Markowitz Approach to optimum portfolio building determines the optimum portfolio for the investor through three of import variable i.e. , return, standard divergence and correlativity coefficient as a step of inter-relationship between the return on assets considered. This theoretical account is called “ Full Covariance Model ” . But this theoretical account is highly demanding in its informations demands and computational demands. Furthermore, in the existent universe of investings, securities analysts typically do non believe in footings of some of the Markowitz input demands such as correlativity inputs for each security, comparative to each other security in the universe utilised. This indicates operational necessity to simplify this procedure to utilize a common “ index ” for looking at the correlativity of each stock instead than the correlativity of each stock to all other stocks. This was done by William Sharpe ( 1963 ) . Sharpe ‘s Mean Variance Approach does non take into consideration the instance of the investors with differentiated hazard antipathy degrees. Mean-Gini attack to analyse hazardous chances and concept optimal portfolios has proved to be more equal than the mean-variance attack for measuring the variableness of a prospect since mean-Gini is consistent with investors ‘ behaviour under uncertainness for a broad category of chance distributions. Gini ‘s average difference may be extended into a household of coefficients of variableness differing from each other in the decision-makers grade of hazard antipathy

This paper is an empirical rating of Mean Variance ( MV ) , Mean-Gini ( MG ) and Mean Extended Gini ( MEG ) approaches to an optimal portfolio choice. Initially these attacks have been reviewed depicting their econometric analysis and the troubles which they raise while doing an optimal portfolio choice. The significance of the difference between MV Betas and MEG Betas and besides the cogency of normalcy premise has been tested for some selected Indian securities utilizing Haussman ‘s trial and D’Agostino ‘s normalcy trial. When security returns are non usually distributed MEG Betas are found to differ significantly from MV Betas. Further, the securities have been ranked harmonizing to their Betas obtained for assorted hazard antipathy degrees. Significance of the difference in the rankings of securities harmonizing to the assorted systematic hazards has besides been examined. The trial ranks the securities in go uping order of Beta for a given hazard antipathy degree and compares the deciles obtained by ranking securities in go uping order of MV Betas. If the security remains in the same decile, so gauging Beta harmonizing to MEG will non supply any extra information to the investor, if the securities move up or down by more than one decile, the MV systematic hazard would impede investor ‘s ability to construct optimal portfolios that diversify the hazard. Here it has been observed that most of the securities move by more than one decile therefore warranting the usage of MEG attack to optimal portfolio choice. To get at an optimum portfolio for assorted risk-aversion degrees Excess Return to Beta ratios have been computed. Last, the paper concludes by ranking the securities harmonizing to their Excess Return to Beta Ratios at assorted risk-aversion degrees, therefore proposing the penchant order of the securities for the investors at assorted risk-aversion degrees.

Portfolio refers to investing in fiscal assets such as portions, unsecured bonds, bonds, securities, common financess etc. The portfolio direction aims to choose the best combinations of assets, which yield maximal sum of return with minimal degree of hazard. This hazard – return tradeoff between assorted degrees of return associated with several hazard is a uninterrupted procedure, which requires a changeless watchfulness on the motions of market monetary values every bit good as on the present and jutting economic scenario, industry status and company public presentation Thus, portfolio direction aims to build an optimal portfolio from assorted securities selected on the footing of risk-return features of the assets, every bit good as the timing of investing determined by the proficient analysis

Traditional portfolio planning called for the choice of those securities that best fit the personal demands and desires of the investor. It deals with analysis of single securities through rating of return and hazard conditions in each security. It is based on the fact that hazard could be measured on each single security through the procedure of happening out the standard divergence and which should be every bit least as possible. Greater variableness and higher divergences showed more hazard than those securities, which have lower fluctuations The modern portfolio theory believes in the maximization of return through a combination of securities. The theory states that overall hazard can be minimized by uniting a security of low hazard with another security of high hazard. Such a variegation can be made by the investor either by holding a big figure of portions of companies in different parts in different industries or those bring forthing different types of merchandise line

Among the Modern Portfolio Theories ( MPT ‘s ) the two good known attacks are Harry Markowitz ‘s ( 1959 ) attack and William Sharpe ‘s ( 1963 ) attack which helped the building of an optimal portfolio. Markowitz was of the position that a portfolio should be analyzed depending upon:

( degree Celsius ) The attitude of the investor towards hazard and return ; and

( vitamin D ) The making of hazard.

