Abstracts of Comparison of Beta Estimation methods

In the current research there is the analysis of the methods that are used to estimate the Beta; beta estimation is done on the daily data from the market data. Consequently, the primary goal of this research is to know the best method to estimate beta and to deliver guidance so that there could be a better estimation of the beta. For the analysis of the beta best method; different methods example conditional capital asset pricing model (CCAPM), from the historical beta its Fama & MacBeth, Bayesian model averaging, exponentially weighted moving average (EWMA), damson beta, covariance/variance method, forecast combinations, shrinkage estimators, by slope method in excel, correlation method, etc. are analyzed so that better evaluation can be done.

The primary and secondary analysis is done in this research. Besides, there is an attention available and the day by day return information from the market, it is investigated in the exploration which exponential weighting plan in the field of macroeconomic is viewed as sustainable. For the secondary analysis is done in this research, literature review is done. Different research or studies are analyzed so that there could be analysis of the methods that are used to estimate the Beta. The survey is conducted from the 100 finance experts by utilizing self-administrated questionnaire in order to know about the best method for calculation beta. It has been observed that the slope method is mostly usable method for calculating beta.

Introduction of Comparison of Beta Estimation methods

In this research, there is an analysis of the methods that are used to estimate the Beta, i.e sensitivities of assets towards some specific risk factors. However, beta can be explained as the fundamental analysis, which is generally performed for identifying the volatility of a portfolio or asset. The beta of the overall market is 1.0; consequently, when the individual stocks are calculated, an analysis is performed for determining just how much the company is deviating from the market. If the stock has a beta greater than 1.0 means the stock deviates more and there are potential or higher risks but higher returns as well. Moreover, if the value of the beta is less than 1.0, then it means that stock moves less and there are fewer risks in the market. However, the low-beta stocks result in lower returns. There is an investigation of the model, which is utilized for the combination of beta estimation and the examination of the exploration is done on the U.S. stock universe; the examination is done of over 50 years with the assistance of an authentic estimator, the system which is considered best for the beta investigation (Bartholdy & Peare, 2005).

Several methods can evaluate or estimate the value of the beta; beta is the risk-reward measure and can help the investors so that they could effectively determine the stock's price variability and also the risks. For the analysis of the beta; different methods example conditional capital asset pricing model (CCAPM), from the historical beta its Fama & MacBeth, Bayesian model averaging, exponentially weighted moving average (EWMA), damson beta, covariance/variance method, forecast combinations, shrinkage estimators, by slope method in excel, correlation method, etc. however, with the help of the beta market risks can be analyzed and there can be security or analysis regarding the variance market returns (Alexander, 2008).

In the decisions of the investments, the most important element that has been frequently used is known as the risk. Meanwhile, it has been defined by the dictionary that the risk is referred as the hazards that is exposures to injury and loss along with the investments. In the various terms the risk can be considered. In the portfolio theory development it has been defined as; the risk is considered as the well-known terms of the stastical measures that is known for the variances. Particularly, the risk has been quantified by the Markowitz as the variance that is required for the expected returns of the assets. Meanwhile the asset’s total risk can be easily measured or evaluated by the variances. The measures of the risk can be easily categorized in the two major types of the risk that are unsystematic risk or systematic risk. The systematic risk has been defined as the portion of the variability of the assets which can be easily attributed for the various common factors. The portion of the assets variability can be defined as the diversified away of an unsystematic risk and returns.

The beta (β) is considered as the parameters that plays an essential role in the modern finance. It is also known as the measure that is required for risk of the assets. The coefficients of the beta (β) are also recognized as the measures of the systematic risk that can easily compare the assets variability along with its historical returns for the entire market. This beta measures is referred as an expected change for the particular percentage changes in the indices of the bench mark. It has been pointed out in the several studies the investors are concerned with the systematic risk while he engaged in making the decisions related to the investments. It is also considered as the risk for the entire market due to the diversified away of the unique risk by well balanced portfolio. Due to this particular reason the (β) beta is only linked and concerned with the particular investors that have the securities values (Aygören, 2007).

There are the several other methods that are relying upon the EOG as well as EED decomposing signals in to the spatial components. It also includes the reconstructing of the EEG as well as identification of artificial components without the observations of the various other artificial components.  For instance, the PCA (principal component analysis) has been utilized by several researchers in order to examine the artificial components. Additionally, the PCA is also utilized by the dipole modelling techniques for computing the topographies of the eye activity. Statically, the signals are decomposes in the PCA for uncorrelated, but it not includes the necessarily independent. It also includes the components which are spatially orthogonal. Importantly for the various purposes and reason of the correction of the artefacts the PCA components can also be utilized for the thoughts of the formed sequentially in order to maximize the remaining variances (Wallstrom, 2004).

