How to Cite:
Guru, B. P. C. S., & Bagrecha, C. (2022). Building an optimal portfolio using Sharpe’s
single index model: A study of BSE Sensex constituent companies. International Journal of
Health Sciences, 6(S2), 11567–11581. https://doi.org/10.53730/ijhs.v6nS2.8137
Building an optimal portfolio using Sharpe's
single index model: A study of BSE Sensex
constituent companies
Mr. B P Chandan Shri Guru
IV Semester, MBA Finance Student, CMS Business School, Jain (Deemed-To-BeUniversity) Bangalore
Corresponding author email: chandan.shriguru@gmail.com
Dr. Chaya Bagrecha
Professor, CMS Business School, Jain (Deemed-To-Be-University) Bangalore
Email: dr.chayabagrecha@cms.ac.in
Abstract---This research paper aims to build an optimal portfolio
using Sharpe’s Index Model. The study has been done on Bombay
Stock Exchange Sensex 30 constituent companies. The monthly stock
prices between August 2017 to August 2021 have been considered for
this study. Various measures such as mean return, Beta coefficient,
Excess return, Standard deviation, Variance, Cut Off Rate, Proportion
of Investment and Portfolio Return are computed. The final results
showed that, twenty-six stocks were bullish during the study period
and delivered positive returns and four stocks showed negative
returns out of the thirty stocks in BSE Sensex. Therefore, the study is
continued on those 26 stocks which generated positive returns to
determine the cut off rate. Further, application of Sharpe’s Index
model highlighted the stocks to be used for constructing the optimal
portfolio. The prices of the stocks have been largely fluctuated
between February 2020 and March 2021 due to the pandemic induced
lockdowns and shut downs and followed by a sharp rise in the prices
of the stocks facilitated by the monetary easing by the Indian
Government and the Reserve Bank of India to maintain liquidity. As
per the results obtained from the study, Optimal Portfolio is built by
selecting seven stocks which are above the cut off rate. This study
shows the detailed method of constructing the portfolio and its
application, which is at the end of the day, advantageous to investors
and in selecting the stocks as part of their portfolio and maximize
their return whilst taking up calculated risk. Also, this study is
limited to understanding on building an optimal portfolio and doesn’t
focus on the exit strategies and manoeuvres over time.
International Journal of Health Sciences ISSN 2550-6978 E-ISSN 2550-696X © 2022.
Manuscript submitted: 27 March 2022, Manuscript revised: 09 April 2022, Accepted for publication: 18 May 2022
11567
11568
Keywords---return, risk, beta, optimal portfolio, excess return beta.
Introduction
India has taken significant steps for economic growth by leveraging its immense
potential in the long term. According to McKinsey Global Institute, average
Indian’s income will triple by 2025 resulting in more investments in the upcoming
years. According to UNCTAD’s World Investment Prospects Survey 2010-2012,
India is the second-most profitable destination for foreign direct investment (FDI)
in the world. Indian markets have significant potential offering prospects of high
profitability and a favourable regulatory regime for investors. Increased income
class will result in increased discretionary money in the hands of the people. This
helps the Indian working-class population of save and invest more in different
financial instruments available in the country.
One such investment platform is the Indian stock market (primary and
secondary) which is tightly regulated and policies that are framed in the favour of
investors. This has led to new companies going public and raising capital from the
retail investors in India. It is a sign that India is on track to attain the status of a
developed economy in the upcoming decade. owever, there is a need to educate
about financial literacy to people before getting into any of the investments that
comes with risk. People can lose money if not advised and taught about the stock
market before investing.
During the pandemic, a lot of retail investors have entered the stock market
through discount brokers such as Zerodha, Upstox etc. We were able to see a
spike in number of new demat accounts opened by the new retail investors. Many
people entered the stock market to avoid the fear of missing out on an
opportunity to make money when the stock market crashed. However, many of
them didn’t have prior knowledge about investing and some learnt the basics of
investing on public platforms like YouTube and other blogs and started investing
which has resulted in overvalued market.