Markowitz attack determines for the investor the optimum portfolio through three of import variable i.e. , return, standard divergence and correlativity coefficient as a step of inter-relationship between the return on assets considered. This theoretical account is called “ Full Covariance Model ” . But this theoretical account is highly demanding in its informations demands and computational demands. Furthermore, in the existent universe of investings, securities analysts typically do non believe in footings of some of the Markowitz input demands such as correlativity inputs for each security, comparative to each other security in the universe utilised. This indicates operational necessity to simplify this procedure by utilizing a common “ index ” for looking at the correlativity of each stock instead than the correlativity of each stock to all other stocks. This was done by William Sharpe ( 1963 ) . ) .

Sharpe ‘s Mean Variance Approach does non take into consideration the instance of the investors with differentiated hazard antipathy degrees. Mean-Gini attack to analyse hazardous chances and concept optimal portfolios has proved to be more equal than the mean-variance attack for measuring the variableness of a prospect since mean-Gini is consistent with investors ‘ behaviour under uncertainness for a broad category of chance distributions. Gini ‘s average difference may be extended into a household of coefficients of variableness differing from each other in the decision-makers grade of hazard antipathy.

This paper is an empirical rating of Mean Variance ( MV ) , Mean-Gini ( MG ) and Mean Extended Gini ( MEG ) approaches to an optimal portfolio choice. For this intent, we have selected 10 reputed companies in different merchandise industries, out of 30 scrips consisting the Bombay Stock Exchange ( BSE ) Sensitive Index which considers 1978-79 as the base twelvemonth because of the monetary value stableness in that twelvemonth. The secondary informations on the month terminal shuting monetary values of all 10 companies and BSE index for 8 old ages ( January 1990, to December 1997 were obtained from Capitaline Ole package as the chief informations beginning. Initially these attacks have been reviewed depicting their econometric analysis and the troubles which they raise while doing an optimal portfolio choice. The significance of the difference between MV Betas and MEG Betas and besides the cogency of normalcy premise has been tested for some selected Indian securities utilizing Haussman ‘s trial and D’Agostino ‘s normalcy trial. Further, the securities have been ranked harmonizing to their Betas obtained for assorted hazard antipathy degrees. Significance of the difference in the rankings of securities harmonizing to the assorted systematic hazards has besides been examined. The trial ranks the securities in go uping order of Beta for a given hazard antipathy degree and compares the deciles obtained by ranking securities in go uping order of MV Betas. If the security remains in the same decile, so gauging Beta harmonizing to MEG will non supply any extra information to the investor, if the securities move up or down by more than one decile, the MV systematic hazard would impede investor ‘s ability to construct optimal portfolios that diversify the hazard. Here it has been observed that most of the securities move by more than one decile therefore warranting the usage of MEG attack to optimal portfolio choice. To get at an optimum portfolio for assorted risk-aversion degrees Excess Return to Beta ratios have been computed. Last, the paper concludes by ranking the securities harmonizing to their Excess Return to Beta Ratios at assorted risk-aversion degrees, therefore proposing the penchant order of the securities for the investors at assorted risk-aversion degrees.

Mean – Discrepancy Approach:

William Sharpe ( 1963 ) suggested that a satisfactory simplification would be to abandon the covariances of each security with each other security and to replace information on the relationship of each security to the market. He suggested the basic market theoretical account of finance which expresses a additive relationship between security returns and the market portfolio. For security ‘i ‘ , this demand implies the being of a true that links security returns X, with the market returns M as follows:

– . combining weight. ( I )

