task report on financial modelling module

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This report aims to investigate stock performance of new listed companies, the companies in which launched initial public offering (IPO) in stock market. Based on theoretical review and empirical studies, five variables are considered as determinants of IPO companies stock returns, namely: age of company, total assets, ownership concentration, founder, rate of return on capital employed (ROCE), and industry or sectors where the company operates . The report, therefore, will assess the notion of these relationships through both descriptive and inferential statistics. 300 samples are selected to conduct the analysis.

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    Full name : La Ode Sabaruddin

    Student ID Number : 139040727

    Program : Accounting and Finance MSc

    Module : Financial Modeling (MN7024)

    Word Count : 1965 (References and appendix are not included)

    1. Introduction

    This report aims to investigate stock performance of new listed companies , the

    companies in which launched initial public offering (IPO) in stock market. Based on

    theoretical review and empirical studies, five variables are considered as determinants

    of IPO companies stock returns, namely: age of company, total assets, ownership

    concentration, founder, rate of return on capital employed (ROCE), and industry or

    sectors where the company operates1. The report, therefore, will assess the notion of

    these relationships through both descriptive and inferential statistics. 300 samples are

    selected to conduct the analysis.

    2. Model Specification, Variables Definitions and Measurements

    Model specification is the process of converting theories into a regression

    model (Lee, et. al., 1999 p. 178). Referring to prior studies, stock returns of IPO

    companies are primarily determined by a linear combination of five explanatory

    variables, as mentioned before. The theoretical model can be written as follows:

    (Adapted from Wooldridge, 2002 p.48)

    Variables definitions and measurements:

    IPOreturn = rate of return three years after IPO launched, P t / Pt-0, where Pt-0

    represents the IPO price, and Pt the trading price three years

    subsequently (%)

    age = age of company (years)

    size = total assets of the company ( million)

    con = ownership concentration, percentage shares of pre-IPO owners post

    floatation (%).

    founder = CEO is also founder of the company:

    1 if yes

    0 if no

    ROCE = average return on capital employed over the year prior to IPO (%)

    1Other determinants of IPO return exist in literature, see, for example, Bansal and Khanna(2012); Bessler and Thies (2007); and Ritter and Welch (2002).

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    industry = Sector in which company operates:

    1 if computer hardware/electronics

    2 if pharmaceuticals

    3 if other manufacturing

    4 if software development

    5 if other servicesu = unobservable random disturbance of error

    3. Statistical Analysis

    3.1. Univariate AnalysisDescriptive Statistics

    Descriptive statistics describes characteristics and spread of data through

    graph and numerical summaries. Table 1 presents characteristics of IPO sample

    companies for continues variables, while categorical variables are presented in table

    2.

    Table 1

    Characteristics of IPO Sample CompaniesContinues Variables

    Continues Variables

    IPOreturn Age Size Con ROCE

    Mean 20.241 14.63 18355.28 28.85 35.48

    Standard deviation 27.910 2.793 9600.135 17.082 24.625

    Normality tests (p-values):- Kolmogorov-Smirnov- Shapiro-walk

    0.000

    0.000

    0.000

    0.001

    0.004

    0.001

    0.000

    0.000

    0.200

    0.268

    From the above table we can see that:

    - IPO return, size, ownership concentration, and ROCE variables have relativelywider data spreads, indicated by high values of standard deviation. On the other

    hand, data of age variable are closer to its mean, indicated by lower value of

    standard deviation.

    - Normality tests indicate that ROCE variable has normal distribution, while othersnot. Central limit theorem, however, says that random variables with large samples

    (i.e. >30) will be normally distributed (Watsham and Parramore, 1997 p.136-137).

    For graphical figures of continues variables, see appendix 1 section a.

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    Table 2

    Characteristics of IPO Sample Companies Categorical Variables

    Frequency Percentage

    Industry Sectors:

    Computer hardware/electronics 53 17.7Pharmaceuticals 17 5.7

    Other manufacturing 113 37.7

    Software development 9 3.0

    Other services 108 36.0

    Total 300 100

    Founder:

    CEO is also founder of the company 88 29.3

    CEO is not founder of the company 212 70.7

    Total 300 100

    In total of 300 IPO sample companies, other manufacturing and other services sectorsare the two largest sample companies with 37.7% and 36% respectively, whereas

    software development sector is the least which occupied only 3% of the total samples.