This study aims to develop an optimum portfolio from BSE Sensex companies
using Sharpe Single Index Model which is one of the effective methods compared
to other models and the simplest for determining the optimal portfolio after
multiple procedural calculations. This study can help understand on how to
derive a portfolio using multiple formulae and calculations. The data is collected
of past five years to weather out the short-term fluctuations and settlements
caused due to various short-term changes.
Review Of Literature
Dr. ARCHANA H N and SRILAKSHMI D (2020) have built an optimal portfolio
using Sharpe Single Index Model from BSE Sensex companies’ list. The closing
price data of the BSE Sensex companies have been conducted for the duration of
one year from (Jan 2019 to Dec 2019). Using Sharpe Single Index Model, the
authors have developed a portfolio of 10 stocks and the proportion of investments
that can be done in order to obtain maximum returns.
11569
R. NALINI (2007) has conducted an empirical study on optimal portfolio using
Sharpe’s model and her study suggests the investors or help them to make
investment in companies depending on the risk and return averse of adjustment
as investors mainly aim for maximum returns over a period of time.
SARAVANAN and A. NATARAJAN.P (2012) The study suggests that optimal
portfolio can be constructed by using Sharpe’s single index model using NSE;
NIFTY FIFTY stocks have been used as market index for constructing the
portfolio. This study uses data on daily bases for a certain period of time which
involves a unique way off formulating known as cut off point and later the
percentage of each stock is selected along with their respective weights and other
variance and covariance. The optimal portfolio considers four best stocks selected
from the nifty fifty short listed stocks or scripts obtaining the return of 0.116%.
DHARMALINGAM N AND BALANAGA GURUNATHAN, K (2016) explored with an
objective to construct an portfolio and also to know the proportion of investment
in each stocks using Sharpe index model with specifically to sugar and metal
industry from 1st April 2012 to 31st March 2016 from National stock exchange.
Total 19 companies were selected from National stock exchange based on simple
random sampling. Finally, researcher constructed a portfolio of 12 stocks based
on cut off rate and weightage of investment in each stock by using single index
model this might help investors to make better decisions.
VARADARAJAN (2011) constructed an optimal equity portfolio consisting of five
stocks. Five years' data was considered i.e., from April 2006 to March 2011
covering 19 companies from banking and information technology sectors.
DEBASISH (2012) developed an optimal portfolio with three stocks, from a total of
14 stocks in the manufacturing industry. This includes the stocks from
automobiles, cement, textiles, paints, oils and refineries. Investment proportions
were decided based on the factors like beta value, return, risk free rate of return
and unsystematic risk.
NAGESWARI (2013) determined the risks and returns of stocks to form an
optimal portfolio that reduces variability of returns. BSE Sensex companies were
considered for the study and their daily closing prices, for the period April 2007 to
March 2012. The cut-off rate of return was determined to select the stocks for
developing a portfolio.
ANANGOSTOPULOS & MAMANIS (2010) The portfolio optimization problem was
formulated by optimizing the objectives involving trade-offs between risk, return
and the number of securities for inclusion in an optimum portfolio. Limits are set
regarding the proportion of the investments in assets, so that the chances of
having smaller proportions of holdings or investments in assets having similar
characteristics is avoided.
TANUJ NANDAN AND NIVEDITA SRIVASTAVA (2017) endeavoured to create a
portfolio by using Sharpe’s single index model of Nifty 50 stocks during 1st
August 2010 to 31st July 2015. The statistical tools were used such as Mean
11570
stock return, mean index return, Standard deviation, and variance, systematic
and unsystematic risk to determine the values of all nifty stocks and the weekly
data of MIBOR has been averaged for the last five years as considered as risk free
rate of return. Finally, 24 companies were chosen to construct a portfolio based
on the cut off rate by using Sharpe’s single index model.
WILLIAM F SHARPE (1963) explicated the process of selecting stocks to form a
portfolio by applying the Markowitz model by using various techniques such as
critical line method, Diagonal model and the analogue of considering 2000
securities. Further says that the diagonal model performed well in representing
the relationship among securities can be used for the initial application of
Markowitz technique.
