Mean–Variance Approach and Portfolio Selection

Abstract

We make an attempt to examine the performance of portfolios formulated on the basis of Mean–Variance approach . For the analysis, monthly adjusted opening and closing prices of composite portfolio of BSE 100 companies have been taken for the period ranging from June 1996 to May 2005. The study has wide-ranging implications for finance professionals and policy makers. Ten portfolios have, first, been formulated and then evaluated by using Sharpe’s excess return to beta approach. Nine portfolios’ expected returns out of ten are significant at 5% level of significance. A cross-sectional analysis of the same set of ten portfolios carried out for three non-overlapping sub-periods (June 1996–December 1999, Jan 2000–December 2002, and Jan 2003–May 2005). The three sub-periods exhibit successive different economic conditions in the Indian economy, viz. decline , recession and growth , respectively. The results so obtained exhibit that portfolio -expected return of all ten portfolios, in three different economic conditions, are optimal.

How many millionaires do you know who have become wealthy by investing in savings accounts? I rest my case.

Robert G. Allen

This chapter draws from the author’s previous publication (Dhankar & Kumar, 2006) Rakesh Kumar, Assistant Professor in the Department of Business Studies, Deen Dayal Upadhyaya College, University of Delhi, New Delhi, and re-used here with permission.

Appendices

Appendix 1

List of companies of BSE 100

Code	Company	Code	Company	Code	Company	Code	Company
c1	ABB Ltd.	c20	Colgate Pamolive Ltd.	c39	ICICI Bank	c58	Lupin Ltd.
c2	Andhra Bank	c21	Container Corporation	c40	I-Flex Solution	c59	Patni Computers
c3	Arvind Mill	c22	Corporation Bank	c41	Kochi Refinery	c60	Pfizer Ltd.
c4	Ashok Leyland	c23	Cummins Ltd.	c42	Kotak Mahindra Bank	c61	Polaris Software Ltd.
c5	Asian Paints	c24	Divi’s Laboratory	c43	Larsen & Turbo	c62	Punjab National Bank
c6	ACC	c25	Dr. Reddy Lab	c44	MTNL	c63	Ranbaxy Ltd.
c7	Bajaj Auto Ltd.	c26	GAIL	c45	Mahindra & Mahindra	c64	Rashtriya Chemical
c8	Bank of Baroda	c27	Glaxosmithkline	c46	Mangalore Refinery	c65	Raymond Ltd.
c9	Bank of India	c28	Grasim Industries Ltd.	c47	Maruti Udoyg Ltd.	c66	Reliance Capital
c10	Bharat Electronics	c29	Great Eastern shipping Ltd.	c48	Matrix Laboratory	c67	Reliance Energy Ltd.
c11	Bharat Forge Ltd.	c30	Gujarat Ambuja Cement	c49	Moser Baer	c68	Reliance Industries
c12	BHEL	c31	HCL Infosystem	c50	MICO	c69	Satyam Computers
c13	Bharat Petroleum	c32	HCL Technologies	c51	National Aluminium	c70	Shipping Corporation
c14	Bharati Televenture	c33	HDFC Bank	c52	Nestle India	c71	Siemens Ltd.
c15	Biocon Ltd.	c34	Hero Honda	c53	Neyveli Lignite	c72	State Bank of India
c16	Cadila Health care Ltd.	c35	Hindalco	c54	Nicholas Piramal	c73	SAIL
c17	Canara Bank	c36	Hindustan Lever Ltd.	c55	Novartis India	c74	Sterlite Industries Ltd.
c18	Chennai Petroleum Ltd.	c37	Hindustan Petroleum	c56	ONGC	c75	Sun Pharmaceuticals
c19	Cipla Ltd.	c38	HDFC	c57	Oriental Bank of Commerce	c76	Tata Chemicals
c77	Tata Iron & Steel	c83	Indian Hotels	c89	Jaiprakash Associate	c96	VSNL
c78	Tata Motor	c84	Indian Oil Corporation	c90	Jammu & Kashmir Bank	c97	Vijaya Bank
c79	Tata Power	c85	Indian Overseas Bank	c91	TVS Motors	c98	Wipro Ltd.
c80	Tata Tea Ltd.	c86	Indian Petrochemicals	c92	Tata Teleservices	c99	Wockhardt
c81	Indian Rayon Ltd.	c87	IDBI c93 UTI Bank	c94	Union Bank of India	c100	Zee Telefilm
c82	ITC Ltd.	c88	Infosys Technologies	c95	United Phosphorus Ltd.

