Does portfolio optimization favor sector or broad market investments?

• Published date: 01 December 2022
• Author: Arunachalam Senthilkumar,Athira Namboothiri,Sreelakshmi Rajeev
• Date: 01 December 2022
• DOI: http://doi.org/10.1002/pa.2752

RESEARCH ARTICLE

Does portfolio optimization favor sector or broad

market investments?

Arunachalam Senthilkumar | Athira Namboothiri | Sreelakshmi Rajeev

Amrita School of Business, Amrita Vishwa

Vidyapeetham, Coimbatore, India

Correspondence

Arunachalam Senthil Kumar, Amrita School of

Business, Amrita Vishwa Vidyapeetham,

Coimbatore 641 112, Tamil Nadu, India.

Email: profask@gmail.com;a_senthilkumar@

cb.amrita.edu

In the Indian context, we have applied the Sharpe Single Index model with Elton's

portfolio optimization framework and Markowitz Portfolio Theory framework for

optimizing intra and inter-sectoral equity portfolios. Literature provide less evidence

on the inter and intra-sector relationships to which we contribute. We compute

11 sector-specific optimal portfolios and one inter-sector optimal portfolio using the

NSE sectoral indices like automobiles, banking, financial services, FMCG, IT, media,

metals, pharmaceuticals, private banks, PSU banks, realty, and broad-market inter-

sector index Nifty50. We use the month-end adjusted closing returns data compris-

ing 15,834 observations from 191 scrips during 2013 to 2019. We create in-sample

optimal portfolios and out-sample mimic portfolios under the Sharpe and Markowitz

models for comparison and validation with optimized weights. Our results show that

inter-sector portfolio performs better than some of the intra-sector portfolios. Also,

the intra-sector portfolios like realty, metals, information technology, and media

generated higher returns with relatively moderate or less risk than their sectoral

peers and benchmark indices. We found that Sharpe's model performs better than

Markowitz's model. We validated our findings with statistical testing. Thereby, we

documented the applicability of the Sharpe Single Index for portfolio optimization in

the Indian context. Our research has several implications. Fund managers can make

use of our optimal portfolio performance matrix to recommend portfolios to their

clients. With our optimized portfolio weights, investors can make sector-level or

inter-sector investments. Regulators can get a synoptic view of the performance of

industry-level portfolios. Researchers can extend the literature by improvising our

portfolio optimization procedure.

KEYWORDS

emerging markets, finance, financial markets, India, Markowitz Portfolio Theory, portfolio

choice, portfolio optimization, sector portfolios, Sharpe Single Index model

1|INTRODUCTION

Portfolio Management refers to the art and science of making an

investment in diversified assets in the right proportion wherein the

objective is to diversify the risk and generate superior returns. An

optimal portfolio aims to achieve the best possible return for a given

level of risk or attain the given level of return with the lowest level of

risk. The concept of optimal portfolio evolved through the modern

portfolio theory (MPT) of Markowitz (1952), where he conceptualized

risk diversification through the mean–variance criterion. The

modern portfolio theory posed a significant challenge of multiple com-

putations of covariance for a large basket of assets. Modeling Marko-

witz mean–variance portfolio optimization theory is a significant

empirical investigation subject for academics and practitioners alike

Received: 23 April 2020 Revised: 1 June 2021 Accepted: 14 August 2021

DOI: 10.1002/pa.2752

J Public Affairs. 2022;22(Suppl. 1):e2752. wileyonlinelibrary.com/journal/pa © 2021 John Wiley & Sons Ltd. 1of19

https://doi.org/10.1002/pa.2752

(Leung et al., 2012). The performance of the estimates of the

Markowitz model has been questioned over time, and studies that

found equal-weighted portfolios outperform Markowitz portfolios

(Sharpe, 1963; Frankfurter et al. 1971; Perold, 1984). The lowest

eigenvalues with the smallest risk are dominated by noise in the MPT

portfolio, making the historical correlation matrix-based MPT inade-

quate (Laloux et al. 1999). To alleviate this inadequacy, Sharpe (1963)

formulated the single-index model (hereafter mentioned as SIM) to

simplify both the informational and computational complexity of the

general model of MPT. He proposed a single index for non-

diversifiable risk instead of the covariance estimates of Markowitz.

Further, the optimization problem was simplified by Elton and

Gruber (1978)andEltonetal.(1976), which saw applications in financial

portfolio investments. Diversification of portfolio with market index

modelproposedbyEltonandGruber(

1978) helps reduce risk and leads

to optimal portfolios (Alexander & Resnick, 1985;Sankaran&

Patil, 1999). The portfolio optimization problem became a research inter-

est over the years. An optimal portfolio is constructed with securities

(hereafter called scrips) from homogeneous or heterogeneous sectors. At

times, investors do not reap the benefits of diversification since they

determine investment risks at an individual asset level, undermining the

portfolio risks (Antony, 2019;Chhatwani,2019; De Bondt, 1998).