MOKTA RANI SARKER (2013) conducted a study on 164 companies listed on
Dhaka Stock Exchange (DSE) for a period from July 2007 to June 2012 and
considered the monthly closing prices to construct a portfolio by using Sharpe
index model during from Dhaka stock exchange. The main objective of the paper
was to construct a portfolio and proportion of investments by calculating cut off
rate and suggest the investors a portfolio. The portfolio was constructed by
selecting 33 stocks out of the total 164 stocks on which the study was conducted.
DILEEP, RAO AND KESAVA (2013) studied the suitability and application of the
Sharpe’s Single Index Model in the Indian context and evaluated the portfolio’s
performance and went on to construct a portfolio in terms of the rate of return
from the 30 stocks that was considered for the study. It was found that only four
companies were included in portfolio. The study concluded that Sharpe’s Single
Index Model was sustainable and applicable to the Indian markets.
DESAI, RADHIKA AND SURTI, MANISHA (2013) constructed an optimal portfolio
using fifty companies that were listed on NSE after studying the past three years’
stock prices. Ten stocks out of the fifty was selected in the optimum portfolio.
Further, investment proportion for each stock was calculated using the Sharpe’s
Single Index Model. The research provided the investors the step-by-step direction
to derive the optimal portfolio.
Objectives of the Study
1. To calculate the return of each security in BSE Sensex for segregating the
securities generating positive return from that of those generating negative
return.
2. To develop an optimal portfolio using Sharpe’s Single Index model from
Sensex 30 companies of Bombay Stock Exchange.
3. To calculate the proportion of investment in each security from the derived
portfolio.
4. To calculate the return of each security w.r.t the proportion of investment in
each security.
5. To calculate the overall return from of the portfolio.
11571
Limitations of the Study
1. The study is conducted using the previous 5 year’s monthly stock prices
(Aug 2017- Aug 2021) under BSE Sensex to derive the optimal portfolio.
2. The study is confined specifically to 30 organization’s stocks from BSE
Sensex and not considered other Index or other stocks in the Exchanges.
3. The study is limited to the calculation of Return (%) of the derived optimal
portfolio.
4. The study is limited to building an optimal portfolio and doesn’t focus on
the exit strategies.
Research Methodology
Sources of Data: The data for this research study has been collected from many
resources which mainly include Bombay Stock Exchange (BSE) website. The
monthly closing price values for the BSE Sensex companies are collected for the
last 5 years i.e. from August 2017- August 2021. The Risk-Free rate is derived
from RBI’s 364 days Treasury Bill Yield issued on 20th August 2021. RBI’s 364
days Treasury Bill Yield on 20th August 2021 is 3.65% p.a which when converted
to monthly Risk Free rate (Rf) is considered to be 3.65/12 = 0.342%.
Period of Study: The period of study is August 2017 to August 2021.
Methodology
 Return (%): The return (%) for each individual closing price of the stock
compared to the previous month closing price of the stock is calculated using:
Where:
Ri = Return in individual security
Pt = Current Closing price of the month
Po = Previous Closing price of the month
 Variance: Variance is the measure of the volatility of a stock. Higher the
variance, higher is the volatility of the stock and vice versa. Variance is
calculated by:
Where,
𝜎𝑚2 = Variance of Stock
Ri = Expected return of a stock
Rbar = Mean return of the stock
n = Number of observations
𝜎𝑚2 =
(𝑅𝑖 − 𝑅𝑏𝑎𝑟)2
𝑛−1
 Standard Deviation (Risk): Standard deviation measures the total risk of the
stock. The square root of the Variance is referred to as standard deviation.
