a SWF s portfolio. How might they go about developing a private equity allocation? MK: Obviously what you want to do is look at the private equity universe; perhaps you might want to sort it by venture capital, buyout funds, or other sub-categories of private equity. Then you would try to identify those funds that you think are going to generate the best performance and figure out a plan for getting exposure to those funds. To get started or as an alternative to private equity you can invest in liquid private equity. It has been shown that approximately three-quarters of the premium of private equity over public equity, on a risk equivalent basis, can be explained by the sector exposures of private equity funds. What that means is that you can invest in public equity sector ETFs or index funds and expect to receive about 75% of the premium of private equity over public equity; at least that has been the case historically. The other 25% of the premium of private equity over public equity is attributable to illiquidity. The fact that there International Forum of Sovereign Wealth Funds 9

10 are lock-ups and fewer disclosure requirements enables private equity managers to do things, or restructure companies, in ways that publicly traded companies cannot. I would think that liquid private equity would be a very good substitute for private equity while you are waiting for your ultimate investment in private equity funds. If you have private equity and have committed capital that has not yet been called, liquid private equity is also a pretty good repository for that committed capital because at least it is delivering a very similar risk profile as you would expect to get from private equity. Q: Along the lines of your comments on private equity and hedge funds we can advance into the next topic on producing estimates of returns, risks, and correlations for asset allocation. Those particular investments, as well as real estate and infrastructure, do present some issues with producing estimates. Can you touch a bit on each of these assets classes and provide some insights as to how you might deal with some of the issues that each of these investments presents? MK: If I were to conduct an asset allocation analysis with both publicly traded and less liquid asset classes, I would estimate expected returns, as a starting point, to be equilibrium returns. Those are the returns that you would expect to earn if all asset classes were fairly priced. In the case of publicly traded assets, the equilibrium returns are those returns that are proportional to their betas. That implies that if a particular asset class is mispriced, investors can trade that asset class and correct the mispricing so that the expected returns are proportional to beta. In the case of illiquid asset classes, if you perceive an illiquid asset class to be mispriced you can t simply just trade and expect that mispricing to be corrected. This is because illiquid asset classes are very expensive to trade. In that case, I would think that the equilibrium returns would be more proportional to the variance of the illiquid asset classes. That is just how I would get started. Then you might have views that you want to incorporate. You may think one asset class should have a return higher than its equilibrium for one particular reason or vice versa. In any event, dealing with illiquid asset classes is tricky for a variety of reasons. One is that, in many cases, the managers are paid performance fees. This has two effects. One is that the measured or the observed volatility of the returns net of fees is lower than the returns gross of fees. So the volatility that you observe actually understates risk. The reason for that is that performance fees cut off the upside. Reducing upside volatility, which is what performance fees do, is not lowering risk. When a manager outperforms and you give some of that outperformance back to managers you are reducing the upside you get you are not lowering risk. It lowers volatility but it doesn t lower risk. The first thing you need to do is reverse engineer the fee calculation so that you get a proper measure of downside volatility. The other problem with some of these asset classes, such as private equity and real estate and, in some cases, hedge funds, is that the values are based on fair value pricing. These prices are typically anchored to prior period International Forum of Sovereign Wealth Funds 10

11 prices so they are smoothed, there is positive autocorrelation. That also understates the true risk of these investments. So what you ought to do is de-smooth the returns. If you do that you get estimates of risk that make much more sense. On the return side, performance fees also cause you problems. For example, it turns out that if you have many managers who charge performance fees, the expected returns of those managers as a group will be less than the average of their individual expected returns. The reason for this is that when a manager outperforms, they collect a performance fee. When a manager underperforms, they do not reimburse you for that underperformance. So the actual average return of the managers is lower than the average of the individual expected returns of the managers. Now, you might argue that there are clawbacks that would prevent that from happening. That is true in principle but, in fact, that is hardly ever the case. It is typically the case that the manager either gets terminated, if the manager underperforms significantly over some period of time or, if you really like the manager, you are going to reset the high-water mark. I would say a good rule of thumb is that the expected return of a group of managers who charge performance fees is about 80 basis points less than the average of their expected returns. When you conduct your asset allocation analysis and you have corrected these issues you ll have lower expected returns and higher risks. That is going to cause your optimal allocation to these types of assets to be lower than if you had not taken these issues into account. Q: When producing estimates for both alternative and traditional assets there are a couple of other things we might want to consider. We know that markets exhibit regime type behavior, so it could be important to incorporate this regime information. Also, institutional investors are often tasked with managing to long-term objectives while also being evaluated over shorter intervals. There is a tension between long-term and short-term objectives that they have to manage. Could you provide some insights as to how we might approach considering risk regimes as well as understanding and addressing risk across different investment horizons when constructing portfolios? MK: The implicit assumption in the way portfolio theory is usually described in the text books is that returns are generated from as single regime, so there is a single distribution that you have to pay attention to. It turns out that, empirically, that has not been the case. One way of categorizing history is to try to categorize it in terms of fragile or turbulent periods versus resilient or calm periods. The way to distinguish these periods is not best done with volatility and correlation. Those are the traditional ways of measuring instability of returns and risk concentration. What I would do is try to describe two regimes, at a minimum. One would be a fragile regime. That would be characterized by market instability and high risk concentration. The other would be a resilient regime. That would be characterized by calm or very stable returns and low concentration of risk. In recent years there International Forum of Sovereign Wealth Funds 11

12 have been two measures that have evolved in the literature to measure instability and risk concentration that are better or, at least, more informative than volatility and correlation. In terms of market instability, there is a measure called financial turbulence. This is literally a measure of how statistically unusual a set of returns is in a given period given their historical pattern of behavior. Where standard deviation deals with one asset class at a time, financial turbulence looks at a whole cross section of asset class returns. It takes into account extreme price moves. That, in a sense, is capturing the same information that you get from volatility. It is also taking into account the decoupling of correlated assets and the convergence of uncorrelated assets. So it is capturing the interaction among the assets as well. You can think of this as capturing two things: One is unusual volatility and the other is correlation surprise. Financial turbulence is a much better measure of market instability than conventional measures such as volatility or credit spreads. It is also the case that it has some very nice empirical features. One is that returns to risk, measured in a variety of different ways, are much lower when markets are turbulent than when they are calm. Furthermore, losses occur when markets are turbulent not when they are calm. The other component of fragility is what we call risk concentration. Literature has shown that you can compute something called the absorption ratio to measure how concentrated risk is. The way this works is that you conduct a principal components analysis to identify the factors that are driving the variability of returns. You then compute the fraction of total variability that is explained by a few of the most important factors. So if this ratio is high, in other words, if these few factors explain a high percentage of the variability of returns, that tells us that markets are very tightly coupled; they are unified. When risk is concentrated that way, conditions are very fragile because shocks travel quickly and broadly. When the same few factors explain a small percentage of the total variation of returns, which means that the absorption ratio is low, that indicates that risk is distributed across many different sources. When that is the state of the world, markets are more resilient. For example, imagine if you had a situation where the absorption ratio was very low, risk was very widely distributed, and you got a shock such as an unexpected jump in oil prices. It might be the case that airlines stocks go down because their operating expenses have gone up unexpectedly. But you wouldn t necessarily expect that shock to travel to other parts of the market where there is no fundamental connection to the price of oil. But if the market were very tightly coupled where returns are moving in unison and you got a shock like that, it would not be at all unusual for the entire market to sell off or to have a system wide response. This is why the absorption ratio is also used by policymakers to measure systemic risk. Just to sum up, you can distinguish fragile market conditions from resilient market conditions by monitoring these measures of financial turbulence and risk concentration. This is something that one should take into account not only in modifying your exposure to risk through time but also in figuring out what your policy portfolio is in the first place. For example, if you want to build a portfolio that is diversified against losses, you don t want to look at the correlations and volatilities that prevailed, on average, across the entire history of returns. It is much more effective to pay attention to the volatilities and correlations that prevailed during these periods of market fragility International Forum of Sovereign Wealth Funds 12

13 because that is when losses typically occur. This also leads to this issue of policy portfolios. You think of a policy portfolio as a set of weights that you are going to hold, on average, through all market environments. It turns out that a set of fixed weights delivers a very unstable risk profile. For example, the typical institutional portfolio going into the financial crisis in 2008 had a trailing annual standard deviation of monthly returns of about three percent. Coming out of the crisis that same portfolio had a trailing annual volatility of about 30 percent. When you think about it, what is the purpose of a policy portfolio? Well, investors want two things, whether they are a SWF or a private investor. They want to grow wealth and to avoid large drawdowns along the way. The purpose of a policy portfolio, or at least one of the purposes, is to balance those two trade-offs which conflict with each other. The more you structure a portfolio to grow wealth the more you expose it to large losses. So the idea of a policy portfolio is to come up with how you want to balance your desire for growth with your aversion for these large drawdowns. Well, it s not really a set of weights that you want. You want the risk profile that you think that set of weights is delivering. What makes more sense in my view, rather than having a policy portfolio of rigid asset class weights, is to have a flexible investment policy. The idea is to target a certain risk profile and then modify your portfolio in some structured and dynamic way to try to maintain that risk profile. What that means is that in periods when markets are very fragile you would try to skew your portfolio towards more defensive assets and in periods when markets are very resilient you would try to orient your portfolio towards growth assets. Q: We haven t yet addressed the issue of long-term versus short-term risk. Could you share your insights on that topic? MK: It is an important topic and I want to make sure we get this issue out on the table. The way people measure risk relies, typically, on two assumptions. One is that correlations do not change depending on the return interval used to estimate them. The academic literature, as well as the software that practitioners use, assume that, over the same sample, the correlation will be the same regardless of whether you are estimate correlations from monthly or annual or daily returns. That turns out not to be true. The other assumption that people make is that volatility, in particular standard deviation, scales with the square root of time. So, for example, if you were to estimate the standard deviation of an asset class based on monthly returns you would multiply that standard deviation by the square root of 12 to get an estimate of the volatility of annual returns. That also is not borne out by the data. It turns out that to the extent autocorrelations are not zero then that square root of time rule does not work. If you have positive autocorrelation that means that the risk of annual returns is going to be greater than the square root of twelve times the volatility of monthly returns. International Forum of Sovereign Wealth Funds 13

14 In the case of correlations, not only do you have to pay attention to the autocorrelations of the two return series you also have to pay attention to the lagged cross correlations. To the extent any of those are not zero then correlations will not be constant across different return intervals. A good example is the correlation between U.S. stocks and emerging market stocks. During the period starting in 1990 through 2013, both emerging market stocks and U.S. stocks had about the same cumulative annualized returns. One had a return of 9.3 percent and the other had a return of 9.5 percent. Moreover, their monthly returns were 69 percent correlated. Yet, there was one three year period when emerging market stocks outperformed U.S. stocks cumulatively by 120 percent and there was another three year period where they underperformed cumulatively by 60 percent. That is somewhat of a puzzle. How can you have you two asset classes that have the same cumulative returns and monthly returns that are highly correlated and experience such divergent performance in these sub-periods? Well, it turns out that the correlation of monthly returns was 69 percent, the correlation over the same sample period of the annual returns was only 40 percent, and the correlation of three year returns was zero. They were uncorrelated at the three year return interval. This is a big deal. When you are building your portfolio, typically you are estimating your risk parameters based on monthly returns and then you are converting them to annual inputs. My presumption is that when you build a portfolio, when you do asset allocation, you are designing a portfolio to be optimal over some multi-year horizon. The risk profile over that multi-year horizon is going to be vastly different than what you are going to infer from volatilities and correlations estimated from monthly returns. This is something that one needs to address. I would also argue that institutions like to say they are long-term investors and they can withstand large drawdowns along the way. I ve been in this business for over forty years and that is not the case. People may like to think that they are long-term investors, but people do care about what might happen along the way. You can say that I ll structure my portfolio based on estimates of long-term risk, but then, if you do that you are going to make your portfolio vulnerable to large interim drawdowns. If you focus on just short-term risk, you are going to expose your portfolio to sub-optimal growth over the long-term. This is something that has to be balanced. Q: So you now have two covariance matrices for different time horizons. How do you go about balancing those? MK: What you would like to be able to do is to estimate correlations and volatilities based on monthly returns and then estimate correlations and volatilities based on three-year returns then come up with two different covariance matrices and introduce both of those into the optimization process. The problem with that approach is that the lagged correlations are not necessarily constant through time. So you may have some periods where there are positive autocorrelations. In which case, longer horizon risk is going to be greater than you would expect. Then there are going to be cases when there are negative lagged correlations, where longer horizon risk is going to be lower than you would expect. International Forum of Sovereign Wealth Funds 14

15 There is a new approach that just recently appeared in the latest issue of the Journal of Portfolio Management which deals with this kind of estimation challenge by measuring the relative stability of covariances and uses that information in the portfolio construction process as a separate component of risk. 1 When we build portfolios we need to estimate returns and risk. We know that those estimates are made with error. I m not going to focus on return right now because most people don t extrapolate historical means to estimate expected returns. They typically use equilibrium returns or they have some fundamental approach to doing that. However, most investors do extrapolate historical covariances. To be clear, when I use the term covariance I am using it interchangeably with volatilities and correlations. When they extrapolate historical covariances it exposes them to several different types of errors. For example, typically what we have is some long history of returns for the asset classes that we care about. It could be decades long. What we are trying to do is to build a portfolio that is optimal for some shorter future period, such as one to three to five years. That means that we are exposed to small sample error because the realized covariances in the small sample that reside within this larger sample are going to be much different than the covariances of the large sample. So we have small sample error. We also have independent sample error because the future period that we are designing the portfolio for is distinct from the history we have used to characterize that future period. Finally, we have what we call interval error. This is what I have just been talking about; that the covariances that you estimate from monthly returns are not easily mapped on to covariances of longer interval or longer horizon returns. So we have these three components of error. What we have developed is a way of measuring the relative stability of the asset class covariances. We are then able to build portfolios that use this information to quantify risk in a more holistic way. One way to think about this is, in terms of standard deviation since getting your head around covariances can be hard, that you can have two assets; one with a higher standard deviation than the other. It could be the case that the asset with the higher standard deviation is more stable. In other words, there is less estimation error around it than the one with the lower standard deviation. In which case, it is possible that the asset with the higher standard deviation is less risky than the asset with the lower standard deviation. This is because out of sample the asset with the lower standard deviation can have a much higher standard deviation. This applies to correlations as well. So, what we are arguing is that the relative stability of the covariances is something that one should account for when building portfolios. The experiments we have done show that this generates much more stable portfolios than ignoring errors. It also generates much more stable portfolios than the conventional approach to dealing with estimation error, which is Bayesian shrinkage. 1 Kritzman, M. and Turkington, D Stability-Adjusted Portfolios. The Journal of Portfolio Management, Vol. 42, No. 5, Special Quantitative Equity Strategies Issue (pp ). International Forum of Sovereign Wealth Funds 15

