Optimal Vs 1/N Diversification and Portfolio Evaluation: A study on Indian Stock Market
V. Harshitha Moulya^{1}, Abuzar Mohammadi^{1}, Dr T. Mallikarjunappa^{2}
^{1}Research Scholar, Department of Business Administration, Mangalore University, Mangalagangothri, Konaje, Mangalore 574199 Karnataka
^{2}Professor, Department of Business Administration, Mangalore University, Mangalagangothri, Konaje, Mangalore 574199 Karnataka
*Corresponding Author Email: harshuwhitetiger@gmail.com, abuzar.mohammadi@gcc.edu.in
ABSTRACT:
The Modern portfolio theory of Markowitz (1952) proposed maximisation of expected utility and minimisation of the risk of the optimal portfolio for the riskaverse investors. We used the linear programming technique to estimate the optimal portfolio weights for the meanvariance efficient optimal portfolio using rebalanced and nonrebalanced portfolios and compared the performances against the 1/N heuristic portfolio. We found that the minimumvariance optimal portfolio performed better than the 1/N heuristic portfolio.
KEYWORDS: Portfolio Optimisation, Markowitz portfolio, Portfolio rebalancing, portfolio returnrisk, NSE
INTRODUCTION:
The Modern Portfolio Theory (MPT) of Markowitz (1952) proposed two axioms for portfolio formation and the efficient frontier of the optimal portfolio for investors viz., the expected utility maximisation and riskminimisation. According to the MPT, investors are riskaverse and have certain beliefs for choosing a portfolio. The riskaverse investors try to maximise the discounted value of their expected returns generated by a maximum utility function where the investors invested all their funds in security that yield maximum anticipated returns. The axiom of expected utility maximisation alone didn’t generate anticipated returns from the optimal portfolio due to market risks and imperfections. The MPT proposed the second axiom viz., the EV rule (Expected returns–Variance in returns) or the MeanVariance (MV) model according to which the investors allots weights on different assets or riskysecurities to form a portfolio for earning the expected returns.
The investors attain expected returns by accepting a variance of returns visàvis reduce the variance in expected returns by giving up expected returns through the process of asset allocation and diversification of securities in a portfolio. The asset allocation process is done by allotting the optimal weights of investments on risky assets. The weights are optimal if the proposed portfolio attains both the objectives of expected utility maximisation and riskminimisation for the riskaverse investors.
There are various measures for measuring the portfolio risk viz., traditional measures– the standard deviation or variance of expected returns; advanced methods – Sortino ratio, the CVaR (Conditional Value at Risk); and the coherent risk measures using quantilebased methods, scenariobased methods (Artzner, Delbaen, Eber, & Heath, 1999) used in the computation of portfolio risk and returns. As the portfolio risk is a function of variance and covariances of asset returns in the portfolio, an optimal portfolio for investors should have lower correlation/ covariance in asset returns for various combination of assets for earnings the maximum expected returns.
In our study, we discuss the vast literature on the portfolio theory and empirically examine the performance of Markowitz’s MV model of optimal portfolio visàvis the 1/N equalweighted portfolio. We considered the singleasset case of riskysecurities, i.e. the equities traded on the NSE for constructing the meanvariance efficient portfolio using the portfolio rebalancing technique for the singleperiod optimisation and multiperiod optimisation scenarios. The stocks traded on the Nifty 50 index is considered for the optimal portfolio as the stocks represent more than 66% of market liquidity in trade and volume for the Indian market. The optimal weights for weight allocation on the equities were estimated using the linear programming technique. Our results show that periodic portfolio rebalancing gives higher expected portfolio returns for the given variance. The minimumvariance MV portfolio performed better than the maximumreturn MV portfolio and the 1/N heuristic portfolio in terms of optimal portfolio returns, Sharpe ratio and minimum variance.