The maximum superiority of the probable parameter’s estimations by the moments that is well-known in the theory of the large sample, while it is difficult for proving the small samples. The use of the estimation moments has been recommended for the numerous parameters of the beta distributions over the MEL (maximum likelihood estimates) while the recommendations is laso depends upon the furious arguments which is the maximum procedure of the likelihood that is leading towards the intractable problem of the computational. There is not any problem and doubt that the estimation from the moments sample is at least considered as the attractive possibility due to the easy observation of the estimates are easily observed on the hand calculator. Therefore, it is for the interest of the few people for comparing performance that is related to the estimates of moments for the small samples of the MLE’s from various random variables along with the distribution of beta (Dishon, 1980).

The particular studies explores or presented the comparison of the specific results that are attained from the sets of the several thousand data that are spans from the range of the various parameters as bivariate and univariate of the beta distributions. This paper also compares the various methods for estimating the beta in order to observe and find out the most important and well method to calculate the beta

Research Objectives of Comparison of Beta Estimation methods

The current research includes the following objectives:

• To analyze the factors of beta models that which model or method proved to be effective.
• To determine the beta estimation from the daily data from the market. The data with the lowest average prediction errors U.S. stock universe is analyzed.
• To evaluate the impact best method to estimate beta and to deliver guidance so that there could be a better estimation of the beta.
• To ascertain the impact of techniques and analyzes techniques through focus on the effects of historical windows, sampling frequencies, forecast adjustments etc.
• To analyze the impact of Bayesian combinations for the estimation and adjustment approaches are analyzed.
• To determine the impact of different methods used for beta include CCAPM, historical beta Fama & MacBeth, Bayesian model averaging, EWMA, forecast combinations, shrinkage estimators, by slope method in excel, correlation method, etc.

Research Questions of Comparison of Beta Estimation methods

The current research includes the following question:

1.      What are some of the factors of beta models that which model or method proved to be effective?

2.      What are some aspects to determine the beta estimation from the daily data from the market and how the data with the lowest average prediction errors proved to be effective from the U.S. stock universe?

3.      What are some impacts of best method to estimate beta and to deliver guidance so that there could be a better estimation of the beta?

4.      How best beta techniques are analyzed through focus on the effects of historical windows, sampling frequencies, forecast adjustments etc.?

5.      What are some aspects to analyze the impact of Bayesian combinations for the estimation and adjustment approaches are analyzed?

6.      How to determine the impact of different methods used for beta include CCAPM, historical beta Fama & MacBeth, Bayesian model averaging, EWMA, forecast combinations, shrinkage estimators, by slope method in excel, correlation method, etc.?

Literature review of Comparison of Beta Estimation methods

In this research, secondary research is performed in the form of literature review. The examinations of the strategies that are utilized to appraise the Beta are clarified in this research     . There is an extensive examination of beta models to determine which model is the most effective. Generally, there is a need of beta assessment for identifying the issues and mistakes. This is carried out by studying different researches.

Different research or studies are analysed for analysing different methods that are used to estimate the Beta. In general, beta is determined so that the volatility of the asset or the portfolio can be known. Several methods can evaluate or estimate the value of the beta; beta is the risk-reward measure and can help in effectively determining the stock's price variability along with risks.

1 Historical beta Fama & MacBeth and CCAPM of Comparison of Beta Estimation methods

According to the research conducted by Guermat & Freeman (2010) there is the focus on the Mone-factor model (CAPM) and Fama and French; however, the researchers analyzed the differences and the effects in both the techniques. However, in the research it is known that both the techniques are effective in order to evaluate the value of the beta. Fama and French indicated as poor model; there are a few shortcomings so breaking down the multifaceted case, it is realized that CAPM improves on account of arrangement of benefits. Also, the CCAPM has a better capability of evaluating expected returns with regards to the beta for the individual stock. However, CAPM is better as compared to the Fama and French because it is a historical technique. Moreover, the CCAPM has better estimating expected returns when it comes to the beta for the individual stock (Guermat & Freeman, 2010).