16 Q: So you are basically incorporating information about the volatility of volatility in the portfolio construction process? MK: Yes. Q: Thank you for those important insights on portfolio construction and risk estimation. It is evident that you have delved much deeper into the portfolio construction process than most of us and we have certainly benefitted from those efforts today. In the time we have left, we did want to address some questions directly from members of the IFSWF. The first question is as follows: It seems that various parts of the world, Europe at first, are going to go through a long period of very low interest rates. How do you think this will change the way we look at these types of investments? MK: You can address that in several ways. One is to define interest rate regimes. You can then characterize your estimates of future return and risk of portfolio components contingent on what regime you expect to be in. When you conduct an optimization, what you are doing is maximizing expected return minus some coefficient of risk aversion times portfolio risk. That portfolio risk is characterized as a covariance matrix. So, what you can do is to collect a long history of returns. You have information about when interest rates were low in history and when interest rates were high in history. Instead of basing the risk of the asset classes on the full sample of historical returns, divide the historical returns into two samples. One sample would be returns when interest rates were below some level and the other would be returns when interest rates were above some level. You would then calculate separate covariance matrices and condition expected returns based on what prevailed in the low interest rate regime versus the high interest regime. Then, when you optimize your portfolio, instead of maximizing expected return minus risk aversion times one covariance matrix, you would maximize expected return minus one risk aversion coefficient times covariances estimated from the low interest rate regime minus another risk aversion coefficient times covariances estimated from the high interest rate regime. So you have two interest rate regimes. Earlier I spoke about a fragile regime and a resilient regime. You can take the same approach but have it be conditioned on these different rate environments. Then the risk aversion coefficient that you assign to these two covariance matrices can either reflect the relative aversion you have toward risk during periods of high or low interest rates or, instead, it can reflect your expectation for what the future will hold. You may argue, and I would argue, that interest rates are more likely to be higher in the future than they have been in the recent past and you might put a higher probability on that when you do your optimization. That is one approach. The other thing to keep in mind is that interest rates historically, at least in the United States, have gone through very long cycles. We had a declining interest rate environment from 1979 through just about the present. Short rates went from about 20 percent down to zero. It is unlikely that that trend can continue. It can t continue without International Forum of Sovereign Wealth Funds 16

17 going significantly negative. I think it s more likely that we ll have a long and gradual increasing interest rate environment. The other thing that this implies is that the risk from fixed income assets is much greater than you think it is. For example, there is a strategy called risk parity. What that means is that you structure a portfolio such that each of the major components of the portfolio contributes the same amount to total portfolio risk. So you should lever up your exposure to bonds and cut your exposure to equities. People have written articles showing that this risk parity strategy approach has outperformed a 60/40 stock/bond portfolio going back to the 1920s. It turns out, that is not true. They based that performance on the Sharpe ratio which has as its denominator standard deviation. They converted the standard deviation of monthly returns to the standard deviation of longer horizon returns using that heuristic I described earlier. If you take into account the lagged correlations of the asset s returns then the 60/40 portfolio outperformed the risk parity portfolio by as much as they argued it underperformed. Anyway, the short answer is and I have trouble giving short answers I would condition my expected returns and risk estimates on the sub-samples of high and low interest rates and use that information to build my portfolio. Q: I like the discussion and identification of this richness of risks and I understand the statistical qualities of these other risk measures. What it presents is added complications regarding optimization and determining what is a best portfolio especially if you have multiple objectives. Generally, my board is happy if we do well versus public plans, if we don t have a high risk of losing money, if we show actuarial progress, or the equivalent of actuarial progress, towards some long-term goal. It sounds like what you are describing is that, in general, the profession has made more advancements in risk measurement than on the optimization side. What is your view? MK: Well, I think there is a lot of misunderstanding of optimization. Let s talk about mean variance for a minute. It turns out that mean variance is much more robust than people give it credit for. I am a big fan of Harry Markowitz, and he and I have had many discussions about this. Mean variance optimization requires one of two things. Either that returns are approximately normally distributed or that investors have preferences that can be reasonably described by just mean and variance. You do not need both of those to be true. You just need one or the other to be true. So, mean variance does a pretty good job. Now, you can amplify mean variance to take into account multiple objectives like you ve just described. For example, you may care about performance relative to your peers and you also may care about your absolute performance. So, just as I described about how you can come up with covariance matrices based on different regimes, you can come up with covariance matrices based absolute returns and covariance matrices based on International Forum of Sovereign Wealth Funds 17

18 relative returns. You can specify the objective function of mean variance optimization to be expected return minus absolute risk aversion times the covariances of absolute returns minus a measure of aversion to relative risk times the covariance matrix of relative returns. So, basically, you are jointly optimizing for both absolute volatility and tracking error relative to some portfolio of peer investors or some benchmark. That is one thing you can do that is trivial to implement. In terms of pension liabilities or actuarial progress, as you describe it, that is a really interesting question. This is research that we are actually doing right now and I ll be giving a talk at Oxford University in a couple of months on the topic. If you want to hedge the monthly volatility of your liabilities, for example, the best hedge would probably be some kind of fixed income asset. This is because high frequency volatility of liabilities is typically a function of changes in discount rates. To be clear, when I say high frequency I mean monthly versus say yearly rather than milliseconds. Bonds would be the best hedge for that. But over the long term, the low frequency volatility of liabilities is a function of wage inflation and productivity growth. Equities are a better hedge against that. Again you can construct an optimization process that balances your aversion to large drawdowns along the way versus your aversion to the gradual erosion of your pension assets relative to your liabilities. That is another thing you can do in the optimization process. To the extent that you or your committee or stakeholders have preferences that can t be well described by mean and variance, there is another thing you can do. A typical example of this would be thresholds. If there is some threshold where if you breached that threshold conditions would be qualitatively worse than if you suffer a loss above that threshold, this is what we call a kinked utility function. If you have a situation where your returns are not normally distributed and you have preferences that are affected by these thresholds then you can t use mean variance optimization. What you would use is what is called full-scale optimization. Full-scale optimization is just plain direct utility maximization through the use of sophisticated search algorithms. So you write down your utility function. You have some sample of returns. You plug those returns into the formula for your kinked utility function and then you plug in a portfolio with one set of asset weights and calculate the utility. Then you plug in another portfolio with another set of asset weights and calculate the utility. You do this over and over again until you find the portfolio that has the highest utility. Now, that is computationally very challenging, especially if you have portfolios that have more than just a few assets in them. However, it turns out that there are optimizers that run full-scale optimization that can sample as many as half a million portfolios in about 30 seconds. So, this is what I would use instead of mean variance optimization in the case where you believe returns not to be approximately normally distributed and you have thresholds. End of discussion International Forum of Sovereign Wealth Funds 18

19 2. Defining and Selecting Asset Classes The starting point for portfolio construction is the identification of the asset classes to be included in the portfolio. One of the key challenges for SWFs is assessing the increasing assortment of investment opportunities available in public and private markets across world. This includes determining whether an investment represents an avenue for capturing a market risk premium or an opportunity to exploit alpha, and whether it provides diversification benefits or if it is even suitable for the objectives of the fund. These are all important considerations for SWFs to contemplate. However, the imprecision with which many investors approach defining asset classes often results in inefficient diversification. Incorrectly determining investments as being similar would result in an SWF neglecting an opportunity to diversify. Alternatively, incorrectly determining investments to be distinct would result in a SWF deploying assets towards redundant investments to little or no benefit. Part of the challenge in addressing these issues is that asset class definitions are often ambiguous. Delineating investment strategies and asset classes requires an understanding of both the qualitative and quantitative aspects of an investment. Defining Asset Classes The first approach to defining an asset class is through their investment attributes. Asset classes are defined as a group of assets with common characteristics that include: 2 Sensitivity to the same major economic and/or investment factors. Risk and return characteristics that are similar. A common legal or regulatory structure. When asset classes are defined in this manner, the relationship between the returns of two different asset classes would be expected to exhibit low correlations. This approach is useful in defining asset classes in general terms. However, some ambiguity remains in terms of the degree to which assets are influenced by specific economic factors and in the extent to which risk and return characteristics are similar. Furthermore, it does not consider the assets currently held by an investor in determining whether it should be considered for inclusion in an investor s portfolio. Asset Class Criteria for Portfolio Inclusion A second approach looks beyond specific investment attributes and allows any group of assets that is treated as 2 F. J. Fabozzi and H. M. Markowitz, The Theory and Practice of Investment Management, John Wiley & Sons, Inc., Hoboken NJ. International Forum of Sovereign Wealth Funds 19

20 an asset class by investment managers to be designated as an asset class as long as it meets the following four criteria for asset class status: 3 1. An asset class should be relatively independent of other asset classes in the investor s portfolio. 2. An asset class should be expected to raise the utility of the investor s portfolio without selection skill on part of the investor. 3. An asset class should be comprised of homogeneous investments. 4. An asset class should have the capitalization capacity to absorb a meaningful fraction of the investor s portfolio. Independence is necessary to avoid investing in assets that do not provide efficiency benefits to the portfolio by considering the redundancy of an asset class candidate against all of the other asset classes held by an investor. Independence can be tested by constructing a portfolio that minimizes tracking error to the proposed asset class by using a combination of the asset classes already held by the investor. If this mimicking portfolio exhibits a high tracking error to the candidate asset class then it is reasonable to assume relative independence. A low tracking error would suggest that the asset class would not provide meaningful benefits to the portfolio. The criterion for increasing the expected utility of the investor s portfolio distinguishes between return and diversification benefits. Because expected utility (Expected Return Risk Aversion x Variance) is a function of both return and risk, an asset class can prove beneficial through either its return or its ability to diversify a portfolio. That is, an asset class can be determined to be beneficial even if the average return it provides is below that of the current portfolio as long as it exhibits sufficient diversification properties. Requiring that utility be increased without the need for skill in asset selection differentiates between benefits provided by an asset class and those afforded by superior active management. The homogeneity requirement is to ensure that opportunities for diversification are not neglected. If assets designated as constituents of an asset class are, in fact, dissimilar then it is likely that greater efficiency can be achieved by partitioning the dissimilar components into another asset class. The fourth requirement addresses the capacity of an asset class. This is of particular importance to SWFs in that they represent some of the largest asset pools in the world. If an asset class is not sufficiently large enough to absorb a significant portion of a SWF s portfolio then it is likely that illiquidity would reduce expected return and increase risk to the point of eroding any expected benefit provided by the asset class. The four criteria detailed for asset class status provide a rigorous framework for defining and evaluating an asset class in the context of an investor s existing portfolio. However, it may be useful to have a simplified approach for assessing the benefits of an asset class or investment. Assuming that an asset class is constrained to a positive 3 M. Kritzman, Towards Defining an Asset Class, Journal of Alternative Investments 2, no. 1(1999): 79. International Forum of Sovereign Wealth Funds 20

21 weight, its impact on the portfolio s Sharpe ratio can be used to evaluate whether it should be considered for inclusion in a portfolio. Exhibit 1 presents an inequality that provides a framework for assessing the benefits of an asset class. 45,6 If the Sharpe ratio of the new asset class is greater than the Sharpe ratio of the portfolio multiplied by the correlation between the new asset class and the portfolio then the new asset class provides an expected benefit to the portfolio. Otherwise, the new asset class provides no benefit and may actually detract from portfolio efficiency. This evaluation framework can be applied to both asset classes as well as individual investments and will be particularly useful for evaluating investments for inclusion in portfolios, especially when considering benefits over different horizons. Exhibit 1: Sharpe Ratio Framework for the Evaluation of Asset Class Benefits Where: E(R new )-R f σ new E(R new ) = expected return of the new asset class σ new = standard deviation of the new asset class R f = risk-free rate E(R p ) = expected return of the portfolio σ p = standard deviation of the portfolio > ( E(R p)-r f ) ρ σ Rnew,R p p ρ Rnew,R p = correlation between the new asset class and the portfolio CFA Program Curriculum Level III, CFA Institute 5 M. Blume, The Use of Alphas to Improve Performance, Journal of Portfolio Management, no. 11 (1984): E. Elton, M. Gruber, and J. Rentzler, Professionally Managed, Publicly Traded Commodity Funds, Journal of Business, Volume 60, Issue 2 (1987): International Forum of Sovereign Wealth Funds 21

22 3. Estimating Asset Class Risk, Returns, and Correlations Markowitz s (1952) seminal work on portfolio theory begins with three simple sentences: The process of selecting a portfolio may be divided into two stages. The first stage starts with observations and experience and ends with beliefs about future performances of available securities. The second stage starts with the relevant beliefs about future performances and ends with the choice of portfolio. 7 It is evident from the very introduction of portfolio theory that beliefs are at the core of the process. This section focuses on stage one, where the identification of the working set of asset classes for portfolio construction proceeds to establishing future beliefs for the expected returns, standard deviations and correlations of those assets. These estimates are the raw materials from which efficient portfolios are developed. While history can (and should) inform those estimates, judgment plays a central role in how those estimates are developed and for what purpose. SWFs are generally tasked with the achievement of specific long-term objectives and are often required to balance those objectives while pursuing short-term opportunities. Furthermore, SWFs will inevitably be evaluated over short-term horizons. The balancing of this tension between short-term and long-term risks requires an understanding of asset class characteristics over different investment horizons. Unfortunately, the standard risk models used by academia and practitioners can underestimate risk over longer horizons. Consequently, it is critical that SWFs inform their portfolio construction decisions using methods that allow them to make the best use of available information in matching their specific objectives. Return A reasonable starting point for estimating expected returns is to assume that markets are fairly priced. This implies that the return provided by an asset class represents a fair compensation for the risk of the asset class within a broadly diversified market. These returns are called equilibrium returns, and are estimated by first calculating the beta of each asset class with respect to a broad market portfolio based on historical standard deviations and correlations. Estimates for the expected return of the market portfolio and the risk-free rate are then used to scale the returns of asset classes according to their betas. Therefore, the equilibrium return for each asset class is calculated as the risk-free return plus its beta multiplied by the excess return of the market portfolio. 7 H. Markowitz, Portfolio Selection, Journal of Finance, March International Forum of Sovereign Wealth Funds 22