where is a perturbation variable. This theoretical account has been tested extensively since its beginning in the sixtiess. M and are handily assumed to be uncorrelated with each other. The variance- of a portion ‘s return where and are the discrepancies of M and severally. The first constituent is called the “ systematic hazard ” or “ market hazard ” of an investing. Since is the same for all portions, systematic hazards will differ among different securities harmonizing to the magnitudes of “ Betas ” . The beta measures sensitiveness of a portion ‘s monetary value motions compared with those of the market index. Securities holding “ Betas ” less than 1 can be said to be defensive. The systematic hazard is caused due to “ macro ” events like oil crisis, an expected alteration in rate of rising prices, etc. The macro events are wide and affect about all securities to one grade or another and they may hold an impact on the general degree of stock market. Therefore one can non cut down systematic hazard by diversifying investing across different securities. Therefore, systematic hazard is frequently called “ non-diversifiable hazard ‘ . The 2nd constituent of discrepancy of portion returns is known as the residuary discrepancy or “ unsystematic hazard ” , or “ diversifiable hazard ” . The beginning of this sort of hazard is ‘micro ‘ events, which have impact on other securities. They may be due to debut of a new merchandise or sudden obsolescence of an old one, labour work stoppage, lockout, surrender or decease of a cardinal individual of the house, dividing up of a concern household, etc. Betas of this theoretical account can be estimated by standard OLS method ( Simple Linear Regression ) . .

Mean – Gini Approach:

Mean – Discrepancy analysis, which forms the most dramatic progress in finance theory, is based on the premise that either chances are usually distributed or the public-service corporation map is quadratic. As a step of systematic hazard, Beta has dominated the universe of finance since its origin in 1960ss. Under Mean-Variance, Beta is estimated utilizing OLS. Mean-Gini attack to analyse hazardous chances and concept optimal portfolios has proved to be more equal than the mean-variance attack for measuring the variableness of a prospect since mean-Gini is consistent with investors ‘ behaviour under uncertainness for a broad category of chance distributions. Therefore, Gini ‘s average difference can replace the discrepancy and concentration ratio based on it can replace for the covariance needed in portfolio theory whenever mean-variance analysis fails to bring forth consistent consequences. By supplying necessary conditions for stochastic laterality, the mean-Gini portfolio choice regulation is appealing to research workers since it prevents them from taking a portfolio which can be considered inferior by all persons i.e. , an another portfolio exists which is preferred by all other investors and, for at least one of them, the chosen portfolio is optimum. In general, the chance distribution of a portfolio is unknown even if all chances are derived from a certain distribution. Mean-variance anal/sis requires the perfect cognition of all chance ‘s chance distribution ; hence, it might neglect to rank portfolios systematically to single penchants when some prospect distribution is non good known. Shalit and Yitzhaki ( 1984 ) have presented Mean-Gini attack to analyse hazardous chances and concept optimal portfolios.

Consequently, Gini ‘s average difference is an index of the variableness of a random variable. It is based on the expected value of the absolute difference between every brace of realisations of the random variables. For a prospect R, if F ( R ) and f ( R ) represent the cumulative distribution and the denseness map severally, and presume that there be and such that F ( a ) = 0 and F ( B ) = 1, so Gini ‘s average difference is defined as follows:

combining weight. { 2 )

where R and R are realization braces of prospect R. This definition is non easy to manage and one finds at least eight different preparations of Gini ‘s average difference in the literature. In finance, it is more convenient to utilize the expression that expresses the Gini as twice the covariance between the returns X and their cumulative chance distribution F ( X ) :

combining weight. ( 3 )

as suggested by Alien and Shalit ( 1999 ) . Equation 3 is easy to measure when the rank of the random variable is used as the cumulative distribution estimation. After the observations are sorted in go uping order, the covariance between the random variable and its rank is computed.

Turning to our market theoretical account as in combining weight. ( 1 ) ; gauging ‘s through OLS assumes that M and, are usually distributed and statistically independent from each other. Under these conditions, the OLS calculator of consequences in mean-variance Beta, besides called MV-systematic hazard. Statistically, the OLS calculator of if the conditional outlook of, given M is zero, and it is efficient if the perturbation variable is homoscedastic, i.e. , . Under these conditions, OLS provides the best indifferent calculator and the most the powerful trials.

