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A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit
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A Post-Crisis Perspective on Diversification for Risk Management - Presentation: Noël Amenc, EDHEC Business School - Middle East Investments Summit

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Professor Noël Amenc, Director, EDHEC Risk Institute, Professor of Finance, EDHEC Business School shared his presentation titled "A Post-Crisis Perspective on Diversification for Risk Management" at …

Professor Noël Amenc, Director, EDHEC Risk Institute, Professor of Finance, EDHEC Business School shared his presentation titled "A Post-Crisis Perspective on Diversification for Risk Management" at the Middle East Investments Summit.

Join the 2014 Middle East Investments Summit along with leading regional investors in an intimate environment for a highly focused discussion on the latest investment strategies in the market.

For more information contact: emailus@marcusevans.com

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  • 1. An EDHEC-Risk Institute Publication A Post-crisis Perspectiveon Diversification for Risk Management May 2011 Institute
  • 2. The authors are grateful to Professor Lionel Martellini for useful comments and suggestions.2 Printed in France, May 2011. Copyright© EDHEC 2011. The opinions expressed in this study are those of the authors and do not necessarily reflect those of EDHEC Business School. The authors can be contacted at research@edhec-risk.com.
  • 3. A Post-Crisis Perspective on Diversification for Risk Management — May 2011Table of ContentsAbstract .................................................................................................................... 5Introduction ............................................................................................................ 71. Advantages and Disadvantages of Diversification .................................... 112. Beyond Diversification: Hedging and Insurance ........................................19Conclusion ..............................................................................................................29Appendices .............................................................................................................31References ..............................................................................................................37About EDHEC-Risk Institute ...............................................................................41EDHEC-Risk Institute Publications and Position Papers (2008-2011) .........45 An EDHEC-Risk Institute Publication 3
  • 4. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 About the Authors Noël Amenc is professor of finance and director of development at EDHEC Business School, where he heads the EDHEC-Risk Institute. He has a masters degree in economics and a PhD in finance and has conducted active research in the fields of quantitative equity management, portfolio performance analysis, and active asset allocation, resulting in numerous academic and practitioner articles and books. He is a member of the editorial board of the Journal of Portfolio Management, associate editor of the Journal of Alternative Investments, member of the advisory board of the Journal of Index Investing, and member of the scientific advisory council of the AMF (French financial regulatory authority). Felix Goltz is head of applied research at EDHEC-Risk Institute and director of research and development at EDHEC-Risk Indices & Benchmarks. He does research in empirical finance and asset allocation, with a focus on alternative investments and indexing strategies. His work has appeared in various international academic and practitioner journals and handbooks. He obtained a PhD in finance from the University of Nice Sophia-Antipolis after studying economics and business administration at the University of Bayreuth and EDHEC Business School. Stoyan Stoyanov is professor of finance at EDHEC Business School and programme director of the executive MSc in risk and investment management for Asia. He has nearly ten years of experience in the field of risk and investment management. He worked for over six years as head of quantitative research for FinAnalytica. He also worked as a quantitative research engineer at the Bravo Risk Management Group. Stoyan has designed and implemented investment and risk management models for financial institutions, co-developed a patented system for portfolio optimisation in the presence of non-normality, and led a team of engineers designing and planning the implementation of advanced models for major financial institutions. His research focuses on probability theory, extreme risk modelling, and optimal portfolio theory. He has published nearly thirty articles in academic journals, contributed to many professional handbooks, and co-authored two books on financial risk assessment and portfolio optimisation.4 An EDHEC-Risk Institute Publication
  • 5. AbstractAn EDHEC-Risk Institute Publication 5
  • 6. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 Abstract Since the global financial crisis of 2008, improving risk management practices— management of extreme risks, in particular— has been a hot topic. The postmodern quantitative techniques suggested as extensions of mean-variance analysis, however, exploit diversification as a general method. Although diversification is most effective in extracting risk premia over reasonably long investment horizons and is a key component of sound risk management, it is ill-suited for loss control in severe market downturns. Hedging and insurance are better suited for loss control over short horizons. In particular, dynamic asset allocation techniques deal efficiently with general loss constraints because they preserve access to the upside. Diversification is still very useful in these strategies, as the performance of well-diversified building blocks helps finance the cost of insurance strategies.6 An EDHEC-Risk Institute Publication
  • 7. 2. xxxxxxxxxxxxxxxxxx Introduction An EDHEC-Risk Institute Publication 7
  • 8. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 Introduction Risk management practices became a general method is related to risk reduction central topic after the financial crisis of as much as it is to improving performance 2008. Improvements to the methods of and, therefore, it is most effective when it risk measurement, many of them made is used to extract risk premia. In short, it is by industry vendors, have drawn on the only one form of risk management. literature on the modelling of extreme events (Dubikovsky et al. 2010; Zumbach The limitations of diversification stem 2007). Although there has been extensive from its relative ineffectiveness in highly research into extreme risk modelling in correlated environments over relatively academe since the 1950s, it is only after shorter horizons. Christoffersen et al. (2010) difficult times that the financial industry conclude that the benefits of international becomes more open to alternative methods.1 diversification across both developed and emerging markets have decreased because From an academic perspective, however, of a gradual increase in the average risk management decision making goes correlation of these markets. Thus, if beyond risk measurement and static asset international markets are well integrated, allocation techniques. In fact, it can be there is no benefit in diversifying across1 - See, for example, thediscussion in Sheikh and Qiao argued that the non-classical methods are them.(2009) about a framework for designed to use two basic techniques instatic asset allocation basedon non-classical models. finance—diversification and hedging—in a The variations of correlation are important2 - Longin and Solnik (2001)base their model on extreme better way, and with the recent focus on not only across markets but also overvalue theory. There are other post-modern quantitative techniques the time; in the short run, then, relying onstudies drawing similarconclusions through models role of diversification as a risk management diversification alone can be dangerous.based on other statisticaltechniques. tool has been over-emphasised. Even though Over longer horizons, Jan and Wu (2008) it is a powerful technique, diversification argue that diversified portfolios on the has limitations that must be understood if mean-variance efficient frontier outperform unrealistic expectations for the real-world inefficient portfolios, an argument that performance of risk management are to adds to the debate that time alone may be avoided. not diversify risks. Although the idea behind it has long The limitations of diversification mean that, existed, a scientifically consistent in certain market conditions, it can fail framework for diversification, modern dramatically. Using a conditional correlation portfolio theory (MPT), was first posited model, Longin and Solnik (2001) conclude by Markowitz (1952). Diversification— that correlations of international equity international diversification, sector and markets2 increase in bear markets. In style diversification, and so on—has since severe downturns, then, diversification become the pillar of many investment is unreliable. Furthermore, it is generally philosophies. It has also become a very incapable of dealing with loss control. So important risk management technique, enhancing the quantitative techniques so much so that it is often considered, behind it by using more sophisticated risk erroneously, synonymous with risk measures and distributional models can lead management. In fact, diversification as a to more effective diversification but not to8 An EDHEC-Risk Institute Publication
  • 9. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 Introduction substantially smaller losses in crashes. Loss subsequent papers generalise the model control can be implemented in a sound by imposing minimum performance way only by going beyond diversification constraints relative to a stochastic, as to hedging and insurance, two other opposed to a deterministic, benchmark. approaches to risk management. Teplá (2001), for example, demonstrates that the optimal strategy in the presence A much more general and consistent of such constraints involves a long position framework for risk management is provided in an exchange option.4 by the dynamic portfolio theory posited by Merton (1969, 1971). The theory The much more general and flexible presents the most natural form of asset dynamic portfolio theory leads to new management, generalising substantially insight into risk management in general the static portfolio selection model and the role of diversification. In this developed by Markowitz (1952).3 Merton framework, diversification provides access (1971) demonstrated that in addition to the to performance through a building block standard speculative motive, non-myopic known as a performance-seeking portfolio long-term investors include intertemporal (PSP). Downside risk control is achieved by3 - In fact, extensions of thedynamic portfolio theory hedging demands in the presence of a assigning state-dependent—and possiblyconcern asset/liability stochastic opportunity set. The model has dynamic—weights to the PSP and to amanagement, but the liabilityside is beyond the scope of been extended in several directions: with portfolio of safe, or risk-free, assets.this paper.4 - See also Martellini stochastic interest rates only (Lioui andand Milhau (2010) and Poncet 2001; Munk and Sørensen 2004), In fact, since the latest financial crisis,the references therein foradditional details. with a stochastic, mean-reverting equity there has been confusion among market risk premium and non-stochastic interest participants not only about the benefits and rates (Kim and Omberg 1996; Wachter limitations of diversification as a method 2002), and with both variables stochastic for risk management but also about how (Brennan et al. 1997; Munk et al. 2004). the methods of hedging and insurance are related to diversification. In this paper, our In addition to these developments, goal is to review diversification and clarify recognising that long-term investors its purpose. Going back to the conceptual usually have such short-term constraints underpinnings of several risk management as maximum-drawdown limits, or a strategies, we see that, in a dynamic asset particular wealth requirement, leads management framework, diversification, to further extensions of the model. hedging, and insurance are complementary Minimum performance constraints were rather than competing techniques for sound first introduced in the context of constant risk management. The paper is organised in proportion portfolio insurance (CPPI) (Black two parts. The first discusses the benefits and Jones 1987; Black and Perold 1992), and and limits of diversification. The second in the context of option-based portfolio moves on to hedging and insurance and insurance (OBPI) (Leland 1980). More discusses diversification as a method of recent papers (Grossman and Zhou 1996) reducing the cost of insurance. demonstrate that both of these strategies can be optimal for some investors and An EDHEC-Risk Institute Publication 9