    In terms of founder, 70.7% of IPO sample companies have CEOs, which also the

    founder, whereas CEOs of 29.3% companies are not the founder. For graphical

    figures of categorical variables, see appendix 1 section b.

    3.2. Bivariate Analysis - Correlations

    Correlation indicates the strength of relationship between two variables. We

    assess correlations among continues variables using Pearson correlation and

    scatterplot, while association between continues variables and categorical variables

    are assessed through analysis of variance (ANOVA) and boxplots. Association among

    categorical variables is examined through chi-square test.

    Correlations between Explanatory Variables and Dependent Variable

    Based on statistical outputs in appendix 2 section a, correlations between

    explanatory variables and dependent variable can be summarized as follows:

    - IPO return has positive relationship and moderate in strength with ROCE, meansthat higher values of ROCE associate with higher values of IPO return (r=0.638).

    Similarly, ownership concentration and size of company have positive

    relationships with IPO return, but very weak in strength (r=0.136 and r=0.120

    respectively). On the other hand, IPO return tends not to correlate with age of

    company (r=-0.056). For the graphical figures, see scatterplots.

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    - Company in which the CEO is also the founder tends to associate with higher IPOreturns, while company in which the CEO is not the founder tends to have lower

    values of IPO returns (ANOVA test shows that these two groups of companies

    have different means, p=0.000). On the other hand, higher or lower IPO returns

    tends not to associate with particular industries or sectors where the companies

    operate (ANOVA test has p=0.868). For the graphical figures, see boxplots.

    Correlations Within Explanatory Variables

    Correlations statistics within explanatory variables as shown in appendix 2,

    section (b) indicate that most of explanatory variables are not correlate each other.

    The exceptions are ownership concentration which has a weak negative relationship

    with age of company (r=-0.318, see also scatterplot), and ROCE which has positive

    association with founder where higher values on the ROCE tends to associate with

    company in which the CEO is also the founder (ANOVA test has p=0.000, see also

    boxplot). Later on, we will assess these correlations in multivariate analysis whether it

    violates multicollinearity assumption or not.

    3.3. Multivariate Analysis - Multiple Linear Regression

    Since the model consists of several explanatory variables (see equation 2 in

    model specification), we run multiple linear regressions to conduct the analysis.

    Statistical outputs as shown in appendix 3, section (a) highlight that p-value for

    regression model F-test is .000 and adjusted R-square=0.519, means explanatory

    variables in the model are simultaneously account for 51.9% to explain variability in

    IPO returns. Partially, size of company, ownership concentration, and founder are

    statistically significant to predict IPO returns (p-values0.05),

    means we find no support that different ages of company or different sectors of

    industry will result in different future stock performance of IPO companies.

    To capture differences in industry sectors, we create dummy variables for each

    sectors of industry, as shown in equation (3).

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    Again, the results (see appendix 3, section b) confirmed that all sectors or industry

    have identic average value of IPO returns, indicated by insignificant p-values of all

    dummy variables for industry. These insignificant outcomes, however, cannot be

    interpreted in a strict sense since this report employs cross-sectional data, which has

    less power to capture such differences.

    Then, we rerun the model while omitting insignificant variables. The result shows

    higher adjusted R-square (0.521) than the previous value (0.519), indicates that

    insignificant variables are irrelevant to predict IPO returns. Hence, estimated model of

    the relationships between IPO return and its explanatory variables can be expressed:

    As IPO return is a linear combination of four explanatory variables in equation (4),

    the model can be interpreted as follows:

    - Intercept: If values of all explanatory variables in the model are zero, then IPOreturn is -29.201%.

    - Slope of continues variables: If other variables in the model are fixed, then foreach change of 1 million in assets (size), then the model predicts that IPO

    returns increases by 0.0004 %; If the ownership concentration increases by 1 %,

    then IPO returns will increase by approximately 0.248% while holding other

    variables constant; For each change of 1 % in ROCE, average increase in the

    mean of IPO returns is about 0.678 % while controlling other variables constant.