23 While markets are rarely, if ever, in equilibrium, market forces tend to have a powerful and persistent pull towards producing long-run asset returns that are consistent with asset risks. Moreover, the expected return of each asset class can be adjusted easily to accord with views about departures from fair value. Consider this example: Suppose an investor estimates the market s expected return to equal 7.0% and the risk-free return to equal 3.0%. Exhibit 2 presents asset class betas with the selected market portfolio along with the respective equilibrium returns. These estimates, together with estimates of beta, are based on monthly returns from December 2000 through September Real Estate refers to listed real estate assets. Direct real estate would be expected to have lower volatility and expected returns. Exhibit 2: Expected Returns (Illustrative) Asset Class β Equilibrium Views Confidence Blend Developed Market Equities % % Emerging Market Equities % % Real Estate % % Global Credit % 4.2% 50.0% 4.5% Global Treasuries % 3.5% 25.0% 3.8% Source: State Street Global Exchange, Datastream Some asset classes may be expected to produce returns that differ from those that would occur if markets were in equilibrium and perfectly integrated, especially if they are not typically arbitraged against other asset classes. Suppose Global Credit is expected to return 4.2% and Global Treasuries to return 3.5% and that an investor has different degrees of confidence in these views. These views can be blended with equilibrium returns to derive expected returns. The blend column in Exhibit 2 shows the expected returns for each of the asset classes in this analysis given specific views and confidence in those views. While a variety of alternative methods to forecasting returns can be used, equilibrium returns serve as a reasonable baseline for comparison. For a thorough discussion of different approaches to estimating expected returns for both traditional and alternative asset classes the reader is directed to Ilmanen (2011). 9 8 The market and asset class proxies used were as follows: Market Portfolio 60% MSCI AC World Index + 40% Bloomberg Barclays Global Aggregate Bond Index Developed Market Equities MSCI World Index Emerging Market Equities MSCI Emerging Market Index Listed Real Estate FTSE EPRA/NAREIT Developed Real Estate Index Global Credit Bloomberg Barclays Global Aggregate Corporate Index Global Treasuries Bloomberg Barclays Global Treasury Index 9 Ilmanen, A. Expected Returns: An Investor s Guide to Harvesting Market Rewards. Chichester, West Sussex, U.K.: John Wiley & Sons, International Forum of Sovereign Wealth Funds 23

24 Risk, Co-movement, Risk Regimes, and the Investment Horizon The goal of a portfolio analysis is to identify the mix of assets that is expected to provide the highest return for the least amount of risk. While expected returns drive the composition of portfolios towards higher returns, estimates for the risk and co-movement characteristics of assets are what inform risk reduction. The challenge for SWFs is in specifying the risks to be mitigated and producing the relevant estimates for those risks. The first step in estimating risks and asset relationships is to understand what risk assets have exhibited historically. This is accomplished by calculating volatilities of asset classes and the correlations between each pair of assets over a relevant historical period. Generally, these historical estimates are calculated using time series of asset class returns at monthly intervals. SWFs will also be concerned with risk over longer intervals, such as 1-, 3-, 5-, or 10-years. Estimates for lowerfrequency, or rather, longer-horizon statistics are routinely extrapolated from higher-frequency monthly statistics using a conventional heuristic. That commonly applied heuristic is the scaling of risk by multiplying by the square root of time. For example, the standard deviation of monthly returns is multiplied by the square root of 12 to estimate the standard deviation of annual returns. A second heuristic is the commonly held belief that correlations are invariant to the time interval used to measure them. For example, the correlation of monthly returns for an asset pair is assumed to Counter to what financial theory suggests, the risk and diversification properties of assets differ depending on the time intervals over which they are measured. Assets that appear highly correlated over monthly intervals may be uncorrelated over multi-year intervals. To strike an effective balance between short- and long-term objectives, SWFs should account for this divergence when evaluating investment opportunities and forming portfolios. be the same as the correlation of annual returns. These methods are regularly used by academics and practitioners and are even programmed into most portfolio construction/management software applications. Unfortunately, they often misestimate the true risk presented by investments and can lead to significantly sub-optimal results for investors with long horizons. The reason for this misestimation is that these approaches assume that all returns are independently and identically distributed (I.I.D.). Contrary to this assumption, financial time series often exhibit serial dependence, mean reversion, trending, and/or risk clustering. This leads to asset values evolving through time in ways that are highly inconsistent with expectations drawn from their high-frequency standard deviations and correlations. To derive estimates that include information about the evolution of asset returns through time it is necessary to account for autocorrelations and lagged cross-correlations. Considering the unique characteristics of financial time series while estimating long-horizon risk can be accomplished by directly using cumulative periodic returns (e.g. 12-month, 36-month, 60-month, or 120 month) International Forum of Sovereign Wealth Funds 24

25 for all complete overlapping periods in the historical sample and then calculating the estimate statistics. This approach may provide a reasonable estimate if the historical period is sufficiently long. Alternatively, the following analytical approach can be used. 10 Estimating long-horizon risk begins with calculating the discrete returns of an asset class X over the high frequency interval. In this instance, a monthly interval is assumed and the percentage change in the price of X from one interval t-1 to the next t is: r t = P t P t-1-1 (1) It follows that the cumulative multi-period return equals the cumulative product of the quantity, one plus the single-period returns, minus one. The continuously compounded return of X is the logarithm of the quantity, one plus the discrete return. For ease of notation going forward, the continuously compounded return of asset X is denoted with a lower-case x: x t = ln ( P t P t-1 ) = ln (1+r t ) (2) The cumulative multi-period continuous return equals the cumulative sum of single-period continuous returns. The standard deviation of the cumulative continuous returns of x over the horizon specified as q periods, x t + +x t+q-1, is given by: σ(x t + +x t+q-1 ) = σ x q+2 q-1 k=1 (q-k)ρ xt,x t+k (3) where σ x is the standard deviation of x measured over single-period intervals. Note that if the lagged autocorrelations of x all equal zero, the standard deviation of x will scale with the square root of the horizon, q. However, to the extent the lagged auto-correlations differ from zero, extrapolating the single-period standard deviation this way to the longer-horizon standard deviation may provide a poor estimate of the actual longerhorizon standard deviation. To estimate long-horizon correlations, a second asset, Y, is introduced whose continuously compounded rate of return over the period t-1 to t is denoted as y t. The correlation between the cumulative returns of x and the cumulative returns of y over q periods, is given by: 10 It is assumed throughout this section that the instantaneous rates of return for all assets are normally distributed with stationary means and variances. International Forum of Sovereign Wealth Funds 25

26 q-1 qρ xt +,y t k=1(q-k)(ρ xt+k ),y t +ρx t,y ρ(x t + +x t+q-1, y t + +y t+q-1 ) = t+k q-1 q-1 q+2 k=1 (q-k)ρ xt,x t+k q+2 k=1 (q-k)ρ yt,y t+k (4) The numerator equals the covariance of the assets taking lagged correlations into account, whereas the denominator equals the product of the assets standard deviations as described by Equation (3). This equation allows for assumed values for the auto-correlations of x and y, as well as the lagged cross-correlations between x and y, in order to compute the correlations and standard deviations that these parameters imply over longer horizons. These values can be drawn from historical estimates or can be adjusted based on expectations. While particular choices for auto-correlation do not uniquely determine cross-correlations, it is important to note that choices for some of the lags do impose bounds on the possible values for other lags. Long horizon estimates calculated using equations 2, 3, and 4 are expressed in units of continuously compounded growth. The following formulas can be used to convert the mean and standard deviation of each asset into discrete units, which is required for optimization: μ d = e μ c +σ c 2 /2-1 (5) σ d = e 2μ c +σ c 2 (e σ c 2-1) (6) where μ d and σ d are the mean and standard deviation of the cumulative discrete returns, and μ c and σ c are the mean and standard deviation of cumulative continuous returns. Similarly, it is also necessary to compute the correlation between the cumulative discrete returns in terms of the means, standard deviations, and correlation ρ c of cumulative continuous returns. ρ d = e ρ c σ x,cσ y,c -1 (e σ 2 x,c -1) (e σ 2 (7) y,c -1) Estimates for long-horizon risk that account for autocorrelation and lagged cross-correlations are important beyond their use in portfolio optimization. Because the standard deviation measure is used in various ways for evaluating the performance of investment strategies and estimating active risk, understanding the implications of long-horizon risks can have an impact on the evaluation and selection of investment strategies. Consider that the Sharpe ratio, a common method of ranking investment strategies, uses standard deviation as the denominator. Estimates of long-horizon tracking error, which is the standard deviation of relative returns, which also incorporates information about asset correlations over longer horizons, can also be affected. Consequently, Information ratios, which equal the average excess return divided by tracking error, would be impacted. Kinlaw, International Forum of Sovereign Wealth Funds 26

27 Kritzman, and Turkington (2015) provide a detailed analysis of the impact of the misestimation of long-horizon risk on performance measurement. 11 Developing estimates that can provide for a more realistic understanding of the long horizon risks presented by investment strategies is an important part of the portfolio implementation and risk management process. Too often, investors rely on long-run averages to characterize the properties of asset classes. In practice, investments behave very differently during quiet markets than during turbulent markets, when risk and correlation are often higher. SWFs can benefit from estimating their risk exposure based on inputs from turbulent periods, when losses are most likely to occur. Full sample estimates of asset risks and correlations from a historical sample of monthly returns provide a reasonable starting point for a portfolio analysis. However, these estimates provide information regarding what occurs on average and mask the fact that risks and correlations are not necessarily stable through time. With respect to managing portfolio risk, it is useful to understand how these parameters change during periods of stress in the financial markets. This requires partitioning the historical sample of returns into normal and abnormal periods and can be accomplished through the use of a risk measure known as turbulence. Financial turbulence is defined as a condition in which asset prices, given their historical patterns of behavior, behave in an uncharacteristic fashion, including extreme price moves, decoupling of correlated assets, and convergence of uncorrelated assets. Financial turbulence often coincides with excessive risk aversion, illiquidity, and devaluation of risky assets. 12 Key benefits of using turbulence versus other measures of risk include the fact that turbulence can be estimated for any set of assets and that it considers the volatilities and correlations of a group of assets simultaneously. To calculate estimates of asset characteristics during turbulent periods it is first necessary to identify periods considered to be turbulent within a historical sample. For any group of assets, financial turbulence can be determined by identifying outliers using the following multivariate distance measure: d t =(y t -μ)σ -1 (y t -μ)' (8) Where: y t = vector of asset returns for period t μ = sample average vector of historical returns Σ = sample covariance matrix of return series y t 11 Kinlaw, W., Kritzman, M., and Turkington, D. The Divergence of High- and Low-Frequency Estimation: Implications for Performance Measurement. The Journal of Portfolio Management, Vol. 41, No Kritzman, M. and Li, Y Skulls, Financial Turbulence, and Risk Management. Financial Analysts Journal, vol. 66, no. 5 (September/October). International Forum of Sovereign Wealth Funds 27

28 The return series y t is assumed to be normally distributed with a mean vector μ and a covariance matrix Σ. For 12 return series, for example, an individual observation of y t would be the set of the 12 asset returns for a specific measurement interval. A tolerance distance is then chosen and the distance, d t, for each vector in the series is examined. If the observed d t is greater than the tolerance distance, the vector is defined as an outlier. For two uncorrelated return series, Equation 8 simplifies to the following equation, which is the equation of an ellipse with horizontal and vertical axes: d t = (y-μ y )2 + (x-μ x ) 2 σ2 y σ2 x (9) If the variances of the return series are equal, Equation 9 simplifies to a circle. For the general n-return normal series case, d t is distributed as a chi-square distribution with n degrees of freedom. Under this assumption, if an outlier is defined as falling beyond the outer 25 percent of the distribution and we have 12 return series, our tolerance boundary is a chi-square score of Using Equation 8, we calculate the chi-square score for each vector in our series. If the observed score is greater than 14.84, that vector is an outlier and considered to fall within the turbulent regime. This process partitions the historical sample of returns into normal and turbulent periods. Alternatively, a Markov switching model can be used to partition historical returns using turbulence or other indicators. 13,14,15 Estimates of asset risk and co-movement for turbulent periods are then calculated using the turbulent historical asset returns. This process can be used with portfolio assets to develop estimates based on intrinsic turbulence, which is turbulence that is specific to portfolio assets. Alternatively, the process can be used with a broad set of global assets, such as developed market equities, emerging market equities, global fixed income, and commodities, to identify a measure of extrinsic turbulence which can then be used to partition portfolio asset historical samples. Regardless of the type of turbulence indicator used, these types of estimates can be useful in constructing portfolios that are more resistant to turbulent periods. Exhibit 3 shows estimates of standard deviations and correlations using the full historical sample of returns, considering a 5-year investment horizon, and using turbulent regime information. Estimates are based on the historical sample of daily returns. A review of turbulent estimates shows higher volatilities and generally higher correlations than those seen in full sample estimates. 13 Kritzman, M., Page, S., and Turkington, D Regime Shifts Implications for Dynamic Strategies Financial Analysts Journal, vol. 68, no. 3 (May/June). 14 Daily returns are used to calculate turbulent estimates so as to include important asset characteristics that might be missed if monthly returns are used. 15 Alternatively, a turbulence index can be calculated and then used to identify periods where turbulence values exceed a particular percentile within a rolling historical sample window. International Forum of Sovereign Wealth Funds 28

29 Exhibit 3: Standard Deviation and Correlation Estimates for Portfolio Assets (Illustrative) Full Long Asset Class Sample Horizon Turbulent 1 Developed Market Equities 15.6% 28.2% 23.2% 2 Emerging Market Equities 22.6% 36.9% 27.6% 3 Real Estate 18.8% 36.8% 27.2% 4 Global Credit 6.3% 8.9% 5.7% 5 Global Treasuries 6.8% 11.1% 7.3% Full Sample Developed Market Equities Emerging Market Equities Real Estate Global Credit Global Treasuries Long-Horizon Developed Market Equities Emerging Market Equities Real Estate Global Credit Global Treasuries Turbulent Developed Market Equities Emerging Market Equities Real Estate Global Credit Global Treasuries Source: State Street Global Exchange, Datastream, FactSet Considerations for Alternative Assets Alternative asset classes such as private equity, real estate, and hedge funds may offer a range of benefits, but they also present analytical challenges. These types of investments have characteristics that differentiate them from traditional asset classes in three important ways: appraisal-based pricing, performance-based fees, and illiquidity. Each of these features can lead to substantial analytical challenges, and the potential for misguided conclusions. Quantitative methods need to be refreshed and adapted to apply to alternative asset classes. The common practice of using lagged appraisal-based pricing for non-traded portfolio companies (for private equity funds) or specific properties (for real estate funds) can lead to a dramatic underestimation of risk. Desmoothing of the illiquid asset returns is required to offset the reduction in the observed standard deviation introduced by appraisals and fair value pricing. This is accomplished by estimating a first order autoregressive model using least squares. International Forum of Sovereign Wealth Funds 29