Financial information, nevertheless, present econometric jobs that might go against these conditions as perturbations may be correlated with the market portfolio taking to biased calculators. Biased OLS calculators have compelled analysis to take other appraisal methods from a assortment of econometric solutions. One most common attack is the usage of instrumental variable which yields consistent calculators for. The ideal Instrumental Variable ( IV ) is chosen to be extremely correlated with M but non with. A variable that would fulfill these standards is the cumulative chance distribution for M, because by its really nature it is correlated with the random variable and less dependent on the error term as suggested by Durbin ( 1954 ) . Here, on the lines of Allen and Shalit ( 1999 ) we use the computed cumulative chance distribution for M, FM ( M ) , defined as the rank of market returns divided by the figure of observations ; as an instrumental variable. The rank of market returns is a vector of whole numbers obtained by screening the sample in go uping order and utilizing the ordinal place as the rank for each observation of M. For the full population of the returns, this calculator becomes:

where Cov is Covariance map. The Betas derived in this mode is precisely the Mean-Gini

Beta derived by Shalit and Yitzhaki ( 1984 ) . ;

Use of Gini has several advantages over the discrepancy as a step of scattering for hazard and portfolio analysis. First, the chief advantage is due to the being of mean-Gini necessary conditions to stochastic laterality. Second, MG sufficient conditions besides exist for all cumulative chance distributions that intersect at most one time. Thus, MG analysis is consistent with expected public-service corporation maximization in instances where MV fails. Third, MG analysis can be extended by showing the Gini as a step of scattering that takes into history the investor ‘s penchants towards hazard, which is expressed by Mean-Extended Gini attack.

## Mean-Extended Gini Approach:

Gini ‘s average difference may be extended into a household of coefficients of variableness differing from each other in the decision-makers grade of hazard antipathy, which is reflected by the parametric quantity v. For prospect R, it can be defined as

= combining weight. ( 5 )

for finite values of ‘a ‘ where 1 & lt ; v & lt ; a?z is a parametric quantity chosen by the user, V expresses the comparative weight given to the assorted sections of the chance distribution. The Covariance preparation suggested by Shalit and Yitzhaki ( 1984 ) which is more handily used in finance can be given as:

combining weight. ( 6 )

for security X. The demand for the mean-extended Gini analysis is motivated by its possible usage in sorting the comparative hazards of chances harmonizing to different hazard averse investors. As an investor applies a larger V ( i.e. , has greater hazard antipathy ) , the lower parts of the distribution go comparatively more of import. A V of 1 represents the coefficient for a hazard impersonal investor, in which instance equation ( 6 ) peers zero, connoting that the investor is interested merely in the expected value of X. A v=a?z represents the weight for a max-min investor who wants to avoid the worst possible result. The investor ‘s job given the hazard coefficient V is to minimise the drawn-out Gini of portfolios capable to the budget restraint and a needed expected return.

For our market theoretical account in combining weight. ( 1 ) , the econometric processs can be extended utilizing Mean- Extended Gini coefficient by utilizing as instrumental variable IV, the increasing monotone transmutations of FM ( M ) , obtaining alternate consistent calculators for I? that are sensitive to the pick of monotone transmutation. Such a transmutation can be done if we use – , v & gt ; 1 as the superior map alternatively Of FM ( M ) giving the MEG betas which are consistent calculators for I? . These betas are dependent upon the power parametric quantity V, which is considered as a coefficient of hazard antipathy. For i-th security these betas can be defined as

combining weight. ( 7 ) =

as suggested by Allen and Shalit [ 1999 ] . They have besides shown that if the returns are usually distributed, all betas obtained under assorted V ‘s converge to the betas derived utilizing the MV attack. Hence MV systematic hazard can be considered as a particular instance of MEG betas. Therefore, whenever executable, the analyst should take MEG betas over MV betas because they are less delusory. Furthermore, Niar [ 1936 ] every bit good as Schetchtman and Yitzhaki [ 1987 ] have shown that when security returns are usually distributed, betas obtained for v=2 are tantamount to MV betas. Again Shalit and Yitzhaki [ 1984 ] have shown that for v=2, MEG coefficient coincides with simple MG coefficient for the security. Thus betas matching to v=2 in mean extended instance are same as MG betas.

## Methodology and Empirical Consequences:

Here we have attempted to through empirical observation measure the Sharpe ‘s theoretical account which is well-known as Mean-Variance attack to portfolio choice. Further, we have highlighted some econometric jobs originating in gauging systematic hazard by Mean-Variance attack and farther we have evaluated Mean-Extended Gini attack of geting at an optimum portfolio which allows for heterogenous hazard antipathy across investors. When security returns are non usually distributed MEG Betas are proved to differ from MV Betas. We have tested the significance of this difference and besides cogency of normalcy premise for some Indian securities. For this intent, we.have selected 10 reputed companies in different merchandise industries, out of 30 scrips consisting the Bombay Stock Exchange ( BSE ) Sensitive Index which consider 1978-79 as the base twelvemonth because of the monetary value stableness in that twelvemonth and propinquity to the current period. As per MPT ‘s, variegation of hazard can be achieved by the investor either by loving a big figure of portions of companies in different parts, in different industries or those bring forthing different types of merchandise lines. Here we use the 2nd attack. Table 1 shows the list of 10 selected reputed companies in different merchandise industries.