  • 10. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 Introduction10 An EDHEC-Risk Institute Publication
  • 11. 1. Advantages and Disadvantages of Diversification An EDHEC-Risk Institute Publication 11
  • 12. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 1. Advantages and Disadvantages of Diversification Diversification and mean-variance where is the covariance analysis matrix of stock returns, w = (w1,…,wn) is the Diversification is one of the most widely vector of portfolio weights, μ is a vector of used general concepts in modern finance. expected returns, m is the target portfolio The principle can be traced back to ancient return, and e = (1,…,1). The objective times, but as far as portfolio construction is function is in fact portfolio variance, concerned, the old saw about not putting the first constraint states that portfolio all your eggs in one basket captures the weights should add up to one and the essence of the approach on a more abstract second constraint sets the portfolio return level—reduce portfolio concentration to target. improve its risk/return profile. The optimisation problem in Eq. 1 implies Portfolio concentration can be reduced in that there are three important inputs—the a number of different ways, from ad hoc standalone characteristics represented by methods such as applying equal weights the vector of expected returns and the to methods based on solid scientific variance of stock returns positioned on the arguments. A landmark publication by main diagonal of the covariance matrix, as 5 - If joint behaviour were unimportant, investing 100% Markowitz (1952) laid the foundations for well as the joint behaviour of stock returns of the capital in the least a scientific approach to optimal distribution represented by the covariance collected in risky stock would always represent the least risky of capital in a set of risky assets. The paper the off-diagonal elements of Σ. The last portfolio. introduced mean-variance analysis and input leads to a very important insight demonstrated that diversification can be indicating that joint behaviour is crucial to achieved through a portfolio construction the notion of efficient portfolios; it explains technique that can be described in two why diversification works.5 alternative ways: (i) maximise portfolio expected return for a given target for In fact, one limitation of the method can be variance or (ii) minimise variance for a given identified by recognising that diversification target for expected return. The portfolios is less effective when asset returns are obtained in this fashion are called efficient more highly correlated. This conclusion and the collection of those portfolios in the follows from the decomposition of portfolio mean-variance space is called the efficient variance into two terms frontier. Therefore, conceptually, the mean-variance analysis links diversification Eq. 2 with the notion of efficiency—optimal diversification is achieved along the efficient frontier. where is the corresponding The principles behind the Markowitz correlation coefficient. The second term model can be formalised in the following is the contribution of correlation to total optimisation problem portfolio variance. If ρij is close to 1 for all assets, then there is a single factor driving the returns of all assets. Therefore, Eq. 1 distributing capital among many assets is just as effective as investing in one asset12 An EDHEC-Risk Institute Publication
  • 13. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 1. Advantages and Disadvantages of Diversification only. More formally, if all correlations are of the S&P 500 from the beginning of 2000 exactly equal to 1, total portfolio variance to 2010. The average correlation increased can be represented as around the dot-com bubble and the 9/11 attacks and in the financial meltdown of 2008. Figure 1: The average correlation of the sectors in the S&P 500 meaning that without a return target calculated over a two-year rolling window the optimal solution to Eq. 1 is a 100% allocation to the least risky asset. In this situation, diversification is ineffective since the optimal solution is a totally concentrated portfolio.6 From an investor perspective, solving the problem in Eq. 1 means optimising the risk/ return tradeoff because risk is minimised conditional on a return target. As a result,6 - We assume that theportfolio is long-only. If diversification as a general method is notunconstrained shorting is only about risk reduction. In fact, assuming In these conditions, as illustrated in figure 2,allowed, then it is possibleto construct a zero-volatility the opposite would imply that the most in which we compare the in-sampleportfolio from any pair ofperfectly positively correlated diversified portfolio is the global minimum performance of two optimised strategies—assets having different variance (GMV) portfolio, which is obtained the maximum Sharpe ratio (MSR) andvolatilities. Since risk can behedged completely using only by dropping the second constraint in Eq. 1. the GMV portfolios—to that of thetwo assets, it follows thatthere is no point in building This statement is arguable, however, as equally weighted (EW) portfolio and thea diversified portfolio under GMV portfolios can be concentrated on the cap-weighted S&P 500, diversification isthese assumptions as well.7 - See appendix 1 for a relatively lower-volatility stocks, which also unhelpful. In all cases, the universe consiststheoretical remark on thestructure of GMV portfolios. implies concentration in such sectors as of the sector indices of the S&P 500. The plot utilities.7 In fact, building well-diversified shows that all strategies, even the optimised portfolios is more about efficient ones, post large losses during the crash of extraction of risk premia than about 2008. These losses are reflected in table 1, mere risk minimisation. This conclusion, which shows the maximum-drawdown however, assumes that diversification is statistics for the strategies in the period designed to work over the long run across between January 2007 and September 2010. different market conditions. Along with the influence of correlation on diversification Table 1: The maximum drawdown experienced by the strategies in figure 2 between January 2007 and September 2010 opportunities, this assumption is another Strategy Max drawdown drawback of the approach. MSR 24.33% GMV 24.45% In a market crash, for example, asset EW 49.43% returns become highly correlated and S&P 500 52.56% the shortcomings of diversification are highlighted. This empirical result is illustrated in figure 1, in which we show the average correlation of the sector indices An EDHEC-Risk Institute Publication 13
  • 14. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 1. Advantages and Disadvantages of Diversification Figure 2: Even though optimised portfolios such as MSR and GMV distributed or if investors have quadratic are well diversified, they suffered large losses during the 2008 crisis. For comparison, the EW portfolio and the cap-weighted utility functions; both of which assumptions S&P 500 are also shown. are overly simplistic. Empirical research has firmly established that—especially at high frequencies—asset returns can be skewed, leptokurtic, and fat-tailed and quadratic utility functions arise in the model as a second-order Taylor series approximation of a general utility function. Using variance as a proxy for risk is also controversial. A disadvantage often pointed out is that it penalises losses and profits symmetrically while risk is an asymmetric phenomenon associated more with the left tail of the return distribution. Therefore, There are, however, good reasons for the a realistic risk measure would be more 9 - See Stoyanov et al. (2011) failure of diversification to reduce losses sensitive to the downside than to the and the references therein. in sharp market downturns. Increased upside of the return distribution. At a given correlation, common in downturns, limits confidence level α, Value-at-Risk (VaR), a diversification opportunities. Perhaps more downside risk measure widely used in the importantly, diversification is designed to industry, is implicitly defined as a threshold extract risk premia in an efficient way loss such that the portfolio loses more than over long horizons, not to control losses VaR with a probability equal to 1 minus the over short horizons. Misunderstanding the confidence level, limitations of the approach can mislead investors into concluding that, since diversification did not protect them from where X is a random variable describing the big losses in 2008, it is a useless concept. portfolio return distribution. Since diversification as a concept goes Diversification and general beyond mean-variance analysis, it has alternative risk models been argued that failure in market crashes Even though diversification is a generic is caused mainly by the inappropriate concept, we use mean-variance analysis to assumptions made by the Markowitz model. exemplify its advantages and disadvantages. If a downside risk measure is used instead of Mean-variance analysis is based on the variance, the portfolio may perform better assumption that risk-averse investors during severe crashes. Which downside risk maximise their expected utility at the measure is appropriate, however, is not investment horizon and take into account clear and VaR is hardly the only alternative. only two distributional characteristics— mean and variance. This assumption is Although different ways of measuring realistic either if asset returns are normally risk have been discussed since the 1960s,14 An EDHEC-Risk Institute Publication
