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Published byEdward Tucker
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Jennifer Bender, PhD Vice President, Applied Research, Americas Optimization Analytics
© All rights reserved. Role of constraints Analyzing the impact of constraints on risk and return Old and new Ex-Ante and Ex-Post Analysis Sensitivity 2
© All rights reserved. Asset managers use constraints for a variety of reasons, including: correct for overly large/small positions limit exposure to certain sources of risk which are either undesirable or for which they have no information achieve a certain risk profile 3
© All rights reserved. And to: lower trading costs comply with institutional requirements, such as no-shorting reduce influence of errors in input estimates Constraints may impair performance 4
© All rights reserved. Unconstrained problem: Optimal portfolio: 5 Risk Return
© All rights reserved. Constrained problem: For each constraint i, we get the a shadow price,, which is the rate at which the portfolio utility increases as we relax the constraint. (These apply only for small changes) The optimal constrained portfolio satisfies: 6
© All rights reserved. Now, 7
© All rights reserved. 8 Active frontier without constraint Active frontier with constraint(s) Risk Alpha
© All rights reserved. The constraint portfolio is the sum of individual constraint portfolios: is the portfolio with the smallest risk per unit exposure to constraint i 9
© All rights reserved. MSCI US Prime Market 750 Index is universe and benchmark (March 2008) Alpha is based on Barra US Short-Term Model (USE3S) Earning Yield factor Risk model = USE3S Constraints Long-Only Size Factor Neutral Budget (Holdings must sum to 1) 10
© All rights reserved. 11
© All rights reserved. We can attribute return to the manager’s information and to the constraints: Unconstrained portfolio: Constraints: 12
© All rights reserved. Risk Contributions: Constraints: 13
© All rights reserved. Constraints act in two ways: - To alter the risk and return without changing the information ratio - To add risk but no return 14
© All rights reserved. The constrained portfolio = Information + Noise: 15 The information ratio is:
© All rights reserved. New holdings decomposition: 16 Individual constraints:
© All rights reserved. Constraints consume the risk budget 17 Original Method
© All rights reserved. We can attribute a manager’s ex-post performance to the information and the constraints Each period, we compute: We compute average realized returns to the information and constraint portfolios To determine the risk contribution from each source, we compute its empirical risk contribution. For example, 18
© All rights reserved. MSCI US Prime Market 750 Index is universe and benchmark Alpha is based on USE3S Earning Yield Risk model = USE3S Manager keeps active risk at 3% forecast active risk every month Constraints Long-Only Neutral to Earnings Variability Budget (Holdings must sum to 1) Backtest period: January 2000 to December
© All rights reserved. 20 Ex-Ante Ex-Post
© All rights reserved. 21 Remove Long-only Constraints Remove Earnings Variability Constraint Was 2.52 Was 3.56Was Was Was 2.55 Was 1.75 Was 1.61
© All rights reserved. We allow some shorting and reign in the industry bets 22
© All rights reserved. As we relax constraint “i” by a little, : where If the constraint portfolios have little covariance, mainly changes ! 23
© All rights reserved. Constraints may force a manager to take unintended bets and incur risk that are unrelated to his information Managers may want to know Which constraints are the most “costly”? What is the effect of constraint(s) on realized performance ? We show how to analyze the impact of individual constraints on the ex-ante and ex-post risk and return of the portfolio 24
© All rights reserved. Grinold, Richard and Kelly Easton (1998), “Attribution of Performance and Holdings,” in Worldwide Asset and Liability Modeling, eds. W.T. Ziemba, John M. Mulvey, Isaac Newton Scherer, Bernd and Xiadong Xu (2007), “The Impact of Constraints on Value-Added,” The Journal of Portfolio Management,
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© All rights reserved. 27 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., 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, including without limitation (as applicable), any liability for death or personal injury to the extent that such injury results from the negligence or wilful default of itself, its servants, agents or sub-contractors. 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. © 2010 MSCI Barra. All rights reserved. RV0110
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