## Table 1 List of Selected Securities

## Sr. No.

## Name of the Company

## Type of Industry/Product

1

Grasim Industry ( GRA )

Textile/Cement/Chemicals/Pulp

2

Reliance Industry Ltd. ( REL )

Textile/Petroleum/Chemicals/Polyester/Polymers/Fibre Mediators

3

Telco Ltd. ( TELCO )

Technology and Locomotive

4

Tisco Ltd. ( TISCO )

Steel

5

L & A ; T Ltd.

Industrial Machinery & A ; Equipments/Cement/Electricals and Electronics/Goods/ Earth Moving Equipments

6

Indian Hotels Ltd.

Tourism Industry/ Hotel

7

Bajaj Auto Ltd. ( Bajaj )

Automobile Industry/2-3 Wheelers

8

ITC Ltd. ( ITC )

Cigarette Industry

9

BSES Ltd. ( BSES )

Power Industry/Distribution of Electric Power

10

RPG Telecom Ltd. ( RPG )

Telecom Industry/Jelly filled Telephone overseas telegrams

Ten values of V [ 1.5, 2, 2.5, 3, 4, 5, 7, 9 and 14 ] are chosen randomly to stand for a big fluctuation in hazard antipathy. For 5 = 2, the consequences become the standard MG Betas.

The secondary informations of shutting monetary value of the month terminal of 10 Indian securities are obtained for the period January, 1990 to December 1997. Tax returns on these securities are computed and BSE indices for the same period were considered as market returns. MV Betas, MG Betas and MEG Betas for theoretical account in combining weight. ( 1 ) obtained for this informations are summarized in Table 2. Although one expects MV Betas to be indistinguishable to MEG Betas when the implicit in returns are usually distributed, the converse is non true. To prove whether these Betas differ, we use Hausman ‘s ( 1978 ) specification trial for non-tested theoretical accounts. To implement the trial we consider two hypotheses ; The nothing H0, where M and, are independent and the option, H1, where M and, are non independent. is obtained through OLS is a consistent and efficient calculator of under H0, whereas it is non consistent under H ; whereas i.e. , MEG Betas are consistent under both H0and H1, although non efficient under H1. Hausman ‘s trial determines the statistical significance of the difference in Betas. Let.Hausman has proved that with as a consistent calculator of the discrepancy of difference, m statistic defined as has a distribution with 1 grade of freedom. In instance of OLS vs. IV defined as, v & gt ; 1, the discrepancy calculator where is the squared correlativity between the market returns and the instrumental variable ( IV ) . Using m-statistic we have tested H0 against H1 and checked whether the difference between MV Betas and MEG Betas is important and whether the MEG theoretical account provides superior econometric consequences to MV theoretical account. The values of m-statistic for assorted betas are shown in parentheses below each value of beta in Table 2.

We have besides examined the normalcy premise for security returns utilizing D’Agostino ‘s statistic which compares the standard divergence with its Gini ‘s average difference. The D-statistic is defined as:

where is the sample ‘s Gini and SK is the sample ‘s standard divergence. D’Agostino shows that is asymptotically usually distributed, as a N ( 0,1 ) variable and can function as an omnibus normalcy trial for big samples.

Table 2

MV and MEG Betas For Various Securities

Securities

MV Beta

V=2

v=1.5

v=2.5

v=3

V=4

V=5

v=7

V=9

V=14

Reliance

1.303433

1.2583018

1.29245

1.239381

1.223527

1 196552

1.153876

1.121851

1.09788

1.0612843

( 39.764595 )

( 0.16400*6 )

( 1.0829659 )

( 1.2092042 )

( 1 4204093 )

( 1.7088624 )

( 1.8M5207 )

( 0.1914714 )

( 1.8262854 )

Bovine spongiform encephalitis

1.268037

1.6710894

1.505023

1.855518

2.07675

2.551253

3.775142

5.532239

8.078038

20.529704

( 48.46107 )

