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Risk Management for Hedge Funds
Risk Management for Hedge Funds
Risk Management for Hedge Funds
Risk Management for Hedge Funds
Risk Management for Hedge Funds
Risk Management for Hedge Funds
Risk Management for Hedge Funds
Risk Management for Hedge Funds
Risk Management for Hedge Funds
Risk Management for Hedge Funds
Risk Management for Hedge Funds
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Risk Management for Hedge Funds

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  • 1. Risk Management for Hedge Funds | January 2008 William Peets Abstract Hedge funds and other long-short investors can use the Barra factor models to manage their risk in a variety of ways covering different complexities. Using the asset-by-asset covariance matrix, which incorporates all information in the estimated factor covariance matrix and the exposures of individual assets to the factors, is the most complete way to assess risk using Barra models. However, often the hedge fund risk officer’s objective is to put in place simple controls that portfolio managers can execute in a straightforward way. This article describes different levels of risk control ranging from the simplest case to the full risk model, focusing on what tradeoffs exist for each use case. Introduction Hedge funds often employ strategies that utilize short selling, derivatives and other complex instruments. Many hedge fund managers also use leverage as a means of increasing the flexibility to exploit return opportunities. The dynamic nature of these strategies requires fund managers to closely monitor their positions and capital allocation. The Barra factor models provide an individual contribution to risk for each asset to the portfolio. This contribution to risk captures the relative riskiness of the asset, taking into account its exposures to the various systematic factors in the market as well as the forecast volatilities and correlations between these factors. However, contribution to risk can be a somewhat unwieldy and unintuitive tool for hedge fund managers. Thus hedge fund risk officers are often looking for simple and intuitive ways to impose risk controls on their managers’ trades. A straightforward method often employed is to impose limits on the exposure of the portfolio to various systematic factors in addition to individual position limits. This approach has the disadvantage of not taking into account the different risk profiles of the individual factors. Controls can then be adjusted to take into account factor volatilities either with, or without, the correlations between factors. Of course, ideally the risk manager wants to use all of the information he has at his disposal without sacrificing tractability in implementing risk controls. In this paper, we discuss the different ways in which hedge funds could potentially implement risk controls. Our goal is to clarify the assumptions for each type of risk control framework and what tradeoffs the hedge fund risk manager faces. 1. Three Use Cases for Hedge Fund Risk Management Exposures and Risk Forecasts in the Barra Factor Models The aim of a fundamental factor model is to explain security level returns using a set of common factors. These factors should be intuitive and robust. In the case of the US long horizon model (USE3L), there are 55 industry factors and 13 style or risk factors. Style factors are created using descriptors that are based on fundamental ratios such as market capitalization, dividend yield, leverage, etc. The exposures of individual securities to these factors are observable and factor returns are estimated via cross-sectional regressions. (Factor returns are estimated by regressing the equity returns of the estimation universe on the set of exposures every day.) Once a history of factor returns is produced, a factor covariance matrix can be constructed. MSCI Barra © 2008 MSCI Barra. All rights reserved. 1 of 11 Please refer to the disclaimer at the end of this document.
  • 2. Risk Management for Hedge Funds | January 2008 The forecast risk for any security or portfolio is then a function of its exposures and the factor covariance matrix.1 It is important to highlight that security exposures are normalized with respect to the estimation universe which consists roughly of the largest 2000 securities in the US equity universe. Normalizing the exposures this way implies that the weighted average of the estimation universe has an exposure of 0 and standard deviation of 1.0 to each of the factors in the model. This allows for a simple interpretation of factor exposures on the asset level. For example, if a security has an exposure of 1.0 to the USE3L Momentum factor, this means it has an exposure that is one standard deviation greater than the average exposure of the estimation universe. If Momentum is expected to increase by 5% and a stock has an exposure of 1.0 to Momentum, then the stock is expected to also increase by 5%, holding all else equal. Portfolio level exposures are simply the weighted average of security level exposures. Case 1: Imposing Limits Using Dollar Exposures One way how some managers control risk is to set limits on a portfolios’ factor exposures. Exposures are easy to compute and interpret since a portfolio’s exposure to a factor is just the weighted average of the stocks’ exposures. Portfolio returns are linearly related to factor returns, as described above, holding all else equal. Managers can convert the exposures to dollar exposures by scaling the exposures by the position or portfolio value, which avoids the need to calculate weights given the ambiguity of using them in the context of long-short portfolios. DE f = PositionValue × X f (1) where: PositionValue = dollar value of the position X f = Barra exposure of the position to factor f Figure 1 illustrates the ease of computing dollar exposures. Figure 1: Computing Dollar Exposures Position USE3L MOM USE3L MOM Security Weight Value Exp $Exp AAPL 82.45% 3,604.40 2.27 $8,193 GOOG 158.35% 6,922.60 0.20 $1,378 - GS -4,550.40 1.42 -$6,466 104.09% MS -36.71% -1,605.00 -0.40 $645.21 $4,372 0.86 $3,749 Weighted Port. Dollar Total Port. Val. Exp Exp. σ P = (wP (X T FX + Δ )wP ) where wP = vector of portfolio weights, X T1/ 2 1 Specifically, the risk of a portfolio is = exposure matrix, F = factor covariance matrix, and Δ = diagonal matrix of specific risk. MSCI Barra © 2008 MSCI Barra. All rights reserved. 2 of 11 Please refer to the disclaimer at the end of this document.