LITERATURE REVIEW:
The seminal works by Tobin (1958), Sharpe (1964), Lintner (1965), Merton (1969, 1973), and Black (1972) studied the meanvariance (MV) efficient portfolio frontier theory of Markowitz (1952) and found the results consistent with the doctrine of investments of expected utility maximization and riskminimization by the riskaverse investors i.e. the investors maximized their expected portfolio returns by minimizing the portfolio variance. Tobin (1958) observed that the proportionate composition of investment made on the riskyassets was independent of the optimal cash holding of the riskaverse investors. He observed that the utility function of the riskaverse investors was quadratic, and the expected returns followed the multivariate normal distribution. Lintner (1965) established a relationship between the expected returns and the rational decision rules of the riskaverse investors given the cash constraints for investing. He postulated that the equilibrium properties of assets determine the optimal portfolio of riskassets. The asset allocation for investors/ institutional investors depends on the factors like  the riskfree rate of return, the market price of the dollar (risk), variance in project’s present value and the aggregate present value returns. Sharpe (1964), Lintner (1965), Jensen (1968) and Black (1972) proposed the asset returns can be estimated as a linear function of market risk using the capital asset pricing model (CAPM) given the consumption of the riskaverse investors and the general equilibrium economy. Merton (1969, 1973) and Fama and French (1992, 1993, 1996) criticised the CAPM as it failed to explain the crosssectional differences in the expected returns of portfolios even when systematic risk or market risks were absent. The followup studies by Merton (1969, 1973) proposed an intertemporal capital asset pricing model (ICAPM) to study the consumption problem and the problem of optimal portfolio selection using constant relativerisk aversion of investors. They got results consistent with both the expected utility maxim and the limited liability of assets propositions of Markowitz (1952) and Tobin (1958) using ICAPM. Fama and French (1992, 1993, 1996) used a multifactor explanation for the crosssectional returns and the return anomalies, and proposed a threefactor model that provided that along with CAPM beta, the nonrisk firm factors like SMB (small minus big) and HML (high minus low) explained the crosssectional variation in the expected returns.
The empirical studies on portfolio optimisation under the MV framework used various measures for risk and optimisation techniques for the efficient portfolio. A study by Chan, Karceski, and Lakonishok (1999) used a factor model to generate a global minimum variance portfolio to obtain factor loadings for the estimation of covariance matrices of asset returns. However, they failed to accurately forecast the asset return covariance matrix for the optimal portfolio. Lauprete, Samarov, and Welsch (2002) simulated a multivariate distribution data to address the estimation problem influenced by marginal heavy tails, applied robust alternative estimation techniques, and found that standard variance minimisation procedure had outlier problems due to marginal heavy tails and multivariate tail dependence, and suggested that alternative estimation techniques gave better results due to lower risks.
De Miguel, Garlappi, and Uppal (2009) performed a comparison of 14 different estimation models for MV optimal portfolio for the US stocks and found that no model performed better than the 1/N heuristic model in terms of Sharpe ratio, and the optimal diversification failed due to estimation errors of asset return moments. Lai, Xing, and Chen (2011) used the stochastic optimisation technique for estimating an efficient frontier and highlighted that the variability in portfolio returns occurred due to variability in plugin weights used for optimisation and estimation of covariance matrices. Lim, Shanthikumar, and Vahn (2011) used a CVaR (conditional Value at Risk) as a measure of risk for estimating conditional VaR for portfolio optimisation. They suggested that the CVaR was weak due to the estimation errors for portfolio returns.
Studies by BaixauliSoler, AlfaroCid, and FernandezBlanco (2011), Lwin, Qu, and MacCarthy (2017) used MODEGL algorithm for the estimation of optimal weights for asset allocation at the stock index level viz., EURSTOXX50 and S&P indices, respectively, and found that the algorithm outperformed MV framework as it gave adequate and better results compared to linear programming techniques or smoothing techniques. Ranković, Drenovak, Urosevic, and Jelic (2016) found that meanGARCH VaR optimisation model outper formed meanmultivariate GARCH VaR model for US stock data, as the results were robust in both low and high volatility samples. On the contrary, (Sukono, Sidi, Bon, & Supian, 2017) used meanVaR framework over MV framework at the individual security level, and found an optimum solution using algebra approach.
The literature analysis shows that the studies have used a variety of optimisation techniques for the optimal portfolio under MV framework. However, none of the techniques was robust to estimation models and different asset classes. A comparative study on the estimation models showed that the heuristics performed better than any of the sophisticated techniques for the US stock market. All the studies assumed singleperiod portfolio scenarios for portfolio optimisation. As portfolio rebalancing is essential for active portfolio management, in our study, we used the singleasset case of using equities as riskysecurities for constructing an optimal portfolio using portfolio rebalancing techniques. We performed the comparative study of the performance of heuristic equalweighted portfolio visàvis MV optimal portfolio. The optimal weights for the MV portfolio were estimated using the linear programming techniques for the Indian stock market.
