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ESG Portfolio Optimization based on the Latent Dimensions within the Thomson Reuters Corporate Responsibility Indices Gordon H Dash*Nina Kajiji**

*College of Business Administration and interdisciplinary Neuroscience Program, University of Rhode Island**Computer Science and Statistics, University of Rhode Island

Email: ghdash@uri.eduEmail: nina@uri.edu

For presentation at:27th European Conference on Operational ResearchJuly 12-15, 2015Glasgow, Scotland

Research was funded by grants from:The College of Business Administration, Univ. of RI; and,The NKD Group, Inc., USA

Motives Two Main ObjectivesFirst, to create a new market pricing factor that captures unexplained market risk within the market returns of ESG designated equities.Despite the investment communities increased reliance on various factor selection methodologies, the debate on how best to estimate an independently priced ESG factor remains a topic of inquiry. We propose the creation of a ESG-related equity pricing factor based upon latent after-market returns volatility within the sample of stocks that comprise the Thomson Reuters US Large Cap Corporate Responsibility Ratings ESG portfolio (TRSRLCP).To demonstrate the pricing efficiency of the new factor by producing comparative multiple objective Sharpe diagonal modelsEURO 2015, July 12-15, 2015Slide: 2 / 20

ESG InvestingESG stands for Environmental, Social and Governance.ESG investing adds value in at least 3 ways:Allows investors to make a social impact beyond just obtaining financial returns.It augments the usefulness of risk-adjusted returns.Integrates non-financial indexes into the portfolio building process.By Contrast, socially responsible (SR) investing applies a screen to deselect sin socks.EURO 2015, July 12-15, 2015Slide: 3 / 20

Literature Contributions: ESG

Extant research reports significant correlation between risk-adjusted returns for ESG-tilted investment plans. Companies with high ESG scores tend to have less company-specific risk (Bouslah, Kryzanowski et al. 2011) and (Oikonomou, Brooks et al. 2012).ESG criteria contribute to overall portfolio diversification ((Hoepner 2010), (Hoepner, Rezec et al. 2013)). Nagy, Z.,et.al. (2013) Examine the efficient characteristics of Three ESG-tilted strategies to demonstrate superiority to non-ESG optimized portfolios.Also, see Deutsche Bank Climate Change Advisers (2012) EURO 2015, July 12-15, 2015Slide: 4 / 20

The Thomson Reuters CR PortfolioThe Thomson Reuters Corporate Responsibility Indices are a suite of benchmarks designed to measure the performance of companies with superior ratings for Environmental, Social and Governance Practices (http://www.trcri.com/). The indices represent a comprehensive benchmarking system for CSR investors and are powered by dynamic ratings based on the Thomson Reuters ASSET4 ESG database.Thomson Reuters US Large Cap Corporate Responsibility Ratings ESG portfolio (TRCRLCP).EURO 2015, July 12-15, 2015Slide: 5 / 20

DataDaily price and dividend data for all trading days from 01-Jan-2014 to 30-June-2015, inclusive (Yahoo Financial): *Newly updatedEstimate daily returns for:243 equity tickers of the TRCRLCP, andS&P 500 (^GSPC)

Create daily market residuals then estimate Vasicek (1973) smart market beta coefficients across sample (also, see Sarker,2013 for international implications of Vasicek beta; Hollstein, et.al., 2014 for estimating efficiency; and, Clark, 2015 for discussion on inter-temporal stability ):

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Exploratory Factor Analysis (EFA)Principal Components Analysis (PCA) with Varimax Rotation243 Market residuals (corresponding to the TRCRLCP securities);375 observations Within the PCA solution, components (C) with eigenvalues 1.0 and above were retained; a methodology which produced 73 factors (see, Jackson, 2005 for a discussion on EFA).Orthogonally rotate (C) factors using the Varimax method.Label the Varimax proxies to correspond to latent traded industry effects within the return generating structure of the TRCRLCP ESG portfolio (e.g. Fertuck, 1975; Kajiji, et.al. 2010).EURO 2015, July 12-15, 2015Slide: 7 / 20