  • 15. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 1. Advantages and Disadvantages of Diversification an axiomatic approach was taken in returns are fat-tailed. A risk measure the 1990s10 with the development of suggested as a more informative, coherent firm-wide risk measurement systems. The (and therefore sub-additive) alternative to first axiomatic construction was that of VaR is Conditional Value-at-Risk (CVaR). coherent risk measures by Artzner et al. It measures the average loss as long as the (1998). The axiom that guarantees that loss is larger than the corresponding VaR. diversification opportunities would be recognised by any coherent risk measure We are interested in whether or not is that of sub-additivity, adopting a downside risk measure results in dramatically different performance in Eq. 3 market crashes. Figure 3: The in-sample performance of GM CVAR and GM VaR where ρ denotes the measure of risk and portfolios, both risk measures at the 95% confidence level, X and Y are random variables describing during the crash of 2008, together—for comparison—with the cap-weighted S&P 500 the returns of two assets, i.e., the risk of a portfolio of assets is less than or equal to the sum of the risks of the assets. It10 - Markowitz (1959)suggested semi-variance is possible to reformulate the portfolioas a better alternative to selection problem in Eq. 1 with any riskvariance as a proxy for risk,as it concerns only adverse measure satisfying Eq. 3 in the objectivedeviations from the mean.11 - See Danielsson et al. function; that is, instead of minimising(2010). variance, we can minimise a sub-additive risk measure subject to the same constraints. An axiomatic approach, however, implies that there could be many risk measures satisfying the axioms, and sub-additivity Although using a downside risk measure axiom in particular. As a consequence, the may help fine-tune the benefits of choice of a particular risk measure for the diversification, it clearly does not help portfolio construction problem becomes much in severe market downturns. Figure difficult and must be made on the basis of 3 and table 2 provide an illustration for the additional arguments. Standard deviation, period from January 2007 to September for example, satisfies the sub-additivity 2010, the same period as that in figure axiom. This conclusion is apparent from 2. Since the point of this illustration is to equation Eq. 2—the second term, which compare results in times of large market involves the correlations, is the reason downturns, we limit the comparison to this sub-additivity holds. VaR is generally time period only. not sub-additive, but it is robust, easy Table 2: The maximum drawdown experienced by the strategies to interpret, and required by legislation in figure 3 between January 2007 and September 2010. and, as a consequence, it is widely used. Strategy Max drawdown Furthermore, recent research11 indicates GM CVAR 22.92% that sub-additivity holds when the GM VaR 29.15% confidence level is high enough and the An EDHEC-Risk Institute Publication 15
  • 16. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 1. Advantages and Disadvantages of Diversification Holding everything else equal, we consider by design, for all coherent risk measures. CVaR and VaR alternative risk measures at a As a result, the dependence structure of standard confidence level of 95% for both. the asset returns determines the presence Figure 3 shows the values of the global of diversification opportunities, whereas 12 - See, for example, minimum CVaR (GM CVaR) and the global the function of the risk measure is to Ekeland et al. (2009) and Rüschendorf (2010). minimum VaR (GM VaR) portfolios through identify them and transform them into 13 - Comonotonicity is in time and table 2 shows the corresponding actual allocations.14 For the worst possible fact a characteristic of the upper Fréchet-Hoeffding maximum-drawdown statistics. The losses in dependence structure, which is that of bound of any multivariate distribution. Since in this table 2 are significant, though the GM CVaR functional dependence, the inequality in Eq. analysis we hold the marginal portfolio leads to drawdown marginally 3 turns into an equality, which means that distributions fixed, it follows that the comonotonic lower that that of the GMV portfolio (see it is not possible to find a portfolio whose behaviour is a property of the dependence structure of table 1). risk is smaller than the weighted average the random vector, or the of the standalone risks. Intuitively, under so-called copula function. As a consequence, the That table 2 shows no significant reduction these circumstances, a 10% drop in one of presence of diversification opportunities is a copula in drawdown is unsurprising. By building the the assets determines exactly the changes property. This statement is in GM VaR portfolio, we are actually minimising in the other assets, since they are increasing line with the conclusion that diversification opportunities the loss occurring with a given probability functions of each other. In a situation such are a function of correlations in the Markowitz framework (5% in the example in the example in figure as this one, holding a broadly diversified since the copula function in 3). There is no guarantee that large losses portfolio is just as good as holding only a the multivariate Gaussian world is uniquely determined will not be observed. Likewise, by building few assets. by the correlation matrix. 14 - We need the technical the GM CVaR portfolio, we are minimising condition sup(X,Y) ρ(X + Y) an average of the extreme losses. Again, As a consequence, we can argue that = ρ(X) + ρ(Y) where the supremum is calculated over having a small average extreme loss does generalising the mean-variance framework all bivariate distributions (X,Y) with fixed marginals. not necessarily imply an absence of large leads to the conclusion that, if securities This condition is introduced losses in market crashes. are nearly functionally dependent in market as a separate axiom in Ekeland et al. (2009). See crashes, then there are no diversification appendix 2 for additional details. In fact, it is possible to make a more general opportunities. Under these conditions, statement that is independent of the choice choosing a risk measure is redundant of risk measure. In the previous section, we because the argument is generic (see argue that diversification opportunities appendix 2 for additional details). disappear when the correlation of asset returns is close to 1. Leaving the multivariate Statistical arguments provide evidence for normal world complicates the analysis, this conclusion as well. Figures 2 and 3 but it is possible to demonstrate12 that show the in-sample performance of the diversification opportunities disappear optimised strategies. In this calculation, if asset returns become comonotonic we assume perfect knowledge of the mean (increasing functions of each other), which and variance in the Markowitz analysis corresponds to perfect linear dependence and perfect knowledge of the multivariate in the Markowitz framework.13 distribution for the GM CVaR and GM VaR examples. Yet in these perfect conditions, In Eq. 3 the joint distribution of X and Y can none of the optimised strategies is able to be any; the property is assumed to hold for provide reasonable loss protection in 2008. all possible multivariate distributions and, In reality, the optimal solutions would be16 An EDHEC-Risk Institute Publication
  • 17. A Post-Crisis Perspective on Diversification for Risk Management — May 20111. Advantages and Disadvantagesof Diversificationinfluenced by the noise coming from our The additional information, however, comesimperfect knowledge of these parameters, at a cost. The coskewness and cokurtosissuggesting that the results may be even parameters increase significantly theworse. However, our results with perfect total number of parameters that need toparameter knowledge show that attempts be estimated from historical data. Thus,to improve the parameter estimators, or the a portfolio of 100 assets would requiremodel for the multivariate distribution, will estimation of more than 4.5 millionbe of little help in reducing the drawdown parameters. Compared to accounting forof optimally diversified portfolios in severe higher-order moments when coskewnessmarket crashes. and cokurtosis parameters are estimated without properly handling estimation risk, a simple mean-variance approach thus tendsDiversification and higher-order to lead to better out-of-sample resultscomoments since it avoids the error-prone estimationAnother way to extend the framework of higher-order dependencies. Nevertheless,beyond the mean-variance analysis is Martellini and Ziemann (2010) demonstrateto consider higher-order Taylor series that, for lower-dimensional problems, ifapproximations of investor’s utility function. the parameter estimation problem isThe higher-order approximation results properly handled, including higher-orderin higher-order moments in the objective comoments adds value to the portfoliofunction of the portfolio optimisation selection problem and can lead to higherproblem given in Eq. 1 (Martellini and risk-adjusted returns, indicating that itZiemann 2010). Using the fourth-order provides access to additional diversificationapproximation, for example, means opportunities. As for protection from lossesincorporating portfolio skewness and in extreme market conditions, however, thiskurtosis in addition to portfolio variance. approach is no more helpful than any of theIn this way, the objective function becomes others discussed in the previous sections.more realistic in the sense that it takesinto account the empirical facts that assetreturns are asymmetric and exhibit excesskurtosis.This problem setup makes it possible toidentify diversification opportunities otherthan those available in the correlation matrixbecause portfolio skewness and kurtosisdepend on the coskewness and cokurtosisof asset returns that represent statisticalmeasures of dependence of the asymmetriesand the peakedness of the stock returndistributions. The coskewness and cokurtosisappear in addition to covariance and describeother aspects of the joint behaviour. An EDHEC-Risk Institute Publication 17
  • 18. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 1. Advantages and Disadvantages of Diversification18 An EDHEC-Risk Institute Publication
  • 19. 2. Beyond Diversification: Hedging and Insurance An EDHEC-Risk Institute Publication 19
  • 20. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 2. Beyond Diversification: Hedging and Insurance The discussion in the previous section Hedging: fund separation and risk illustrates the benefit of diversification, reduction which is to extract risk premia, and two The mean-variance framework introduced key shortcomings: (i) it is unreliable in by Markowitz (1952) does not consider highly correlated markets and (ii) it is not a risk-free asset; the investable universe an efficient technique of loss control in the consists of risky assets only. Tobin (1958), short term. Complaints that diversification however, argued that, in the presence of has failed are somewhat misleading, as a risk-free asset, investors should hold it was never meant to provide downside portfolios of only two funds—the risk-free protection in market crashes. From a asset and a fund of risky assets. The fund practical viewpoint, it is important to of risky assets is the maximum Sharpe ratio transcend diversification and to identify (MSR) portfolio constructed from the risky techniques that can complement it and assets. Furthermore, the risk aversion of offset its shortcomings. investors does not change the structure of the efficient MSR fund; it affects only the One potential technique is hedging, relative weights of the two funds in the 15 - This rate is used in all generally used to offset partially or portfolio. This arrangement is the result of calculations unless stated completely a specific risk. Hedging can a so-called two-fund separation theorem, otherwise. be done in a variety of ways; the best which posits that any risk-averse investor example, perhaps, is through a position can construct portfolios in two steps: (i) in futures. Suppose that a given portfolio build the MSR portfolio from the risky has a long exposure to the price of oil, a assets and (ii) depending on the degree risk the portfolio manager is unwilling to of risk-aversion, hedge partially the risk take over a given horizon. One possibility present in the MSR portfolio by allocating a is to enter into a short position in an oil fraction of the capital to the risk-free asset. futures contract. If the portfolio has an Figure 4: The in-sample efficient frontier of the risky assets undesirable long exposure to a given sector (in blue) and the CML (capital market line) together with the (financials, say), another hedging strategy is tangency portfolio, the GMV portfolio, and the portfolio with the same risk as the GMV on the CML. The annualised risk-free to short sell the corresponding sector index. rate is set to 2%.15 Depending on the circumstances, the hedge can be perfect, if the corresponding risk is completely removed, or imperfect (partial), leading to some residual exposure. In the following section, we discuss the advantages and disadvantages of combining hedging and diversification. The limitations of this combination stem largely from the static nature of hedging. Insurance, which is dynamic in nature—and the second topic of this section—can be used to overcome From a geometric perspective, adding a these limitations. risk-free asset to the investable universe results in a linear efficient frontier called the20 An EDHEC-Risk Institute Publication