DATA AND METHODOLOGY:
We used the monthly closing price data of the NSE listed stocks viz.., equities traded under the Nifty50 index for the period between January 2013 and December 2017. The data is referred from the NSE website.
The MV framework:
We used the singleasset case for the proposed portfolios viz., the MV portfolio and the equalweighted portfolio, where Nifty50 stocks are used for asset allocation and portfolio diversification purposes. The equalweighted 1/N heuristic portfolio is considered by allotting equal weights on the Nifty50 stocks.
The MV portfolio is the one which maximises the expected returns at given a variance visavis reduces variance for the given level of expected returns under the given conditions. The expected portfolio returns are measured as the weighted average discounted expected return of securities at a time ‘t’, and the portfolio risk is calculated as the covariance between securities’ returns at a time ‘t’. The portfolio return and risk of the proposed MV portfolio are mathematically represented as (1) and (2).
(1)
Where,
represents the expected portfolio returns; _{} is the return on the security ‘i’ at the time ‘t’; _{} is the discounting rate at time ‘t’; _{} refers to the weight of investment allotted on the security ‘i’ and n is the number of securities in the portfolio.
(2)
Where, is portfolio variance; represent returns on securities ‘i’ and ‘j’ respectively at a time ‘t.’
The MV framework (Markowitz, 1952) recommends diversification of assets, maximisation of expected utility for investors under the fullinvestment and longonly constraints, and minimisation of portfolio variance.
The MV portfolio is proposed under the two constraints viz., 1) fullinvestment constraint, where, all the investible fund is used for the assetinvestment. The summation of allocation weights should be equal to unity. 2) The longonly constraint, where, all the allocation weights are positive, i.e. no shortselling is admissible. The fullinvestment and longonly constraints are mathematically expressed as (3) and (4), respectively.
(3)
Where represent the allocation weights for optimal portfolio, _{} refers to the fullinvestment constraint.
(4)
Estimation of optimal weights for the MV portfolio using linear programming technique
For the estimation of the optimal weights for the proposed MV portfolio, we used the linear optimisation technique. The linear programming achieves optimisation (maximisation/minimisation) under a linear objective function, subject to the linear equality and linear inequality constraints. The solution of the linear programming problem is the objective function that gives the optimal value of the linear expression, subject to the constraints expressed as inequalities.
The objective function of the portfolio optimisation problem should maximise expected returns _{} for given variance or minimise the variance _{} for the given expected returns for the given constraints of fullinvestment and longonly constraints. The objective functions and the constraints are mathematically represented in (5), (6), (7) and (8) respectively.
(5)
(6)
Where _{} represents a vector of optimal weights, Q represents the estimated covariance matrix of asset returns.
Constraints:
, (7)
, i=1,2…n (8)
Portfolio optimisation scenarios:
We carried out portfolio optimisation under twoscenario viz., a) Singleperiod optimisation, and b) Multipleperiod optimisation. Under the singleperiod case, optimal weights are estimated at the beginning of the portfolio formation period for one time. Under the multipleperiod case, the MV portfolio is rebalanced by altering the allocation weights on the assets at the beginning of every quarter. Thus, we carried out four optimisations of the MV portfolio under the given scenarios.
RiskReturn of MV portfolios and Portfolio evaluation:
The portfolio return and risk of the optimised portfolios (for both rebalanced and nonrebalanced) and the equalweighted using equation (1) and (2). We used the Sharpe ratio (Sharpe, 1963) for comparing the returnrisk performances of the optimised MV portfolios visàvis the 1/N heuristic portfolio. The annualised Sharpe ratio is measured as the ratio of annualised portfolio return to the annualised portfolio risk. The higher value of the Sharpe ratio implies a higher riskadjusted return for taking higher risk. We have assumed riskfree rate as zero in the study. The mathematical representation of the Sharpe ratio is given in (9).
(9)
RESULTS AND DISCUSSION:
Table 1 provides the descriptive statistics of the Nifty50 stocks. We found that 29 stocks (57%) have average positive returns, 28 stocks (55%) have average returns higher than the crosssectional average (0.01%). 13 stocks (25%) have a higher variance than the crosssectional average variance (0.09%). The frequency distribution of the returns of the stock shows that the returns are highly leptokurtic and skewed to the right. The SBIN (0.17%) has the highest mean returns; MARUTI (0.14%) has the lowest mean returns. SBIN (6.73%) has the highest average volatility, and HDFCBANK (1.26%) has the lowest average volatility.