11572
σi = SQRT
Where,
σi = Standard deviation of the stock
Ri = Expected return of the stock
Rbar= Mean return of the stock
n = Number of observations
(𝑅𝑖 − 𝑅𝑏𝑎𝑟)2
𝑛−1
 Systematic risk (β): Beta refers to the measurement the volatility of the stock
w.r.t the stock market (index). Greater the value of Beta, higher is the volatility
of the stock and vice versa. Beta is calculated by:
β=
Where,
Ri = Expected return of a stock
Rm = Return from market (index)
𝑪𝒐𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆 (𝑹𝒊 ,𝑹𝒎)
𝑽𝒂𝒓𝒊𝒂𝒏𝒄𝒆 (𝑹𝒎)
 Unsystematic risk: Unsystematic risk is the difference between the total risk
and the systematic risk. The Unsystematic risk is calculated as:
Unsystematic risk (𝜎𝑒𝑖 2 ) = Variance of stock (𝜎𝑖 2 ) – 𝛽 2 * Variance of market (𝜎𝑚2 )
 Excess Return to Beta ratio: The excess return is the difference between the
individual stock’s return and the risk-free rate of return offered on the
government security such as Treasury bill.
In this study, we have taken into account one year or 364-day Treasury bill rate,
which is 3.65% as the risk-free rate of interest/return.
Excess return to beta measures the additional return earned for bearing risk per
unit.
Where:
Ri = Expected return on individual stock
Rf = Risk free rate of return
β = Systematic risk of individual stock
 Cut off rate by using Sharpe Index Model: Cut off rate is calculated by using
the following formula:
11573
Where,
Ri = Expected return of stock
Rf = Risk free rate of return
β = Systematic risk of the stock
𝜎𝑚2 = Variance of Stock
𝜎𝑒𝑖 2 = Unsystematic risk
 Proportion of Investment in each stock from the derived portfolio: The
proportion of investment in each stock which is a part of the derived portfolio
is calculated using the following formula:
Where,
X i = Proportion of investment in individual stock
Ri = Expected return of stock
Rf = Risk free rate of return
β = Systematic risk of the stock
C = Cut off point
𝜎𝑒𝑖 2 = Unsystematic risk
 Portfolio Return: Portfolio return is calculated using the following formula:
Rp = Σ (X i * Rbar)
Where,
Rp = Return of the portfolio
X i = Proportion of investment in individual stock
Rbar= Mean return of the stock
Data Analysis and Interpretation
Table 1- Industry Classification Of BSE Sensex 30 Companies
Sl
No.
1
2
3
Scrip
Code
532977
500520
532500
Company
Industrial Classification
Bajaj Auto Ltd
Mahindra & Mahindra Ltd
Maruti Suzuki India Ltd
Automobiles
11574
4
500124
5
524715
6
7
8
9
10
500696
500875
500790
500034
532978
11
500010
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
532555
532898
500209
532281
532540
532755
532215
500180
532174
532187
500247
500112
532454
500820
500510
500325
Dr Reddy's Laboratories Ltd
Sun Pharmaceutical Industries
Ltd
Hindustan Unilever Ltd
ITC Ltd
Nestle India Ltd
Bajaj Finance Ltd
Bajaj Finserv Ltd
Housing Development Finance
Corp
NTPC Ltd
Power Grid Corp of India Ltd
Infosys Ltd
HCL Technologies Ltd
Tata Consultancy Services Ltd
Tech Mahindra Ltd
Axis Bank Ltd
HDFC Bank Ltd
ICICI Bank Ltd
IndusInd Bank Ltd
Kotak Mahindra Bank Ltd
State Bank of India
Bharti Airtel Ltd
Asian Paints Ltd
Larsen & Toubro Ltd
Reliance Industries Ltd
28
500470
Tata Steel Ltd
29
30
500114
Titan Co Ltd
532538
UltraTech Cement Ltd
Source- Bombay Stock Exchange website
Pharmaceuticals & Biotechnology
FMCG
Other Financial Services
Electric Utilities
IT Software & Services
Banks
Telecom Services
Furniture,Furnishing,Paints
Construction & Engineering
Integrated Oil and Gas
Iron & Steel and Intermediary
Products
Textiles, Apparels & Accessories
Cement and Cement Products
Analysis: Table 1 shows that the BSE Sensex 30 companies are spread among
different business sectors in India. This also showcases the diversity of the
companies in the Sensex Index.
Table 2- Return, Risk And Beta Values For BSE Sensex 30 Stocks
Sl No.