( 51.882032 )

‘53.697005 )

( 83.3-34381 )

( 136.40129 )

( 324.60945 )

( 693.93883 )

( 1420.5104 )

( 7811.151 )

aˆ?aˆ? c-

ITC

1.212346

1.62S3759

1.433932

1.832948

2.051 135

2.545448

3.845438

5,733139

8.488597

22.262738

( 99.11318 )

( 45.170531 )

( 131.^8817 )

( 172.50205 )

( 28J.36392 )

( 684.03498 )

( 490.064 )

( 3098.3226 )

( 17822.857 )

L & A ; T

1.212C77

1.1505628

‘ , .184319

1.136315

1.127865

1.119317

1.117775

1,254561

1.137037

1.1688482

( 2.7002783 )

( 1.7027624 )

( 2.4499743 )

( 2.1772019 )

( 1.7300144 )

( 1.0986089 )

( 0.0945197 )

( 0.412624 )

( 0.0941155 )

TI’SCO

1.062273

1.0684545

1.054636

1.080286

1.089099

1.100152

1.10861

1.110357

1.110417

1.1087957

( 0.03560385 )

( 0.16745266 )

( 0.18081919 )

( 0.28700418 )

( 0.37477305 )

( 0.34458635 )

( 0.27420523 )

( 0.22064415 )

( 0.1415069 )

IND

0.860964

0.7018842

0.774458

0-B89438

0.633497

0.5936706

0.542584

0.509329

0.486385

0.4561547

( 11.20991434 )

( 10.2651413 )

( ? 99. 848546 )

( 9.8S016E=6 )

( ? , .914426 )

( 7.77327396 )

( 7.006895 )

( 6.3820817 )

( 5.1229885 )

GRASIM

0.797487

0.7Gf,7579

0.7S4437

0.75975

0.760355

0.759852

0.7562

0.751988

0.748305

0.743559

( 1.4322001 )

3.229753

( 0.81334237 )

( 0.5663759 )

( 0.38104792 )

( 0.28177339 )

( 0.2528716 )

( 0.2371626 )

( 0.1959776 )

JELCO

0-709635

0.7918282

0.74034

0.825751

OJ85299

0.695319

0.947555

0.974377

0.988182

0.9980154

( 3.5180556 )

( 0.1520395 )

( 4.199765 )

( 4.604054 )

( 5.5884349 )

( 5 10317305 )

( 4.6693177 )

( 4.148959 )

( 3.0556628 )

Bajaj

0.547483

0.6368824

0.58057

0.72293

0.832416

1. 11948

1.C96943

3.04595

4.718207

13.035891

( 3.21 12S )

11.3621371 )

( 7.3976C 67 )

( 4.03348 )

( 36.0695915 )

( 126.667989 )

( 320.86526 )

( 901.1613319 )

( 4792.7485 )

RPG

0.529S41

C.8055351

0.67858

0.926726

1.040891

1.238062

1.596659

2.007686

2.546035

4.8947412

( 16.59962 )

( 14.9802983 )

( 20.T7491B7 )

( 24,5221378 )

( 30.1918008 )

( 42.983249 )

( 60.9480f ; 36 )

( 91.047914 )

( 293.2577 )

## Empirical Consequences:

Table 2 shows that the variableness of MEG Betas and their difference from MV Beta alterations for house to tauten. D’Agostino ‘s trial of normalcy shows that security returns of Reliance and Grasim are usually distributed whereas those for other securities are non usually distributed.

In instance of Reliance, the MEG Betas are found non to be significantly different from MV Beta and besides the normalcy trial classifies it as being usually distributed and therefore nil would hold been gained by utilizing the MEG attack. Same is the instance with Grasim. L & A ; T, Telco.and TISCO even are classified being non-normal but their Betas are once more non significantly different from MV Betas. So for these securities the period is well less volatile. Merely minor alterations exist in assorted Betas. In instance of TISCO Betas are significantly different for higher hazard antipathy degrees i.e. , v7.