Table 1: Descriptive statistics of asset returns
Equities 
Mean 
SD 
Variance 
Kurtosis 
Skewness 
SBIN 
0.17% 
6.73% 
0.45% 
1038.12 
30.58 
BANKBARODA 
0.14% 
5.26% 
0.28% 
702.94 
22.68 
ASIANPAINT 
0.11% 
6.67% 
0.44% 
1124.37 
32.52 
ICICIBANK 
0.10% 
4.92% 
0.24% 
879.78 
27.02 
GRASIM 
0.08% 
4.76% 
0.23% 
970.77 
29.19 
AXISBANK 
0.07% 
4.98% 
0.25% 
869.01 
26.80 
BHEL 
0.07% 
2.76% 
0.08% 
42.39 
2.92 
INFY 
0.06% 
3.28% 
0.11% 
332.08 
15.66 
TECHM 
0.04% 
4.32% 
0.19% 
879.83 
27.10 
ONGC 
0.03% 
2.23% 
0.05% 
75.45 
4.24 
YESBANK 
0.03% 
5.14% 
0.26% 
751.12 
23.98 
IDEA 
0.02% 
2.49% 
0.06% 
6.97 
0.68 
LT 
0.02% 
2.35% 
0.06% 
115.46 
6.83 
MM 
0.02% 
2.62% 
0.07% 
478.58 
17.11 
SUNPHARMA 
0.02% 
2.67% 
0.07% 
318.55 
12.86 
WIPRO 
0.02% 
2.49% 
0.06% 
517.35 
18.34 
COALINDIA 
0.01% 
1.78% 
0.03% 
3.56 
0.08 
ITC 
0.01% 
1.91% 
0.04% 
123.69 
6.42 
NTPC 
0.00% 
1.65% 
0.03% 
6.32 
0.48 
ACC 
0.01% 
1.55% 
0.02% 
1.33 
0.19 
DRREDDY 
0.01% 
1.72% 
0.03% 
8.49 
0.82 
RELIANCE 
0.01% 
2.51% 
0.06% 
469.37 
16.87 
TATAMOTORS 
0.01% 
2.17% 
0.05% 
2.05 
0.05 
TATAMTRDVR 
0.01% 
2.25% 
0.05% 
1.72 
0.10 
AMBUJACEM 
0.02% 
1.75% 
0.03% 
2.21 
0.09 
BHARTIARTL 
0.02% 
1.90% 
0.04% 
1.69 
0.32 
BPCL 
0.02% 
3.09% 
0.10% 
253.97 
11.66 
GAIL 
0.02% 
2.04% 
0.04% 
45.33 
2.79 
LUPIN 
0.02% 
1.77% 
0.03% 
11.55 
1.18 
BAJAJAUTO 
0.03% 
1.48% 
0.02% 
2.56 
0.08 
CIPLA 
0.03% 
1.59% 
0.03% 
3.07 
0.03 
HCLTECH 
0.03% 
2.64% 
0.07% 
428.99 
15.92 
TATASTEEL 
0.03% 
2.29% 
0.05% 
2.73 
0.01 
INFRATEL 
0.04% 
2.20% 
0.05% 
1.89 
0.02 
KOTAKBANK 
0.04% 
2.53% 
0.06% 
467.50 
16.79 
POWERGRID 
0.04% 
1.42% 
0.02% 
4.91 
0.34 
HINDALCO 
0.05% 
2.50% 
0.06% 
1.37 
0.11 
BOSCHLTD 
0.06% 
1.63% 
0.03% 
2.58 
0.52 
HDFC 
0.06% 
1.69% 
0.03% 
1.65 
0.11 
ULTRACEMCO 
0.06% 
1.69% 
0.03% 
1.60 
0.09 
TCS 
0.07% 
1.46% 
0.02% 
2.40 
0.19 
HDFCBANK 
0.08% 
1.26% 
0.02% 
4.04 
0.14 
ZEEL 
0.08% 
1.87% 
0.03% 
1.05 
0.16 
ADANIPORTS 
0.09% 
2.41% 
0.06% 
2.60 
0.13 
AUROPHARMA 
0.09% 
3.06% 
0.09% 
188.42 
8.37 
INDUSINDBK 
0.11% 
1.82% 
0.03% 
3.32 
0.30 
MARUTI 
0.14% 
1.62% 
0.03% 
2.94 
0.32 
Source: Authors’ computation
Table 2 shows the estimated portfolio weights using a linear programming technique under the Singleperiod optimisation scenario. It is observed that 24 stocks (47%) have an estimated optimal weight ≥ 0.17%, TCS (13.28%) has the highest estimated optimal weight followed by POWERGRID (1.084%), HDFCBANK (10.31%), DRREDDY (7.60%) and BOSCHLTD (6.29%).