30 The model is specified as: r t = A 0 +A 1 +r t-1 +ε (8) To de smooth the time series, returns are computed as: Where: r t ' = r t-a 1 r t-1 1-A 1 (9) r t ' = de smoothed return observation at time t r t = return observation at time t A 0 = intercept A 1 = regression coefficient ε = error term Alternative asset classes such as real estate and private equity present a range of analytical challenges to SWFs. Several features of these investments including the fees they charge, the way they are priced, and their illiquidity can lead investors to significantly underestimate their risk. It is essential for SWFs to adjust for these considerations when forming portfolios and evaluating risk. The asymmetric nature of performance-based fees is another consideration for alternative assets. These fees can counterintuitively make returns seem less risky, if they are not accounted for properly. Consider a fund charging 2% and a 20% performance fee. Estimating the standard deviation of the fund using net returns would underestimate risk due to the 20% performance fee for returns above the hurdle rate. It is necessary to correct for the downward bias in the observed standard deviation of the illiquid asset arising from the effect of performance fees. For a single fund that accounts for performance fees on an annual basis, the returns of the illiquid asset net of fees can be converted to returns gross of fees, as shown below. r n = r g -b - (max 0,p (r g -b)) (10) r n + b for r n <0 r g = { r n 1-p + b for r n 0 (11) Where r n = return net of fees r g = return gross of fees b = base fee p = performance fee International Forum of Sovereign Wealth Funds 30

31 In practice, a simulation can be performed to estimate the volatility dampening effect of performance fees when fee accrual accounting is used. On average, the true standard deviation is estimated to be approximately 1.09 times larger than the standard deviation estimated from monthly net returns with fee accrual. 16 It has already been shown that performance fees cause the observed standard deviation of a fund to understate its risk. Performance fees also reduce the expected return of a group of funds which charge performance fees beyond the average reduction of the individual funds expected returns. Consider, for example, a fund that charges a base fee of 2% and a performance fee of 20%. A fund that delivers a 10% return in excess of the benchmark on a $100 million portfolio will collect a $2 million base fee (2% x 100,000,000) and a $1.6 million performance fee (20% x (10,000,000 2,000,000)), for a total fee of $3.6 million. The investor s return net of fees, therefore, is 6.4%. Now suppose an investor hires two funds that each charges a base fee of 2% and a performance fee of 20%. Assume as well that these funds both have expected returns of 10.0% in excess of the benchmark. The expected fee for each fund is 3.6% (2% + 20% x (10% 2%)). Therefore, the investor might expect an aggregate return net of fees from these two funds equal to 6.4%. This expectation would be justified, however, only if both funds returns exceed the base fee. If, instead, one fund produces an excess return of 30.0% and the other a 10.0% excess return, and an equal amount of capital is allocated to each fund, the investor would pay an average fee of 4.8% rather than 3.6%, and the average return to the investor would equal 5.2% rather than 6.4%, even though the funds still have an average excess return of 10%. 17 These results are summarized in Exhibit 4. Exhibit 4: Multi-Fund Return Impact Excess Return Manager Fee Return to Investor Fund % 3.6% 6.4% Fund % 3.6% 6.4% Average 10.0% 3.6% 6.4% Fund % 7.6% 22.4% Fund % 2.0% -12.0% Average 10.0% 4.8% 5.2% Impact 1.2% Source: State Street Global Exchange 16 This is based on a simulation of 1,000 years of monthly fund returns from a normal distribution with an annualized mean of 8% and an annualized standard deviation of 8%. It is assumed that an annual base fee of 2% and an additional annual hurdle rate of 3.5% before performance fees are charged. We record a 20% annual performance fee on an accrual basis. 17 This difference is equivalent to the difference in value between a portfolio of options and an option on a portfolio. International Forum of Sovereign Wealth Funds 31

32 This result is specific to the assumptions of this example. Nevertheless, it is easy to determine the typical reduction in expected return by applying Monte Carlo simulation. Consider investment in 10 funds, each of which has an expected excess return of 70%, a standard deviation of 15.0%, and a correlation of 0% with the other funds. Also assume that LIBOR equals 4.0%. With these assumptions, the reduction to the collective expected return of the funds equals about 0.7%. If the funds correlations were higher, the reduction would be smaller and vice versa. This reduction in the collective return is a hidden fee arising from the fact that investors pay for outperformance but are not reimbursed for underperformance. In principal, this effect could be somewhat muted because most performance fee arrangements include claw back provisions which require funds to offset prior losses before collecting performance fees. In most cases, though, underperforming funds are either terminated, or the performance fees are reset without reimbursement for prior losses. One of the most important characteristics of alternative investments that must be assessed is liquidity, or rather, the fact that they are generally less liquid than traditional assets. There are two aspects to consider. First, how much of an illiquidity premium should be demanded from an alternative asset? Second, how should investors account for illiquidity in the portfolio selection process? While there is little consensus amongst academics regarding how much of a liquidity premium markets actually provide, it is possible to determine the premium an investor should demand based on an investor s specific uses of liquidity. Locking up capital imposes a cost. This is because the portion of the portfolio allocated to illiquid investments is no longer available for passive rebalancing, market timing, raising cash to meet periodic demands, exiting unproductive investments, or taking advantage of new opportunities that might arise in the future. The size of this cost is different for every investor, but it can be quantified. To the extent an investor foregoes some portion of the benefits provided by liquidity, an allocation to illiquid assets should be justified by an offsetting expected return that is equal to or greater than the penalty imposed by illiquidity. The framework for incorporating liquidity in the portfolio construction context treats liquidity as a shadow allocation that either bestows benefits or imposes penalties. If an investor deploys liquidity to raise a portfolio s expected utility beyond its original expected utility, a shadow asset is attached to tradable assets. If instead an investor deploys liquidity to prevent a portfolio s expected utility from falling, a shadow liability is attached nontradable assets. Because the impact of illiquidity is path dependent, the value of these assets and liabilities must be estimated using simulation methods. This allows for a great deal of flexibility in extending this type of analysis to address real-world concerns. Changing risk regimes, different investment horizons, varying degrees of liquidity, trading costs, capital calls, and future cash outflows, amongst other things, can all be accounted for within this framework. The first step for an SWF is to identify its specific uses of liquidity. The ability to trade can be used to play International Forum of Sovereign Wealth Funds 32

33 defense, for example responding to capital calls and rebalancing the portfolio. It can also be used to play offense, such as engaging in market timing or seizing new investment opportunities. Using realistic assumptions, thousands of hypothetical future portfolio return paths can be generated that account for the fund s specific uses of liquidity. Two set of portfolio returns are simulated. The first, assumes all assets are liquid and tradable. The second uses the liquidity characteristics of the assets being considered. This highlights an important benefit of this approach; it allows investors to address absolute and partial illiquidity within a single framework. The differences between the two simulations are measured using certainty equivalent returns to account for the differences in return as well as the differences in risk. 18 For an investor with log wealth (meanvariance) utility, the certainty equivalent return is computed as: r CE =μ T w-λw T Σw (12) Where: r CE = certainty equivalent return μ = expected returns Σ = covariance matrix λ = coefficient of risk aversion w = portfolio weights The analytical construct of this framework can be demonstrated using a two-asset example. First, a meanvariance analysis is used to solve for optimal allocations to liquid equity and liquid bonds without considering the effect of liquidity. 19 Optimal weights are identified by maximizing expected utility: E(U)= r e w e -r b w b -λ(σ 2 e w 2 e +σ 2 b w 2 b +2ρ b,e σ e σ b w e w b ) (13) Where: E(U) = expected utility r e = expected equity return r b = expected bond return σ e = equity standard deviation σ b = bond standard deviation w e = equity weight w b = bond weight 18 The certainty equivalent return for a given portfolio is the amount of risk free return required such that a given investor is indifferent between receiving that return and holding a particular risky portfolio. 19 While mean-variance optimization is used in this illustration, it can be applied to any portfolio formation process, including full-scale optimization, multi-period models, and even heuristic approaches. International Forum of Sovereign Wealth Funds 33

34 λ = coefficient of risk aversion ρ b,e = correlation of equity and bonds The weights that equate the marginal utilities of equities and bonds, as shown below, are those that are optimal. U w e = r e -λ(2σ e 2 w e +2ρ b,e σ e σ b w b ) (14) U w b = r b -λ(2σ b 2 w b +2ρ b,e σ e σ b w b ) (15) Next illiquid equity is substituted for liquid equity. However, two adjustments are required. First, the downward bias in the illiquid asset s observed standard deviation that results from the effect of performance fees is corrected. Second, illiquid equity returns are de-smoothed to offset the reduced observed standard deviation introduced by appraisals and fair-value pricing. A shadow asset is then attached to the bond portion of the portfolio and the expected return, standard deviation, and correlation are re-stated to account for the presence of the shadow asset, as shown in equations (16), (17), and (18). 20 r bl = r b +r l (16) σ 2 bl = σ 2 2 b +σ l (17) ρ bl,e = ρ b,e σ b σ bl (18) Where: r bl = expected return of bonds with shadow liquidity asset r l = expected return of shadow liquidity asset σ bl = standard deviation of bonds with shadow liquidity asset σ b = standard deviation of shadow liquidity asset ρ bl,e = correlation of bonds (with shadow liquidity asset) and equity Exhibit 5 presents a simple numerical illustration of the analytical framework. It shows how the required return for equities changed as liquid equities are switched to illiquid equities and then, step by step, adjusted for the effects of performance fees, smoothing, and the inclusion of the shadow asset. 20 It is assumed that the shadow asset is uncorrelated with both stocks and bonds; an assumption that can be relaxed. International Forum of Sovereign Wealth Funds 34

35 Exhibit 5: Required Return for Liquid and Illiquid Equities Liquid Equity Illiquid Equity Correct for Fee Correct for Correct for Unadjusted Asymmetry Smoothing Liquidity Required equity return 8.75% 5.31% 5.75% 13.75% 15.5% Bond return 5.00% 5.00% 5.00% 5.00% 7.00% SLA return 2.00% 2.00% 2.00% 2.00% 2.00% Equity standard deviation 20.00% 7.50% 10.00% 30.00% 30.00% Bond standard deviation 5.00% 5.00% 5.00% 5.00% 7.07% SLA standard deviation 5.00% 5.00% 5.00% 5.00% 5.00% Equity/bond correlation Risk Aversion Equity weight 50% 50% 50% 50% 50% Bond weight 50% 50% 50% 50% 50% Marginal utility equities Marginal utility bonds Derivative difference Source: State Street Global Exchange, Datastream Column 1 shows that it is optimal to split the portfolio equally between liquid equity and liquid bonds, given the indicated assumptions for their expected returns, standard deviations, and correlation, and assuming that an the investor s risk aversion coefficient equals 1. Notice that their marginal utilities are equal; demonstrating that expected utility cannot be improved by altering weights. At this point, the expected return and risk of the shadow asset have not yet been considered. In column 2, illiquid equity is substituted for liquid equity. It is now necessary to solve for the return required to produce the same weight, given the illiquid equity s observed standard deviation. Biases introduced by performance fees and smoothing have not yet been corrected. In column 3, the effect of performance fees on the observed standard deviation and the illiquid equity correlation is corrected using equations (10) and (11). This correction raises the illiquid equity s required return. In column 4, equations (8) and (9) are used to correct for fair-value pricing, which shows that investors should require a premium to justify the substitution of illiquid equity for liquid equity. In column 5, the shadow liquidity asset is introduced and the bond component s expected return and standard deviation, as well as its correlation with illiquid equity is adjusted using equations (16), (17), and (18). This final step gives the total expected return required of illiquid equity, taking into account the distortions introduced by performance fees and smoothing and the opportunity cost of forgoing liquidity. The required illiquidity premium equals the difference between the required return in column 5 and the required return in column 4, which in this example 1.75%. This required illiquidity premium is less than the shadow liquidity asset s 2% expected return, because the shadow asset introduces risk as well as incremental expected International Forum of Sovereign Wealth Funds 35

36 return to the portfolio. Suppose that illiquid equity has an expected return of 14.70% instead of 15.50%, offering an illiquidity premium of only 0.95%, compared to the required illiquidity premium of 1.75%. In this case, the optimal allocation to illiquid equity would fall from 50% to 45%, assuming all other assumptions remained unchanged. Alternatively, a 50% allocation to illiquid equity can be maintained. It would then be necessary to solve for the shadow asset s required return, given an expected return of 14.70% for illiquid equity. In this case, an expected return of only 1.20% would be required for the shadow asset instead of 2%. 21 It is important to note that while there may be a single market price for liquidity, investors do not benefit equally from liquidity. Two investors with identical expectations and preferences, but different in the extent to which they benefit from liquidity, should not hot the same portfolio, just as investors with higher tax rates should be more inclined than investors with low tax rates to hold tax-favored assets, such as municipal bonds. 21 This analytical framework is presented for expository purposes. In practice, one could simply introduce the shadow asset as an overlay that does not require capital and constrain its weight to equal the sum of the liquid assets. International Forum of Sovereign Wealth Funds 36

37 4. Portfolio Construction for the Short- and Long-term This section proceeds to stage two of the portfolio analysis process described by Markowitz (1952) where future beliefs about the assets classes are transformed into concrete portfolio weights and ultimately efficient portfolios. With the various estimates and adjustments presented in the previous section, a SWF can now shape the portfolio analysis to address specific investment objectives. Multi-Risk Optimization: Balancing Short- and Long-Horizon Risks If investors care only about performance over short horizons or within long horizons they could construct portfolios that reflect aversion to risk based on the covariances of monthly returns. Alternatively, if they are concerned only with performance at the conclusion of long horizons, they could estimate the covariance matrix from long-horizon returns, such as three years. Or, as is the most likely case, they care about performance over both short and long horizons and could include separate estimates of risk; one based on a covariance matrix of monthly returns and one based on a covariance matrix of triennial returns. It is straightforward to augment the standard Markowitz framework to include additional terms for aversion to long-horizon risk and long-horizon variance. 22 E(U)=μ-λ H σ H 2 -λ L σ L 2 (19) In Equation 19, E(U) is expected utility, µ equals portfolio expected return, λ H is aversion to risk estimated from high-frequency returns, σ 2 H is portfolio variance based on high-frequency returns, λ L is aversion to low-frequency 2 risk, and σ L is portfolio variance based on low-frequency returns. It also possible to preserve the original Markowitz format by blending the two covariance matrices in accordance with one s relative aversion to high-and low-frequency risk. E(U)=μ-λ B σ B 2 (20) To provide an example of how balancing these risks affect the composition of portfolios, Exhibit 6 presents an iso-expected return curve. The portfolios along this curve all have the same expected return, but have different combinations of monthly and triennial risk. This curve is constructed by solving for optimal weights using Equation (19), initially assuming no aversion to triennial risk. This first optimization provides the extreme upperleft portfolio on the curve. The aversion to triennial risk is then progressively increased while holding expected 22 Chow, Jacquier, Lowry, and Kritzman [1999] deploy the same methodology to construct portfolios for which the investor has different degrees of aversion to risk during turbulent regimes and to risk during quiet regimes. International Forum of Sovereign Wealth Funds 37