  • 21. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 2. Beyond Diversification: Hedging and Insurance capital market line (CML), a line tangential with the same risk on the CML. The in-sample to the efficient frontier generated by the performance of the two portfolios is shown risky assets. Since the point of tangency is in figure 5. Both portfolios are equally risky the MSR portfolio, it is also known as the in terms of volatility but the one on the tangency portfolio. Figure 4 illustrates the CML performs better. geometric property.16 The components of the portfolio account Introducing a risk-free asset and partial for its better risk/return tradeoff. The hedging as a technique for risk reduction efficient MSR portfolio is constructed to raises the following question. For a given provide the highest possible risk-adjusted risk constraint, which portfolio construction return. Therefore, it is in the construction technique is better? Taking advantage of of this portfolio that we take advantage of diversification, maximising expected return diversification to extract premia from the subject to the risk constraint and choosing risky assets. The MSR portfolio is in fact the portfolio on the efficient frontier of responsible for the performance of the the risky assets, or taking advantage of overall strategy. The risk-free asset, by the fund-separation theorem and, instead contrast, is there to hedge risk. In fact,16 - The risky assetsgenerating the efficient of building a customised portfolio of risky the fund-separation theorem implies thatfrontier on the plot are assets, partially hedging the risk of the there is also a functional separation—thethe sector indices of theS&P 500. We consider the MSR portfolio with the risk-free asset to two funds in the portfolio are responsibleten-year period from 2000to 2010. The weights in the meet the risk constraint? From a theoretical for different functions.optimisation problem are perspective, the second approach is superiorbetween -40% and 40%. Therisk-free asset is assumed because the risk-adjusted return of all Although volatility is kept under control,to yield an annual return of2%, a return representative portfolios on the CML is not smaller than both the GMV portfolio and the GMV matchof the average three-month those on the efficient frontier of the risky on the CML (see figure 4) post heavy lossesTreasury bill rate from 2000to 2010. assets. in the crash of 2008. Unlike diversification, however, hedging can be used to control Figure 5: The performance and the dynamics of the maximum drawdown of the GMV portfolio and the GMV match on the extreme losses. In theory, the risk-free asset capital market line has universal hedging properties. If the portfolio is allocated entirely to the risk-free asset, then, in theory, it grows at the risk-free rate. Appropriate allocation to the risk-free asset can thus hedge partially all aspects of risk arising from the uncertainty in the risky assets. We can easily, for example, construct a portfolio on the CML with an in-sample maximum drawdown of no more than 10%. For our dataset, it turns out that a portfolio with this property is obtained with a 40% allocation to the MSR portfolio. Explicit To check this conclusion in practice, we loss control of this type is not possible if choose the GMV portfolio on the efficient the investor relies only on diversification. frontier of the risky assets and the portfolio An EDHEC-Risk Institute Publication 21
  • 22. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 2. Beyond Diversification: Hedging and Insurance Figure 6: The in-sample performance of the GMV (in green), the symmetrically the right tail of the return GMV match on the CML (in blue), and a portfolio on the CML constructed such that it has a maximum drawdown of 10% (in red) distribution. As a consequence, this approach can lead to limited drawdown but at the cost of lower upside potential. Insurance: dynamic risk management In the previous example, the reason for the lower upside potential is the fact that hedging is a static technique. The entire analysis takes place in a single instance and the optimal portfolio is, essentially, a buy-and-hold strategy. As a consequence, the weight of the MSR does not depend on time or on A comparison of the performance of three the state of the market. Ideally, investors portfolios—the GMV portfolio, the GMV would demand an improved downside match on the CML, and a portfolio on the and an improved upside at the same time. 17 - In the particular case of the dataset used for figure 6, CML with an in-sample maximum drawdown This, however, is not feasible with a static v = 0.4 results in the portfolio of 10% —is shown in figure 6. Hedging makes technique. with a 10% in-sample maximum drawdown. it possible to match in-sample any maximum drawdown, regardless of its size. Since the Simple forms of dynamic risk management, portfolio return distribution is a weighted also called portfolio insurance, were suggested average of the return distribution of the MSR in the late 1980s. Black and Jones (1987) portfolio and a constant, and Black and Perold (1992) were the first to suggest constant proportion portfolio Eq. 4 insurance (CPPI). This strategy is a dynamic trading rule that allocates capital to a risky where 0 ≤ v ≤ 1 is the weight of the MSR asset and cash in proportion to a cushion portfolio and rƒ the risk-free rate, it follows that is the difference between the current that by changing v the portfolio return portfolio value and a selected protective floor. distribution is scaled up or down. Using The resulting payoff at the horizon is option- Chebychev’s inequality, it is possible to like because the exposure to the risky asset demonstrate that the probability of large approaches zero if the value of the portfolio losses can be made infinitely small by approaches the floor. The overall effect is reducing v, similar to that of owning a put option—CPPI guarantees that the floor will not be breached. Another popular insurance strategy is option- in which is the variance of the MSR based portfolio insurance (OBPI) (Grossman portfolio. Even though this approach is and Vila 1989). This strategy basically consists capable of controlling the downside of of buying a derivative instrument so that the return distribution,17 there is a caveat. the left tail of the payoff distribution at the Along with the left tail, scaling influences horizon is truncated at a desired threshold.22 An EDHEC-Risk Institute Publication
  • 23. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 2. Beyond Diversification: Hedging and Insurance The derivative instrument can be a simple • A rolling-performance floor. This floor European call option or an exotic product is defined by depending on additional path-wise features we would like to engineer. where t* is a predefined period of time, Even though CPPI and OBPI are conceptually twelve months, for example. The rolling- simple, they seem to be based on separate performance floor guarantees that the techniques rather than on a more basic performance will stay positive over period framework. Nevertheless, since the option t*. can, in theory, be replicated dynamically, both CPPI and OBPI can be viewed as • A maximum-drawdown floor. A members of a single family of models. In drawdown constraint is implemented by fact, a much more general extension is valid. The dynamic portfolio theory developed by Merton (1969, 1971) can be extended with absolute or relative constraints on asset where α is a positive parameter less than value and it is possible to show that both 1 and At portfolio wealth at time t. A18 - See Amenc et al. (2010b)for additional information in CPPI and OBPI arise as optimal strategies for maximum-drawdown floor implies thatthe context of the dynamic investors subject to particular constraints the value of the portfolio never falls belowcore-satellite approach. (Basak 1995, 2002). a certain percentage, 100(1 – α)%, of the maximum value attained in the past. This The treatment of the constraints in constraint was initially suggested as an continuous-time dynamic portfolio theory absolute constraint but can be reformulated is generic; they are introduced in terms of as a relative one.18 a general floor. The floors can be absolute or relative to a benchmark portfolio. An • A relative-benchmark floor. This relative absolute floor, for instance, can be any of floor is defined by the following: • A capital-guarantee floor. The floor is where k < 1 is a positive multiplier and calculated by the formula Bt is the value of a benchmark at time t. This floor guarantees that the value of the portfolio will stay above 100k% of the value where rƒ is the risk-free rate, T-t calculates of the benchmark. the time to horizon, A0 is the initial portfolio wealth, and k < 1 is a positive multiplier. Several floors can be combined together in This floor is usually used in CPPI and a single floor by calculating their maximum, non-violation of this floor guarantees that . The new floor can the strategy will provide the initial capital then be adopted as a single floor in the at the horizon. dynamic portfolio optimisation problem. It follows from the definition that if is not violated, then none of the other floors will be, either. An EDHEC-Risk Institute Publication 23
  • 24. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 2. Beyond Diversification: Hedging and Insurance Solving a dynamic asset allocation problem weights of the building blocks. In Eq. 4, the with an implicit floor constraint results in weights are static, whereas in Eq. 5 they are an optimal allocation of the following form, state- and, potentially, time-dependent. This is the improvement that makes insurance Eq. 5 an adequate general approach to downside risk management. Figure 7: The in-sample performance of the 10% maximum- drawdown strategy on the CML and a dynamic strategy with a where PSP is the generic notation for the 10% maximum-drawdown constraint weights of a performance-seeking portfolio, SAFE the weights in the safe assets, γ the degree of risk aversion, Ft the value of the selected floor at time t, and the value of the optimal constrained portfolio (see appendix 3 for additional details). The solution in Eq. 5 is a fund-separation 19 - The same portfolio is represented by the red line in theorem in a dynamic asset allocation figure 6. setting. The optimal weight equals a 20 - The dynamic portfolio is implemented as a dynamic weighted average of two building blocks core-satellite strategy with a multiplier of six and a constructed for different purposes. The PSP An illustration of the improvement of risk-free instrument yielding is constructed for access to performance insurance strategies on hedging is provided an annual return of 2%. See Amenc et al. (2010b) through efficient extraction of risk premia; in figure 7. In the upper part of the figure, for further details on core-satellite investing. in fact, under fairly general assumptions it we compare the in-sample performance is the MSR portfolio. of the 10% maximum-drawdown strategy obtained through the static methods of The general goal of the SAFE building block hedging19 and a dynamic strategy20 with is to hedge liabilities. In the very simple a maximum-drawdown floor of 10%. The example of the previous section, SAFE lower part of the figure shows a plot of consists of a government bond maturing the dynamics of the allocation to the MSR at the investment horizon. In a dynamic portfolio and illustrates how insurance setting, depending on the institution strategies control downside losses. When constructing the strategy, SAFE has a there is a market downturn and the value different structure. For example, critical of the portfolio approaches the floor, the factors for pension funds are interest rates allocation to the PSP building block, or and inflation. As a result, the SAFE portfolio the MSR portfolio in this case, decreases. for a pension fund would contain assets When the value of the portfolio hits the hedging interest rate risk and inflation risk floor, as it nearly does in the crash of 2008 (see appendix 3 for additional details). (see figure 7), allocation to the risky MSR portfolio stops altogether and the portfolio Even though Eq. 5 is much more general is totally invested in the SAFE building block. than Eq. 4, considering only the building Since the SAFE asset is supposed to carry no blocks, the greatest difference is in the risk, it is not possible, in theory, to breach24 An EDHEC-Risk Institute Publication