1
2
3
4
5
6
7
8
Company Name
Asian Paints Ltd
Axis Bank Ltd
Bajaj Auto Ltd
Bajaj Finance Ltd
Bajaj Finserv Ltd
Bharti Airtel Ltd
Dr Reddy's Laboratories Ltd
HCL Technologies Ltd
Return
2.362
1.622
0.977
4.155
3.471
1.323
2.107
1.408
Risk
7.170
10.896
8.805
14.553
14.557
9.139
8.445
11.303
β
0.54
1.52
0.97
1.79
1.75
0.75
0.18
0.83
11575
9
10
HDFC Bank Ltd
Hindustan Unilever Ltd
Housing Development Finance
11
Corp
12
ICICI Bank Ltd
13
IndusInd Bank Ltd
14
Infosys Ltd
15
ITC Ltd
16
Kotak Mahindra Bank Ltd
17
Larsen & Toubro Ltd
18
Mahindra & Mahindra Ltd
19
Maruti Suzuki India Ltd
20
Nestle India Ltd
21
NTPC Ltd
22
Power Grid Corp of India Ltd
23
Reliance Industries Ltd
24
State Bank of India
Sun Pharmaceutical Industries
25
Ltd
26
Tata Consultancy Services Ltd
27
Tata Steel Ltd
28
Tech Mahindra Ltd
29
Titan Co Ltd
30
UltraTech Cement Ltd
Source- Computed by Author
0.361
1.864
10.122
6.017
1.01
0.21
1.285
8.166
1.15
2.357
0.658
1.972
-0.392
1.561
1.201
-0.104
0.220
2.281
-0.517
-0.198
1.605
1.673
9.811
16.469
10.534
6.544
8.304
8.699
13.199
9.500
5.677
7.269
7.050
12.368
12.599
1.32
2.31
0.82
0.73
0.96
1.13
1.44
1.14
0.25
0.65
0.54
1.22
1.46
1.456
9.263
0.69
1.567
2.458
2.922
2.860
1.762
10.666
12.365
8.515
9.654
8.393
0.64
1.29
0.74
0.92
0.88
Analysis: Table 2 shows the Return (%) of all the stocks in Sensex Index. Bajaj
Finance Ltd has generated the highest returns followed by Bajaj Finserv Ltd.
Indusind Bank Ltd has the highest risk followed by Bajaj Finance Ltd and Bajaj
Finserv Ltd. It is visible that there are 4 company’s stocks that will generate
negative returns. Out of those, NTPC Ltd has generated maximum negative return
followed by ITC Ltd, Power Grid Corp of India Ltd and Mahindra & Mahindra Ltd.
Also, it can noted that 12 company’s Beta value of greater than 1 which means
that out of the 30 companies’ stocks, 12 companies’ stock are highly volatile w.r.t
market.
Table 3- List Of BSE Sensex Companies’ Stocks Generating Positive Returns
Sl No.
1
2
3
4
5
6
7
8
Company Name
Asian Paints Ltd
Axis Bank Ltd
Bajaj Auto Ltd
Bajaj Finance Ltd
Bajaj Finserv Ltd
Bharti Airtel Ltd
Dr Reddy's Laboratories Ltd
HCL Technologies Ltd
Return
2.36
1.62
0.98
4.15
3.47
1.32
2.11
1.41
Risk
7.17
10.90
8.80
14.55
14.56
9.14
8.45
11.30
Beta
0.54
1.52
0.97
1.79
1.75
0.75
0.18
0.83
11576
9
HDFC Bank Ltd
10
Hindustan Unilever Ltd
11
Housing Development Finance Corp
12
ICICI Bank Ltd
13
IndusInd Bank Ltd
14
Infosys Ltd
15
Kotak Mahindra Bank Ltd
16
Larsen & Toubro Ltd
17
Maruti Suzuki India Ltd
18
Nestle India Ltd
19
Reliance Industries Ltd
20
State Bank of India
21
Sun Pharmaceutical Industries Ltd
22
Tata Consultancy Services Ltd
23
Tata Steel Ltd
24
Tech Mahindra Ltd
25
Titan Co Ltd
26
UltraTech Cement Ltd
Source- Computed by Author
0.36
1.86
1.29
2.36
0.66
1.97
1.56
1.20
0.22
2.28
1.60
1.67
1.46
1.57
2.46
2.92
2.86
1.76
10.12
6.02
8.17
9.81
16.47
10.53
8.30
8.70
9.50
5.68
12.37
12.60
9.26
10.67
12.37
8.52
9.65
8.39
1.01
0.21
1.15
1.32
2.31
0.82
0.96
1.13
1.14
0.25
1.22
1.46
0.69
0.64
1.29
0.74
0.92
0.88
Analysis: Table 3 depicts that the companies’ stocks generating negative returns
have been screened out. Further calculations to derive the optimal portfolio will
be done on the 26 positive returns generating companies’ stocks.