  • 3. Risk Management for Hedge Funds | January 2008 Dollar exposures capture how much money is exposed to the volatility of systematic risk and can be calculated with respect to any of the factors in a model. For example, the manager may be asked to control his or her dollar exposure to any of the USE3 factors--for example Momentum, Value, Growth, Size, or Leverage. A simple way of imposing risk limits is to cap the dollar exposure any one manager can be exposed to for a certain factor. A similar use of dollar exposures is to instruct portfolio managers to be dollar-factor-neutral or confined within some bound. For instance, portfolio managers may be required to have their net (long plus short) style factor exposures within a given range of the single-side book value.2 Enforcing constraints like these are very common in market-neutral and portable alpha strategies where a manager’s success in isolating alpha depends on his or her ability to remain factor-neutral. Note that one pitfall with dollar exposures is that they may sometimes be unintuitive in that the total dollar exposure of a portfolio can exceed the actual value of the portfolio. Thus if the hedge fund has a 2.0 exposure to Momentum on a USD 1 billion portfolio, then the dollar exposure is USD 2 billion. This may at first glance seem counterintuitive but does in fact represent the true dollar exposure of the position though it does not offer insights into the risk coming from the Momentum exposure. Case 2: Risk-adjusted Exposure Limits and Volatility Budgeting So far, we have not accounted for differences in volatility across factors. In a later example, we see that, Momentum has been a more volatile factor than Value. Thus, when setting limits using dollar exposures, a hedge fund manager may want to consider the individual factor volatilities. Specifically, dollar exposures can be adjusting using the forecasted risk for the relevant factor: DollarsatRisk f = PortValue × X f × σ f (2) where X f = the exposure of the portfolio to factor f σf = the forecast volatility of factor f The quantity in Equation 2 is often called “dollar volatility” or “dollars-at-risk” and represents the actual portfolio value at risk coming from the factor in question. Similar to dollar exposures, a hedge fund risk manager can set limits on the dollars-at-risk for each factor which explicitly will take into account the risk coming from the factor. Dollars-at-risk can also be useful as a first step in volatility budgeting. Given some total dollar amount at risk (the portfolio’s total value perhaps scaled for risk), the risk manager can set a budget for each individual systematic factor. For example, he might state that no more than 20% of dollar volatility can come from any one factor. Therefore, for a portfolio of USD 100 million, no more than USD 20 million can be allocated to any one factor. The risk manager can then compare his dollars-at-risk (from Equation 2) against this budget. Alternatively he can set the maximum dollar exposure for each factor as: PortfolioValue * k MaxDollarExposure f = (3) σf where k is the maximum allocation to any one factor (i.e., 20% in this example). 2 For instance, assume a manager has a portfolio that is invested USD 100M long and USD 100M short, with the style factor budget being +/-10% of the single side book size. The hedge fund manager may wish to target some net exposure to a factor, for instance, 0.05 to the Barra Momentum factor. The dollar exposure limit can then be used in an optimizer. The resulting portfolio might have a long dollar exposure to Momentum of USD 20M, a short dollar exposure of -USD 15M, with the net dollar exposure ending up as USD 5M. This ends up being equivalent to 5% of a single-side book value and translates into the desired 0.05 (USD 5/USD 100) exposure to Momentum. MSCI Barra © 2008 MSCI Barra. All rights reserved. 3 of 11 Please refer to the disclaimer at the end of this document.