  • 25. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 2. Beyond Diversification: Hedging and Insurance the floor.21 In a recovery, the return from The results are summarised in figure 8. The the safe asset can be used to build up a plot on the left shows the histograms of the new cushion and invest again in the MSR annualised return distribution for the two portfolio. In this way, exposure to extreme strategies superimposed. The blue histogram risks is limited and access to the upside indicates better access to the upside is preserved through the MSR portfolio performance of the dynamic strategy. The because it is designed to extract premia plot on the right shows the corresponding from risky assets by taking full advantage histograms for the maximum-drawdown of the method of diversification. distribution. The great difference stems from the inability of the static approach to Table 3: The maximum and the average drawdown of the two strategies in figure 7 between January 2007 and September 2010 keep losses under control. In some states Strategy Average Max drawdown of the world, the maximum drawdown drawdown reaches more than 20%, even though the Dynamic strategy 2.9% 9.2% same static strategy was designed to have Static strategy 2% 10% a 10% in-sample maximum drawdown. In contrast, there is no single state of the The drawdown characteristics of the world in which the dynamic strategy has21 - In a practical two strategies are shown in table 3. a maximum drawdown greater than 10%.implementation, a breach ofthe floor may occur because, To all appearances, they both exhibitas a result of turnoverconstraints, trading may need similar in-sample average and maximum Figure 8: The annualised return distribution and the maximum- drawdown distribution of the dynamic and the static strategiesto be less frequent, which can drawdown. The dynamic strategy, however, calculated from 5,000 sample pathsresult in a breach occurringbetween rebalancing dates, or has greater upside potential, a result of thebecause a perfect hedge withthe SAFE portfolio may not be design of the MSR portfolio.possible as a result of marketincompleteness, whichimplies that there may be The difference in the properties of theresidual risks in the portfolio.Nevertheless, dynamic asset static and the dynamic approaches areallocation is the right general best illustrated in a Monte-Carlo study.approach to controllingdownside risks. Figure 7 compares the performance of only two paths, but in practice we need more than two to gain insight into the difference in the extreme risk exposure of the two strategies. We fitted a geometric Brownian motion (GBM) to the MSR sample path and generated 5,000 paths with a ten-year horizon. For each path, which represents one state of the world in this setting, we calculated the dynamic strategy with a 10% maximum drawdown. The static strategy is a fixed-mix portfolio with a 40% allocation to the MSR portfolio. Then, in each state of the world, we calculated the annualised returns and the maximum drawdown of the two strategies. An EDHEC-Risk Institute Publication 25
  • 26. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 2. Beyond Diversification: Hedging and Insurance Table 4: The risk-return characteristics of the dynamic and the We did a Monte-Carlo study to illustrate static strategies calculated from the distributions in figure 8 this effect on an insurance strategy with a Strategy Annualised Average max Largest max average drawdown drawdown maximum-drawdown constraint. The PSP return building block is modelled as a GBM, Dynamic 9.56% 8% 9.64% strategy Static 8.26% 10.32% 28.3% Eq. 6 strategy where λ is the Sharpe ratio of the strategy. The risk-return characteristics calculated We adopt the parameter values calibrated in from the distributions shown in figure 8 are Munk et al. (2004)23 and have the Sharpe shown in table 4. The annualised average ratio be λ = 0.24, which corresponds to return of the dynamic strategy is higher the long-term ratio for the S&P 500.24 We than that of the static strategy, as expected, generated 5,000 sample paths from the and the big difference in the maximum- model in Eq. 6 with an investment horizon drawdown distributions is apparent. The of ten years. For each sample path, we average maximum drawdown of the static calculated the dynamic insurance strategy strategy is near the in-sample figure of 10%. and computed its average annual return, 22 - Diversification can involve the transaction as well as the average annual return of the costs arising from additional PSP component. trading. 23 - The model in Munk et Diversification and the cost of Figure 9: The return distribution of a dynamic strategy compared al. (2004) is more general as it allows for a stochastic insurance to that of the PSP component. The top pair of plots is produced interest rate. The parameter Diversification can be implemented, at least with the default value of λ = 0.24 and the bottom pair of plots values used in the simulation is produced with λ = 0.36, which is a 50% improvement on the are σS = 14.68% and rƒ = in theory,22 at no cost, but insurance always default value. SP is shortfall probability—the probability that 3.69%, the value for rƒ being the long-term mean in the has a cost. The cost of insurance is easiest the annualised average return will be negative. mean-reversion model fitted to spot in the OBPI strategies in which a by Munk et al. (2004). 24 - See Amenc et al. (2010a). certain amount of capital is invested in a derivative instrument. In this case, the cost is the price of the derivative. Since the derivative can usually be replicated by a dynamic portfolio, it is clear that such costs can be present in other types of dynamic insurance strategies. In such cases, however, they materialise as implicit opportunity costs. One way to illustrate the cost of insurance is to look at the return distribution of the dynamic strategy at the investment horizon and the corresponding histogram of the PSP building block. The opportunity cost of insurance appears as a lower expected return for the dynamic strategy.26 An EDHEC-Risk Institute Publication
  • 27. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 2. Beyond Diversification: Hedging and Insurance Although cap-weighted indices are popular in the industry, there is ample empirical evidence that they are poorly diversified and highly inefficient (Haugen and Baker 1991; Grinold 1992; Amenc et al. 2006). The reason is that capitalisation weighting leads to high concentration in a handful of stocks. In fact, equally weighted portfolios, although naïvely diversified, have been found to provide higher risk-adjusted returns.25 Although it has been shown that even naïvely diversified portfolios dominate the corresponding cap-weighted portfolios, equal weighting provides optimal diversification from the standpoint of25 - See, for example, DeMiguel et al. (2009). mean-variance analysis if and only if all securities have identical expected returns, The top pair of plots in figure 9 compares volatility, and if all pairs of correlation are the two distributions. The annualised the same. Since this hypothesis is highly expected return of the dynamic strategy unrealistic, there is a clear indication is 6.72%, whereas that of the PSP building that, by carefully estimating the risk and block is 8.46%. Although the difference in return parameters, it would be possible the annualised return distribution seems to construct risk-efficient MSR portfolios large on the plot, it must be kept in mind providing superior risk-adjusted returns. that drawdown protection results in good path-wise properties that are hard to spot Successful implementation of an MSR in the histogram of the dynamic strategy portfolio is critically dependent on the in figure 9. The good path-wise properties quality of the parameter estimators. Amenc materialise as a significantly smaller et al. (2010a) do an empirical study for shortfall probability (SP). the S&P 500 universe from January 1959 to December 2008. They show that using One way to offset the cost of insurance parameter estimation techniques resulting is to improve the building blocks of the in robust estimates of the risk and the dynamic strategy. Since the PSP is devoted return parameters leads to an optimised to performance, it must be constructed as strategy with a Sharpe ratio more than a well-diversified portfolio. In practice, the 50% higher than the Sharpe ratio of the common approach is to adopt a standard S&P 500 index. stock market index, a cap-weighted portfolio. If improving diversification makes possible a 50% improvement in the Sharpe ratio of the PSP, it is interesting to see to what An EDHEC-Risk Institute Publication 27
  • 28. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 2. Beyond Diversification: Hedging and Insurance degree it can offset the implicit cost of insurance. So we regenerated the scenarios from the model in Eq. 6, keeping the same parameter values and increasing the Sharpe ratio to 0.36. The histograms of the return distributions of the dynamic strategy before and after the Sharpe ratio improvement are compared in the bottom pair of plots in figure 9. The annualised expected return of the dynamic strategy improves from 6.72% to 8.19%, a jump that, in this context, implies that improving the Sharpe ratio of the PSP by 50% very nearly compensates for the cost of insurance.28 An EDHEC-Risk Institute Publication
  • 29. ConclusionAn EDHEC-Risk Institute Publication 29
  • 30. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 Conclusion The global financial crisis of 2008 has preserving access to the upside through shifted the attention of all investors to the PSP. In this context, a well-diversified risk management. In a broad context, risk portfolio is a building block of crucial management is about maximising the importance. A carefully designed PSP probability of achieving certain objectives with an improved Sharpe ratio resulting at the investment horizon while staying from good diversification can reduce the within a risk budget. Diversification, implicit cost of insurance. hedging, and insurance can be relied on to make optimal use of risk budgets. These three techniques involve different aspects of risk management, but they are complementary techniques rather than competing ones. Diversification provides investors with the best reward per unit of risk through a smart combination of individual assets. It is designed to work in the long run across different market conditions and is, therefore, helpless in such specific conditions as severe market downturns. Since the purpose of diversification is efficient extraction of risk premia, it is most effective in the construction of performance-seeking portfolios. Hedging can be combined with diversification to reduce risks that cannot be diversified away. Hedging is achieved through a portfolio of safe assets, or simply through cash, which is another dedicated building block. A non-diversifiable risk that can be handled in this way is the risk of a large drawdown. Insurance, unlike diversification and hedging, combines the safe building block and the PSP optimally to comply with the corresponding risk budgets. So downside risk control is best achieved through dynamic asset allocation. This technique makes it possible to control the downside of the return distribution while30 An EDHEC-Risk Institute Publication
  • 31. AppendixAn EDHEC-Risk Institute Publication 31