Table 2: Optimal weights for the MV Portfolio (Singleperiod Optimization)
Stock 
Optimal weights estimated (%) 
TCS 
13.28% 
POWERGRID 
10.84% 
HDFCBANK 
10.31% 
DRREDDY 
7.60% 
BOSCHLTD 
6.29% 
LUPIN 
6.24% 
INFRATEL 
4.82% 
COALINDIA 
4.54% 
ITC 
4.54% 
NTPC 
4.47% 
CIPLA 
4.31% 
BAJAJ_AUTO 
3.99% 
WIPRO 
3.59% 
BHARTIARTL 
3.29% 
HCLTECH 
2.83% 
ACC 
2.43% 
MARUTI 
2.19% 
INFY 
1.38% 
MM 
0.92% 
ZEEL 
0.73% 
IDEA 
0.52% 
RELIANCE 
0.48% 
SUNPHARMA 
0.23% 
GAIL 
0.17% 
Others 
0.17% < _{} ≥ 0.01% 
Source: Authors’ computation
Table 3 shows the returnrisk measures and the Sharpe ratio for the optimised MV portfolios under the singleperiod scenario (nonrebalanced). It is observed that the maximumreturn MV portfolio and the equalweighted portfolio gave an optimal portfolio return of 0.06% with a portfolio variance of 1.021%, and Sharpe ratio of 0.006. The maximumreturn MV portfolio has mimicked the performance of a 1/N heuristic portfolio of equalweight allocation on the stocks. The minimumvariance MV portfolio has an estimated portfolio return of 0.035% with a portfolio variance of 0.755% and a Sharpe ratio of 0.046. The higher portfolio return and Sharpe ratio and lower portfolio variance values indicate that the minimisation of variance has better performance than the 1/N portfolio and the maximumreturn MV portfolio.
Table 3: Optimal portfolio performance measures (Singleperiod optimisation scenario)
Optimal Portfolios 
Portfolio Return 
Portfolio Risk (std. dev in %) 
Sharpe ratio 
Minimum Variance 
0.035% 
0.755% 
0.046 
Maximum Return 
0.006% 
1.021% 
0.006 
Equalweighted Portfolio 
0.006% 
1.021% 
0.006 
Source: Authors’ computation
Table 4 shows the estimated portfolio returnrisk for the optimised MV portfolios using the quarterly portfoliorebalancing technique. It is observed that the rebalanced risk for the minimumvariance MV portfolio has been increasing over the rebalancing periods, while the quarterly rate of return is decreasing. The lowest rebalanced risk is 0.35%, with a quarterly return of 0.64% recorded during the first quarter (January – March 2013). For maximumreturns MV portfolio, the highest quarterly return (1.33%) is recorded in the first quarter (January  March 2013) with a standard deviation of (0.19%).
Table 4: Portfolio returnrisk for MV portfolios using portfolio rebalancing under multiperiod optimization scenario
Rebalancing Dates 
Minimum Variance Portfolio 
Maximum Return Portfolio 

Rebalanced Risk (%) 
Quarterly Return (%) 
Rebalanced Return (%) 
Quarterly Risk (%) 

28032013 
0.35% 
0.64% 
0.19% 
1.33% 
28062013 
0.58% 
0.05% 
0.10% 
0.05% 
30092013 
0.69% 
0.03% 
0.12% 
0.15% 
31122013 
0.69% 
0.15% 
0.08% 
0.19% 
31032014 
0.67% 
0.04% 
0.34% 
0.11% 
30062014 
0.68% 
0.24% 
0.44% 
0.27% 
30092014 
0.68% 
0.21% 
0.16% 
0.05% 
31122014 
0.70% 
0.04% 
0.24% 
0.10% 
31032015 
0.72% 
0.03% 
0.15% 
0.06% 
30062015 
0.75% 
0.04% 
0.01% 
0.06% 
30092015 
0.78% 
0.03% 
0.28% 
0.15% 
31122015 
0.78% 
0.04% 
0.02% 
0.03% 
31032016 
0.80% 
0.07% 
0.16% 
0.08% 
30062016 
0.80% 
0.11% 
0.15% 
0.12% 
30092016 
0.79% 
0.05% 
0.05% 
0.03% 
30122016 
0.79% 
0.16% 
0.15% 
0.16% 
31032017 
0.78% 
0.07% 
0.02% 
0.15% 
30062017 
0.77% 
0.11% 
0.09% 
0.04% 
29092017 
0.77% 
0.01% 
0.24% 
0.11% 
29122017 
0.76% 
0.03% 
0.01% 
0.09% 
20022018 
0.76% 
0.08% 
0.12% 
0.14% 
Source: Authors’ computation
Figure 4 provides a graphical representation of the estimated optimal weights for the MV portfolios under the multiperiod rebalancing scenario.