  • 4. Risk Management for Hedge Funds | January 2008 Case 3: Controlling Risk Through Beta The last case we describe concerns the use of betas for controlling risk. Using betas to understand the risk of the portfolio to the market as well as the individual factors has all the advantages of the previous cases in that betas are tractable and relatively easy to work with. They also make full use of the information in the risk model. Expected profit and loss at the portfolio and individual asset level can be linked to the exposures and the volatility of the factors through betas. The standard concept of beta links a security’s return to aggregate market movements; in other words beta captures the sensitivity to market- wide risk. Within the Barra factor model, betas are called “fundamental betas” and capture the risk from all sources of systematic or common factor risk. In addition, a variety of betas can be computed, not just that of the beta to the market. Examples include: The beta of a stock or portfolio to a market index The beta of a factor (i.e., a factor-mimicking portfolio) to a market index The beta of a stock or portfolio to some other portfolio The beta of a stock or portfolio to a factor The beta of one stock to another Fundamental betas make use of the factor covariance matrix and the exposures of the individual assets. They are calculated for a portfolio or security as: cov(ri , rm ) wiT XFX T wm + wiT Δwm β i ,m = = (4) σm 2 σm 2 where σ m = market volatility wi = vector of N weights for a portfolio i wm = vector of N weights for market portfolio X = exposure matrix of N assets to K factors F = K x K factor covariance matrix Δ = N x N diagonal matrix of specific risk Returning to our previous cases where the objective was to understand the risk of the portfolio arising from some factor like Momentum, we introduce the concept of “factor betas.” Factor betas are the betas of the Barra factors to the market. Then we can use the factor betas to compute the beta of individual assets to the market purely due to its exposure to an individual factor f . β i , f = xi , f β f (5) where xi , f is the exposure of the stock to the factor and β f is the beta of the factor to the market. Note that this representation is not the same as a stock’s beta to the market β i ,m . The beta shown in Equation 5 is the beta of a stock to the market arising solely from (i.e., holding all else equal) a factor. To illustrate the use of these betas, consider the securities shown in Figure 2 with their exposures to a handful of factors as of November 2007. MSCI Barra © 2008 MSCI Barra. All rights reserved. 4 of 11 Please refer to the disclaimer at the end of this document.
  • 5. Risk Management for Hedge Funds | January 2008 Figure 2: Portfolio Position Exposures in BarraOne US Momentum US Growth US Leverage US Volatility Asset Name Mkt Value Exp Exp Exp Exp Apple $3,604 2.273 0.779 -0.120 0.755 Computers Google $6,923 1.421 3.671 -0.556 0.135 Goldman Sachs -$4,550 0.199 0.715 1.381 0.448 Morgan Stanley -$1,605 -0.402 0.362 1.451 -0.028 Figure 2 tells us that the exposure of Apple to US Momentum is much higher than the other three assets shown. Apple’s exposures to other factors shown—Growth, Leverage, and Volatility—are not quite as large. But without knowing how volatile these factors are, we cannot say how risky these exposures really are. Figure 3 shows these volatilities. Figure 3: Sample Factor Exposure Report in BarraOne Factor Volatility US Volatility 4.79 US Momentum 3.81 US Earnings Yield 3.14 US Size Non-Linearity 2.39 US Size 1.74 US Earnings Variation 1.53 US Trading Activity 1.52 US Value 1.46 US Leverage 1.42 US Growth 1.26 US Yield 1.19 US Currency Sensitivity 1.14 From Figures 2 and 3, we glean that for a USD 1M holding of Google, the position value of Google is expected to change by +/-USD 54,102 [USD 1M*1.42 (Exposure of Google to Momentum) *3.81% (US Momentum Volatility) =USD 54,102] with a 68% probability over the course of the next year through its exposure to US Momentum, assuming changes in Momentum do not affect any of the other factors.3 In reality, a change in one factor usually does not take place in isolation but in conjunction with other factor movements, meaning that we may be better off using beta in Equation 5, which accounts for factor relationships. 3 Of course the portfolio manager must also be wary of deviations from normality since the distribution of certain factor returns can be leptokurtic. This suggests the occurrence of a one sigma event is much more common and the frequency of 4 or 5 sigma events is much higher than if factor returns were normally distributed. See MSCI Barra Research Bulletins, “Risk Management During Turmoil” (August 13, 2007) and “The End of the Momentum Run?” (November 15, 2007). MSCI Barra © 2008 MSCI Barra. All rights reserved. 5 of 11 Please refer to the disclaimer at the end of this document.