    - Slope of categorical variable: Company in which the CEO is also the founder hashigher IPO return average of 16.004% than company in which the CEO is not the

    founder.

    Testing the Assumptions of OLS Linear Regression Model

    Assumption testing of OLS regression is necessary to obtain a valid model. In

    this report, assumption tests include multicollinearity, heteroscedasticity, normality of

    residuals and model specification. The tests use STATA program and the results are

    summarized as follows (Appendix 4):

    - Collinearity statistics show that all variables have VIF values around 1 andtolerance values around 0.9, means multicollinearity doesnt existin the model.

    - Heteroscedasticity is assessed through Whites test and Breusch-Pagan test. Bothtests confirmed that the model has heteroscedasticity problem (p-values < 0.05),

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    means the variance is not homogenous. The plotted residuals is also supported the

    arguments (see rvfplot).

    - Normality of residuals is examined by plotting ordered values of standardizedresiduals against expected values from standard normal distribution. The plots

    include kernel density plot, P-P plot (pnorm plot), and quantiles plot (qnorm plot).

    The results show a slight deviation from normality. These results are also

    confirmed by Shapiro-Wilk W test (p-value=0.00571). However, since we have

    large samples, central limit theorem can be applied.

    - Model specification is evaluated by linktest and Ramsey Reset test. Linktest showsthat predicted values squares (hatsq) is significant, means the model has a

    specification error. Likewise, the Ramsey Reset test is significant, indicates that

    there could be omitted variable in the model, which it should. In conclusion, both

    tests indicate that the model may not be correctly specified.

    Interaction Terms

    Refer to estimated model in equation (4), we check whether interaction terms

    between dummy variable and other explanatory variables in the model exist or not

    through regress equation (5).

    The results show that the effects of company size, ownership concentration, and

    ROCE are higher in a company where the CEO is also the founder (p-values < 0.05).

    4. Conclusion and Limitations

    This report examines whether age of company, size, ownership concentration,

    founder, ROCE, and industry or sectors where the company operates can predict stock

    return performance of IPO companies. The major findings are summarized as follows:

    - Size of company, ownership concentration, founder and ROCE are statisticallysignificant to influence the stock return of IPO companies, which account for

    52.1%, while 47.9 remains unexplained. On the other hand, we find no support

    that age of company and industry sectors can predict future stock performance of

    IPO companies.

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    - The company in which the CEO is also the founder has higheraverage of IPOreturns than the company in which the CEO is not the founder.

    - The effects of company size, ownership concentration and ROCE to stock returnof IPO companies are higher in a company where the CEO is also the founder.

    Having said that, this report has some limitations:

    1. There may be a problem of error specification and potential omitted variable biasin the model, as the model doesnt satisfy the specification test. In addition, the

    model also has a problem of heteroscedasticity.

    2. Coefficient determination of the model is relatively low, and therefore it isadvisable to include other powerful explanatory variables in future empirical

    research.

    3. The model only employs linear approach, while real-world financial time series arelikely to have both linear and nonlinear patterns, and therefore an approach, which

    combines linear-nonlinear method will produce a more precise result.

    4. As the employed data is cross section, it may less accurate to capture inter-company or industry sector differences as well as intra-company or sector

    dynamics. Using panel data and larger sample size will give greater capacity to

    capture the complexity of the relationships, include controlling the impact of

    omitted variables.

    References

    Bansal, R. and Khanna A., 2012. Determinants of IPOs Initial Return: Extreme

    Analysis of Indian Market. Journal of Financial Risk Management, 1 (4), pp. 68-

    74.

    Bessler, W. and Thies, S., 2007. The long-run performance of initial public offerings

    in Germany.Managerial Finance, 33 (6), pp. 420-441.

    Lee, C.F., Lee, J.C. and Lee, A. C., 1999. Statistics for Business and FinancialEconomics.Singapore: World Scientific Publishing.

    Ritter, J.R. and Welch, I., 2002. A Review of IPO activity, pricing and allocations.

    Journal of Finance, 57(4), pp. 1795-1828.

    Watsham, T.J. and Parramore, K., 1997. Quantitative Methods in Finance. Singapore:

    South Western Cengage Learning.

    Wooldridge, J.M., 2002. Econometric Analysis of Cross Section and Panel Data.