38 Long-Horizon Risk (Triennial) Asset Allocation for the Short- and Long-Term return constant, which moves the optimal portfolio down and right along the curve. This curve represents the available choices to an investor who cares about aversion to both short-term and long-term losses. Exhibit 6 shows that it is possible to construct portfolios that simultaneously optimize short- and long-term risk in a manner that is consistent with an investor s relative aversion to two measures of risk. Exhibit 7 then shows the weights and expected returns of three selected portfolios along the curve as well as their monthly and triennial risk. Exhibit 6: Iso-Expected Return Curve Balancing Short-and Long-Horizon Risk 13.65% 13.60% P % 13.50% 13.45% 13.40% 13.35% 13.30% P % 13.20% P % 11.54% 11.55% 11.56% 11.57% 11.58% 11.59% 11.60% 11.61% Short Horizon Risk (Annual) Source: State Street Global Exchange Exhibit 7: Weights, Expected Returns, and Standard Deviations of Selected Portfolios Source: State Street Global Exchange Asset Class Portfolio 1 Portfolio 2 Portfolio 3 Short-Horizon Blended Long-Horizon Developed Market Equities 60.71% 54.48% 49.03% Emerging Market Equities 6.22% 12.11% 16.09% Real Estate 1.75% 0.00% 0.00% Global Credit 0.00% 0.00% 0.00% Global Treasury 31.32% 33.41% 34.88% Expected Return 7.37% 7.37% 7.37% Full Sample Standard Deviation 11.55% 11.57% 11.61% Long- Horizon Standard Deviation 13.58% 13.26% 13.19% International Forum of Sovereign Wealth Funds 38

39 This same approach can be used to balance other combinations of risks. For example, because investors are often measured against some benchmark or peer group, it may be useful to balance absolute and relative risks. Here an investor could incorporate their aversion to absolute risk and their aversion to relative risk (tracking error) in the optimization process. This simultaneously addresses concerns about absolute performance and relative performance. However, instead of producing an efficient frontier in two dimensions the optimization process produces an efficient surface in three dimensions: expected return, standard deviation, and tracking error. The efficient surface is bounded on the upper left by the traditional mean-variance efficient frontier, which comprises of efficient portfolios in dimensions of expected return and standard deviation. The left most portfolio on the mean-variance efficient frontier is the minimum risk asset. The right boundary of the efficient surface is the mean-tracking error efficient frontier. It comprises portfolios that offer the highest expected return for varying levels of tracking error. The left most portfolio on the mean-tracking error efficient frontier is the benchmark portfolio because it has no tracking error. The efficient surface is bounded on the bottom by combinations of the minimum risk asset and the benchmark portfolio. All of the portfolios that lie on this surface are efficient in three dimensions. However, it does not necessarily follow that a three-dimensional efficient portfolio is always efficient in any two dimensions. Consider, for example, the minimum risk asset. Although it is on both the mean-variance efficient frontier and on the efficient surface, if it were plotted in dimensions of just expected return and tracking error, it would appear very inefficient if the benchmark included high expected return assets such as stocks and long-term bonds. This asset has a low expected return compared with the benchmark and yet a high degree of tracking error. Risk Regimes and Conditioned Covariance To identify optimal portfolios based on views and attitudes toward two risk regimes, the standard mean variance objective function is first augmented to include a normal covariance matrix Σ N and an event covariance matrix Σ E that reflects returns that occur during specific events such as periods of high turbulence, which are then assigned probabilities. The vector of returns has a mean µ and a covariance matrix Σ. We replace the full-sample covariance matrix Σ with pσ N +(p-1)σ E (21) where p is the probability of falling within the normal sample and 1 p is the probability of falling within the event sample. Substituting these two covariance matrixes into the standard equation for the expected utility, EU, of a portfolio with a weight vector w yields: International Forum of Sovereign Wealth Funds 39

40 EU=w ' μ-λ[pw ' Σ N w+(1-p)w ' Σ E w] (22) where λ equals aversion to full-sample risk. Equation (22) allows an investor to express views about the respective probabilities of the two risk regimes, but it assumes that they are equally averse to both regimes. To differentiate aversions to the two regimes, values are assigned to reflect the relative aversion to each of the regimes. Those values are then rescaled so that they sum to 2. For example, suppose aversion to normal risk equals 2 and aversion to event risk equals 3. Aversions are then rescaled to equal 0.80 for normal risk and 1.20 for event risk as follows: λ N * = 2λ N λ N +λ E (23) λ E * = 2λ E λ N +λ E (24) The probability-weighted normal and event covariance matrixes are then multiplied by their respective rescaled risk aversions: EU=w ' μ-λ[λ N * pw ' Σ N w+λ E * (1-p)w ' Σ E w] (25) Although Equation (25) has the virtue of transparency, it is somewhat cumbersome. It can be simplified by defining a grand or conditioned covariance matrix to equal: Σ * =λ N * pσ N +λ E * (1-p)Σ E (26) This definition allows the recasting of the objective function to EU=w ' μ-λ(w ' Σ * w) (27) which is the original Markowitz objective function. The conditioned covariance, Σ *, can then be used as part of the standard portfolio optimization framework. A probability-weighted covariance matrix as given by equation (21) can also be used for portfolio construction or in calculating forward looking risk estimates that are aligned with a SWF s probability beliefs about the likelihood of normal and event periods in the future. International Forum of Sovereign Wealth Funds 40

41 Risk Regimes and Tactical Shifts While the identification of risk regimes was presented as a backward looking exercise in partitioning a historical sample to develop regime specific estimates of asset characteristics, the process can also be used to inform tactical portfolio allocation decisions to respond to changing risk conditions. This can provide for improved performance as well as for more stable portfolio risk characteristics through time. Financial turbulence, presented in Section 3, has been shown to be an effective risk measure for informing tactical shifts. The differential performance of risky strategies during turbulent and nonturbulent periods, together with the persistence of turbulence, can make it particularly useful in conditioning exposure to risk. Another measure of risk that has been shown to be useful in measuring and predicting systemic risk in the financial markets and informing tactical shifts is the absorption ratio. The absorption ratio measures systemic risk and is calculated by measuring the proportion of variation in asset returns that is explained or absorbed by a fixed number of factors. Rather than attempt to select specific relevant factors, a well-known statistical procedure called Principal Components Analysis is used to identify the factors (or eigenvectors) that are most important in terms of their contribution to overall variation in asset returns. Equation (28) shows the formula for calculating systemic risk. AR= n i=1 N j=1 σ 2 Ei σ 2 Aj (28) Where: AR = absorption ratio N = number of assets n = number of eigenvectors in numerator of absorption ration σ 2 Ei = variance of the i th eigenvector σ 2 Aj = variance of the j th asset The absorption ratio measure captures the extent to which a set of assets is unified or tightly coupled. A high absorption ratio indicates that assets are tightly coupled and are collectively fragile in the sense that negative shocks can travel more quickly and broadly than when assets are loosely linked. In contrast, a low absorption ratio implies that risk is distributed broadly across disparate sources; hence, the assets are less likely to exhibit a unified response to bad news. In short, the absorption ratio can be used to distinguish fragile market conditions from resilient market conditions. While the level of absorption does provide a measure of market fragility, the level is not particularly useful as a tactical signal as market fragility may remain elevated for extended periods of International Forum of Sovereign Wealth Funds 41

42 time. What is useful is to identify significant changes in the level of absorption. To do this, an investor can calculate the standardized shift in the level of an absorption index which is equal to today s value minus the previous year s average, divided by the standard deviation over the previous year. High risk or fragile periods can then be identified as those when the absorption ratio exhibits a 1-sigma increase and more resilient periods can be identified as those when the absorption ratio sees 1-sigma decrease. It should be noted that a high absorption ratio does not necessarily lead to asset depreciation or financial turbulence. It is simply an indication of fragility. Financial turbulence and systemic risk measures can generally be applied to any set of asset returns. They can be used individually to provide specific information about risk or in concert to provide a more holistic view of the risk environment. Furthermore, the risk measures can be used with portfolio asset returns in order to provide a measure of intrinsic or portfolio specific risk or they can be calculated using a broad set market index returns to measure extrinsic or broad market risk. The identification of a risk regime can be accomplished through the calculation of a selected risk measure (or combination of risk measures) and determining if a specified threshold has been breached, or through the use of a Markov switching model to determine if the current period falls within a particular risk regime. Portfolio allocations can then be adjusted in a variety of ways given the determination of being in one risk regime or another. For example, exposure to risk can be scaled according to pre-determined levels of turbulence such that an investor accepts increasing amounts of risk when exposure to risk is most likely to provide rewards and decreases exposure to risk when exposure to risk has a high probability of resulting in a loss. Alternatively, an investor can identify tilts away from assets that tend to underperform towards assets that tend to outperform given a particular risk regime. Investor Utility Preferences Institutional investors typically employ mean-variance optimization to create portfolios, in part because it only requires knowledge of the expected returns, standard deviations and correlations of the portfolio s components. The approach is aligned with the use of log wealth utility which is well documented and can be approximated by a quadratic that is a function of mean (expected return) and variance. The significance of approximation is that if log-wealth utility can be well approximated using mean and variance for a sufficiently wide range of returns, then maximizing a function of mean and variance will approximately maximize expected utility. In the case of log wealth utility, maximizing utility is the equivalent of maximizing the geometric mean (long run growth rate) of the portfolio since the log of 1+geometric mean is the average of the logs of (1+return). International Forum of Sovereign Wealth Funds 42

43 While the classical portfolio construction framework does not make assumptions about investment returns conforming to a normal, bell-curve distribution, it does assume that investor satisfaction adjusts smoothly to changes in wealth and that the level of satisfaction can be approximated by mean and variance. In many cases, these assumptions hold, and this approach produces reasonable results. However, some investors may have alternative concerns. A full-scale approach to portfolio construction can provide increased flexibility and useful insights in such cases. The table in Exhibit 8 shows log-wealth utility at various return levels alongside utility calculated using a quadratic approximation based on mean and variance. Returns within the range of approximately -30% and +40% are virtually identical to one another. 23 Although differences appear at - 40% and +50%, the approximation still provides fairly reasonable results. Outside of this range the approximation deteriorates at an increasing rate. The chart in Exhibit 8 provides a graphical comparison of the log-wealth utility function and the quadratic approximation. In 1956, Markowitz developed the Critical Line Algorithm (CLA) that provides an efficient approach to tracing out a mean-variance efficient frontier. Significant advances in computing power since then now allow for direct utility maximization, also known as full-scale optimization, to be used as an alternative. With this approach a sophisticated search algorithm is used to identify a single optimal portfolio or to trace out an efficient frontier of portfolios based on any description of investor utility preferences. 24 The process uses a sample of asset returns and calculates a portfolio s utility for every period in the sample and the sums the utilities, iteratively searching to identify the combination of asset weights that yields the highest expected utility over the entire sample. 25 When used with mean and variance, full-scale optimization provides (virtually) identical results to the CLA approach. Therefore, full-scale optimization is most useful when considering alternative utility preferences or risk measures. 23 Markowitz, H. Portfolio Selection, Malden, MA: Blackwell Publishing, Adler, T. and Kritzman, M., Mean-Variance versus Full-Scale Optimisation: In and Out of Sample, Journal of Asset Management, Vol. 7, 5, , (2007). 25 Full scale optimization generally incorporates a historical sample of returns rescaled to reflect forward-looking risk and return estimates. The relationships between assets are retained in the return series used rather than being provided explicitly. Because actual returns are used, it incorporates all of the features of the asset returns in the empirical sample that are not captured by descriptive summary statistics (mean, variance, and correlations), including skewness and kurtosis. Therefore, the historical period used should be sufficiently long to be representative of asset characteristics and relationships. International Forum of Sovereign Wealth Funds 43

44 Utility Asset Allocation for the Short- and Long-Term Exhibit 8: Comparison of Log Wealth Utility and a Quadratic Approximation of Log Wealth Utility R Ln(1+R) Quadratic Approximation (R 0.5 R 2 ) -50% % % % % % % % % % % % -40% -30% -20% -10% 0% 10% 20% 30% 40% 50% Return Log Wealth Utility Ln(1+R) Quadratic Approximation (R R 2 ) An example of an alternative utility preference is one that assumes log wealth utility above a particular return threshold and a sharply decreasing utility (increasing loss aversion) below that threshold. This is known as a kinked utility function because the function changes abruptly, or kinks, at the threshold return level. The threshold can be set at zero to describe in investor with a high aversion to loss or can be set at some other threshold to describe an investor that requires a minimum level of returns to meet important long-term objectives. Exhibit 9 presents a kinked utility function with the return threshold, θ, equal to 5% and the degree of loss aversion, α, equal to 5. International Forum of Sovereign Wealth Funds 44

45 Utility Asset Allocation for the Short- and Long-Term Exhibit 9: Comparison of Kinked Utility (θ = 5%, α = 5) and Log Wealth Utility Functions % -40% -30% -20% -10% 0% 10% 20% 30% 40% 50% Return Kinked Utility ln(1+r), for R > θ U(R)= { - ( 1+R 1+θ ) ln(1+θ), for R θ Log Wealth Utility Ln(1+R) Full scale optimization can accommodate a wide range of investor preferences including kinked utility. However, the implications of optimizing to specific utility functions or using alternative risk measures should be considered carefully as investor preferences that might be described by alternative functions could defy the most basic levels of common sense. There are return trade-offs to be considered as well. Markowitz (1959) presents a thorough discussion about the desirability of using alternative measures of risk and the utility functions implied by those risk measures (e.g. semi-variance, expected value of loss, expected absolute deviation, probability of loss, and maximum loss). 26 Markowitz and Blay (2013) explore additional alternative measures of risk including mean absolute deviation, Value-at-Risk, and Conditional Value-at-Risk. 27 Stability-Adjusted Portfolio Optimization One of the criticisms of portfolio optimization is that it relies on estimates about the future risk, return, and relationship characteristics that are likely to be wrong and that optimizers will tend to maximize errors by loading up on assets for which returns are overestimated and risk is underestimated. Unfortunately, critics fail to point to a viable alternative to using observations, experience, beliefs, and judgment in determining how to confront an uncertain future. It should be understood that even the most thoughtful and careful analyst relying on 26 Markowitz, H. Portfolio Selection, Malden, MA: Blackwell Publishing, Blay, K., and Markowitz. H. Risk-Return Analysis: The Theory and Practice of Rational Investing (Volume One). New York, NY: McGraw Hill, International Forum of Sovereign Wealth Funds 45