Table 4- Computation Of Cut Off Rate, Excess Return To Beta Ratio, Standard
Deviation, Variance And Unsystematic Risk
Sl
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Company Name
Asian Paints Ltd
Axis Bank Ltd
Bajaj Auto Ltd
Bajaj Finance Ltd
Bajaj Finserv Ltd
Bharti Airtel Ltd
Dr Reddy's Laboratories Ltd
HCL Technologies Ltd
HDFC Bank Ltd
Hindustan Unilever Ltd
Housing Development Finance
Corp
ICICI Bank Ltd
IndusInd Bank Ltd
Infosys Ltd
Kotak Mahindra Bank Ltd
Larsen & Toubro Ltd
2.36
1.62
0.98
4.15
3.47
1.32
2.11
1.41
0.36
1.86
Excess
Return
(R - Rf) %
2.06
1.32
0.67
3.85
3.17
1.02
1.80
1.10
0.06
1.56
1.29
2.36
0.66
1.97
1.56
1.20
Return
(%)
0.54
1.52
0.97
1.79
1.75
0.75
0.18
0.83
1.01
0.21
Excess
Return
Beta
3.79
0.87
0.70
2.15
1.81
1.36
9.86
1.33
0.06
7.43
0.98
1.15
0.85
21
2.05
0.35
1.67
1.26
0.90
1.32
2.31
0.82
0.96
1.13
1.56
0.15
2.03
1.30
0.79
14
24
8
17
22
β
to
RANKING
4
20
23
7
10
15
1
16
25
3
11577
17
18
19
20
21
22
23
24
25
26
Maruti Suzuki India Ltd
0.22
-0.08
1.14 -0.07
26
Nestle India Ltd
2.28
1.98
0.25 7.90
2
Reliance Industries Ltd
1.60
1.30
1.22 1.07
18
State Bank of India
1.67
1.37
1.46 0.94
19
Sun Pharmaceutical Industries
1.46
1.15
0.69 1.67
12
Ltd
Tata Consultancy Services Ltd
1.57
1.26
0.64 1.96
9
Tata Steel Ltd
2.46
2.15
1.29 1.67
11
Tech Mahindra Ltd
2.92
2.62
0.74 3.54
5
Titan Co Ltd
2.86
2.56
0.92 2.77
6
UltraTech Cement Ltd
1.76
1.46
0.88 1.66
13
Source: Computed by Author
Analysis: Rf taken as 3.65% p.a which when converted to monthly Rf is 3.65/12
= 0.342%.
Table 4 shows that the stocks are generating excess return to beta which also
means, the excess returns earned for taking up one unit of systematic risk. The
ranking is done for all these stocks in high to low “excess return of beta values”
order of the stocks. Excess returns per unit systematic risk taken are highest in
Dr. Reddy’s Laboratories Ltd, followed by Nestle India Ltd and Hindustan Uniliver
Ltd.
Table 5- Computation Of Cut Off Rate Using Sharpe’s Single Index Model (Table
Headings are detailed below the table due to lack of space)
Source- Computed by Author
11578
Analysis: Table 5 shows the various measures calculated using different formulae
as mentioned in the Techniques used for data analysis sub topic in Chapter 3.