According to the research conducted by Bartholdy & Peare (2005) it is analyzed that CCAPM has better portfolio returns, however, the main objective two models but still the research compare the performance of the models and know that CAPM is better as can be obtained using different time frames so it is efficient one. Fama and French showed very poor performance as a model; there are several weaknesses so analyzing the multi-factor case, it is known that CAPM does much better in the case of portfolios of assets. The research found that CAPM is the standard technique for beta or testing assets (Bartholdy & Peare, 2005).

It has been argued that the alone market beta is not appropriate and sufficient for exploring and explaining the expected returns. They have struggles to improve and developed their model along with the addition of the various two extra factors.  It includes the book to book market equity ratio and size for calculating the CAPM. This particular model is also recognized by the French and Fama three factors model. This model has been gradually adopted by the financial community for the academic and financial purposes. The two traditional assets pricing model has been examined by the various researchers as well as it has been concluded the estimates for the  expected returns that is computed by utilizing the particular two models that are not reliable. The research has also been conducted for this particular topic for the alternative ways in order to estimates the expected returns.

The information related to the dispersed as beta dissemination has been examined by various researchers. They utilized analysis of the linear regression for evaluating the beta distribution; however this work had been continued change of the reaction variable and after that pre-owned it in direct regression analysis. There are numerous researchers who are engaged in taking the beta dissemination and its applications, and some of them take the general status of the Beta conveyance it also includes the four parameters Beta dispersion.

There are the various other methods that are utilized for the beta estimations such as the MLE estimation on account of the reliant variable finishes the Beta circulation the examination between the OLS and BMLE dependent on recreations depending on the proficiency scale just as depend on the test between the evaluated qualities and the estimations of beta. They clarified how utilized the beta dissemination as an underlying conveyances related with binomial appropriation which are utilized in the Bayesian appraisals, additionally that year 2004 contemplated the situation when the reaction variable follows the beta dispersion to any perception esteem inside period.  They have taken a shot at a transformation to reaction variable to a straight relationship with the logical factors. What's more, they utilizing genuine information for two applications were created estimator parameters of beta relapse and afterward tried expansion to finding the level of symptomatic measures.

2 Bayesian model averaging of Comparison of Beta Estimation methods

According to the research conducted by Chmielecki & Raftery (2011) it is known that the Bayesian model averaging (BMA) is proved to be an effective approach for the beta analysis because in the research it is considered to be best for the predictive probability density functions. However, after analysing the translation algorithm in the research or after analysing the visibility forecasts, it is known that forecasts can be effectively done based on the technique and as the research done the regression-based visibility forecasts and explored a method that is proved to be effective for the additional predictors. The Bayesian model averaging (BMA) is proved to be an effective approach as it can also increase precision (Chmielecki & Raftery, 2011).

For the Bayesian estimation, we can officially locate the earlier dissemination and the conjugate back conveyance of the parameters of the beta appropriation. In any case, this back circulation is as yet characterized with a combination articulation in the denominator to such an extent that the shut type of the back dispersion is systematically obstinate. It has been proposed a down to earth Bayesian estimation calculation dependent on the Gibbs examining technique which mimics the back circulation around instead of processing it. The strategy proposed in could forestall the over fitting issue yet at the same time experiences high computational expense in view of the Gibbs inspecting, particularly when the information are in a high dimensional space (N. Bouguila, 2006.).

3 Exponentially weighted moving average (EWMA)

According to the research conducted by Glova (2013) EWMA technique is proved to be effective for the correlation structure of beta, it is the forecasting techniques that also given value by the Economist Harry Markowitz (1952); however, it is known that EWMA can effectively analyze the systematic risk and specific risk from the static perspective. EWMA can give the quantitative perspective on portfolios fluctuation and there are better choices for the speculation extent or riskless venture (Glova, 2013).

The method is improved and dynamized with time. The EWMA can do an effective analysis of the variance and covariance forecast for the beta coefficient. In the research, there is the analysis of the Harry Max Markowitz (1959) in the research and it is known that EWMA can provide the quantitative view of portfolios variance and there are better decisions for the investment proportion or riskless investment. it is realized that EWMA can adequately break down the efficient hazard and explicit hazard from the static point of view. The researchers noticed that EWMA is the efficient frontier or the quadratic technique for the observation of stock prices as well as the security returns. Focused on the Modern portfolio theory (MPT) it is known that EWMA proved to be effective for the mean-variance analysis (Glova, 2013).