The instance of Indian Hotels indicates that for v3 the MEG Betas are found to be significantly different than MV Betas, and therefore more risk-averse have investors over-evaluated true Betas by utilizing MV attack. While the instance of BSES, ITC and RPG show the clear advantage of the MEG attack and the period was more disruptive for them. The difference between and MV are extremely statistically important. Therefore, investors with differentiated hazard antipathy in these instances would hold clearly mistakened about the true Beta if they had used MV attack. In instance of Bajaj Auto Ltd. , MEG Betas are found to be extremely important for v2.5 bespeaking that extremely risk-averse investors puting in this security would hold over-estimated the aggressiveness of their investings. For all securities which are found to be non-normal and have significantly different Betas from MV Betas, the investor should utilize and allow value of V to suit one ‘s sensitiveness of hazard from amongst the decreased set of statistically different Betas.

Last, we examine how important are the differences in ranking securities harmonizing to the assorted systematic hazards. Our trial ranks the securities in go uping order of Beta for a given V and compares the deciles obtained by ranking securities in falling order of MV Betas.

If the security remains in the same decile, so gauging Beta harmonizing to MEG will non supply any extra information to the investor. Table 3 shows the rankings of different securities for given degree of hazard antipathy.

Table 3 Rankings of Securities Harmonizing to Betas

## Rank MV – Betas

## V = 2

## V = 1.5

## V = 2.5

## V = 3

## V = 4

## V = 5

## V = 7

## V = 9

## V = 14

1

RPG

Bajaj

Bajaj

Bajaj

IND

IND

IND

IND

IND

IND

2

Bajaj

IND

RPG

GRA

GRA

GRA

GRA

GRA

GRA

GRA

3

TELCOCO

GRA

Telephone company

Telephone company

Bajaj

Telephone company

Telephone company

Telephone company

Telephone company

Telephone company

4

GRA

Telephone company

GRA

RPG

Telephone company

TISCO

TISCO

TISCO

REL

REL

5

IND

RPG

IND

TISCO

RPG

Bajaj

L & A ; T

REL

TISCO

TISCO

6

TISCO

TISCO

TISCO

L & A ; T

TISCO

L & A ; T

REL

L & A ; T

L & A ; T

L & A ; T

7

L & A ; T

L & A ; T

L & A ; T

REL

L & A ; T

REL

RPG

RPG

RPG

RPG

8

ITC

REL

REL

ITC

REL

RPG

Bajaj

Bajaj

Bajaj

Bajaj

9

Bovine spongiform encephalitis

ITC

ITC

Bovine spongiform encephalitis

ITC

ITC

Bovine spongiform encephalitis

Bovine spongiform encephalitis

Bovine spongiform encephalitis

Bovine spongiform encephalitis

1010

REL

Bovine spongiform encephalitis

Bovine spongiform encephalitis

IND

Bovine spongiform encephalitis

Bovine spongiform encephalitis

ITC

ITC

ITC

ITC

If the securities move up or down by more than one decile, the MV systematic hazard would impede investor ‘s ability to construct optimal portfolios that diversify the hazard. Here it is assumed that most of the securities move by more than one decile therefore warranting the usage of MEG attack in optimum portfolio choice.

To get at an optimum portfolio for assorted risk-aversion degrees we need to calculate Excess Return to Beta ratio which is defined as – where Ri = expected return on stock I, Rf = return on hazard free plus and – expected alteration in rate of return on security I. Here we assume return on hazard less plus to be 8 % which is common for Indian Capital Market. Table 4 snows the extra return to beta ratios for MV betas every bit good as MEG betas harmonizing to assorted degrees of hazard antipathy. Table 5 indicates the rankings of the securities harmonizing to their extra return to beta ratios for MV betas every bit good as MEG betas. Thus the investors must take their securities in the above order as indicated by Table 5 depending upon their degrees of hazard antipathy in order to get at an optimal portfolio.