46 multi-decade samples of historical data to forecast covariances will be faced with at least three sources of estimation error. First, small-sample error arises when covariances from a long sample are used to forecast covariances of a specific smaller sample. Even though the true covariances of a long sample may be known, the realization of those covariances in shorter sub-samples can be meaningfully different. Second, independentsample error arises when known covariances from one sample are projected onto a separate, independent sample. Third, interval error arises when covariances of high-frequency returns, such as monthly returns, differ from covariances of longer-period returns, such as five-year returns. While estimation errors are a virtual inevitability, it is an aspect of the portfolio construction process that should be addressed. Investors typically deal with estimation error by reducing reliance on the historical data which is error-prone. For example, one popular technique is called Bayesian shrinkage, in which the estimate of an asset s volatility, for example, is blended with the average volatility of all the assets under consideration. This process makes portfolio assets appear more similar to each other, effectively limiting the likelihood of errors influencing optimization outcomes. Stability adjusted optimization takes a different approach. 28 Rather than attempting to mitigate estimation error by debasing the information content of historical covariances, it explicitly incorporates information about estimation error into the portfolio formation process. It accomplishes this by measuring the estimation error, or stability, of portfolio assets and then producing stability-adjusted return distributions that incorporate the estimation error. Efficient portfolios are then identified by optimizing with the adjusted return distributions. Producing stability-adjusted return distributions that account for a composite measure of estimation error comprising small sample error, independent sample error, and interval error is accomplished using the following process: 1. Select a large sample of returns for the assets under consideration. 2. Select a sub-sample from this large sample and compute its covariance matrix based on returns of the same interval as the investment horizon Subtract the sub-sample covariances from the covariances estimated from the remaining observations in the large sample. These differences represent a composite error comprising small-sample error, independent-sample error, and interval error. 4. Select a new sub-sample that partly overlaps with the first sub sample and again compute the differences from the covariances estimated from the remaining observations of the large 28 Kritzman, M. and Turkington, D Stability-Adjusted Portfolios. The Journal of Portfolio Management, Vol. 42, No. 5, Special Quantitative Equity Strategies Issue (pp ). 29 For example, the original sample may comprise monthly returns, but the investment horizon may be five years. Therefore, the covariance matrix using five-year, overlapping returns would need to be estimated. Log returns are used to calculate covariance matrices in order to remove the effect of compounding. In particular, each return observation is transformed by taking the natural logarithm of one plus the return. The multi-period compounded returns of a normally distributed asset will be highly skewed due to compounding and therefore not normally distributed; however the logarithms of the long-period returns will be normally distributed. International Forum of Sovereign Wealth Funds 46

47 sample Proceed in this fashion until errors in covariances from all overlapping sub-samples are computed For all sub-samples, add the errors to the covariances of a base-case sample, which, for example, could be the median sub-sample. 32,33 Then, assuming normality, generate simulated return samples from each error-adjusted covariance matrix. 7. Combine these return samples into a new large sample, which can be thought of as a stabilityadjusted return sample. There are several features of this process that should be noted. First, the composite errors incorporate all three sources of error. They reflect small-sample error because the sub-samples are smaller than the original sample. They reflect independent-sample error, because each sub-sample is distinct from the remaining observations in the large sample. And they capture interval error, because the sub-sample covariances are estimated from longer-interval returns than the returns used to estimate the large-sample covariances. It should also be noted that the resultant return distribution will not be normal despite the distributions of the sub samples as well as the Central Limit Theorem. The stability-adjusted return distribution should be expected to have fatter tails than a normal distribution. The Central Limit Theorem states that the sum of independent random variables, which themselves need not be individually normally distributed, will approach normality as the quantity of random variables increases. 34 But we are not summing random variables. We are combining distributions. For example, suppose the daily returns of a particular asset for a given month are approximately normally distributed around a mean of 0.5%. And suppose their returns in the following month are again approximately normal, but this time around a mean of -0.5%. If these daily returns are summed for the first day of the two months, the second day of the two months, and so on, the 20 summed observations will also be normally distributed, but around a mean of 0.0%. However, the 40 daily returns for the two-month period will not be normally distributed. They will have a bimodal distribution with some observations clustering around a peak of 0.5% and others clustering around a peak of -0.5%. Constructing efficient stability-adjusted portfolios is a matter of identifying the desired utility function (e.g.: log- 30 Overlapping samples are used to mitigate the distortion that could be caused by choosing a particular start date with independent samples. For example, it could be that a particular period has very high risk and the subsequent period has very low risk. If we were to choose a start date such that we combined half of the first period with half of the subsequent period, we would not capture these extreme episodes of risk. 31 Any strong directional bias from the distribution of errors is removed by subtracting the median error from each individual sub-sample error. 32 The full-sample covariance matrix should not be used as the base case because the full sample embeds the small-sample error of all the sub samples. 33 Some of the sub-sample covariance matrices may not be positive semi-definite. Therefore standard corrections are applied to render all covariance matrices invertible. 34 In addition to independence, the Central Limit Theorem also assumes finite variances. International Forum of Sovereign Wealth Funds 47

48 wealth or kinked) and then using full-scale optimization with stability-adjusted return samples. 35 While mean variance optimization can provide reasonable results, the use of full-scale optimization accounts for every feature of the data, even beyond kurtosis and skewness and is thus suitable for use with stability-adjusted distributions and for utility functions that cannot be described by mean and variance. The stability-adjusted optimization approach yields portfolios with different asset weights than when ignoring errors or using Bayesian shrinkage for a fixed level of expected return. Stability-adjusted portfolios also exhibit more stable risk over time. Other applications of the approach where accounting for errors has proven beneficial are index tracking, proxy hedging for expensive currencies, and tracking liabilities or inflation. 35 Although it could be prohibitively challenging to test every possible asset mix in small increments, there are search algorithms that yield a reasonably reliable solution in a few seconds. A particular algorithm based on evolutionary biology initiates several searches simultaneously and iteratively terminates those searches that are sure to fail, thus transferring the search energy to the remaining feasible searches. International Forum of Sovereign Wealth Funds 48

49 5. Evaluating Portfolio Risk Investors typically measure risk as the probability of a given loss or the amount that can be lost with a given probability at the end of their investment horizon. This view of risk only considers the result at the end of the investment horizon and ignores what might happen along the way. This section focuses on techniques for measuring and communicating the risks associated with portfolios and considers various aspects of those risks that can help inform strategic portfolio choice as well as active decisions. Risk and the Investment Horizon Exhibit 10 illustrates the distinction between risk based on ending outcomes and risk based on outcomes that might occur along the way. Each line represents the path of a hypothetical investment through four periods. The horizontal line represents a loss threshold, which in this example equals 10%. Exhibit 10 reveals that only one of the five paths breaches the loss threshold at the end of the The approach to estimating risk exposure that is espoused by most financial textbooks contains a crucial flaw. This approach typically measures the probability (or size) of a loss that might occur at the END of an investment horizon, whether that horizon is a day, a month, or many years. In practice, most investors are equally concerned with how interim losses might accumulate along the way. Indeed, to reach the long-term, an investor much first survive the short term. horizon; hence we might conclude that the likelihood of a 10% loss equals 20%. However, four of the five paths at some point during the investment horizon breach the loss threshold, although three of the four paths subsequently recover. If we also care about the investment s performance along the way to the end of the horizon, we would instead conclude that the likelihood of a 10% loss equals 80%. One might argue that calculation of daily value at risk measures a strategy s exposure to loss within an investment horizon, but this is not true. Knowledge of the value at risk on a daily basis does not reveal the extent to which losses may accumulate over time. Moreover, even if daily value at risk is adjusted to account for prior gains and losses, the investor still has no way to know at the inception of the strategy, or at any other point, the cumulative value at risk to any future point throughout the horizon, including interim losses that later recover. We estimate probability of loss at the end of the horizon by: 1.) calculating the difference between the cumulative percentage loss and the cumulative expected return, 2.) dividing this difference by the cumulative standard deviation, and 3.) applying the normal distribution function to convert this standardized distance from the mean to a probability estimate, as shown in Equation (29). International Forum of Sovereign Wealth Funds 49

50 Wealth Asset Allocation for the Short- and Long-Term Exhibit 10: Risk of Loss: Ending Wealth versus Interim Wealth (Illustrative) $120 $110 $100 $90 $ Time Path 1 Path 2 Path 3 Path 4 Path 5 Source: State Street Global Exchange P E =N [ ln(1+l)-μt ] (29) σ T Where, P E = probability of loss at the end of the investment horizon N[ ] = cumulative normal distribution function ln = natural logarithm L = cumulative percentage loss in periodic units = annualized expected return in continuous units T = number of years in horizon = annualized standard deviation of continuous returns The process of compounding causes periodic returns to be lognormally distributed. The continuous counterparts of these periodic returns are distributed normally, which is why the inputs to the normal distribution function are in continuous units. International Forum of Sovereign Wealth Funds 50

51 To estimate value at risk, this calculation is turned around by specifying the probability and solving for the loss amount, as shown in equation (30): VaR = -(e μt-zσ T -1)W (30) Where, e = base of natural logarithm ( ) Z = normal deviate associated with chosen probability (e.g. Z=1.645 for a 5% probability) W = initial wealth Both of these calculations pertain only to the distribution of values at the end of the horizon and therefore ignore variability in value that occurs throughout the horizon. To capture this variability, a statistic called first passage time probability is used. 36 This statistic measures the probability (P W ) of a first occurrence of an event within a finite horizon. The following equation gives the probability of loss within the investment horizon, P W, which is the probability that an investment will depreciate to a particular value over some horizon if it is monitored continuously. P W = N [ ln(1+l)-μt σ T ] +N [ ln(1+l)+μt σ T 2μ ] (1+L) σ 2 (31) Note that the first part of this equation is identical to the equation (29) for the end of period probability of loss. It is augmented by another probability multiplied by a constant, and there are no circumstances in which this constant equals zero or is negative. Therefore, the probability of loss throughout an investment horizon must always exceed the probability of loss at the end of the horizon. Moreover, within horizon probability of loss rises as the investment horizon expands in contrast to end of horizon probability of loss, which diminishes with time. This effect supports the notion that time does not diversify all measures of risk and that the appropriate equity allocation is not necessarily horizon dependent. We can use the same equation to estimate continuous value at risk. Whereas value at risk measured conventionally gives the worst outcome at a chosen probability at the end of an investment horizon, continuous value at risk gives the worst outcome at a chosen probability from inception to any time during an investment horizon. It is not possible to solve for continuous value at risk analytically. Numerical methods must be used. Estimating continuous value at risk is accomplished by setting equation (31) equal to the chosen confidence level and solving iteratively for L. Continuous value at risk equals L times initial wealth. 36 The first passage probability is described in Karlin, S. and Taylor, H., A First Course in Stochastic Processes, 2nd edition, Academic Press, International Forum of Sovereign Wealth Funds 51

52 Risk Regimes and Stress Testing Most risk measures weight a sample s observations equally in order to estimate risk parameters. Although this procedure may produce reasonable estimates for the full investment horizon, it likely misrepresents a portfolio s risk attributes during periods of turbulence or financial crisis when asset and manager returns tend to become more volatile and more highly correlated. Thus, the diversification that characterizes the sample, on average, disappears when it is most needed. The conventional approach for measuring VaR uses the full-sample covariance matrix to compute the portfolio s standard deviation and considers the probability distribution only at the end of the investment horizon. Exposure to loss can be measured more reliably by estimating covariances from the turbulent subperiods, when losses are more likely to occur, and by accounting for interim losses as well as losses that occur only at the conclusion of the investment horizon. Exhibit 11 shows three portfolios conservative to aggressive together with assumptions for their expected returns and two estimates of standard deviation. One estimate of standard deviation, Full-sample risk, is based on the full-sample covariance matrix of monthly returns beginning in January 1977 and ending in December The other estimate of standard deviation, labeled Turbulent risk, is based on the covariance matrix from the turbulent subsample. Turbulence was calculated according to Equation 8, in which each return vector consisted of returns of the five asset-level indices for a particular month, and average vector μ and covariance matrix Σ were calculated from monthly returns during the entire 30-year history. The threshold for identifying turbulent periods was set at 75 percent, which means that roughly 25 percent of the months fell within turbulent subperiods. 37 Note how risk increases for each portfolio when turbulence risk is used. If the financial crisis is considered as a once-in-a-century event, Exhibit 12 shows that the conventional approach to measuring exposure to loss badly underestimated the riskiness of these portfolios. The turbulencebased approach, in contrast, anticipated the exposure to loss of these portfolios much more accurately. To be clear, it should be noted that the turbulence-based approach does not offer a more reliable estimate of when an extreme event will occur; rather, it gives a more reliable estimate of the consequences of such an event. Also note that turbulence is a relative measure. If the world becomes more turbulent, for example, the threshold for separating turbulent periods from nonturbulent periods will rise. 37 The results are not particularly sensitive to the 75th percentile threshold. International Forum of Sovereign Wealth Funds 52

53 Exhibit 11: Efficient Portfolios, Expected Returns, and Two Risk Estimates Asset Class Conservative Portfolio Moderate Portfolio Aggressive Portfolio U.S. Stocks 22.86% 35.23% 48.15% Non-U.S. Stocks 16.59% 24.22% 32.19% U.S. Bonds 49.95% 32.81% 14.89% Real Estate 3.85% 2.59% 1.28% Commodities 6.75% 5.16% 3.49% Expected Return 7.60% 8.37% 9.17% Full-sample Risk 7.77% 10.12% 12.86% Turbulent Risk 10.68% 13.68% 17.33% Note: Full-sample risk was estimated from the full-sample covariance matrix; Turbulentsample risk was estimated from the covariance matrix of the turbulent sample. Source: State Street Global Exchange Exhibit 12: VaR and Realized Returns Portfolio VaR for Full Sample, End of Horizon VaR for Full Sample, End of Horizon Maximum Loss from Inception (Jan/07-Sep/09) Maximum Drawdown (Jan/07-Sep/09) Conservative 2.10% 26.20% 19.60% 25.80% Moderate 9.90% 35.10% 29.42% 35.50% Aggressive 10.70% 45.00% 38.96% 45.30% Note: The horizon is five years. Source: State Street Global Exchange, Datastream International Forum of Sovereign Wealth Funds 53