Cut- Off rate using Sharpe Single Index Model is calculated for each stock. It is
observed that the cut off rate increases in ascending order and at 7 th Ranked
stock- Bajaj Finance Limited, the cut off rate is highest (2.0943). Beyond Rank no
7th stock, the cut off rate values is observed to be descending. Therefore, the
stocks below the highest cut off rate are not considered in the portfolio. The
portfolio is constructed using the 7 stocks for the period under study.
Table 6- Construction Of Portfolio And Proportion Of Investment In Each Stock
Source: Computed by Author
Analysis: Table 6 shows the computation of the proportion of funds that needs to
be invested in different stocks from the derived portfolio.
The computation shows that 23% of the total funds must be invested in Tech
Mahindra Ltd, 23% of the total funds must be invested in Asian Paints Ltd., 20%
of the total funds must be invested in Nestle India Ltd, 13% of the total funds
must be invested in Titan Co Ltd, 11% of the total funds must be invested in
Hindustan Uniliver Ltd, 6% of the total funds must be invested in Dr. Reddy’s
Laboratories Ltd, 2% of the total funds must be invested in Bajaj Finance Ltd
stock.
Table 7- Calculation Of Portfolio Return
Portfolio Return
RAN
K
1
2
3
4
5
Company Name
Dr
Reddy's
Laboratories Ltd
Nestle India Ltd
Hindustan
Unilever
Ltd
Asian Paints Ltd
Tech Mahindra Ltd
X
proportion
of
Investmen
t
Return
(Rbar) (%)
0.06356
0.02107
0.00134
0.20692
0.02281
0.00472
0.11341
0.01864
0.00211
0.23027
0.23361
0.02362
0.02922
0.00544
0.00683
Return on
Portfolio (%)
the
11579
6
Titan Co Ltd
7
Bajaj Finance Ltd
Source- Computed by Author
0.12934
0.02289
0.02860
0.04155
Total monthly return of Portfolio
Total yearly return of the Portfolio
0.00370
0.00095
2.51%
30.11%
Analysis: Table 7 illustrates the total return that can be expected to earn from the
derived portfolio. The annual return of the derived portfolio is 30.11%.
Figure 1- Proportion Of Investments To Be Done In Different Stocks From The
Dervied Portfolio
Source- Computed by Author
Interpretation: Figure 1 illustrates the proportion of investments that needs to be
done in each of the companies from the derived portfolio in a doughnut chart
view. The maximum proportion of the investment amount i.e., 24% of the
investment amount needs to be invested in Tech Mahindra Limited stock followed
by 23% of the investment amount in Asian Paints Limited.
Findings from the Study
 Out of the 30 companies from Sensex, only 26 companies were chosen to
conduct a study and derive a portfolio since the rest 4 companies generated
negative returns when calculated.
 The performances of the stocks were determined using the calculation of
excess return to beta ratio and ranked accordingly.
 Study was able to determine that there are few stocks that are negatively co
related to the market.
 The study found that 12 companies’ stocks have Beta value greater than 1.
 IndusInd bank’s stock is the most volatile stock containing beta value of
2.31 among the 30 stocks in Sensex index.
 Dr. Reddy’s Laboratories Ltd had the highest Excess returns per unit
systematic risk.
11580
 The Cut- Off point is 2.0943.
 Out of 30 stocks from BSE Sensex, only 7 stocks are chosen as part of the
optimal portfolio.
 The computations of the proportion of funds that needs to be invested in
different stocks from the derived portfolio shows that:
 23% of the total funds must be invested in Tech Mahindra Ltd.
 23% of the total funds must be invested in Asian Paints Ltd.
 20% of the total funds must be invested in Nestle India Ltd.
 13% of the total funds must be invested in Titan Co Ltd.
 11% of the total funds must be invested in Hindustan Uniliver Ltd.
 6% of the total funds must be invested in Dr. Reddy’s Laboratories Ltd.
 2% of the total funds must be invested in Bajaj Finance Ltd stock.