## Table 4

## Excess Return To Beta Ratios For Various Securities

Securities

Mean Return

Excess Return

MV Betas

V=2

v=1.5

v=2.5

v=3

V=4

V=5

v=7

V=9

V=14

Reliance

20.45

12.45

9.55

9.89

9.63

10.05

10.17

10.41

10.78

11.1

11.34

11.73

Bovine spongiform encephalitis

20.91

12.91

10.18

7.73

8.57

6.92

6.22

5.06

3.41

2.33

1.6

0.63

ITC

16.67

8.67

7.15

5.32

6.05

4.73

2.23

3.41

2.25

1.51

1.02

0.39

L & A ; T

12.27

9.27

7.65

8.05

7.83

8.15

8.22

8.28

8.29

7.39

8.15

7.93

TI’SCO

14.25

6.25

5.88

5.85

5.93

5.79

5.73

5.68

5.63

5.83

5.63

5.17

IND

13.73

5.73

6.63

8.16

7.39

2.74

9.04

9.65

10.56

11.25

11.78

12.56

GRASIM

11.89

3.89

4.88

5.13

5.08

5.12

5.11

5.11

5.14

5.17

5.2

5.23

Telephone company

10.54

2.54

3.58

3.21

3.43

3.08

2.98

2.84

2.68

2.61

2.57

2.55

Bajaj

6.87

-11.13

-20.33

-17.47

-19.17

-15.39

-13.37

-10.01

-5.86

-3.65

-2.36

-0.85

RPG

7.25

-0.75

-1.37

-0.93

-1.11

-0.81

-0.72

-0.61

-0. 47 —

## –

-0.37

-0.29

-0.15

## Table 5 Rankings of Securities Harmonizing To Excess Return To Beta Ratios

## Rank MV – Betas V = 2

## ________________________________________

## v=1.5

## v=2.5

## V = 3

## v=4

## V = 5

## V = 7

## V = 9

## v=14

## 1

Bovine spongiform encephalitis

REL

REL

REL

REL

REL

REL

IND

IND

IND

## 2

3

REL

IND

Bovine spongiform encephalitis

L & A ; T

IND

IND

IND

REL

REL

REL

3

4444

L & A ; T

L & A ; T

L & A ; T

Bovine spongiform encephalitis

L & A ; T

L & A ; T

L & A ; T

L & A ; T

L & A ; T

L & A ; T

4

ITO

Bovine spongiform encephalitis

IND

TISCO

Darmstadtium

TISCO

TISCO

TISCO

TISCO

GRA

5

IND

TISCO

ITC

GRA

TISCO

GRA

GRA

GRA

GRA

TISCO

6

TISCO

ITC

TISCO

ITC

GRA

Bovine spongiform encephalitis

Bovine spongiform encephalitis

Telephone company

TELCO TELCO

7

GRA

GRA

GRA

Telephone company

ITC

ITC

Telephone company

Bovine spongiform encephalitis

Bovine spongiform encephalitis

Bovine spongiform encephalitis

8

Telephone company

Telephone company

Telephone company

INO

Telephone company

Telephone company

ITC

ITC

ITC

ITC

9

RPG

RPG

RPG

RPG

RPG

RPG

RPG

RPG

RPG

RPG

10

Bajaj

Bajaj

Bajaj

Bajaj

Bajaj

Bajaj

Bajaj

Bajaj

Bajaj

Bajaj

Summarv and Decisions:

Choosing securities harmonizing to their hazard and average return is an indispensable challenge for investors who want to do investing determinations consistent with hazard antipathy. The ranking of assets with regard to their extra return to systematic hazard ratios has been the standard pattern for choosing an optimal portfolio. However, gauging systematic hazard depending upon assorted grades of risk- antipathy is more advisable, particularly whenever one can non presume usually distributed returns to guarantee the cogency of MV theoretical account since these estimations provide rather different optimum portfolio than that obtained by MV attack and which is more good to an investor. This is being provided by MG and MEG attacks to gauging systematic hazard.

From our survey we conclude the undermentioned chief consequences:

From the selected Indian securities returns of lone Reliance and Grasim are found to be usually distributed harmonizing to D’Agostino ‘s trial and MV betas are appropriate estimations of systematic hazard for these securities.

Hausman ‘s trial indicates that except for Reliance, Grasim, L & A ; T and Telco, remainder of the securities have significantly different betas as compared to MV betas, therefore bespeaking MEG attack to be a superior one than MV attack for gauging the systematic hazard.

Ranking of securities harmonizing to their betas show that most of the securities move up or down by more than one decile of the ranks and therefore show that MV systematic hazard would impede investor ‘s ability to construct optimal portfolios that diversify the hazard.

Last, penchant orders of the securities for different investors harmonizing to their risk- antipathy degrees has been obtained by ranking the securities harmonizing to their extra return to beta ratios, to get at optimal portfolios with differentiated degrees of hazard antipathy.