 

The Exponentially Weighted Moving Average (EWMA) model was determined by JP Morgan in 1989 for their systems of the Risk Metrics from a Gaussian conveyance. The EWMA technique is particularly used for figuring instability laid more accentuation on later returns. The purpose for is that on-going value development is the best indicator of future development. This was an improvement to the basic unpredictability technique. There are various strategies for the alignment of the parameters of the EWMA model. A broad diagram of these methodologies is given in further stressed the primary thoughts of these methodologies. He further expressed that parameter and alludes to the quantity of verifiable perceptions used to create the gauge and an alternate gauge of this parameter doesn't essentially impact the precision of the estimate  (Adewuyi, 2016).

4 Slope method in excel of Comparison of Beta Estimation methods

According to the research conducted by Wang & Huang (2012), the slope method in excel can also help to analyze the beta. However, in the excel there is the use of the slope function through which the data can be analyzed. Nevertheless, the Microsoft Excel SLOPE function help to analyze the slope of the regression through using the correlation method so it can effectively have calculated (Wang & Huang, 2012).

In the terms of the finance, the beta of a firm alludes to the affectability of its share price regarding a file or benchmark. For instance, think about the theoretical firm US CORP (USCS). Google Finance gives a beta to this organization of 5.48, which implies that as for the chronicled varieties of the stock contrasted with the Standard and Poor's 500, US CORP expanded on normal by 5.48% if the S&P 500 rose by 1%. Then again, when the S&P 500 is down 1%, US CORP Stock would will in general normal a decrease of 5.48%.

Usually, the list of one is chosen for the market record, and if the stock acted with more unpredictability than the market, its beta worth will be more prominent than one. In the event that the inverse is the situation, its beta will be a worth short of what one. An organization with a beta of more prominent than one will in general enhance showcase developments (for example the case for the financial division), and a business with a beta of short of what one will in general straightforwardness advertise developments.

Beta can be viewed as a proportion of the measure of the risk: the higher the beta of an organization, the higher the normal return ought to be to make up for the abundance chance brought about by unpredictability. The Beta coefficient is a proportion of affectability or relationship of a security or a speculation portfolio to developments in the general market. We can infer a factual proportion of hazard by looking at the profits of an individual security/portfolio to the profits of the general market and recognize the extent of hazard that can be ascribed to the market.

All of these variables are utilized as the thoughts of the using slope by which the intercept framework where;

 Re = y

B= slope

(Rm-Rf) = X

Rf= y-intercept

An essential is gained from this particular frame work; at where the assets are expected for generating at least risk factors that are free of returns. If the beta of an individuals as well as portfolio or stocks is equal to 1. The assets and its returns become equals to the average returns market. The slope is represented by the beta coefficients related to the lines of the best fits for each;

Re – Rf (y)

Rm – Rf (x)

It also includes the excess return of pair.

5 Correlation method of Comparison of Beta Estimation methods

Correlation method is another technique that is used to analyze the beta through dividing market’s standard deviation to the assets of the standard deviation of returns and then its multiplied by the correlation of returns that can be the market’s return and the security’s return (Wallstreetmojo, 2020).

If we talk about the area of pattern recognition, the statistical approach is what that is studies intensively and commonly. The underlying source generate some set of observations and assumptions, major work of statistical modelling is to develop a model that can specify the observation patterns, get their underlying distribution and can explain the statistical characteristics of the source. The mixture model has powerful and flexible property for analysing multivariate data as well as univariate data. In order to efficiently model the data by beta mixture model (BMM) that will carry less model complexity as compared to GMM, data is bounded with support property of beta distribution.

The estimation approach of Bayesian is required for BMM, in order to avoid the problem of over lifting when determining the model parameter of the data. following principles of getting conjugate priors of exponential family can help out in finding conjugate prior of beta distribution, it can be saying the both these prior and corresponding posterior distributions are relatable. In this way few approximations are required. With the help of VI framework, we describe a Bayesian estimation approach in order to determine the distribution of parameters and derive as solution that will be independent of iterative numerical calculation at the time of each update round  (Zhanyu Ma, 2011).

A lot of efforts are required by beta estimation. For example, stability of beta over time, results of return interval and time area of investors. Stability of beta estimate with regards of time are the focus of some researchers. Low correlations for betas through time is reported by Blume (1971) and Levy (1971). It is studied by Blume that is it possible of estimated betas to have a power to regress in direction of great means of all betas. . Cheng and Boasson (2004) used a method that was weighted as least square method in order to determine betas of developing markets and came to know that betas of these markets do shift with time change. In other hand, potential asymmetry and beta instability are determined and explained by Braun et al. (1995) and found weaker evidence of time-varying betas (Lee, 2007).