    Massachusetts: MIT Press.

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    Appendix 1 - Univariate Analysis

    a. Continues VariablesData Distribution

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    b. Categorical Variables Data Distribution

    Appendix 2Bivariate Analysis

    a. Relationships between explanatory variables and dependent variable

    Pearson Correlation - Continues explanatory variables and dependent variable

    Correlations

    Iporeturn age size con Roce

    iporeturn

    Pearson Correlation 1 -.056 .120* .136

    * .638

    **

    Sig. (2-tailed) .338 .038 .018 .000

    N 300 300 300 300 300

    Age

    Pearson Correlation -.056 1 -.009 -.318**

    -.007

    Sig. (2-tailed) .338 .874 .000 .910

    N 300 300 300 300 300

    Size

    Pearson Correlation .120* -.009 1 .019 -.065

    Sig. (2-tailed) .038 .874 .748 .258

    N 300 300 300 300 300

    Con

    Pearson Correlation .136* -.318

    ** .019 1 -.059

    Sig. (2-tailed) .018 .000 .748 .306

    N 300 300 300 300 300

    Roce

    Pearson Correlation .638** -.007 -.065 -.059 1

    Sig. (2-tailed) .000 .910 .258 .306

    N 300 300 300 300 300

    *. Correlation is significant at the 0.05 level (2-tailed).

    **. Correlation is significant at the 0.01 level (2-tailed).

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    Scatterplots - Continues explanatory variables and dependent variable

    Analysis of Variance (ANOVA):

    Categorical explanatory variables and Continues dependent Variable

    ANOVA - IPO return and Founder

    Iporeturn

    Sum of Squares df Mean Square F Sig.

    Between Groups 40475.336 1 40475.336 62.679 .000

    Within Groups 192433.990 298 645.752

    Total 232909.327 299

    ANOVAIPO return and Industry

    Iporeturn

    Sum of Squares df Mean Square F Sig.

    Between Groups 988.124 4 247.031 .314 .868

    Within Groups 231921.202 295 786.174

    Total 232909.327 299

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    BoxplotsCategorical explanatory variables and continues dependent variable

    b. Relationships within explanatory variables

    Pearson CorrelationCorrelations between Continues explanatory variables

    Correlations

    age size con roce

    age

    Pearson Correlation 1 -.009 -.318**

    -.007

    Sig. (2-tailed) .874 .000 .910

    N 300 300 300 300

    size

    Pearson Correlation -.009 1 .019 -.065

    Sig. (2-tailed) .874 .748 .258

    N 300 300 300 300

    con

    Pearson Correlation -.318**

    .019 1 -.059

    Sig. (2-tailed) .000 .748 .306

    N 300 300 300 300

    roce

    Pearson Correlation -.007 -.065 -.059 1

    Sig. (2-tailed) .910 .258 .306

    N 300 300 300 300

    **. Correlation is significant at the 0.01 level (2-tailed).

    Scatterplots Correlations between continues explanatory variables

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    Analysis of Variance (ANOVA):

    Categorical explanatory variables and Continues explanatory Variables

    ANOVA Founder and Continues Explanatory Variables

    Sum of Squares df Mean Square F Sig.

    age

    Between Groups 10.748 1 10.748 1.380 .241

    Within Groups 2321.438 298 7.790

    Total 2332.187 299

    size

    Between Groups 284679531.259 1 284679531.259 3.111 .079

    Within Groups 27271932811.221 298 91516553.058

    Total 27556612342.480 299

    roce

    Between Groups 8842.276 1 8842.276 15.278 .000

    Within Groups 172464.640 298 578.740

    Total 181306.917 299

    con

    Between Groups 385.340 1 385.340 1.322 .251

    Within Groups 86856.910 298 291.466

    Total 87242.250 299

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    ANOVAIndustry and Continues Explanatory Variables

    Sum of Squares df Mean Square F Sig.