54 6. Reference Portfolios While the methods detailed in this paper are presented in the context of a traditional portfolio construction framework it is important to acknowledge the reference portfolio framework that has recently gained the attention of SWFs as a method of increasing implementation flexibility and accommodating the inclusion of private market investments, such as hedge funds and private equity, in the portfolio management process. To do this the approach replaces the policy portfolio with a reference portfolio. A reference portfolio is a notional diversified portfolio designed to achieve specific goals that is implemented with only simple, passive, low cost, liquid investments. It provides a baseline for investment performance and is used to determine the effectiveness of active portfolio management efforts. Although the reference portfolio and the actual portfolio share the same goals, the composition of the two portfolios can differ substantially due to active portfolio management decisions implemented to exploit opportunities to add value relative to the returns offered by the traditional assets used in the reference portfolio. The use of a reference portfolio as a benchmark allows for greater versatility in asset selection and portfolio composition relative to a bucketed policy benchmark approach. In effect, investors increase flexibility in implementation at the expense of the implicit risk controls imposed by a policy benchmark. Consequently, the management of active risk depends, to a great extent, on investor judgement. The methods and approaches discussed in this paper are not at all incongruent with the reference portfolio approach and can only serve to better inform portfolio and risk management decisions. The distinction between a portfolio of traditional assets and one of active and/or alternative assets does not preclude investors from seeking to construct reference and active portfolios that are efficient in terms of expectations for the capital markets or from seeking a more holistic understanding of the risks borne by exposure to financial markets and those that result from active decisions. In fact, establishing pre-determined limits on active risk can be a useful method of retaining important risk controls for those applying this approach. While generally not part of the reference portfolio framework, the determination and use of a reasonable tracking error budget relative to the reference portfolio imposes discipline in selecting and implementing active decisions. Determining an active risk budget is not a trivial exercise as it demands a thoughtful and deliberate determination of a suitable reference portfolio as well as a clear understanding of how a SWF expects to generate excess returns. Furthermore, the active risk budget may consider both short- and long-term investment horizons. If not chosen carefully, the reference portfolio and/or the active risk budget could impose unintended constraints on a portfolio manager s ability to add value. The identification of the reference portfolio and active risk budget can be accomplished simultaneously using the following framework: International Forum of Sovereign Wealth Funds 54

55 1. Specify the SWF s specific investment goal A key characteristic of a reference portfolio is that it should be appropriate for achieving specified investment goals. Consequently, the identification of a reference portfolio is, first and foremost, a function of the SWF s goals. This may include quantifying the level of risk a SWF is willing to bear in seeking to maximize return or provide for broader goals such as maintaining the fund s reputation relative to peers. 2. Define the opportunity set of reference and active portfolio assets The selection of investments used in the reference portfolio should be a deliberate process that includes the development of criteria for the inclusion of assets in the reference portfolio. These criteria would then be applied to the universe of assets available to a SWF in order to determine the opportunity set of assets for use in the construction of the reference portfolio. The opportunity set of active portfolio assets, which are assets that are expected to be used to add value in excess of reference portfolio assets, should also be identified. 3. Develop estimates of return and covariance for reference and active portfolio assets The results of a portfolio analysis are a function of the inputs used. This paper has detailed a number of different approaches to forming beliefs about the future performances of investments. Special consideration must be given to unlisted and/or illiquid assets as risks for these types of investments are often under-estimated due to periodic valuation biases and the asymmetric nature of performance fees. The estimates developed in this step will be used as part of the portfolio optimization process as well as for determining ex-ante tracking error estimates of possible portfolio implementations. 4. Define portfolio constraints Portfolio constraints are used to incorporate professional judgment in limiting risks that are not adequately expressed as a function of volatility. Additional constraints can include limitations on domestic or foreign assets as well as limitations on private/illiquid assets. 5. Conduct a portfolio analysis with reference assets and identify a suitable reference portfolio A portfolio analysis is conducted to identify the set of efficient portfolios based on the estimates in step 3 and the constraints identified in step 4. The selection of a reference portfolio would begin with identifying the subset of efficient portfolios that exhibit return and risk characteristics acceptable to the SWF. Portfolios can be evaluated using various criteria including: Multi-period returns: The outputs of a portfolio analysis are presented in terms of expected return and standard deviation. The expected return for a portfolio is the weighted sum of the expected returns of portfolio constituents. These expected returns are arithmetic means (expected values) and not geometric International Forum of Sovereign Wealth Funds 55

56 means (compound returns). Approximations to geometric mean using portfolio arithmetic mean and standard deviation can be used to estimate the long-run return provided by portfolios. Alternatively, simulation could be used to assess portfolio outcomes. This provides an understanding of a portfolio s ability to achieve long-term goals. Stress testing of portfolios assuming multiple risk regimes: Understanding portfolio characteristics in both normal markets and turbulent markets is useful in determining an appropriate reference portfolio. End-of-horizon and within-horizon exposure to loss: Investors typically measure risk as the probability of a given loss at the end of their investment horizon. Exposure to loss within the investment horizon is substantially greater than investors normally assume and is an important characteristic to consider in selecting a portfolio Evaluate the tracking error of possible active portfolio implementations and identify a suitable active risk budget Estimates of ex-ante tracking error are calculated using estimates developed in step 3 and possible active portfolio weights. Possible active weights should consider the SWF s methods and expertise in pursuing excess returns. Considering some investor approaches, such as determining the tracking error impact of opportunistically shifting active portfolio weights over time, may require the use of simulation methods. An important by-product of this exercise is that additional portfolio constraints may be identified that may help in the management of active risk. A mean variance tracking error framework that considers both absolute risk and relative risk can then be used to implement and update the active portfolio on an ongoing basis to keep allocations within active risk budgets. Alternatively, the fund can be allocated using other methods with desired allocations being informed by estimates of active risk. 38 Kritzman, M. and Rich, D The Mismeasurement of Risk. Financial Analysts Journal, vol. 58, no. 3 (May/June). International Forum of Sovereign Wealth Funds 56

57 7. Survey Results: The Experience of Sovereign Wealth Funds As the financial markets have evolved, SWFs have had to balance the application of financial theory with the complexities presented by real world circumstances. To gain insight as to the specific challenges faced by SWFs, how their approaches, organizations, and fund allocations have adapted to changing markets, and how they are positioning themselves for the future, the working group conducted a survey of IFSWF members. The survey focused on current fund asset allocations, the evolution of those allocations, private market investments, and how fund organizations have evolved to facilitate change. Ten funds participated in the survey. The funds were broadly distributed across the world and represented a variety of fund types. Despite the wide range of different investment objectives and disparate geographic locations of these funds, the results provide insight into how SWFs have evolved. In the interest of protecting each fund s anonymity, responses are not attributed to any specific SWFs or their investment teams. The complete survey is provided in Appendix. Current Fund Asset Allocations This section of the survey focuses on identifying the asset classes currently held by SWFs and the distribution of those asset classes across markets. Details regarding allocations across various asset segments were also explored. While the unique nature of the SWFs surveyed limits drawing firm conclusions about specific allocations, they can be indicative of general asset preferences. Exhibit 13 presents the current average allocation across broad asset classes for diversified SWFs. This indicates that the diversified SWFs in the survey group are primarily allocated to more traditional investment categories and are more heavily weighted to fixed income than equity. Allocations to infrastructure/real estate and hedge funds are comparatively much smaller. Additional detail regarding these allocations can be gained by reviewing allocation the preferences across various asset segments presented in Exhibit 14. International Forum of Sovereign Wealth Funds 57

58 Exhibit 13: Current Average Allocation for Diversified Sovereign Wealth Funds 8% 5% 34% 53% Equities Fixed income Infrastructure/Real Estate Hedge funds Source: IFSWF Survey Completed July 2016 This shows that SWF investments are focused primarily in foreign markets. This may be a function of preferences or due to specific policies. Interestingly, only a small amount of assets currently devoted to emerging market investments with the majority of assets being directed to the developed world. Actively managed investments are favored over passive investments by only a small margin and listed investments outweigh nonlisted investments by a ratio of three-to-one. The survey also delved into the distribution of allocations to specific asset classes across geographic regions. Exhibit 15 shows the percentage of surveyed SWFs that currently have assets allocated to specific regions. Here it can be seen that listed equity allocations received allocations from most funds across all of the global regions (notable values are highlighted in orange). The region receiving the greatest percentage of fund allocations is, unsurprisingly, North America followed by Europe and then Asia. This is confirmed by survey responses that list the United States, the United Kingdom, and Japan as the top three countries for investments and also aligns closely with the fact that these three countries represent the largest markets in the world as measured by market capitalization. 39 Only a small percentage of funds have allocations within the MENA region. It is notable that European listed equities are the only assets common to all funds. With regard to how SWFs access specific investments across different regions, the survey suggests that funds are flexible in that they invest both directly and through funds with traditional assets (listed equities, government and corporate bonds) being the top areas where SWFs had only direct investments. 39 Bank of America/Merrill Lynch s Transforming World Atlas: Investment Themes Illustrated by Maps March International Forum of Sovereign Wealth Funds 58

59 Exhibit 14: Fund Allocation Across Various Asset Segments 7.5% 28.5% 71.5% 92.5% Domestic Markets Foreign Markets Developed Markets Emerging Markets 26.8% 54.0% 46.0% 73.2% Passive Active Listed Non-Listed Source: IFSWF Survey Completed July 2016 International Forum of Sovereign Wealth Funds 59

60 Exhibit 15: Percentage of Funds Allocated to Specific Assets Across Regions North America Asia Europe MENA Rest of World Listed Equities 90% 90% 100% 70% 80% Private Equity 40% 50% 50% 10% 40% Venture Capital 30% 10% 20% 0% 10% Government Bonds 80% 70% 70% 30% 50% Corporate Debt 80% 60% 70% 30% 50% Infrastructure 40% 30% 40% 20% 30% Real Estate 30% 30% 50% 10% 20% Hedge Funds 40% 30% 30% 20% 20% Liquid Assets 60% 20% 20% 10% 0% Other Assets 20% 0% 0% 0% 0% Source: IFSWF Survey Completed July 2016 The Evolution of Fund Allocations This section of the survey presents information on the evolution of SWF asset allocations beginning with how SWFs have been altering their allocation over the recent past (3-5 years) and ending with how SWF anticipate changing their portfolios in the future. As with the exploration of current asset allocations the survey first looks into changes in broad asset categories and then probes further into various asset segments. Exhibit 16 presents the percentage of funds with specific changes in allocations across broad asset classes in both domestic and foreign markets over the recent past (notable values are highlighted in orange). Here we find that, within domestic markets, there is no consensus in the percentage of funds making changes to any particular asset class. The most significant area of agreement is in increasing Private Equity. Across foreign markets there appears to have been more agreement as to how SWFs have actively changed their allocations. Here we find that the areas where the highest percentages of funds have actively increased their allocations were listed equity, private equity, and real estate asset classes. These increases appear to have been funded with decreases in both government and corporate fixed income. This aligns with survey responses where listed equities, private equities, and real assets were amongst the most commonly listed relevant asset classes introduced to portfolios over the last three to five years. Exhibit 17 presents the percentage of SWFs with specific allocation changes across various asset segments in the recent past (3-5 Years) versus future expectations. Here we see that there has been some agreement as to where changes have been made in the recent past with the highest percentage of funds agreeing in increasing infrastructure/real estate along hedge funds and other assets. Emerging market assets saw the greatest agreement in increases with half of the funds having increased allocations. Non-listed assets were also a focus for funds. The greatest agreement in decreases came in the listed assets and developed market segments. International Forum of Sovereign Wealth Funds 60

61 Exhibit 16: Percentage of Funds with Specific Allocation Changes Across Broad Asset Categories in the Recent Past (3-5 Years) Equities Fixed Income Infrastructure / Real Estate Hedge Funds and Other Assets Domestic Markets Increase No Change Decrease N/A Listed Equities 10% 20% 20% 50% Private Equity 30% 20% 0% 50% Venture Capital 20% 10% 0% 70% Government Bonds 0% 10% 10% 80% Corporate Debt 20% 10% 0% 70% Infrastructure 20% 20% 0% 60% Real Estate 20% 0% 20% 60% Hedge Funds 10% 30% 0% 60% Liquid Assets 0% 20% 0% 80% Other Assets 20% 0% 0% 80% Equities Fixed Income Infrastructure / Real Estate Hedge Funds and Other Assets Foreign Markets Increase No Change Decrease N/A Listed Equities 50% 10% 20% 20% Private Equity 50% 0% 0% 50% Venture Capital 20% 10% 0% 70% Government Bonds 0% 20% 50% 30% Corporate Debt 20% 20% 30% 30% Infrastructure 20% 20% 0% 60% Real Estate 30% 10% 10% 50% Hedge Funds 10% 20% 10% 60% Liquid Assets 10% 20% 10% 60% Other Assets 10% 10% 0% 80% Source: IFSWF Survey Completed July 2016 With regard to anticipated changes in the future, the survey suggests the majority of funds expect that they will not adjust current allocations. A small percentage of funds will continue with existing trends that have seen increases in allocations to infrastructure/real estate, non-listed assets, and emerging market assets. The limited percentage of funds indicating future changes in the survey could be an indication of uncertainty regarding the evolution of the capital markets in the future. International Forum of Sovereign Wealth Funds 61