In many applications of finance this estimation of systematic risk is critical. In various methods like estimating expenses of capital, examining portfolio strategies, risk management implementation methods and using different valuation models, practitioner totally rely on beta estimates. On the other hand, researcher is all dependent on estimates of beta for many applications like determining risk relatively, testing strategies of trading, testing asset pricing models and for model study conduct. A large amount of energy is required by beta estimation, beta coefficient is unobservable (Estrada, 2000).

On return f portfolio of the market, unobservability of beta can be resolved simply by regression of asset returning in market using data of time series as long as the returns of assets are stationary. It is stated by Groenewold and Fraser (1999) when talking in practice the assets return are not stationary which can cause beta instability with change in time. It is conducted in early studies that portfolio betas are also instable and they force themselves to regress toward 1 over time. The logic of economy here state that riskiness of firm will force to move toward average firm riskiness (AVRAMOV, 2006).

Standard market model is used to determine beta which is expressed as the following:

 Rit i iRmt it = α + β + ε (1)

where Rit is the realized return on security i over return interval t; Rmt is the realized return on the market index over return interval t; αi is the constant term for security i; βi is the sensitivity of security i returns to the market index returns measured as cov(Ri,Rm)/var(Rm. εit is the error/residual term for security i for return interval t, εit ~ N(0, σt 2), cov(εit, εit-1)=0, cov(εit, Rmt)= 0. t is return interval over which the return is measured t= 1,2,3,………,T (CHENG, 2004).

Botosan (1997) applied the mode of equity valuation which was developed by Ohlson (1995) to determine the rate of capitalization as a proxy for result that was expected. He did not used the CAPM in order to estimate equity capital cost. This method is quite common in use by practitioner but the operation of use is simple and also it is in use in academia for the purpose of research. This estimate is referred to as “implied cost-of-equity capital” (ICE, hereafter) and this approach is also called as ICE approach with this regard because this was the rate that market was assuming for all of the future that was expected in order to estimate present price of stock (Lee S. &., 2008).

One critical stand against the extant ICE literature is analysing the upcoming capability of ICE approximation functioned with the help of multiple equity  valuation structures which includes dividend, residual income valuation, and Ohlson-Juettner models based on future realized returns (Chen et al., 2004; Gode and Mohanram, 2003; Guay et al., 2004; Shro¨der, 2004). The approximations calculated with the use of these structures or multiple variants of the similar model show difference due to the reason of the operationalizations process In implementing every model being different from one another. Therefore, in order to analyse which suitable model provides the approximate with the largest upcoming or predictive capacity based on future realized returns turns out to be an empirical question

Even though many other ICE studies refer that the residual income value model facilitates the ICE approximate with the highest upcoming capacity, a mixture of results still involved. Moreover, the empirical requirements stay the same even if ICE literature purposely endorse one suitable model or its version whether the given model delivers the approximate with the most predictive capability in scenario of the lodging industry. This due to the reason that lodging industry shows multiple characteristics from the wide economy (Keiser, 1998; Lee, 1984; Lee and Upneja, 2007; Powers, 1992; Winata and Mia, 2005).

The suggested cost-of-equity (ICE) procedure is not a method which was created currently. Financial professionals have been implementing this procedure for quite a time and typical textbooks of finance describes the capitalization rate concept which is equal to the ICE diameter. in the previous times, the most common accounting and finance literature totally relied on implementing the average realized return as a backup for the analysed market return to test asset pricing theories.

Financial professionals calculated that the ICE assessments might be fruitful in testing the asset costing theory due to the reason of  this practice,  researchers doesn’t require to attain help from the average realized returns which was widely involved in criticism for its inaccuracy as a proxy for the analysed market return return (Elton, 1999; Fama and French, 1997). On the other side, the ICE proceedings might be deficient due to the reason that approach implements the analysts’ forecasting data. The practice of using economic professional’s data has been cross checked by many theories, and it’s been widely acclaimed that the analyst’s measurement and approximations of the data tend to be highly optimistic and sluggishly updated (Dechow and Sloan, 1997; Lys and Sohn, 1990). On measuring the reliable estimated of the cost-of-equity by using the ICE approach these issues might have a negative impact but no other way is present to overcome the defects due to the reason they are not resolvable by researchers with ease.