  • 6. Risk Management for Hedge Funds | January 2008 Figure 4 shows the beta of the USE3L style factors relative to the MSCI US Prime Market 750 Index. Figure 4: Factor Betas in BarraOne Beta (MSCI US Prime US Style Factor Market 750 Index) US Currency Sensitivity -0.0103 US Earnings Variation 0.0053 US Earnings Yield 0.0051 US Growth 0.0107 US Leverage -0.0013 US Momentum -0.0110 US Size Non-Linearity -0.0472 US Size 0.0291 US Size Non-Linearity 0.0424 US Trading Activity 0.0767 US Value -0.0004 US Volatility 0.3073 US Yield -0.0218 Combining the factor betas in Figure 4 with the exposures in Figure 2, we expect that given a 5% return in the market, Apple is expected to move 1.16% due to Volatility, -0.125% due to Momentum and so forth. Lastly, we show the common factor, idiosyncratic, and total risk forecast for each of the securities in our example in Figure 5. Style risk in Figure 5 reflects risk coming from the 13 US styles while industry risk reflects risk due to the stock’s industry membership. Note that style and industry variance sums to common factor variance, and that common factor variance and selection variance sums to total variance, which we discuss in more detail in the next section. Figure 5: Portfolio Position Risk in BarraOne Common Style Industry Selection Total Asset Name Factor Risk Risk Risk Risk Risk Apple Computers 11.14 13.36 20.93 35.46 41.18 Google 8.93 19.23 24.31 33.18 41.13 Goldman Sachs 6.18 19.54 23.72 28.02 36.71 Morgan Stanley 6.28 19.30 20.68 21.50 29.83 It is important to highlight that in Figure 5, selection risk dominates risk for these four stocks. For most individual stocks, the larger portion of risk comes from the idiosyncratic risk, not common factors. This implies that using factor betas and exposures to manage risk has a greater impact at the portfolio level than the stock level. At the stock level, the selection risk must be managed separate from the factor exposures. Still, asset-level analysis can be helpful in understanding the drivers of individual stock movements. In sum, analyzing individual asset exposures and betas to certain factors and looking at betas to the market via individual factors can be extremely useful for long-short portfolio managers. Managers can moreover use this type of analysis in conjunction with their fundamental or proprietary information including company comparisons, cash flow models, dividend discount MSCI Barra © 2008 MSCI Barra. All rights reserved. 6 of 11 Please refer to the disclaimer at the end of this document.
  • 7. Risk Management for Hedge Funds | January 2008 models, etc. Barra exposures and betas may help to red flag certain positions, particularly those for which the portfolio manager is less confident. In some instances, managers may identify large unintended bets which can then be neutralized. 2. Additional Risk Tools The previous three cases provide successively more detailed means of evaluating risk, each using incrementally more information from the risk model. For a more comprehensive risk analysis, additional tools are available to help augment trade decisions and better understand the risk exposures and their sources. First, a correlation report can be used in conjunction with a factor exposures report to better understand the potential impact of factor return movements. Looking at Figure 6, which shows a handful of correlations as of November 2007, we see that there is a moderate positive predicted correlation between US Growth and US Volatility. This might suggest that a portfolio manager be more sensitive to an asset that has a positive exposure to both Growth and Volatility. Figure 6: Factor Correlation Report in BarraOne USE3L Factor US Momentum US Leverage US Growth US Volatility US Momentum 1.000 US Leverage -0.202 1.000 US Growth -0.127 -0.139 1.000 US Volatility -0.093 -0.051 0.234 1.000 Similar to the factor betas, this view addresses the impact of factor correlations. To better capture the degree to which factor exposures contribute to or reduce risk, we can look at a risk decomposition report in conjunction with a factor exposures report for either a portfolio or individual security. Figure 7, for example, shows how risk can be decomposed for Apple Computers to understand what are the biggest sources or contributors of risk.4 Figure 7 also shows the exposures of Apple to the factors shown above in Figure 6. 4 The risk decomposition report shown in Figure 7 is performed using an adaptation of the BarraOne risk decomposition which is described in Menchero (2006). See Menchero, J. “Portfolio Risk Attribution,” Journal of Performance Measurement, Spring 2006. MSCI Barra © 2008 MSCI Barra. All rights reserved. 7 of 11 Please refer to the disclaimer at the end of this document.