 The study shows that annual return of the derived portfolio is 30.11%.
Conclusion
Diversification of any investment is very essential in order to spread the risk and
so is it in the stock market as well. Diversifying an investment in stock markets
needs to be carefully done after careful and type of analysis based on the tenure
and need of the investment returns. Analysing the risk and return of each stock
in a stock market before adding into the portfolio is highly important. Also,
understanding the co-relation between the stocks in the portfolio is also highly
essential in order to balance the negative returns sometimes. Thus, this research
paper is prepared with an attempt to compute the return, risk and excess to beta
ratios of each stock before developing a portfolio to understand the overall
riskiness of the stocks in BSE Sensex 30 companies. The excess beta ratio
calculation plays a major role in eliminating those companies’ stocks which is not
efficient for the study. Further, the study is progressed with the usage of Sharpe’s
Single Index model’s cut-off point formulae to describe the securities which are
above the cut-off point. Those stocks above the cut-off point have been considered
for developing the portfolio. Lastly, the proportion of investments that are to be
done in each stock is determined based on the percentage of returns the stocks in
the portfolio have generated earlier.
Jel Classification: G11, G14
References
[1] Archana, H. N., & Srilakshmi, D. (2020). Building an Optimal Portfolio Using
Sharpe’s Single Index Model: An Empirical Study With Refernce To Indian
Capital
Markets. Journal
of
Xi'an
University
of
Architecture
&
Technology, 12(8), 1233-1244.
[2] Nalini, R. (2014). Optimal Portfolio construction using Sharpe’s Single Index
Model-A study of selected stocks from BSE. International Journal of Advanced
Research in Management and Social Sciences, 3(12), 72-93.
[3] Saravanan, A., & Natarajan, P. (2012). Optimal portfolio construction with
Nifty stocks (An analytical prescription for investors). Advances in
Management.
[4] Dharmalingam, N., & Gurunathan, K. B. (2021). Portfolio construction using
the Sharpe index model with reference to sugar and metal sector on
11581
India. ACADEMICIA: AN INTERNATIONAL MULTIDISCIPLINARY RESEARCH
JOURNAL, 11(1), 1132-1143.
[5] Debasish, S. S., & Khan, J. S. (2012). Optimal Portfolio Construction in Stock
Market: An Empirical Study on Selected Stocks in Manufacturing Sector of
India. International Journal of Business Management, 2(2), 37-44.
[6] Nageswari, P., Selvam, M., & Bhuvaneswari, P. (2013). An empirical analysis
of optimal portfolio selection using Sharpe's optimization. Asian Journal of
Research in Business Economics and Management, 3(11), 209-221.
[7] Anagnostopoulos, K. P., & Mamanis, G. (2010). A portfolio optimization model
with three objectives and discrete variables. Computers & Operations
Research, 37(7), 1285-1297.
[8] Nandan, T., & Srivastava, N. (2017). Construction of optimal portfolio using
sharpe’s single index model: an empirical study on nifty 50 stocks. Journal of
Management Research and Analysis, 4(2), 74-83.
[9] Sharpe, W. F. (1963). A simplified model for portfolio analysis. Management
science, 9(2), 277-293.
[10] Varadharajan, P. (2012). Construction of equity portfolio of large caps
companies of selected sectors in India with reference to the Sharpe Index
Model. International Journal of Physical and Social Sciences, 2(8), 37-50.
[11] Sarker, M. R. (2013). Markowitz portfolio model: evidence from Dhaka Stock
Exchange in Bangladesh. International Organization of Scientific Research
Journal of Business and Management, 8(6).
[12] Dileep, S., & Rao, G. K. (2013). A STUDY ON SUITABILITY OF WILLIAM
SHARPE’S SINGLE INDEX MODEL IN SENSEX IN THE INDIAN
CONTEXT. International Journal of Administrative, Management and Business
(IJAMBU), 1(1), 48-54.
[13] Desai, R., & Surti, M. (2013). Optimal Porfolio Construction: Sharpe’s Single
Index Model. International Journal of Scientific Research, 2(9), 250-251.