Appendix 2

Correlation Matrix for Portfolio 1

• c95c42 = 0.18, c95c88 = 0.24, c95c54 = 0.12, c95c1 = 0.1, c95c100 = 0.12, c95c0.05 = –0.01, c95c98 = 0.13, c95c89 = 0.16, c95c31 = 0.14

• c42c88 = 0.58, c42c54 = –0.28, c42c1 = 0.08, c42c100 = 0.05 c42c69 = 0.34, c42c98 = 0.08, c42c89 = –0.03, c42c31 = 0.17

• c88c54 = –0.28, c88c1 = 0.08, c88c100 = 0.05, c88c69 = –0.13, c88c98 = 0.33, c88c89 = 0.08, c88c31 = –0.11

• c54c1 = 0.17, c54c100 = 0.22, c54c69 = 0.18, c54c98 = 0.10, c54c89 = 0.18, c54c31 = 0.27

• c1c100 = 0.25, c1c69 = 0.23, c1c98 = 0.24, c1c89 = 0.19, c1c31 = 0.23

• c100c69 = 0.29, c100c98 = 0.02, c100c89 = 0.16, c100c31 = 0.36

• c69c98 = –0.02, c69c89 = 0.08, c69c31 = 0.35

• c98c89 = 0.15, c98c31 = 0.16

• c89c31 = 0.32

Correlation Matrix for Portfolio 2

• c33c71 = 0.13, c33c68 = 0.18, c33c52 = 0.12, c33c19 = 0.12, c33c47 = 0.25, c33c45 = 0.10, c33c50 = 0.21, c33c27 = 0.11, c33c7 = 0.18

• c71c68 = 0.34, c71c52 = 0.10, c71c19 = 0.24, c71c47 = 0.30, c71c45 = 0.61, c71c50 = 0.13, c71c27 = 0.29, c71c7 = 25

• c68c52 = 0.18, c68c19 = 0.41, c68c47 = 0.29, c68c45 = 0.37, c68c50 = 0.21, c68c27 = 0.38, c68c7 = 0.43

• c52c19 = 0.24, c52c47 = 0.1, c52c45 = 0.09, c52c50 = 0.19, c52c27 = 0.35, c52c7 = 0.26

• c19c47 = 0.35, c19c45 = 0.36, c19c50 = 0.09, c19c27 = 0.4, c19c7 = 0.29

• c47c45 = 0.61, c47c50 = 0.09, c47c27 = 0.05, c47c7 = 0.13

• c45c50 = 0.06, c45c27 = 0.05, c45c7 = 0.29

• c50c27 = 0.24, c50c7 = 0.16

• c27c7 = 0.39

Correlation Matrix for Portfolio 3

• c77c44 = 0.31, c77c28 = 0.48, c77c61 = 0.06, c77c36 = 0.12, c77c32 = 0.28, c77c24 = 0.04, c77c25 = 0.41, c77c6 = 0.43, c77c63 = 0.27

• c44c28 = 0.31, c44c61 = 0.19, c44c36 = 0.14, c44c32 = 0.33, c44c24 = –0.33, c44c25 = 0.19, c44c6 = 0.52, c44c63 = 0.28

• c28c61 = 0.27, c28c36 = 0.22, c28c32 = 0.50, c28c24 = –0.04, c28c25 = 0.35, c28c6 = 0.51, c28c63 = 0.39

• c61c36 = 0.28, c61c32 = 0.53, c61c24 = 0.35, c61c25 = 0.20, c61c6 = 0.28, c61c63 = 0.31

• c36c32 = 0.34, c36c24 = 0.14, c36c25 = 0.28, c36c6 = 0.14, c36c63 = 0.33

• c32c24 = 0.27, c32c25 = 0.36, c32c6 = 0.43, c32c63 = 0.32

• c24c25 = 0.41, c24c6 = 0.18, c24c63 = 0.40

• c25c6 = 0.37, c25c63 = 0.54

• c6c63 = 0.43

Correlation Matrix for Portfolio 4

• c82c74 = 0.01, c82c62 = -0.06, c82c43 = 0.23, c82c94 = 0.31, c82c10 = 0.28, c82c30 = 0.21, c82c26 = 0.12, c82c34 = 0.06, c82c35 = 0.27