 (Kotz, 2006) created a stack of beta distribution attributes and features, which also included the symmetry attribute, where ( α,b) are identical if x ~ Beta (α, β) then (1-x) ~ Beta (β, α) and there were many professionals who studied the beta and its connection with α,b distribution function attributes. Through processing operations to study more properties like these you can be go through reference [10].

n 2012 Mahmoud learned in his paper, the highest likelihood approximate are calculated for the couple unknow parameters of the Beta-Weibull(B-W) distribution under type II censored samples also asymptotic variances and covariance matrix of the approximators are provided.  An iterative methodology is implemented to calculate the approximation mathematically with the help of Mathcad Package in processing results which are involve in different sample sizes

In stock repurchase tender, the offers by small companies are generally impart negative abnormal returns before the announcement of the offer. But the common relief here is under price criterion of the stock. Companies that are involved in taking over consist of high level of performance before the announcement that was related to corporate control changes by Jensen (1986). Roll (1988) finds that firms that are involved in condition of taking over are directly associated for the biggest improvement in market model and model of multi factor at the time of excluded news dates. It is studied well OLS that is ordinary least squares estimator of the beta is actually sensitive for the presence of outliers and specifically departures from normality. The stock returns distribution can be “fat tailed” as compared to normal distribution, resulting in outlier (Chan, 1992).

Research Type of Comparison of Beta Estimation methods

Various kinds of research can be used according to the topic and requirements of the study. All of these kinds of studies are explores here from which the types of study that best fitted for this topic are explained in good ways. These types are includes as;

Experimental Research of Comparison of Beta Estimation methods

Usually, it is known as the cornerstone of science and defined as creative research. These kinds of research are usually concerned with the cause and effects. Even under these kinds of research, the interesting variables are defined in effective manners. The relationship between the dependent and independent variables explain under this kind of research. These kinds of research are required to examine the changes in cause and effect independent and independent variables.

Source of data collection of Comparison of Beta Estimation methods

There are two major sources of data collection from which the first one is the primary source of data collection and another one secondary source of data collection. Both of these kinds of sources are important and essential factors for conducting this kind of research. The said study is conducted by utilizing both the source of data collection. It includes primary and secondary.  As the under considerations and above discusses topic “comparisons of the beta estimation methods” is wider topic and it requires a lot of data collection that’s why both sources of data collection are particularly used in the said study.

In the primary source data collection; it includes information processed and collected that is directly conducted by the researchers, for instance, focus group, observations, interviews, and surveys. The particular information is included in the secondary source data collection that is retrieved by using the pre-existing resource such as library searches, research articles and browsing on the topic from the internet.

Research Methods of Comparison of Beta Estimation methods

There are two major kinds of research methods that are adopted for this study. These methods are; qualitative and quantitative. Both of these research methods are utilized to attain the particular objective of the research study. For the said study qualitative is one of the most important and well-known methods to conduct a particular study. The most important and major characteristic of qualitative research is that it is the most important and well-known technique for the small samples meanwhile its results and outcomes can be easily measurable and quantifiable.

The numerical data is always collected in quantitative research. This study is quantitative in its research methods because the data that will be collected by conducting the survey will be coded and recoded in the numerical configuration for collecting accurate data. In the quantitative research methods, it also includes the implementation and generation of the charts tables and graphs that are required to manipulating and generating the data in extensive manners.

Research approach of Comparison of Beta Estimation methods

The research approach that was being used to follow the purposes of the said study was known as the deductive research approach. Because the set of the hypothesis has been formulated for the said study and to attain the objective of the research that why it will follow the deductive research approach and for measuring the risk impacts of the risk management on the productivity the formulation of the hypothesis is necessary. Developing the hypothesis is always concerned with the deductive approach that rebased upon the existing theories. After developing a hypothesis; it includes the designing of the research strategy to test the hypothesis for conducting various kinds of results.

Research Philosophy of Comparison of Beta Estimation methods

According to the nature of the study, the best-fitted paradigm for examining the best method of the beta estimation is the positivism paradigm. Thus study follows the quantitative research methods and deductive research approach in which the formulation and developments of the hypothesis are observed. That's why the positivism paradigm is considered as the best philosophy in order to conduct this research on a particular topic (Caldwell, 2015). In the positivism philosophy, it has been believed that reality is stable and it can easily describe and observed from the objective viewpoints. It is easily being studied without interfering along with the phenomena.