Figure 4: Estimated optimal Weights for MV Portfolio under the multiperiod scenario
Table 5 shows the annualised performance measures of optimised MV portfolios using the rebalancing technique. The minimumvariance MV portfolio has an annualised portfolio return of 3.727% with an annualised risk of 14.47% and a Sharpe ratio of 0.258. The maximumreturn MV portfolio mimick the 1/N heuristic portfolio with an annualised return of 0.311%, annualised portfolio risk of 16.484% and a Sharpe ratio of 0.019.
Table 5: Portfolio returnrisk performance of rebalanced portfolios
Optimal Portfolios 
Annualized Portfolio Rebalancing Return 
Annualized Portfolio Rebalancing Risk (std. dev in %) 
Annualized Sharpe ratio 
Minimum Variance 
3.727% 
14.447% 
0.258 
Maximum Return 
0.311% 
16.484% 
0.019 
Equalweighted Portfolio 
0.311% 
16.484% 
0.019 
Source: Authors’ computation
DISCUSSION:
The findings (Table 3 and Table 5) indicate that the multiperiod optimisation of MV portfolio using the portfolio rebalancing technique has given an optimal annual return of 3.727% with the highest Sharpe ratio of 0.258 compared to the other portfolios. The 1/N heuristic portfolio and the maximumreturn MV portfolios have lower return and Sharpe ratio and highest risk compared to the minimumvariance MV portfolio under all the scenarios. Therefore, our findings do not support the results of (DeMiguel et al., 2009). We found that the estimated optimal weights varied over the rebalancing period resulting in the variation of optimal portfolio returns. Our observation abides by (Lai et al., 2011) that the portfolio variance is a linear function of portfolio weights.
FINDINGS AND CONCLUSION:
The study empirically tested the Markowitz’s MeanVariance optimal portfolio using the linear programming optimisation technique. The twinobjectives of portfolio optimisation is to achieve maximum expected utility for investors at minimum variance. We tested the objective functions of maximumutility and minimumvariance for MV portfolios under the constraints of fullinvestment and longonly conditions. The portfolio optimisation was performed under the singleperiod scenario and the multiperiod scenarios using the portfolio rebalancing technique. We found that the minimumvariance portfolio outperformed the 1/N heuristic portfolio in terms of optimal returnrisk and Sharpe ratio in both scenarios of singleperiod and multipleperiod optimisations. Our findings contrast (DeMiguel et al., 2009). The study showed that though the portfolio rebalancing gave better returns for given risk for minimumvariance portfolio, the variability in portfolio returns is attributed to the variability in the allocation of estimated weights, in support of (Lai et al., 2011).
The linear optimisation technique didn’t perform well as the technique didn’t optimise the allocation weights for the maximumreturns portfolio. The estimation The estimation failed due to the presence of asset returns properties to the asset returns properties, i.e. the skewness and excess kurtosis in the asset returns and the associated marginal heavy tails (Lauprete et al., 2002). There is a lot of future research scope as the study can be improved by using sophisticated nonlinear estimation techniques for estimating optimal weights for Markowitz optimisation, and estimation of asset returns moments. This study has contributed to the field of portfolio management by highlighting the importance of periodic portfolio rebalancing for achieving optimal returns.
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Received on 08.06.2019 Modified on 21.06.2019
Accepted on 10.07.2019 ©AandV Publications All right reserved
Asian Journal of Management. 2019; 10(3): 248254.
DOI: 10.5958/23215763.2019.00039.8