We apply Sharpe's Single Index Model in the Indian context. A

study on the Indian context is relevant here. Indian economy is the

third-largest economy in the world by purchasing power terms (World

Bank, 2019); the Indian financial markets are comparatively well-

regulated and remained resilient during the global financial crisis

(Kumar & Srividya, 2014; Thomas & Kumar, 2019); integrated with

global markets and rely on the banking system at large (Antony, 2019;

Kumar & Palanisamy, 2019). According to SEBI (2019), the Indian

stock market is the second largest in Asia with a market capitalization

of USD 2184 billion, which is 2.8% of the total global stock market

capitalization and 8.7% of the stock market capitalization of the Asia-

Pacific region. National Stock Exchange of India (NSE), established in

1994, is the leading technology-driven stock exchange in India with a

market share of 46.9% of Indian stock market capitalization. NSE is

the second largest globally by the number of equity trades and

second-largest in Asia-Pacific by a market capitalization to GDP ratio

of 78.6%. Therefore, it is apt to research the Indian stock market,

focusing on the NSE indices.

The significance of our study is established through the following

contributions it makes to the optimal portfolio literature. The studies

of Kumar (2009), Chitnis (2010), Ravichandra (2014), and Lal (2016)

applied SIM for broad-based NIFTY/SENSEX stocks. Also, we see

studies on select sector-specific indices of the NSE of India like Auto-

mobile sector stocks (Mallikharjunarao & Anithadevi, 2017), Banking

(Kumar & Bogarappu, 2016), and IT indices (Poornima &

Remesh, 2015) among others. It is evident that earlier studies con-

structed portfolios with scrips drawn from different sectors; however,

the optimal portfolios within sectors and across sectors remain

unexplored. In our research, we have used all the 11 sectoral indices

listed in the NSE of India to construct sectoral portfolios, which in our

humble opinion, is a unique contribution. The previous studies have

constructed the optimal portfolios but have not tested for their valid-

ity in the out-sample period, a gap we have identified. Though Kumar

and Bogarappu (2016) has validated the optimal portfolio, the size of

the out-sample is too small to provide any conclusive evidence.

Furthermore, we have constructed optimal portfolios and mimic

portfolios using an alternative portfolio optimization approach based

on Markowitz Portfolio Theory (MPT). This helps us assess whether

SIM portfolios are better optimized than the MPT portfolios in the

Indian context. Therefore, our next contribution comes through

the creation of mimic portfolios, also known as out-of-sample portfo-

lios with SIM and MPT, and statistically validate the returns & risk

with the in-sample optimal portfolios. Such comparison will indicate

the effectiveness of the optimally constructed portfolios with the

actual market performance. Finally, we have proposed a matrix sum-

marizing the recommended portfolios at the sector-level and

broad-market level in the Indian context, making our study attractive

to academia and practice. Hence, our research is motivated to contrib-

ute to the literature of the optimal portfolio by answering the follow-

ing questions:

1. Can investors generate superior returns with moderate risk by

making sectoral investments or broad-based investments?

2. Do the Sharpe Index Model (SIM) and Elton's optimal portfolio

framework work better than the Markowitz Portfolio framework in

the Indian context?

Our research objectives are to study the risk & return of the sectoral

and broad-based equity indices and their constituent stocks; to con-

struct hypothetical portfolios with sector-specific and broad-based

stocks; to construct out-sample or mimic portfolios and compare their

performance with the hypothetical portfolios.

Following the studies of Behr and Miebs (2013), Al-Janabi et al.

(2017), and Dai and Wang (2019), we hypothesize that there exists a

statistically significant difference in the performance of in-sample

portfolios, out-sample portfolios, and benchmark indices constructed

using the SIM and MPT portfolio optimization models, respectively.

We intend to validate the same using appropriate hypothesis tests.

The rest of the article gets organized as follows. The section 2will

present the review of previous studies in the portfolio literature, the

section 3explains the research methodology, the section 4presents

the results with discussion, the section 5discusses the managerial

implications of our research, the section 6provides the conclusion,

and the final section 7presents the limitations and further scope of

research.

2|LITERATURE REVIEW

The literature on portfolio optimization has studies proposing asset

selection based on financial performance indicators (e.g., Edirisinghe &

Zhang, 2007; Sharma & Mehra, 2017; Xidonas et al., 2009) and stud-

ies on asset selection based on market risk-adjusted return indicators

(e.g., Lehhmann & Modest, 2003; Bilbao et al., 2006 to name a few).

2of19 SENTHILKUMAR ET AL .