Sampling techniques and size of Comparison of Beta Estimation methods

By considering all of these stages of the sampling technique that was adopted for the said study are one of stratified sampling as well as simple random sampling. These results from the fact that there is a need to first classify the target population into those in management positions and those working on the industrial equipment. The other reason for the selection of stratified sampling is because of the need to eliminate the possibility of sampling bias. Sampling bias is normally witnessed in a case where the resulting sample consists of the population with the same characteristics. Sampling has been done in such a way that the employees whose jobs directly relate to risk management as well as who are engaged in performing the duties at the financial departments of the various firms. These are given more slots as compared to the rest. This will be done in order to guarantee high-quality data is obtained from the research sample. The research sample will consist of 100 individuals. This sampling technique is chosen as the best way to conduct this study.

The target population of the project will be workers or professionals who will be taken from various financial firms in the Poland. The various firms of the industries will be selected from those involved in the financial services, risk calculating and assets management.

Instruments of the Research of Comparison of Beta Estimation methods

There are several tools that can be utilized to collecting the data from the respondents by conducting an accurate survey. For the said study the questionnaire is considered as one of the most important and well-known techniques for collecting the data from the respondents. Under the inductive research approach the quantitative research methods this is the most important essential tools that can be employed in this study collecting the data and knowing the reviews of the people on a particular topic (Colton, 2007). This questionnaire contains the two major sections. The first section explains the demographic profile of the respondents meanwhile another one explains the detail related to the various constructs that are exploring the questions related to the various other factors of the study. This questionnaire has been designed in very easy language and the section of the vocabulary is quite accurate according to the standards of the respondents.

Results and analysis of Comparison of Beta Estimation methods

There are two kinds of particular analyses that have been conducted in order to measure comparison of the beta analysis methods. These analyses are descriptive and inferential analysis. The descriptive analysis is particularly utilized in order to explain the frequencies of the variables as well as the reliability of the variables. Meanwhile, inferential analyses are utilized to explain the relationships and effects of variables on each other. The responses of the respondents are better evaluated through the frequency distribution. The following is given the frequency distribution along with the respective pie-charts for the demographic variables.

Interpretation

The information related to the frequency distribution and the relevant percentages for the respondents of the age is given in the above table. 6% of the respondents are a part of the age range of fewer than 25 years and the frequency for the said age range is 36% of the respondents belong to the age range of 25-35 years and the relevant frequency is 36respondents. The respondents who belong to the age range of 35-45 years and 45 years plus have a frequency of 37 and 21 respondents along with the relevant percentages of 37 21% respectively. Most of the respondents are part of the age range of fewer than 25 years with 6.2%.

 

Interpretation of Comparison of Beta Estimation methods

            The varying percentages for the respondents of the age are shown with various attractive colors in the above pie-chart. The major area of the pie-chart is covered by grey color which is showing the frequency of the age range 35-45 years. The second, third, and fourth number is the age ranges 25-34 years, 45 years plus and less than 25 years which are shown in the pie-chart by the colors green, blue and purple, respectively.

 

Interpretation of Comparison of Beta Estimation methods

The details related to the frequency distribution and the relevant percentages for the respondents of the gender are given in the above table. 75.6% of the respondents are a part of the gender male with the frequency 189. 24.4% of the respondents are a part of the gender female with frequency 61. This frequency distribution shows that most of the respondents are male.

Interpretation of Comparison of Beta Estimation methods

            The varying percentages for the respondents of the gender are shown with various attractive colors in the above pie-chart. The major area of the pie-chart is covered by blue color which is showing the frequency of the male gender. The second number is the gender female who is shown in the pie-chart by the blue color.

 

Interpretation of Comparison of Beta Estimation methods

The information related to the frequency distribution for the educational level and the relevant percentages for the said respondents is given in the above table. 49.2% of the total respondents are a part of the bachelor’s degree and the frequency for the said educational level is 123. 27.6% of the respondents belong to the Master's degree and the relevant frequency is 69 respondents. The respondents who belong to the M-Phil and the Intermediate educational level have a frequency of 46 and 12 respondents, along with the relevant percentages of 18.4% and 4.8% respectively. Most of the respondents are part of the educational level Bachelor with the frequency 123.

Interpretation of  Comparison of Beta Estimation methods

            The varying percentages for the respondents of the educational level are shown with various attractive colors in the above pie-chart. The major area of the pie-chart is covered by blue color which is showing the frequency of the educational level bachelor. The second, third, and fourth numbers are the respondents from the Bachelors, Others, and Masters, Mphill and intermediate which are shown in the pie-chart by the colors blue, purple, and green, respectively.