62 Exhibit 17: Percentage of Funds with Specific Allocation Changes Across Various Asset Segments in the Recent Past (3-5 Years) versus Future Expectations Asset Categories Target Markets Geographies Recent Past Increase No Change Decrease N/A Equities 20% 60% 20% 0% Fixed Income 10% 60% 20% 10% Infrastructure / Real Estate 30% 40% 10% 20% Hedge Funds and Other Assets 30% 30% 10% 30% Domestic Markets 10% 70% 0% 20% Foreign Markets 0% 80% 10% 10% Listed 10% 60% 30% 0% Non-Listed 40% 40% 10% 10% Actively Managed 20% 70% 10% 0% Passively Managed 20% 50% 20% 10% Developed Markets 0% 60% 40% 0% Emerging Markets 50% 30% 0% 20% North America 20% 70% 0% 10% Europe 10% 80% 10% 0% Asia 20% 70% 0% 10% MENA 10% 70% 0% 20% Rest of the World 20% 50% 10% 20% Asset Categories Target Markets Geographies Future Expectations Increase No Change Decrease N/A Equities 20% 70% 0% 10% Fixed Income 0% 70% 10% 20% Infrastructure / Real Estate 20% 50% 0% 30% Hedge Funds and Other Assets 10% 40% 10% 40% Domestic Markets 0% 70% 0% 30% Foreign Markets 10% 70% 0% 20% Listed 0% 80% 0% 10% Non-Listed 20% 60% 10% 20% Actively Managed 10% 80% 0% 10% Passively Managed 0% 70% 10% 20% Developed Markets 0% 90% 0% 10% Emerging Markets 20% 50% 0% 30% North America 0% 70% 10% 20% Europe 0% 90% 0% 10% Asia 10% 70% 0% 20% MENA 10% 60% 0% 30% Rest of the World 10% 60% 0% 30% Source: IFSWF Survey Completed July 2016 International Forum of Sovereign Wealth Funds 62

63 Private Markets One of the greatest challenges faced by SWFs is in allocating to private market investments. These investments have unique characteristics that must be understood as well as higher fees that must be considered as part of the decision to invest in these assets. Generally, this requires intellectual resources with the professional aptitude and skillset necessary to fully comprehend the legal and operational complexities of these types of investments. This section of the survey focuses on gaining greater insight regarding what SWFs perceive to be the challenges of investing in private markets and what they believe to be the keys to the successful navigation of private market investments. For additional information on how SWFs are addressing the challenges of private market investing please see the IFSWF s whitepaper titled Comparison of Member s Experiences Investing in Public versus Private Markets which provides insights gathered from interviews with various SWFs, one of the world s foremost academic researchers of private markets, and an extensive review of academic literature. Exhibit 18 ranks the biggest challenges to investing in private markets identified by SWFs along with what they believe to be the keys to successfully investing those markets. Interestingly, fees and insufficient in-house resources rank below concerns about lack of transparency and illiquidity. This is consistent with the ranking of the keys to success where investment and operational due diligence along with institutional relationships and manager alignment are ranked highest. These two items are the primary methods portfolio managers have for decreasing the opacity often present in private markets and to increasing comprehension of risks, such as illiquidity, that transcend those implied by measures of volatility. Exhibit 18: Private Market Investments: Risks and Key for Success Rank What are the greatest challenges to investing in private markets? 1 Lack of Transparency 2 Illiquidity 3 Lack of appropriate benchmark 4 Fees 5 Insufficient in-house resources Source: IFSWF Survey Completed July 2016 Rank What are the key for success in private market investing? 1 Investment and operational due diligence process 2 Institutional relationships & manager alignment 3 In-house resources & human resources policies 4 Governance structure & stakeholder communication 5 Speed of decision making 6 Sophistication of risk management systems 7 Size of assets under management International Forum of Sovereign Wealth Funds 63

64 Fund Organization To this point SWF challenges have been primarily viewed as issues that emanate from sources outside of the control of SWFs. This section of the survey turns the focus to SWFs as investment management organizations and explores how they are adapting and organizing themselves to manage change and the expansion into new asset classes. The survey first explored the organizational solutions implemented to access the human and intellectual resources needed to manage new asset classes. Respondents were asked to indicate whether they have implemented the full in-house management of new asset classes, worked through partnership/cooperation to manage assets, or outsourced the management of assets to an external manager. The results show that SWFs are comfortable outsourcing asset management to external managers when new assets were traditional investments such as listed equities and fixed income. When it came to private market investments, SWFs demonstrated a preference towards fully managing in-house and, to a lesser extent, in partnering or cooperating with an outside resource. This suggests that SWFs view the management of traditional assets as a commodity and the management of private or alternative assets as an area that requires specialized resources and/or competencies. Because the additional resources need for private assets are primarily intended to address issues with transparency and risk management, having the organization play an active role in gathering and sharing objective insights to inform asset management decisions is preferred. This coincides with interest from IFSWF members in how to build out the human and intellectual resources within their organizations to manage private assets. The second area of inquiry for this section was to understand how SWFs have organized themselves to manage the expansion into new asset classes. In this section respondents were asked to indicate whether they have created a new business division to manage the new assets, created a new team within an existing business division, added new resources to current teams, or made no changes to resources/organization. By a wide margin, the approach taken by SWFs has been to add new resources to existing teams. Establishing new business divisions was indicated twice for private assets and once for listed equities. Only a small number of respondents indicated that no new resources were required. The final area of focus for the survey was to understand SWF perceptions of the most relevant competencies required in expanding to new asset classes. An overarching theme across the responses provided by SWFs, outside of the obvious need for analytical aptitude and commercial acumen, was the importance of being able to build and maintain relationships. Whether it is was with regard to building internal capacity through cooperation with outside resources, through establishing relationships with consultants/advisors, or through establishing communication channels with external managers, the key competency mentioned revolved around relationship building. This has important implications for identifying external investment resources, for hiring investment talent, and for establishing and maintaining a collaborative culture within investment teams. International Forum of Sovereign Wealth Funds 64

65 8. Appendix IFSWF Member Survey The working group prepared a list of survey questions intended to gain insight as to the specific challenges faced by SWFs, how their approaches, organizations, and fund allocations have adapted to changing markets, and how they are positioning themselves for the future.the survey questions are presented below for reference. International Forum of Sovereign Wealth Funds 65

66 Section I: Current Asset Allocation Overview Question 1: Assets Under Management: Please provide an indication of the amount of assets under management: $ Billions. Question 2: Asset Categories: What is the relative allocation of your current investments between the following asset categories? Portfolio % Equities (Both Listed and Private Equity) Fixed Income Infrastructure / Real Estate Hedge Funds and Other Assets Question 3: Target Market: What is the relative allocation of your current investments between the following markets? Domestic Markets Foreign Markets Listed Assets Non-Listed Assets Actively Managed Passively Managed % of Portfolio Question 4: Geographic Distribution: What is the relative allocation of your current investments between the following geographies? Developed Markets Developed Markets North America Europe 40 Asia MENA 41 Rest of World % of Portfolio Please indicate the top 3 countries of your current investments Top 3 Countries 40 Excluding Turkey and Russia as they are grouped with Asia. 41 MENA: Middle East North Africa region International Forum of Sovereign Wealth Funds 66

67 Section II: Evolution of Asset Allocation Question 5: Asset Evolution: How would you describe the recent past evolution (e.g. the last 3-5 years) of previous categories? Which are the expectations for their evolution in the near future? Please provide a qualitative indication using the following indicators: : Increase = : Stable : Decrease Asset Categories Equities Fixed Income Infrastructure / Real Estate Hedge Funds and Other Assets Recent Evolution Future Expectation Target Markets Domestic Markets Foreign Markets Listed Non-Listed Actively Managed Passively Managed Geographies Developed Markets Emerging Markets North America Europe Asia MENA Rest of the World International Forum of Sovereign Wealth Funds 67

68 Section III: Details on Current Asset Allocation Question 6: Asset Class Matrix: Which of the following asset classes are currently present within your investments portfolio? Please mark with an X the asset classes present in your portfolio: Equities Fixed Income Infrastructure / Real Estate Hedge Funds and Other Assets Listed Equities Private Equity Venture Capital Government Bonds Corporate Debt Infrastructure Real Estate Hedge Funds Liquid Assets (e.g. Mutual Funds, Money Market) Other Assets (Please Specify): Domestic Market Foreign Markets Direct Through Funds Direct Through Funds Question 7: Regional Asset Class Matrix: Which of the following asset classes are currently present within your investments portfolio? Please mark with an X the asset classes present in your portfolio: Equities Fixed Income Infrastructure / Real Estate Hedge Funds and Other Assets Listed Equities Private Equity Venture Capital Government Bonds Corporate Debt Infrastructure Real Estate Hedge Funds Liquid Assets (e.g. Mutual Funds, Money Market) Other Assets (Please Specify): North America Asia Europe MENA Rest of World International Forum of Sovereign Wealth Funds 68

69 Section IV: Details on Evolution of Asset Allocation Question 8: Portfolio Diversification: Which are the most relevant asset classes that have been introduced in the recent past in your portfolio (e.g. the last 3-5 years)? What are the expectations for possible introductions in the near future? Please indicate the most relevant three asset classes: Asset Classes Recently Introduced Asset Classes Under Consideration Question 9: Asset Matrix Evolution: How has the allocation of the various asset classes evolved in the recent past in your portfolio (e.g. the last 3-5 years)? Please provide a qualitative indication using the following indicators: : Increase = : Stable : Decrease Equities Listed Equities Private Equity Venture Capital Domestic Markets Foreign Markets Fixed Income Government Bonds Corporate Debt Infrastructure / Real Estate Infrastructure Real Estate Hedge Funds and Other Assets Hedge Funds Liquid Assets (e.g. Mutual Funds, Money Market) Other Assets (Please Specify): International Forum of Sovereign Wealth Funds 69

70 Section V: Private Markets Question 10: Challenges: What are the biggest challenges you face investing in private markets? Please rank the following from 1 to 6 (with 1 representing the biggest challenge): Lack of transparency Lack of appropriate benchmark Fees Illiquidity Insufficient resources in-house Other (Please Specify) Ranking Question 11: Success Factors: What are the key success factors for private markets? Please rank the following from 1 to 7 (with 1 representing the greatest success factor): Investment and operational due diligence In-house resources and human resource policies Institutional relationships and manager alignment Governance structure and stakeholder communication Speed of decision making Sophistication of risk management systems Amount of assets under management Ranking International Forum of Sovereign Wealth Funds 70

71 Section VI: Organization Question 12: Management: How have you decided to manage the expansion towards new asset classes? Please indicate the new asset class and mark with an X the implemented organizational solution: Indicate new asset class here Fully managed in-house Through Partnership /Co-operation External Manager New Asset Class Name Question 13: Organizational Set-up: How have you organized to be able to manage the expansion towards new asset classes? Please indicate the new asset class and mark with an X the implemented organizational solution: Indicate new asset class here New business division New team in current business division New resources in current team No new resources / organization New Asset Class Name Question 14: Competencies: What additional competencies have you implemented to be able to manage the expansion towards new asset classes? Please indicate the new asset class and the three most relevant competencies: Indicate new asset class here New Asset Class Name International Forum of Sovereign Wealth Funds 71

72 References Adler, T. and Kritzman, M. (2007). Mean-Variance versus Full-Scale Optimisation: In and Out of Sample, Journal of Asset Management, Vol. 7, no. 5: Blay, K., and H. Markowitz. Risk-Return Analysis: The Theory and Practice of Rational Investing (Volume One). New York, NY: McGraw Hill, Blume, M. (1984) The Use of Alphas to Improve Performance, Journal of Portfolio Management, no. 11: Chow, G Portfolio Selection Based on Return, Risk, and Relative Performance. Financial Analysts Journal, vol. 51, no. 2 (March/April): Chow, G., Jacquier, E., Kritzman, M., and Lowry, K Optimal Portfolios in Good Times and Bad. Financial Analysts Journal, vol. 55, no. 3 (May/June): Elton, E., Gruber, M., and Rentzler, J. (1987) Professionally Managed, Publicly Traded Commodity Funds, Journal of Business, Volume 60, Issue 2: F. J. Fabozzi and H. M. Markowitz, The Theory and Practice of Investment Management, John Wiley & Sons, Inc., Hoboken NJ. Ilmanen, A. Expected Returns: An Investor s Guide to Harvesting Market Rewards. Chichester, West Sussex, U.K.: John Wiley & Sons, Karlin, S. and Taylor, H., A First Course in Stochastic Processes, 2nd edition, Academic Press, Kinlaw, W., Kritzman, M., and Turkington, D The Divergence of High- and Low-Frequency Estimation: Causes and Consequences. The Journal of Portfolio Management, Vol. 40, No. 5 (40th Anniversary). Kinlaw, W., Kritzman, M., and Turkington, D The Divergence of High- and Low-Frequency Estimation: Implications for Performance Measurement. The Journal of Portfolio Management, Vol. 41, No. 3. Kinlaw, W., Kritzman, M., and Turkington, D Liquidity and Portfolio Choice: A Unified Approach. The Journal of Portfolio Management, vol. 39, no. 2 (Winter). Kinlaw, W., Kritzman, M., and Turkington, D Toward Determining Systemic Importance. Journal of Portfolio Management, vol. 38, no. 4 (Summer): Kritzman, M. The Portable Financial Analyst: What Practitioners Need to Know. Hoboken, NJ: John Wiley & Sons, Inc., Kritzman, M Risk Disparity. Journal of Portfolio Management, vol. 40, no. 1 (Fall): Kritzman, M., Li, Y., Page, S. and Rigobon, R Principal Components as a Measure of Systemic Risk. Journal of Portfolio Management, vol. 37, no. 4 (Summer). Kritzman, M. and Li, Y Skulls, Financial Turbulence, and Risk Management. Financial Analysts Journal, vol. 66, no. 5 (September/October). Kritzman, M., Lowry, K., and Van Royen, A Risk, Regimes, and Overconfidence. The Journal of Derivatives, vol. 8, no. 3 (Spring): Kritzman, M. and Rich, D The Mismeasurement of Risk. Financial Analysts Journal, vol. 58, no. 3 (May/June). International Forum of Sovereign Wealth Funds 72

73 Kritzman, M., Page, S., and Turkington, D Regime Shifts: Implications for Dynamic Strategies. Financial Analysts Journal, vol. 68, no. 3 (May/June). Kritzman, M., and Turkington, D Stability-Adjusted Portfolios. The Journal of Portfolio Management, Vol. 42, No. 5, Special Quantitative Equity Strategies Issue: Kritzman, M Towards Defining an Asset Class, Journal of Alternative Investments 2, no. 1:79. Luu, B. V., Sharaiha, Y., Doskov, N., Patel, C. and Turkington, D "The Shadow Price of Liquidity in Asset Allocation: A Case Study. Journal of Investment Management, vol. 12, no. 2. Markowitz, H. Portfolio Selection, Malden, MA: Blackwell Publishing, Markowitz, H. Portfolio Selection, Journal of Finance, March International Forum of Sovereign Wealth Funds 73

74 Legal Disclaimers The material presented is for informational purposes only. The views expressed in this material are subject to change based on market and other conditions and factors, moreover, they do not necessarily represent the official views of State Street Global Exchange SM and/or State Street Corporation and its affiliates. International Forum of Sovereign Wealth Funds 74