  • 32. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 Appendix Appendix 1: Are GMV Portfolios to tilt the portfolio further towards the Generally Concentrated in lower-volatility assets. When all assets are Low-Volatility Stocks? perfectly positively correlated, the GMV If a non-degenerate covariance matrix is long-only portfolio is concentrated entirely assumed, the optimisation problem in Eq. in the lowest-volatility stock. 1 without the expected return constraint makes possible the following analytic A way to illustrate this idea is to consider, for solution, the sake of simplicity, a constant correlation model and different ranges for the stock Eq. 7 volatilities. The case in which all stocks have one and the same volatility is not of interest where is the inverse of the covariance because the GMV portfolios are trivial— matrix. The factor in Eq. 7 equally weighted for any correlation. The ensures that the weights add up to one expectation is that the more we allow the and, therefore, the optimal solution stock volatilities to vary, the stronger the is proportional to the vector . This departure from equal weighting will be. solution is, for all intents and purposes, In this illustration, we choose the inverse the GMV portfolio. of the Herfindahl index as a measure of concentration which, in a vector notation, Suppose that returns of the assets in the takes the form, portfolio are not correlated. The inverse of the covariance matrix then has the following very simple structure, where w is a vector of weights (e.g., the optimal solution in Eq. 7). For an equally weighted portfolio, H-1 = n, which stands for the number of stocks in the universe, and for a portfolio totally concentrated in one asset, H-1 = 1. The concentration metric H-1 is between 1 and n for any other where σjj is the variance of the return of long-only portfolio. the j-th asset. In this case, the optimal solution as given in Eq. 7 is proportional To preserve this interpretation, we calculate to the inverse of the squared volatilities. the GMV portfolios using the optimisation As a result, the more diverse the volatilities problem in Eq. 1 with the additional in the universe are, the more highly the constraint that the weights should be GMV portfolio is concentrated in the lower- non-negative. We consider a hypothetical volatility assets. universe of 100 stocks, the annualised volatilities of which are equally spaced in It is expected that increasing correlations the following ranges: [16%, 18%], [15%, from zero to a positive number will lead to 19%], [13%, 21%], and [10%, 24%]. In the even greater concentration in the lower- three cases, the average volatility is one volatility assets since, as a result of some and the same; the only difference is the common factors, it would be optimal dispersion of the volatilities around the32 An EDHEC-Risk Institute Publication
  • 33. A Post-Crisis Perspective on Diversification for Risk Management — May 2011Appendixaverage. On these assumptions, we calculate volatility stocks increases monotonically,numerically the GMV portfolios for degrees an increase that is offset by a monotonicof correlation ranging from 0 to 0.99 and decrease of the total weight allocated towe estimate the concentration metric H-1 the group of higher-volatility stocks. Forfor each of them. correlation more than 0.6, the portfolio is concentrated entirely in the group ofFigure 10: The inverse of the Herfindahl index of long-only GMVportfolios as a function of correlation in a constant correlation lower-volatility stocks.model. The volatilities are equally spaced between the lowerand the upper bounds, which are provided in annualised terms. Figure 11: The sum of the GMV weights corresponding to three groups of stocks of equal size ranked by their volatility. The volatilities of the stocks are equally spaced in the interval [16%, 18%].The plot of H-1 as a function of correlationis provided in figure 10. As expected, therelationship is monotonic in the fourcases and, all other things equal, a wider This numerical illustration correspondsrange of volatility corresponds to greater to the fairly homogeneous case in whichconcentration. stock volatilities do not vary much. The conclusions would be stronger if we allowedThe plot in figure 10 indicates that a greater degree of non-homogeneity.concentration increases, but it is notclear if it does so as a result of the higherrelative weight of the low-volatility stocks. Appendix 2: DiversificationTo explore this question, we rank the GMV Opportunities Are Determinedstocks into three groups of equal size and by the Multivariate Dependencethen calculate the sum of the weights of Structure of Asset Returnsthe stocks in each group. Figure 11 shows In this appendix, we examine more closelythe sum of these weights as a function the claim that the functional dependenceof correlation, assuming that the stock of asset returns leaves no room forvolatilities are in the interval [16%, 18%]. diversification. The analysis is general in theIf the stock returns are non-correlated, sense that we do not limit the discussion tothe total weight allocated to the three the mean-variance setting alone. Rather, wegroups of stocks is almost the same, which is work with a general risk measure, denotedconsistent with the value of H-1 being near by ρ here, making as few assumptions as100 in figure 10. As correlation increases, possible while extending the Markowitzthe total weight allocated to the lower- setting. An EDHEC-Risk Institute Publication 33
  • 34. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 Appendix Suppose, to start, that the investable universe Eq. 9 consists of n assets, the joint behaviour of the returns of which is described by the where U is uniformly distributed in [0, 1], or random vector (X1,…, Xn). We distinguish 2. The multivariate distribution function of between marginal distributions, describing Y can be represented as the elements of the random vector on a standalone basis, and the joint distribution, Eq. 10 describing the joint behaviour of all stocks. Let ρ be a general risk measure that is The definition in Eq. 9 indicates that the sub-additive (i.e., it satisfies Eq. 3) and components of a comonotonic random positively homogeneous26 ρ(aX) = aρ(X) vector can be represented as increasing for positive a; assume that it satisfies the functions of each other. Eq. 10 shows that structure neutrality condition (Ekeland et the upper Fréchet-Hoeffding bound, al. 2009), Eq. 8 Eq. 11 26 - Technically, these which is an upper bound of any multivariate two properties guarantee distribution function, is the distribution convexity of ρ. where the supremum is taken with function of a comonotonic random vector. 27 - See, for example, the original publications of respect to all possible joint distributions; Since the marginal distributions of the Hoeffding (1940) and Fréchet (1951). however, the marginal distributions are upper bound are the same, it follows that 28 - See Rüschendorf (2010) fixed—that is, we vary only the dependence comonotonicity is, essentially, a property of and the references therein. structure. This condition implies that the copula, or the dependence structure, the dependence structure for which of the random vector. the supremum is attained—call it the worst possible dependence structure— In fact, the worst possible dependence leads to a linear decomposition of the structure turns out to be that of risk measure. If this condition does not comonotonicity. It is possible to show that hold, then by the sub-additivity property for any convex risk measure that satisfies for the worst Eq. 8, the following inequality holds,28 possible dependence structure. However, the strict inequality means that we must exclude volatility and the multivariate normal distribution as a possible setup. Additional motivation for this condition which can be restated in terms of portfolio can be found in Ekeland et al. (2009). risk and standalone risks as Eq. 12 To characterise the worst possible dependence structure, we need the notion of comonotonicity. A random vector Y is said to be comonotonic if,27 That is, holding the marginal distributions fixed, any risk measure satisfying the 1. The following representation holds assumptions above has an absolute34 An EDHEC-Risk Institute Publication
  • 35. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 Appendix maximum when stock returns are increasing We can conclude that diversification functions of each other. Furthermore, for opportunities are determined essentially this dependence structure the risk of any by the joint behaviour of stock returns. portfolio equals the weighted average of The function of risk measures in this more the risks of the portfolio constituents, which general setting is to provide an objective means that the risk measure becomes a to translate those opportunities into actual linear function of portfolio weights. allocations. If there are no diversification opportunities, however, the choice of As a result, under the assumption of objective is irrelevant. comonotonicity, the extension of the mean-variance analysis in Eq. 1 with a general risk measure in the objective Appendix 3: Dynamic Portfolio function turns into a linear programming Choice in Continuous Time with an problem. And assuming that no short- Implicit Lower Bound selling is allowed, any point on the efficient In this appendix, we provide in detail the frontier generated by the extended version assumptions and the problem setup leading of Eq. 1 is a portfolio of no more than two to the particular solution given in Eq. 5. In29 - The statement refers tothe general case of distinct assets,29 indicating that diversification is terms of assumptions, we do not considerstandalone risks. pointless. Trivially, the global minimum risk the most general setting.30 - See Martellini andMilhau (2010) for additional portfolio is totally concentrated in the stockdetails. with the smallest standalone risk. Likewise, Consider an economy whose uncertainty is the global maximum return portfolio is represented through a standard probability totally concentrated in the stock with the space (Ω, A, P) and a finite time span maximum expected return. The result for denoted by T.30 Investors trade n assets, the intermediate points follows from the the prices of which, represented by the linearity of the risk measure. The reasoning elements of a vector St, evolve as is independent of the choice of ρ. If the vector of returns is not comonotonic, then diversification opportunities are in which z is an n-dimensional Brownian determined by the degree to which the motion and diag(St) is a diagonal matrix multivariate distribution function can with the elements of St on the main deviate from its upper Fréchet-Hoeffding diagonal, rt is a non-stochastic risk-free bound (see Eq. 11). This is one factor that rate, λt is the market price of risk vector, determines the potential for portfolio risk to and σt is a time-dependent n x n matrix. deviate from its upper bound, which is the The market is assumed to be complete. weighted average of the standalone risks (see Eq. 12). The other factor is, of course, the A portfolio strategy is described by a risk measure ρ and its properties. Trivially, vector process of weights wt adapted if ρ is constant for any portfolio, then it to the filtration of the probability space is unable to identify any diversification augmented with the natural filtration of the opportunities n-dimensional Brownian motion. Letting the value process of the strategy be A, we An EDHEC-Risk Institute Publication 35
  • 36. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 Appendix obtain the following expression describing its dynamics, . in which is the asset value of the optimal solution and: In addition, we assume that there is a Eq. 14 benchmark evolving according to the equation Eq. 15 Eq. 16 and that the floor is a multiple of the benchmark, Ft = kBt. Because we assume that the market is complete, it follows that The expression in Eq. 14 stands for the the benchmark can be replicated by the weights of the PSP, Eq. 15 for the weights traded securities. of the benchmark replicating portfolio, and Eq. 16 defines as the stochastic process The investors’ utility functions take the of the benchmark-replicating portfolio following form, constructed such that . where is the CRRA utility function and γ is the risk-aversion parameter. This definition results in infinite disutility if x < k. Investors maximise expected utility at the terminal time instant T by solving the following expected utility maximisation problem subject to a budget constraint: Eq. 13 where A0 is the initial capital and MT the pricing kernel. In addition, there is also a liquidity constraint AT ≥ 0 in an almost-sure sense for all t ≤ T. On these assumptions, the solution to the expected utility maximisation problem in Eq. 13 is given by36 An EDHEC-Risk Institute Publication
