On outperforming social-screening-indexing by multiple-objective portfolio selection

Abstract

Socially responsible investment has been rapidly growing over the past two decades and is typically fulfilled by screening and indexing. Recently, scholars propose multiple-objective portfolio selection for corporate social responsibility (CSR). The proposal raises the question whether multiple-objective portfolio selection can outperform screening and indexing. The question is not fully answered although researchers have made some encouraging trial. By formulating multiple-objective portfolio selection for CSR, I propose a theorem to demonstrate that investors can outperform screening and indexing in expected CSR with identical or better expected return and with identical variance, and can outperform screening and indexing in expected return with identical or better expected CSR and with identical variance. I empirically test the outperformance by component stocks of Dow Jones Industrial Average and report the results.

Appendix

1.1 The proof of Theorem 1

Proof

I start by studying the intersection between Z and plane $z_1=z_1^S$ and depict the intersection as shaded in $(z_2, z_3)$ space in Fig. 5. Because Qi et al. (2017) prove the minimum-variance surface of (10) as a paraboloid (11), the intersection’s boundary is an ellipse. Moreover, the paraboloid is typically rotated with ${\mathbf{d }^2}^T \varvec{\varSigma } \mathbf{d }^3 \ne 0$ of (11) (i.e., unrotated with ${\mathbf{d }^2}^T \varvec{\varSigma } \mathbf{d }^3 = 0$); the ellipse is also typically rotated. I depict the cases of unrotated, clockwisely rotated, and counterclockwisely rotated ellipses in the left, middle, and right parts of Fig. 5, respectively. I also depict the intersection between the nondominated set and the plane by thick curves, and label the end points as $\mathbf{z }^H$ and $\mathbf{z }^V$. The proofs of the three cases are basically identical, so I’ll focus on the clockwisely rotated ellipse in the middle.

If $\mathbf{z }^S$ is to the right of the broken line $z_2=z_2^H$ (i.e., $z_2^S \ge z_2^H$) in the left part of Fig. 6, I draw a thin vertical line passing through $\mathbf{z }^S$; the intersection between the thin line and the thick curve is $\mathbf{z }^S_C$. I depict a rare case with $\mathbf{z }^S$ as nondominated (i.e., $\mathbf{z }^S$ on the thick curve) in the middle part of Fig. 6; then, $\mathbf{z }^S_C$ doesn’t exist. Otherwise (i.e., $z_2^S < z_2^H$), I take $\mathbf{z }^H$ as $\mathbf{z }^S_C$ in the right part of Fig. 6.

If $\mathbf{z }^S$ is above the broken line $z_3=z_3^V$ (i.e., $z_3^S \ge z_3^V$) in the left part of Fig. 7, I draw a thin horizontal line passing through $\mathbf{z }^S$; the intersection between the thin line and the thick curve is $\mathbf{z }^S_R$. Similarly, I locate $\mathbf{z }^S_R$ in the middle part of Fig. 7 with $\mathbf{z }^S$ as a boundary point. Otherwise (i.e., $z_3^S < z_3^V$), I take $\mathbf{z }^V$ as $\mathbf{z }^S_R$ in the right part of Fig. 7.

Theorem 1 holds by the choice of $\mathbf{z }^S_C$ and $\mathbf{z }^S_R$ and definition of dominate. $\square$

Fig. 5

The intersection between Z and plane $z_1=z_1^S$

Fig. 6

Locating $\mathbf{z }^S_C$

Fig. 7

Locating $\mathbf{z }^S_R$

1.2 Rating CSR

For rating CSR, KLD adopts the following categories: community, corporate governance, diversity, employee relations, environment, human rights, product, alcohol, gambling, tobacco, firearms, military, and nuclear power. KLD typically divides a category into two subcategories: strengths and concerns, but some categories (e.g., alcohol) have only concerns. Altogether, 139 binary variables are set under all the subcategories.

I compute a category measurement by adding all the strengths variables under the category and then subtracting all the concerns variables under the category. Then, I add all the category measurements to get the CSR rating and report the five stocks’ rating from 1999 to 2013 in the following table:

Year	AAPL	BA	DIS	KO	UTX	Year	AAPL	BA	DIS	KO	UTX
1999	2	$-$ 6	4	2	0	2007	0	$-$ 1	$-$ 2	$-$ 2	$-$ 1
2000	0	$-$ 9	3	$-$ 3	1	2008	$-$ 1	$-$ 5	$-$ 3	$-$ 1	$-$ 3
2001	0	$-$ 6	$-$ 1	$-$ 5	0	2009	$-$ 1	$-$ 5	$-$ 3	$-$ 1	$-$ 3
2002	1	$-$ 4	1	$-$ 2	1	2010	$-$ 1	$-$ 4	4	0	$-$ 1
2003	0	$-$ 4	$-$ 2	$-$ 4	0	2011	1	$-$ 1	8	5	2
2004	0	$-$ 3	0	$-$ 5	1	2012	$-$ 2	7	9	3	4
2005	2	0	0	$-$ 3	$-$ 3	2013	0	11	6	7	4
2006	0	$-$ 1	$-$ 2	$-$ 3	0