  • 8. Risk Management for Hedge Funds | January 2008 Figure 7: Apple Computers: X-Sigma-Rho Risk Analysis Report Apple Computers Risk Source Portfolio Risk Portfolio Variance % Portfolio Risk Local Market Risk 41.18 1,695.87 100.00% Common Factor Risk 20.93 438.18 25.84% Industry 13.36 178.50 10.53% Style 11.14 124.14 7.32% Factor Interaction N/A 135.54 7.99% Selection Risk 35.46 1,257.70 74.16% Total Risk 41.18 1,695.87 100.00% % Contribution to Total Risk Factor Volatility Exposure Risk MCTR Cont. from from Total to TR Volatility Covariance US Volatility 4.79 0.76 3.62 0.02 2.58 0.77% 2.41% 3.18% US Momentum 3.81 2.27 8.66 0.01 3.27 4.42% -0.38% 4.04% US Leverage 1.42 -0.12 0.17 0.00 0.03 0.00% 0.04% 0.04% US Growth 1.26 0.78 0.98 0.00 0.23 0.06% 0.22% 0.28% Style Factors 6.110 5.25% 2.29% 7.54% Total Portfolio Risk Source Portfolio Risk Portfolio Variance % Portfolio Risk Local Market Risk 54.81 3,004.52 100.000% Common Factor Risk 25.34 642.07 21.370% Industry 15.55 241.86 8.050% Style 14.42 207.82 6.917% Factor Interaction N/A 192.39 6.403% Selection Risk 48.61 2,362.45 78.630% Total Risk 54.81 3,004.52 100.000% % Contribution to Total Risk Factor Volatility Exposure Risk MCTR Cont. from from Total to TR Volatility Covariance US Volatility 4.79 0.38 1.82 0.01 0.42 0.11% 0.25% 0.36% US Momentum 3.81 4.06 15.49 0.01 7.33 7.98% -1.81% 6.18% US Leverage 1.42 -2.95 4.20 0.00 1.76 0.59% 0.90% 1.48% US Growth 1.26 5.58 7.01 0.00 2.24 1.63% 0.25% 1.89% Style Factors 11.744 10.32% -0.41% 9.90% Figure 7 shows that although US Volatility contributes a substantial amount to the total risk of Apple, it plays a relatively minor role in the total risk of the portfolio. Furthermore, it shows that US Leverage and US Growth have a larger impact on the total risk of the portfolio than they do to Apple individually, and that the covariances between the factors at the portfolio level actually reduce total risk. MSCI Barra © 2008 MSCI Barra. All rights reserved. 8 of 11 Please refer to the disclaimer at the end of this document.
  • 9. Risk Management for Hedge Funds | January 2008 Conclusion Hedge funds and other long-short investors can use the information in Barra factor models to manage their risk in a variety of ways. First, Barra exposures can be a useful metric for designing limits on individual and portfolio positions. Second, adjusting these exposures for their respective factor volatilities provides important additional information, for instance in setting up a risk budget. Third, factor betas can help illuminate how correlations between factors impact portfolio risk. Overall, factor models provide a flexible framework to allow risk managers to slice and dice the components of risk in the manner he or she finds most valuable. MSCI Barra © 2008 MSCI Barra. All rights reserved. 9 of 11 Please refer to the disclaimer at the end of this document.
  • 10. Risk Management for Hedge Funds | January 2008 Contact Information clientservice@mscibarra.com Americas Americas 1.888.588.4567 (toll free) Atlanta + 1.404.949.4529 Boston + 1.617.856.8716 Chicago + 1.312.706.4999 Montreal + 1.514.847.7506 New York + 1.212.762.5790 San Francisco + 1.415.576.2323 Sao Paulo + 55.11.3048.6080 Toronto + 1.416.943.8390 Europe, Middle East & Africa Amsterdam + 31.20.462.1382 Cape Town + 27.21.683.3245 Frankfurt + 49.69.2166.5325 Geneva + 41.22.817.9800 London + 44.20.7618.2222 Madrid + 34.91.700.7275 Milan + 39.027.633.5429 Paris 0800.91.59.17 (toll free) Zurich + 41.1.220.9300 Asia Pacific China Netcom 10800.852.1032 (toll free) China Telecom 10800.152.1032 (toll free) Hong Kong + 852.2848.7333 Singapore + 65.6834.6777 Sydney + 61.2.9033.9333 Tokyo + 813.5424.5470 www.mscibarra.com MSCI Barra © 2008 MSCI Barra. All rights reserved. 10 of 11 Please refer to the disclaimer at the end of this document.