  • 37. References An EDHEC-Risk Institute Publication 37
  • 38. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 References • Amenc, N., F. Goltz, and A. Grigoriu. 2010a. Risk control through dynamic core-satellite portfolios of ETFs: Applications to absolute return funds and tactical asset allocation. Journal of Alternative Investments 13 (2): 47-57. • Amenc, N., F. Goltz, and V. Le Sourd. 2006. Assessing the quality of stock market indices. EDHEC-Risk Institute Publication (September). • Amenc, N., F. Goltz, L. Martellini, and P. Retkowsky. 2010b. Efficient indexation: An alternative to cap-weighted indices. EDHEC-Risk Institute Publication (January). Forthcoming in Journal of Investment Management. • Artzner, P., F. Delbaen, J.-M. Eber, and D. Heath. 1998. Coherent measures of risk. Mathematical Finance 6: 203-228. • Basak, S. 1995. A general equilibrium model of portfolio insurance. Review of Financial Studies 8: 1059-90. • Basak, S. 2002. A comparative study of portfolio insurance. Journal of Economic Dynamics and Control 26 (7-8): 1217-41. • Black, F., and R. Jones. 1987. Simplifying portfolio insurance. Journal of Portfolio Management 14 (1): 48-51. • Black, F., and A. Perold. 1992. Theory of constant proportion portfolio insurance. Journal of Economic Dynamics and Control 16:403-426. • Brennan, M., E. Schwartz, and R. Lagnado. 1997. Strategic asset allocation. Journal of Economic Dynamics and Control 21 (8-9):1377-1403. • Christoffersen, P., V. Errunza, K. Jacobs, and X. Jin. 2010. Is the potential for international diversification disappearing? (March 16). Available online at SSRN: http://ssrn.com/ abstract=1573345 • Danielsson, J., C. de Vries, B. Jorgensen, S. Mandira, and G. Samorodnitsky. 2010. Fat tails, VaR and subadditivity. Available online at: http://www.riskresearch.org/?papid=35&catid=0 • De Miguel, V., L. Garlappi, and R. Uppal. 2009. Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? Review of Financial Studies 22 (5): 1915-53. • Dubikovsky, V., M. Hayes, L. Goldberg, and M. Liu. 2010. How well can the risk of financial extremes be forecast? Whitepaper, MSCI Barra, Research Insights. • Ekeland, I., A. Galichon, and M. Henry. 2009. Comonotonic measures of multivariate risks. Available online at SSRN: http://ssrn.com/abstract=1115729 • Fréchet, M. 1951. Sur les tableaux de corrélation dont les marges sont données. Ann. Univ. Lyon Sect. A Série 3 (14): 53–77. • Grinold, R. C. 1992. Are benchmark portfolios efficient? Journal of Portfolio Management 19 (1): 34-40.38 An EDHEC-Risk Institute Publication
  • 39. A Post-Crisis Perspective on Diversification for Risk Management — May 2011References• Grossman, S. J., and J.-L. Vila. 1989. Portfolio insurance in complete markets: A note.Journal of Business 62:473-76.• Grossman, S., and Z. Zhou. 1996. Equilibrium analysis of portfolio insurance. Journalof Finance 51 (4): 1379-1403.• Haugen, R. A., and N. L. Baker. 1991. The efficient market inefficiency of capitalizationweighted stock portfolios. Journal of Portfolio Management 17 (3): 35-40.• Hoeffding, W. 1940. Masstabinvariante Korrelationstheorie. Schriften des mathematischenInstituts und des Instituts für angewandte Mathematik der Universität Berlin 5:179-233.• Jan, Y.-C., and Y.-L. Wu 2008. Revisit the debate of time diversification. Journal ofMoney, Investment and Banking 6:27-33.• Kim, T., and E. Omberg. 1996. Dynamic nonmyopic portfolio behavior. Review of FinancialStudies 9 (1): 141-61.• Leland, H. 1980. Who should buy portfolio insurance? Journal of Finance 35 (2): 581-94.• Lioui, A., and P. Poncet. 2001. On optimal portfolio choice under stochastic interestrates. Journal of Economic Dynamics and Control 25 (11): 1841-65.• Longin, F., and B. Solnik. 2001. Extreme correlation of international equity markets.Journal of Finance 56 (2): 649-676.• Markowitz, H. M. 1952. Portfolio selection. Journal of Finance 7 (1): 77-91.• Markowitz, H. M. 1959. Portfolio selection: Efficient diversification of investments.New York: Wiley.• Martellini, L., and V. Milhau. 2010. Hedging versus insurance: Long-term investing withshort-term constraints. Working paper, EDHEC-Risk Institute.• Martellini, L., and V. Ziemann. 2010. Improved estimates of higher-order comomentsand implications for portfolio selection. Review of Financial Studies 23 (4): 1467-1502.• Merton, R. C. 1969. Lifetime portfolio selection under uncertainty: The continuous timecase. Review of Economics and Statistics 51: 247-57.• Merton, R. C. 1971. Optimum consumption and portfolio rules in a continuous-timemodel. Journal of Economic Theory 3:373-413.• Munk, C., and C. Sørensen. 2004. Optimal consumption and investment strategies withstochastic interest rates. Journal of Banking and Finance 28 (8): 1987-2013.• Munk C., C. Sørensen, and T. Vinther. 2004. Dynamic asset allocation under mean-revertingreturns, stochastic interest rates, and inflation uncertainty: Are popular recommendationsconsistent with rational behaviour? International Review of Economics and Finance13:141-66.• Rüschendorf, L. 2010. Worst case portfolio vectors and diversification effects. Forthcomingin Finance and Stochastics. An EDHEC-Risk Institute Publication 39
  • 40. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 References • Sheikh, A. Z., and H. Qiao. 2009. Non-normality of market returns: A framework for asset allocation decision making. Whitepaper, J.P. Morgan Asset Management, JPMorgan Chase & Co. • Stoyanov, S. V., S. Rachev, B. Racheva-Iotova, and F. Fabozzi. 2011. Fat-tailed models for risk estimation. Journal of Portfolio Management 37 (2): 107-17. • Teplá, L. 2001. Optimal investment with minimum performance constraints. Journal of Economic Dynamics and Control 25 (10): 1629-45. • Tobin, J. 1958. Liquidity preference as behavior towards risk. Review of Economic Studies 25:65-86. • Wachter, J. 2002. Optimal consumption and portfolio allocation under mean-reverting returns: An exact solution for complete markets. Journal of Financial and Quantitative Analysis 37:63-91. • Zumbach, G. O. 2007. The RiskMetrics 2006 methodology. Available online at SSRN: http://ssrn.com/abstract=142018540 An EDHEC-Risk Institute Publication
  • 41. About EDHEC-Risk Institute An EDHEC-Risk Institute Publication 41
  • 42. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 About EDHEC-Risk Institute Founded in 1906, EDHEC is The Choice of Asset Allocation An Applied Research Approach one of the foremost French and Risk Management In an attempt to ensure that the research business schools. Accredited by the three main international EDHEC-Risk structures all of its research it carries out is truly applicable, EDHEC academic organisations, work around asset allocation and risk has implemented a dual validation EQUIS, AACSB, and Association management. This issue corresponds to a system for the work of EDHEC-Risk. of MBAs, EDHEC has for a genuine expectation from the market. All research work must be part of a research number of years been pursuing a strategy for international programme, the relevance and goals of excellence that led it to set up On the one hand, the prevailing stock market which have been validated from both an EDHEC-Risk in 2001. situation in recent years has shown the academic and a business viewpoint by With sixty-six professors, limitations of diversification alone as a risk the Institutes advisory board. This board research engineers, and research associates, EDHEC-Risk has management technique and the usefulness is made up of internationally recognised the largest asset management of approaches based on dynamic portfolio researchers, the Institutes business partners, research team in Europe. allocation. and representatives of major international institutional investors. Management of the On the other, the appearance of new asset research programmes respects a rigorous classes (hedge funds, private equity, real validation process, which guarantees the assets), with risk profiles that are very different scientific quality and the operational from those of the traditional investment usefulness of the programmes. universe, constitutes a new opportunity and challenge for the implementation of Six research programmes have been allocation in an asset management or asset- conducted by the centre to date: liability management context. • Asset allocation and alternative diversification This strategic choice is applied to all of the • Style and performance analysis Institutes research programmes, whether • Indices and benchmarking they involve proposing new methods of • Operational risks and performance strategic allocation, which integrate the • Asset allocation and derivative alternative class; taking extreme risks instruments into account in portfolio construction; • ALM and asset management studying the usefulness of derivatives in implementing asset-liability management These programmes receive the support of approaches; or orienting the concept a large number of financial companies. of dynamic “core-satellite” investment The results of the research programmes management in the framework of absolute are disseminated through the EDHEC-Risk return or target-date funds. locations in London, Nice, and Singapore.42 An EDHEC-Risk Institute Publication
  • 43. A Post-Crisis Perspective on Diversification for Risk Management — May 2011About EDHEC-Risk InstituteIn addition, EDHEC-Risk has developed a • The Benefits of Volatility Derivativesclose partnership with a small number of in Equity Portfolio Management,sponsors within the framework of research in partnership with Eurexchairs or major research projects: • Solvency II Benchmarks,• Regulation and Institutional Investment, in partnership with Russell Investmentsin partnership with AXA InvestmentManagers The philosophy of the Institute is to• Asset-Liability Management and validate its work by publication inInstitutional Investment Management, international journals, as well as to makein partnership with BNP Paribas Investment it available through its position papers,Partners published studies, and conferences.• Risk and Regulation in the EuropeanFund Management Industry, Each year, EDHEC-Risk organises a majorin partnership with CACEIS international conference for institutional• Structured Products and Derivative investors and investment managementInstruments, professionals with a view to presentingsponsored by the French Banking the results of its research: EDHEC-RiskFederation (FBF) Institutional Days.• Dynamic Allocation Models and NewForms of Target-Date Funds, EDHEC also provides professionals within partnership with UFG-LFP access to its website, www.edhec-• Advanced Modelling for Alternative risk.com, which is entirely devoted toInvestments, international asset management research.in partnership with Newedge Prime The website, which has more than 42,000Brokerage regular visitors, is aimed at professionals• Asset-Liability Management Techniques who wish to benefit from EDHEC’sfor Sovereign Wealth Fund Management, analysis and expertise in the area ofin partnership with Deutsche Bank applied portfolio management research.• Core-Satellite and ETF Investment, Its monthly newsletter is distributed toin partnership with Amundi ETF more than 700,000 readers.• The Case for Inflation-Linked Corporate EDHEC-Risk Institute: Key Figures,Bonds: Issuers’ and Investors’ Perspectives, 2009-2010in partnership with Rothschild & Cie Nbr of permanent staff 66• Advanced Investment Solutions for Nbr of research associates 18Liability Hedging for Inflation Risk, Nbr of affiliate professors 6in partnership with Ontario Teachers’ Overall budget €9,600,000Pension Plan External financing €6,345,000• Exploring the Commodity Futures Nbr of conference delegates 2,300Risk Premium: Implications for Asset Nbr of participants at EDHEC-Risk 582 Indices & Benchmarks seminarsAllocation and Regulation, Nbr of participants at EDHEC-Riskin partnership with CME Group 512 Institute Risk Management seminars• Structured Equity Investment Strategies Nbr of participants at EDHEC-Risk 247for Long-Term Asian Investors, Institute Executive Education seminarsin partnership with Société GénéraleCorporate & Investment Banking An EDHEC-Risk Institute Publication 43