Interpretation:

The details related to the frequency distribution for the employment status and the relevant percentages for the said respondents are given in the table. 49.2% of the respondents are serving as the private officials and the frequency for the said employment status is 123. 27.6% of the respondents are the government officials and the relevant frequency is 69 respondents. The respondents who belong to the other employment status have a frequency of 46 respondents, along with the relevant percentage of 18.4%. Most of the respondents are the part of the employment status as the government officials with the frequency 123.

Interpretation

            The varying percentages for the respondents of the employment status are shown with various attractive colors in the above pie-chart. The major area of the pie-chart is covered by blue color which is showing the frequency of the employment status of private officials. The second and the third number are the respondents from the government sector and others which are shown in the pie-chart by the colors blue and skin, respectively. The purple color shows the frequency of the respondents who did not mention their employment status.

Data Reliability Analysis

The data reliability is accessed by using the Cronbach Alpha Value for the current study variables. The idea of Cronbach Alpha was introduced in 1951 by Cronbach. The range for the Cronbach Alpha lies between 0 and 1. It shows that all the items of the questionnaire are better evaluated on the similar concept & idea. The data set for which the value of Cronbach Alpha is more than 0.70; it means that the data is highly reliable (Nunnallly, 1978). For the present research work, the overall value of the Cronbach Alpha is shown in the below-given table.

            The above-given table is showing that the overall Value of Cronbach Alpha is greater than 0.70 such as 0.738. It means that the data items are highly reliable.

Correlation Analysis

The association of the study variables can better be determined by the Pearson product-moment correlation coefficient. It was developed by Karl Pearson in 1985. The test results for this coefficient lie between +1 and -1. For a positive correlation, the test result is +1. For no relationship, the test result is 0. The negative relation between the variables is depicted by -1. The correlation analysis and its results are shown in the below-given table.

 

The relationship of the study dependent and the independent variables are determined by using the Pearson correlation coefficient. For p<0.01, the value of the Pearson coefficient is showing that there exists a strong positive correlation between the study dependent and the independent variables. These variables are positively significantly associated with each other.

Regression Analysis

 

a. Predictors: (Constant), Bayesianmodelaveraging

 

 

Interpretation

In the regression model, the value of R-Square provides the measure for the goodness-of-fit. This value tends to depict the %age variance change in the dependent variable due to the independent variables. Based on the regression analysis for the current data set, it is evaluated that the value of R is 0.955. As far as the value of R-square for the current study variables is concerned, it is 0.911. This value is determining a significant percentage change on the dependent variable (beta estimation methods) due to the study independent variables (i.e Bayesian model averaging and various other methods) are the good techniques for estimating beta. The value of adjusted R-square provides for a comparison between the study models. This value is 0.911 which shows that out of total variation narrated by the regression line, the variation %age is significant. In case we talk about the value of p for the regression model, this value is less than 0.05 for all the study independent variables.

The value of p<0.05 shows that the study independent variables (i.e., Bayesian model averaging and various other methods) are positively significantly associated with the study dependent variable (i.e., beta estimation techniques). It can be said that these parameters better help to determine the effects of beta estimation by which it can have varying reasons to take place. It has been observed that Bayesian model averaging and various other methods is positively affected by the beta estimation techniques because these techniques can be used by finance experts to evaluate the risk. It has been observed that most of the firms are engaged in the using slope method for estimating the beta. That’s why few of the researchers considered it the most effective and good approach for estimating beta.

Conclusion of Comparison of Beta Estimation methods

By summing up entire discussion it has been concluded that there are several methods that can be utilized to estimating beta. All of these methods are compared by conducting this research. The most unique methods have been adopted in order to conduct this research in which the survey is conducted from the experts of the finance. Their views and arguments are also known for getting the information related to the most usable methods in the organizations. These entire professional has argued about the methods that they are using in their firms for estimating and calculating methods.

There are five major methods that have been utilized to calculate and estimate the beta. These methods are; Historical beta Fama & MacBeth and CCAPM, Bayesian model averaging, Exponentially weighted moving average (EWMA), Slope method in excel and Correlation method. It has been observed that the mostly usable methods for calculating beta are slope method in which the Excel is utilized to estimating the beta. The correlation method  is also best fitted method  for estimating and calculating the beta  but there are the fewer firms or organization that are using this method  due to its inaccuracy. Few of the researchers perceived that it is not good method for calculating beta.

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