• c74c62 = 0.12, c74c43 = 0.33, c74c94 = 0.03, c74c10 = 0.25, c74c30 = 0.29, c74c26 = 0.13, c74c34 = 0.20, c74c35 = 0.34

• c62c43 = 0.37, c62c94 = 0.07, c62c10 = 0.24, c62c30 = 0.10, c62c26 = 0.16, c62c34 = 0.20, c62c35 = 0.15

• c43c94 = 0.12, c43c10 = 0.41, c43c30 = 0.41, c43c26 = 0.38, c43c34 = 0.26, c43c35 = 0.36

• c94c10 = 0.22, c94c30 = 0.16, c94c26 = 0.-0.05, c94c34 = –0.03, c94c35 = 0.16

• c10c30 = 0.36, c10c26 = 0.35, c10c34 = 0.24, c10c35 = 0.38

• c30c26 = 0.24, c30c34 = 0.21, c30c35 = 0.32

• c26c34 = 0.27, c26c35 = 0.16

• c34 c35 = 0.16

Correlation Matrix for Portfolio 5

• c72c86 = 0.21, c72c78 = 0.51, c72c80 = 0.02, c72c14 = 0.50, c72c23 = 0.31, c72c11 = 0.28, c72c55 = 0.45, c72c91 = 0.44, c72c81 = 0.18

• c86c78 = 0.05, c86c80 = 0.08, c86c14 = 0, c86c23 = –0.02, c86c11 = 0.03, c86c55 = 0.12, c86c91 = –-0.12, c86c81 = 0.18

• c78c80 = 0.27, c78c14 = 0.41, c78c23 = 0.30, c78c11 = 0.08, c78c55 = 0.28, c78c91 = 0.21, c78c81 = 0.31

• c80c14 = 0.01, c80c23 = 0.12, c80c11 = 0.11, c80c55 = 0.09, c80c91 = –0.05, c80c28 = 0.28

• c14c23 = 0.12, c14c11 = 0.15, c14c55 = 0.43, c14c91 = 0.51, c14c81 = –0.36

• c23c11 = 0.18, c14c55 = 0.17, c23c91 = 0.20, c23c81 = 0.10

• c11c55 = 0.23, c11c91 = 0.23, c11c81 = 0

• c55c91 = 0.44, c55c81 = 0.20

• c91c81 = –0.26

Correlation Matrix for Portfolio 6

• c83c57 = –0.08, c83c53 = 0.10, c83c22 = 0.10, c83c56 = 0.26, c83c8 = 0.23, c83c38 = 0.16, c83c51 = 0.14, c83c17 = 0.26, c83c90 = 0.06

• c57c53 = 0.18, c57c22 = 0.24, c57c56 = 0.21, c57c8 = 0.41, c57c38 = 0.22, c57c51 = 0.19, c57c17 = 0.29, c57c90 = 0.37

• c53c22 = 0.15, c53c56 = 0.36, c53c8 = 0.27, c53c38 = 0.10, c53c51 = 0.07, c53c17 = –0.11, c53c90 = 0.35

• c22c56 = 0.07, c22c8 = 0.53, c22c38 = 0.09, c22c51 = 0.30, c22c17 = 0.44, c22c90 = 0.38

• c56c8 = 0.32, c56c38 = 0.20, c56c51 = 0.22, c56c17 = 0.42, c56c90 = 0.16

• c8c38 = 0.31, c8c51 = 0.21, c8c17 = 0.63, c8c90 = 0.24

• c38c51 = 0.12, c38c17 = 0.42, c38c90 = 0.22

• c51c17 = 0.32, c51c90 = 0.18

• c17c90 = 0.39

Correlation Matrix for Portfolio 7

• c67c65 = 0.28, c67c39 = 0.14, c67c9 = 0.27, c67c2 = 0.46, c67c75 = 0.29, c67c13 = 0.22, c67c37 = 0.31, c67c40 = 0.02, c67c84 = –0.11

• c5c39 = 0.05, c5c9 = 0, c5c2 = –0.08, c5c75 = 0.27, c5c13 = 0.16, c5c37 = 0.26, c5c40 = –0.14, c5c84 = –0.28

• c39c9 = 0.38, c39c2 = 0.18, c39c75 = 0.13, c39c13 = 0.33, c39c37 = 0.22, c39c40 = 0.23, c39c84 = –0.18

• c9c2 = 0.58, c9c75 = 0.32, c9c13 = 0.36, c9c37 = 0.24, c9c40 = 0.12, c9c84 = 0.43