Factor Extraction Latent Industry domains within the ESG Portfolio (see, Fertuck, 1975; Kajiji, et.al.,2010)Fk - Latent DomainSec loadings > 0.4% of Var.Cum %1. Oil & Gas215.781 5.781 2. Energy144.69610.477 3. Financial163.28113.758 4. Device Mfgs123.01316.771 5. Apparel81.54918.320

Given an eigenvalue 1.0, 73 factors (Fk) account for 75.49% of the variation in the after-market-residuals of TRCRLCP tickers.The contribution of the first five factors (18%) as shown below (eigenvalue 1.5)Domain Factor ScoresFactor scores are composite variables that represent an orthogonal set of latent industry factors.For each (C) Latent factor, we compute a vector of factor scores such that each factor score vector has n-observations.Factor scores are computed using Thomson (1951) Maximum Validity (or regression) method it states that, if fr is the score of the rth factor corresponding to a response of x, then we estimate fr by a linear combination of the xi:

We choose ar such that is minimized. The solution is estimated by:

where is the factor loading matrix, the covariance matrix, and x the original data matrix. From each set of responses x we obtain the vector of factor scores f.

Index Derivation from Factor Score DomainsThe factor score index (FSI) value at time t is calculated as a simple average across the C=73 factor scores (fti) as computed from Varimax rotated factors (recall: 73 Factors were retained in the study).

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CorrelationS&P 500MSCINA Mid/L Cap ESG IndexFSI S&P 5001.0000.997-0.010MSCI1.0000.007FSI1.000Comparative Efficient SetsEURO 2015, July 12-15, 2015Slide: 11 / 20

Markowitz dominatesFSI Multiple FactorSingle FactorCorrelated Multiple Factor ModelKajiji et.al. (2010) apply a 5 year coincident methodology to the insurance industry. Among alternative efficient sets, they find:Sharpe Diagonal ModelKey Advantages of Index-based Sharpe Diagonal Portfolio model (SDM)Sharpe (1964)Quadratic ProgramRequires N+1 terms No Cross Product Terms.All variables are SeparableKey Properties of Markowitz Mean VarianceQuadratic Program[(N2-N)/2]+N terms Complete Covariance MatrixSeparability would require problem expansion in both variables and constraints EURO 2015, July 12-15, 2015Slide: 12 / 20

The SDM with Smart BetasEURO 2015, July 12-15, 2015Slide: 13 / 20

The Multiple Factor Smart Beta SDM: Vasicek and ESG-FSIThe Multiobjective (NLGP) SDMDash, G.H., and Kajiji, N. (2014): Multiobjective portfolio optimization with combinatorial methods to dynamically hedge interim period performance.Kwon, R., Stoyan, Steven J. (2011): incorporated a wide set of real-world trading constraints to the mean-variance portfolio framework. Solved both MV and MAD. Focus: MIP and trading system constraintsAnagnostopoulos, K.P and Mamanis, G. (2010): formulated the MV problem as a bi-objective linear mixed integer optimization problem.Xidonas, P; Mavrotas, G; and, Psarras, J. (2010): Multiple Criteria Decision-Making Approach. MO/MCFabozzi, Frank; et.al. (2010): Survey of recent contributions in robust portfolio strategies from OR and Finance

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Canononical NLGP Formulation of SDMEURO 2015, July 12-15, 2015Slide: 15 / 20

Equation (1) is the objective functionEquation (2) and (3) capture the unsystematic and systematic risk for n investment securities across L indicesThe systematic risk level of individual asset, sp is captured in (3)Equation (4) forces the portfolio to be fully invested (short-sales are not permitted)Equation (5) is the goal constraint for the managerially determined portfolio return RRp Equation (6) is a summary metric of the portfolio return generated from the optimal diversification planThe Equally Weighted PortfolioThe equally weighted portfolio requires n additional goal constraints as shown below:

The augmented objective function is inserted as equation 1

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Comparative Efficient SetsEURO 2015, July 12-15, 2015Slide: 17 / 20

