Abstract
In this article we extend the research on risk-based asset allocation strategies by exploring how using an SRI universe modifies properties of risk-based portfolios. We focus on four risk-based asset allocation strategies: the equally weighted, the most diversified portfolio, the minimum variance and the equal risk contribution. Using different estimators of the matrix of covariances, we apply these strategies to the EuroStoxx universe of stocks, the Advanced Sustainability Performance Index (ASPI) and the complement of the ASPI in the EuroStoxx universe from March 15, 2002 to May 1, 2012. We observe several impacts but one is particularly important in our mind. We observe that risk-based asset allocation strategies built on the entire universe, concentrate their solution on non-SRI stocks. Such risk-based portfolios are therefore under-weighted in socially responsible firms.
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Notes
Some of the implementation choices will be discussed in this paper, in the section on data and methodology.
Fundamental allocations define the weights as a function of issuers’ fundamental statistics see Arnott et al. (2005).
The EuroStoxx is a subset of the EuroStoxx 600 that contains a variable number of stocks, roughly 300, traded in Eurozone countries. The ASPI universe is a subset of EuroStoxx that contains the 120 best rated stocks. This social performance rating is given by VIGEO. The complement of the ASPI universe in the EuroStoxx universe is the universe of about 180 stocks that are in the EuroStoxx but not in the ASPI universe.
IEM is the firm in charge of calculation methodology for the ASPI. VIGEO is a provider of social performance ratings and sponsor of the ASPI.
By construction EuroStoxx is a Euro Zone universe.
As previously stated, the EuroStoxx is a subset of the EuroStoxx 600 that contains a variable number of stocks, roughly 300 depending on the methodology stated by STOXX.
For 2 rebalancing dates ASPI is defined by \(\hbox {N}=118\) and \(\hbox {N}=119\).
The empirical VCV matrices is \(VCV_e = \frac{1}{n-1} * \sum _{i=1}^n (r_i - \bar{r})(r_i - \bar{r})'\). The constant correlation matrix is a VCV matrix with empirical variances on the diagonal and average of empirical covariances on lower and upper part of the VCV matrix.
See also Maillet et al. (2015) for an approach that is robust to parameter uncertainty.
For some stocks historical series are shorter than the VCV estimation window. For the ASPI universe, this concerns two stocks out of 238, the smallest window is 100 days. For EuroStoxx and complement of ASPI universe, this concerns 53 stocks out of 536, the smallest windows is 12 days.
Risk budget is defined as the product of the weight of component i combined with its volatility.
The benchmark used is our replication of EuroStoxx CW indice.
Our results are confirmed by measures \(D_2\).
We recall that \(D_1\), our difference in weight, is one minus the sum of the lowest weights of stocks that are in the two portfolios based on the two different universes. As ASPI rules discard about 60 % of the EuroStoxx stocks, while we observe only 30 % of weight differences, the remaining 40 % stocks then must concentrate about 70 % of the weights. Consistent with this explanation by size of firms, on average the market values of firms in the ASPI are 3.74 times greater than the market values of firms in complement of ASPI in EuroStoxx universe. Finally, the relative mean differences of weights in the CW ASPI we calculate in the next sub-section indicate that firms in the ASPI are in general larger than in the EuroStoxx.
The RMD is closely related to the Gini coefficient. The closer the relative mean difference gets to zero the less concentrated the distribution is.
When we focus on the degree of diversification of strategies built on the same universe, we observe rankings similar to Maillard et al. (2010). The most diversified are the EW and the ERC, followed by the CW, and finally the MDP and the MV, which are the most concentrated in risk and weights. When we focus on the degree of diversification of strategies over the three universes and the five measures, we observe no modification in ranking when switching from ASPI to EuroStoxx or to the complement of the ASPI in the EuroStoxx universe of stocks.
Four further observations emerge from the regressions: first, adding bounds to the MV and MDP strategies improves diversification but this improvement is not statistically significant; second, the complement of the ASPI universe is also correlated with more diversified distributions; once again, however this is not statistically significant. Third, portfolio size is positively related to diversification of distributions: the larger the portfolio, the more diversified it is. Fourth, regressions confirm that the four risk-based strategies yield more diversified distributions than the CW strategy, and that the EW and ERC strategies are the most strongly correlated with higher diversification.
The weight turnover is the lowest for EW portfolios (Fig. 3), the second lowest turnover being for the CW strategy. The CW strategy is not the one with the lowest turnover in our case, contrary to Carvalho et al. (2012). The third lowest turnover is for the ERC strategy. MV and MDP portfolios have similar weight turnovers, those of the MV portfolios, however, being more volatile than the turnovers of the MDP portfolios. Similarly, component turnover is the lowest for the EW, the CW and the ERC strategies. However, when measure \(T_2\) is used, the three strategies have the same component turnover. Since they invest in the entire available universe, this component turnover requests solely from universe modifications. MV and MDP strategies have similar component turnovers; however the turnover of the MV strategy is more volatile than that of the MDP strategy. No modification in these results is observed when switching from ASPI to EuroStoxx or to the complement of the ASPI in the EuroStoxx universe of stocks.
We do not report the results because of space constraints. They are available from the authors upon request.
Please see also Bertrand and Lapointe (2015) for a detailed analysis of the effect of using a SRI universe on performance of risk-based strategies.
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Acknowledgments
We benefited from comments by Lloyd Kurtz, Raul Leote de Carvalho, Thierry Roncalli and Guillaume Weisang. We also benefited from comments by referee of the 1st Geneva Summit on Sustainable Finance and by participants to the 5th ARCS Conference at the University of Berkeley, the 30th AFFI Conference at the EM Lyon Business School and the 3rd FEBS International Conference at the ESCP Europe Business School. We are grateful to Vigeo for granting us access to their data. We thank Fouad Benseddik and Antoine Begasse from Vigeo for their support in understanding the methodology of these data. An early version of this work was presented in a working paper entitled “Smart Beta Strategies: the Socially Responsible Investment case”.
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Bertrand, P., Lapointe, V. Risk-based strategies: the social responsibility of investment universes does matter. Ann Oper Res 262, 413–429 (2018). https://doi.org/10.1007/s10479-015-2081-4
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DOI: https://doi.org/10.1007/s10479-015-2081-4