• c2c75 = 0.14, c2c13 = 0.23, c2c37 = 0.18, c2c40 = –0.06, c2c84 = 0.30

• c75c13 = 0.24, c75c37 = 0.23, c75c40 = 0.32, c75c84 = –0.13

• c13c37 = 0.69, c13c40 = –0.09, c13c84 = 0.15

• c37c40 = –0.05, c37c84 = 0.03

• c40c84 = 0.28

Correlation Matrix of Portfolio 8

• c12c79 = 0.22, c12c49 = 0.28, c12c20 = 0.51, c12c18 = 0.33, c12c48 = 0.33, c12c93 = 0.50, c12c70 = 0.42, c12c73 = 0.29, c12c3 = 0.17

• c79c49 = 0.35, c79c20 = 0.36, c79c18 = 0.08, c79c48 = 0.35, c79c93 = 0.06, c79c70 = –0.12, c79c73 = 0.14, c79c3 = 0.31

• c49c20 = 0.32, c49c18 = 0.21, c49c48 = 0.10, c49c93 = 0.06, c49c70 = –0.013, c49c73 = 0.10, c49c3 = 0.18

• c20c18 = 0.29, c20c48 = 0.05, c20c93 = –0.15, c20c70 = 0.19, c20c73 = 0.35, c20c3 = 0.36

• c18c48 = 0.17, c18c93 = 0.21, c20c70 = 0.07, c18c73 = 0.43, c18c3 = 0.27

• c48c93 = 0.26, c48c70 = 0.02, c48c73 = 0.14, c48c3 = –0.01

• c93c70 = 0.18, c93c73 = 0.22, c93c3 = 0.28

• c70c73 = 0.16, c70c3 = 0.22

• c73c3 = 0.37

Correlation Matrix of Portfolio 9

• c58c41 = 0.01, c58c60 = 0.15, c58c76 = 0.18, c58c59 = 0.41, c58c96 = 0.09, c58c64 = 0.29, c58c4 = 0.21, c58c29 = 0.41, c58c29 = 0.22

• c41c60 = 0.09, c41c76 = 0.43, c41c59 = –0.05, c41c96 = 0.18, c41c64 = 0.21, c41c4 = 0.36, c41c29 = 0.29, c41c92 = 0.30

• c60c76 = 0.22, c60c59 = –0.25, c60c96 = –0.03, c60c64 = 0.03, c60c4 = 0.08, c64c29 = –0.01, c60c92 = –0.04

• c76c59 = 0.04, c76c96 = 0.19, c76c64 = 0.20, c76c4 = 0.34, c76c29 = 0.37, c76c92 = 0.19

• c59c96 = 0.40, c59c64 = –0.35, c59c4 = –0.48, c59c29 = 0.08, c59c92 = –0.51

• c96c64 = 0.03, c96c4 = 0.15, c96c29 = 0.21, c96c92 = 0.58

• c64c4 = 0.02, c64c29 = 0.15, c64c92 = 0.08

• c4c29 = 0.35, c4c92 = 0.30

• c29c92 = 0.43

Correlation Matrix of Portfolio 10

• c65c15 = 0.47, c65c99 = 0.09, c65c16 = 0.20, c65c21 = –0.06, c65c85 = 0.39, c65c46 = 0.04, c65c87 = 0.13, c65c97 = 0.14, c65c66 = 0.46

• c15c99 = –0.20, c15c16 = 0.01, c15c21 = –0.40, c15c85 = 0.26, c15c46 = 0.56, c15c87 = –0.15, c15c97 = 0.00, c15c66 = 0.61

• c99c16 = 0.01, c99c21 = 0.05c61, c99c85 = 0.22, c99c46 = 0.0, c99c87 = 0.48, c99c97 = 0.45, c99c66 = 0.33

• c16c21 = 0.26, c16c85 = 0.16, c16c46 = –0.13, c16c87 = 0.07, c16c97 = 0.33, c16c66 = 0.20

• c21c85 = 0.04, c21c46 = 0.08, c21c87 = 0.11, c21c97 = 0.23, c21c66 = 0.20

• c85c46 = 0.35, c85c87 = 0.16, c85c97 = 0.19, c85c66 = 0.32

• c46c87 = -0.06, c46c97 = 0.02, c46c66 = 0.29

• c87c97 = 0.56, c87c66 = 0.35

• c97c66 = 0.