MultiIndex v/s Single IndexEURO 2015, July 12-15, 2015Slide: 18 / 20

MultiIndex v/s Single IndexEURO 2015, July 12-15, 2015Slide: 19 / 20

Summary & ConclusionsDistinguish between ESG investing and SI/SR approachesCreated an ESG-influenced factor index from the residual returns or all n securities populating the TRCRLCP portfolio.Optimized an equally weighted multi-factor - multiple objective SDM portfolio for the non-profit GSRI by incorporating the market and FSI factors.EFA efficiently located latent industry effects in the return residuals of ESG stocksA return-generating index was created by averaging across maximum validity factor scores.Compared to the single-index SDM, the multiple index model (market & FSI) produced a dominant equally allocated portfolio at an equivalent return level.Future research questions:Time invariant..???Stability of FSI beta (time scale)Ease of implementationEURO 2015, July 12-15, 2015Slide: 20 / 20

Selected ReferencesBouslah, K., Kryzanowski, L., and MZali, B.: Relationship Between Firm Risk and Individual Dimensions of Social Performance. In: Proceedings of the Annual Conference of the Administrative Science Association of Canada, Montreal, (Canada). 32(1), 105-122 (2011)Daryl, C.R.M. and Shawn, L.K.J.: The Attenuation of Idiosyncratic Risk under Alternative Portfolio Weighting Strategies: Recent Evidence from the UK Equity Market. International Journal of Economics and Finance. 4(11), 1-14 (2012)Dash, G.H. and Kajiji, N.: A Nonlinear Goal Programming Model for Efficient Asset-Liability Management of Property-Liability Insurers. Information Systems and Operational Research. 43(2), 135-156 (2005)Dash, G.H. and Kajiji, N.: Efficient Multiple Objective Neural Network Mapping of State-Wide High School Achievement. Journal of Applied Operational Research. 4(3) (2012)Dash Jr., G.H. and Kajiji, N.: On Mulitobjective Combinatorial Optimization and Dynamic Interim Hedging of Efficient Portfolios. International Transactions in Operational Research. DOI: 10.1111/itor.12067, (2014)Hemmerle, W. J. "An Explicit Solution for Generalized Ridge Regression." Technometrics 17(3): 309-314 (1975).Hoepner, A.G.F.: Portfolio Diversification and Environmental, Social or Governance Criteria: Must Responsible Investments Really Be Poorly Diversified? Social Science Research Network Working Paper Series. Available at http://ssrn.com/abstract=1599334 (2010)Hoepner, A.G.F., Rezec, M., and Siegl, K.S.: Does Pension Funds' Fiduciary Duty Prohibit the Integration of Environmental Responsibility Criteria in Investment Processes?: A Realistic Prudent Investment Test. Social Science Research Network Working Paper Series. Available at http://ssrn.com/abstract=1930189 (2013)Hoerl, A. E. and R. W. Kennard. "Ridge Regression: Biased Estimation for Nonorthogonal Problems." Technometrics 12(3): 55-67. (1970)Oikonomou, I., Brooks, C., and Pavelin, S.: The Impact of Corporate Social Performance on Financial Risk and Utility: A Longitudinal Analysis. Financial Management. 41(2), 483-515 (2012)Pennanen, T., Introduction to Convex Optimization in Financial Markets. Mathematical Programming. 134(1), 91-110 (2012)Thomson, G. H. The Factorial Analysis of Human Ability. London, University of London Press. (1951)Tikhonov, A. and V. Arsenin. Solutions of Ill-Posed Problems. New York, Wiley (1977)Urwin, R., Allocations to Sustainable Investing. Towers Watson Technical Paper No. 1656955. Available at http://ssrn.com/abstract=1656955 (2010)EURO 2015, July 12-15, 2015Slide: 21 / 20

QUESTIONS???Contact Info: Gordon H. Dash, Jr.ghdash@uri.eduwww.ghdash.net

ESG Portfolio Optimization based on the Latent Dimensions within the Thomson Reuters Corporate Responsibility Indices