  • 11. Risk Management for Hedge Funds | January 2008 Notice and Disclaimer This document and all of the information contained in it, including without limitation all text, data, graphs, charts (collectively, the “Information”) is the property of MSCI Inc. (which is registered to do business in New York under the name NY MSCI), Barra, Inc. (“Barra”), or their affiliates (including without limitation Financial Engineering Associates, Inc.) (alone or with one or more of them, “MSCI Barra”), or their direct or indirect suppliers or any third party involved in the making or compiling of the Information (collectively, the “MSCI Barra Parties”), as applicable, and is provided for informational purposes only. The Information may not be reproduced or redisseminated in whole or in part without prior written permission from MSCI or Barra, as applicable. The Information may not be used to verify or correct other data, to create indices, risk models or analytics, or in connection with issuing, offering, sponsoring, managing or marketing any securities, portfolios, financial products or other investment vehicles based on, linked to, tracking or otherwise derived from any MSCI or Barra product or data. Historical data and analysis should not be taken as an indication or guarantee of any future performance, analysis, forecast or prediction. None of the Information constitutes an offer to sell (or a solicitation of an offer to buy), or a promotion or recommendation of, any security, financial product or other investment vehicle or any trading strategy, and none of the MSCI Barra Parties endorses, approves or otherwise expresses any opinion regarding any issuer, securities, financial products or instruments or trading strategies. None of the Information, MSCI Barra indices, models or other products or services is intended to constitute investment advice or a recommendation to make (or refrain from making) any kind of investment decision and may not be relied on as such. The user of the Information assumes the entire risk of any use it may make or permit to be made of the Information. NONE OF THE MSCI BARRA PARTIES MAKES ANY EXPRESS OR IMPLIED WARRANTIES OR REPRESENTATIONS WITH RESPECT TO THE INFORMATION (OR THE RESULTS TO BE OBTAINED BY THE USE THEREOF), AND TO THE MAXIMUM EXTENT PERMITTED BY LAW, MSCI AND BARRA, EACH ON THEIR BEHALF AND ON THE BEHALF OF EACH MSCI BARRA PARTY, HEREBY EXPRESSLY DISCLAIMS ALL IMPLIED WARRANTIES (INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES OF ORIGINALITY, ACCURACY, TIMELINESS, NON-INFRINGEMENT, COMPLETENESS, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE) WITH RESPECT TO ANY OF THE INFORMATION. Without limiting any of the foregoing and to the maximum extent permitted by law, in no event shall any of the MSCI Barra Parties have any liability regarding any of the Information for any direct, indirect, special, punitive, consequential (including lost profits) or any other damages even if notified of the possibility of such damages. The foregoing shall not exclude or limit any liability that may not by applicable law be excluded or limited. Any use of or access to products, services or information of MSCI or Barra or their subsidiaries requires a license from MSCI or Barra, or their subsidiaries, as applicable. MSCI, Barra, MSCI Barra, EAFE, Aegis, Cosmos, BarraOne, and all other MSCI and Barra product names are the trademarks, registered trademarks, or service marks of MSCI, Barra or their affiliates, in the United States and other jurisdictions. The Global Industry Classification Standard (GICS) was developed by and is the exclusive property of MSCI and Standard & Poor’s. “Global Industry Classification Standard (GICS)” is a service mark of MSCI and Standard & Poor’s. The governing law applicable to these provisions is the substantive law of the State of New York without regard to its conflict or choice of law principles. © 2008 MSCI Barra. All rights reserved. About MSCI Barra MSCI Barra is a leading provider of investment decision support tools to investment institutions worldwide. MSCI Barra products include indices and portfolio analytics for use in managing equity, fixed income and multi-asset class portfolios. The company’s flagship products are the MSCI International Equity Indices, which are estimated to have over USD 3 trillion benchmarked to them, and the Barra risk models and portfolio analytics, which cover 56 equity and 46 fixed income markets. MSCI Barra is headquartered in New York, with research and commercial offices around the world. Morgan Stanley, a global financial services firm, is the majority shareholder of MSCI Barra. MSCI Barra © 2008 MSCI Barra. All rights reserved. 11 of 11 Please refer to the disclaimer at the end of this document.

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