  • 44. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 About EDHEC-Risk Institute Research for Business improved risk/reward efficiency compared The Institute’s activities have also given to cap-weighted indices. The weighting rise to executive education and research of the portfolio of constituents achieves service offshoots. EDHEC-Risks executive the highest possible return-to-risk education programmes help investment efficiency by maximising the Sharpe ratio professionals to upgrade their skills with (the reward of an investment per unit advanced risk and asset management of risk). These indices provide investors training across traditional and alternative with an enhanced risk-adjusted strategy classes. in comparison to cap-weighted indices, which have been the subject of numerous The EDHEC-Risk Institute PhD in critiques, both theoretical and practical, Finance over the last few years. The index series is www.edhec-risk.com/AIeducation/PhD_Finance based on all constituent securities in the The EDHEC-Risk Institute PhD in Finance FTSE All-World Index Series. Constituents is designed for professionals who aspire are weighted in accordance with EDHEC- to higher intellectual levels and aim to Risk’s portfolio optimisation, reflecting redefine the investment banking and asset their ability to maximise the reward- management industries. It is offered in two to-risk ratio for a broad market index. tracks: a residential track for high-potential The index series is rebalanced quarterly graduate students, who hold part-time at the same time as the review of the positions at EDHEC, and an executive track underlying FTSE All-World Index Series. for practitioners who keep their full-time The performances of the EDHEC-Risk jobs. Drawing its faculty from the world’s Efficient Indices are published monthly best universities and enjoying the support on www.edhec-risk.com. of the research centre with the greatest impact on the financial industry, the EDHEC-Risk Alternative Indexes EDHEC-Risk Institute PhD in Finance creates www.edhec-risk.com/indexes/pure_style an extraordinary platform for professional The different hedge fund indexes available development and industry innovation. on the market are computed from different data, according to diverse fund selection FTSE EDHEC-Risk Efficient Indices criteria and index construction methods; www.edhec-risk.com/indexes/efficient they unsurprisingly tell very different FTSE Group, the award winning global stories. Challenged by this heterogeneity, index provider, and EDHEC-Risk Institute investors cannot rely on competing hedge launched the first set of FTSE EDHEC-Risk fund indexes to obtain a “true and fair” Efficient Indices at the beginning of 2010. view of performance and are at a loss when Offered for a full global range, including selecting benchmarks. To address this All World, All World ex US, All World issue, EDHEC Risk was the first to launch ex UK, Developed, Emerging, USA, UK, composite hedge fund strategy indexes Eurobloc, Developed Europe, Developed as early as 2003. The thirteen EDHEC-Risk Europe ex UK, Japan, Developed Asia Alternative Indexes are published monthly Pacific ex Japan, Asia Pacific, Asia Pacific on www.edhec-risk.com and are freely ex Japan, and Japan, the index series aims available to managers and investors. to capture equity market returns with an44 An EDHEC-Risk Institute Publication
  • 45. EDHEC-Risk Institute Publications and Position Papers (2008-2011) An EDHEC-Risk Institute Publication 45
  • 46. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 EDHEC-Risk Institute Publications (2008-2011) 2011 • Amenc, N., L. Martellini, F. Goltz, and D. Sahoo. Is there a risk/return tradeoff across stocks? An answer from a long-horizon perspective (April). • Amenc, N., L. Martellini, F. Goltz, and L. Tang. Improved beta? A comparison of index- weighting schemes (April). • Sender, S. The elephant in the room: Accounting and sponsor risks in corporate pension plans (March). • Martellini, L., and V. Milhau. Optimal design of corporate market debt programmes in the presence of interest-rate and inflation risks (February). 2010 • Amenc, N., and S. Sender. The European fund management industry needs a better grasp of non-financial risks (December). • Amenc, N., S, Focardi, F. Goltz, D. Schröder, and L. Tang. EDHEC-Risk European private wealth management survey (November). • Amenc, N., F. Goltz, and L. Tang. Adoption of green investing by institutional investors: A European survey (November). • Martellini, L., and V. Milhau. An integrated approach to asset-liability management: Capital structure choices, pension fund allocation decisions and the rational pricing of liability streams (November). • Amenc, N., F. Goltz, Martellini, L., and V. Milhau. New frontiers in benchmarking and liability-driven investing (September). • Martellini, L., and V. Milhau. From deterministic to stochastic life-cycle investing: Implications for the design of improved forms of target date funds (September). • Martellini, L., and V. Milhau. Capital structure choices, pension fund allocation decisions and the rational pricing of liability streams (July). • Sender, S. EDHEC survey of the asset and liability management practices of European pension funds (June). • Goltz, F., A. Grigoriu, and L. Tang. The EDHEC European ETF survey 2010 (May). • Martellini, L., et V. Milhau. Asset-liability management decisions for sovereign wealth funds (May). • Amenc, N., and S. Sender. Are hedge-fund UCITS the cure-all? (March). • Amenc, N., F. Goltz, and A. Grigoriu. Risk control through dynamic core-satellite portfolios of ETFs: Applications to absolute return funds and tactical asset allocation (January). • Amenc, N., F. Goltz, and P. Retkowsky. Efficient indexation: An alternative to cap-weighted indices (January). • Goltz, F., and V. Le Sourd. Does finance theory make the case for capitalisation-weighted indexing? (January).46 An EDHEC-Risk Institute Publication
  • 47. A Post-Crisis Perspective on Diversification for Risk Management — May 2011EDHEC-Risk Institute Publications(2008-2011)2009• Sender, S. Reactions to an EDHEC study on the impact of regulatory constraints on theALM of pension funds (October).• Amenc, N., L. Martellini, V. Milhau, and V. Ziemann. Asset-liability management inprivate wealth management (September).• Amenc, N., F. Goltz, A. Grigoriu, and D. Schroeder. The EDHEC European ETF survey (May).• Sender, S. The European pension fund industry again beset by deficits (May).• Martellini, L., and V. Milhau. Measuring the benefits of dynamic asset allocation strategiesin the presence of liability constraints (March).• Le Sourd, V. Hedge fund performance in 2008 (February).• La gestion indicielle dans limmobilier et lindice EDHEC IEIF Immobilier dEntrepriseFrance (February).• Real estate indexing and the EDHEC IEIF Commercial Property (France) Index (February).• Amenc, N., L. Martellini, and S. Sender. Impact of regulations on the ALM of Europeanpension funds (January).• Goltz, F. A long road ahead for portfolio construction: Practitioners views of an EDHECsurvey. (January).2008• Amenc, N., L. Martellini, and V. Ziemann. Alternative investments for institutionalinvestors: Risk budgeting techniques in asset management and asset-liability management(December).• Goltz, F., and D. Schroeder. Hedge fund reporting survey (November).• D’Hondt, C., and J.-R. Giraud. Transaction cost analysis A-Z: A step towards best executionin the post-MiFID landscape (November).• Amenc, N., and D. Schroeder. The pros and cons of passive hedge fund replication(October).• Amenc, N., F. Goltz, and D. Schroeder. Reactions to an EDHEC study on asset-liabilitymanagement decisions in wealth management (September).• Amenc, N., F. Goltz, A. Grigoriu, V. Le Sourd, and L. Martellini. The EDHEC European ETFsurvey 2008 (June).• Amenc, N., F. Goltz, and V. Le Sourd. Fundamental differences? Comparing alternativeindex weighting mechanisms (April).• Le Sourd, V. Hedge fund performance in 2007 (February).• Amenc, N., F. Goltz, V. Le Sourd, and L. Martellini. The EDHEC European investmentpractices survey 2008 (January). An EDHEC-Risk Institute Publication 47
  • 48. A Post-Crisis Perspective on Diversification for Risk Management — May 2011 EDHEC-Risk Institute Position Papers (2008-2011) 2010 • Amenc, N., and V. Le Sourd. The performance of socially responsible investment and sustainable development in France: An update after the financial crisis (September). • Amenc, N., A. Chéron, S. Gregoir, and L. Martellini. Il faut préserver le Fonds de Réserve pour les Retraites (July). With the EDHEC Economics Research Centre. • Amenc, N., P. Schoefler, and P. Lasserre. Organisation optimale de la liquidité des fonds d’investissement (March). • Lioui, A. Spillover effects of counter-cyclical market regulation: Evidence from the 2008 ban on short sales (March). 2009 • Till, H. Has there been excessive speculation in the US oil futures markets? (November). • Amenc, N., and S. Sender. A welcome European Commission consultation on the UCITS depositary function, a hastily considered proposal (September). • Sender, S. IAS 19: Penalising changes ahead (September). • Amenc, N. Quelques réflexions sur la régulation de la gestion dactifs (June). • Giraud, J.-R. MiFID: One year on (May). • Lioui, A. The undesirable effects of banning short sales (April). • Gregoriou, G., and F.-S. Lhabitant. Madoff: A riot of red flags (January). 2008 • Amenc, N., and S. Sender. Assessing the European banking sector bailout plans (December). • Amenc, N., and S. Sender. Les mesures de recapitalisation et de soutien à la liquidité du secteur bancaire européen (December). • Amenc, N., F. Ducoulombier, and P. Foulquier. Reactions to an EDHEC study on the fair value controversy (December). With the EDHEC Financial Analysis and Accounting Research Centre. • Amenc, N., F. Ducoulombier, and P. Foulquier. Réactions après l’étude. Juste valeur ou non : un débat mal posé (December). With the EDHEC Financial Analysis and Accounting Research Centre. • Amenc, N., and V. Le Sourd. Les performances de l’investissement socialement responsable en France (December). • Amenc, N., and V. Le Sourd. Socially responsible investment performance in France (December). • Amenc, N., B. Maffei, and H. Till. Les causes structurelles du troisième choc pétrolier (November). • Amenc, N., B. Maffei, and H. Till. Oil prices: The true role of speculation (November).48 An EDHEC-Risk Institute Publication
  • 49. A Post-Crisis Perspective on Diversification for Risk Management — May 2011EDHEC-Risk Institute Position Papers(2008-2011)• Sender, S. Banking: Why does regulation alone not suffice? Why must governmentsintervene? (November).• Till, H. The oil markets: Let the data speak for itself (October).• Amenc, N., F. Goltz, and V. Le Sourd. A comparison of fundamentally weighted indices:Overview and performance analysis (March).• Sender, S. QIS4: Significant improvements, but the main risk for life insurance is nottaken into account in the standard formula (February). With the EDHEC Financial Analysisand Accounting Research Centre. An EDHEC-Risk Institute Publication 49
  • 50. For more information, please contact:Carolyn Essid on +33 493 187 824or by e-mail to: carolyn.essid@edhec-risk.comEDHEC-Risk Institute393 promenade des AnglaisBP 311606202 Nice Cedex 3 — FranceEDHEC Risk Institute—Europe10 Fleet Place - LudgateLondon EC4M 7RB - United KingdomEDHEC Risk Institute—Asia1 George Street#07-02Singapore 049145www.edhec-risk.com

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