    age

    Between Groups 32.294 4 8.073 1.036 .389

    Within Groups 2299.893 295 7.796Total 2332.187 299

    size

    Between Groups 609291110.615 4 152322777.654 1.668 .158

    Within Groups26947321231.86

    5295 91346851.633

    Total27556612342.48

    0299

    roce

    Between Groups 1513.115 4 378.279 .621 .648

    Within Groups 179793.802 295 609.471

    Total 181306.917 299

    con

    Between Groups 2055.916 4 513.979 1.780 .133

    Within Groups 85186.334 295 288.767

    Total 87242.250 299

    BoxplotsCategorical explanatory variables and continues explanatory variables

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    Pearson Chi-Square

    Categorical explanatory variables

    Chi-Square TestsFounder and Industry

    Value df Asymp. Sig. (2-sided)

    Pearson Chi-Square 1.561a 4 .816

    Likelihood Ratio 1.483 4 .830

    Linear-by-Linear Association .126 1 .723

    N of Valid Cases 300

    a. 2 cells (20.0%) have expected count less than 5. The minimum expected count is2.64.

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    Appendix 3Multivariate Analysis

    a. Multiple Linear RegressionAll variables

    Model Summaryb

    Model R R Square Adjusted R Square Std. Error of the

    Estimate

    1 .727a .529 .519 19.34867

    a. Predictors: (Constant), industry Industry, founder Founder, con, size, roce, age

    b. Dependent Variable: iporeturn

    ANOVAa

    Model Sum of Squares df Mean Square F Sig.

    1Regression 123218.578 6 20536.430 54.856 .000

    b

    Residual 109690.748 293 374.371

    Total 232909.327 299

    a. Dependent Variable: iporeturn

    b. Predictors: (Constant), industry Industry, founder Founder, con, size, roce, age

    Coefficientsa

    Model Unstandardized

    Coefficients

    Standardized

    Coefficients

    t Sig. Correlations Collinearity

    Statistics

    B Std. Error Beta Zero-order Partial Part Tolerance VIF

    1

    (Constant) -36.015 8.735 -4.123 .000

    Age .228 .426 .023 .534 .593 -.056 .031 .021 .883 1.133

    Size .000 .000 .133 3.279 .001 .120 .188 .131 .976 1.025

    Con .263 .070 .161 3.779 .000 .136 .216 .151 .885 1.130

    founder 16.051 2.545 .262 6.308 .000 .417 .346 .253 .930 1.076

    Roce .681 .047 .601 14.490 .000 .638 .646 .581 .934 1.071

    industry .810 .778 .042 1.041 .299 -.017 .061 .042 .973 1.027

    a. Dependent Variable: iporeturn

    b. Multiple Linear RegressionAll variables + Dummy variables for industry sectors

    Model Summaryb

    Model R R Square Adjusted R

    Square

    Std. Error of

    the Estimate

    1 .729a .531 .516 19.41089

    a. Predictors: (Constant), d4_sector4, age, roce, d2_sector2, size,d1_sector1, founder Founder, con, d3_sector3

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    b. Dependent Variable: iporeturn

    ANOVAa

    Model Sum of Squares df Mean Square F Sig.

    1

    Regression 123642.326 9 13738.036 36.461 .000b

    Residual 109267.001 290 376.783

    Total 232909.327 299

    a. Dependent Variable: iporeturn

    b. Predictors: (Constant), d4_sector4, age, roce, d2_sector2, size, d1_sector1, founder Founder, con,

    d3_sector3

    Coefficientsa

    Model Unstandardized

    Coefficients

    Standardized

    Coefficients

    t Sig. Correlations Collinearity

    Statistics

    B Std. Error Beta Zero-order Partial Part Tolerance VIF

    1

    (Constant) -31.614 7.888 -4.008 .000

    Age .211 .429 .021 .490 .624 -.056 .029 .020 .876 1.141

    Size .000 .000 .131 3.178 .002 .120 .183 .128 .958 1.043

    Con .253 .071 .155 3.569 .000 .136 .205 .144 .861 1.161

    founder 16.276 2.564 .266 6.348 .000 .417 .349 .255 .922 1.085

    Roce .679 .047 .599 14.362 .000 .638 .645 .578 .929 1.077

    d1_sector1 -3.003 3.287 -.041 -.914 .362 .018 -.054 -.037 .799 1.251

    d2_sector2 -1.263 5.131 -.010 -.246 .806 .031 -.014 -.010 .893 1.120

    d3_sector3 -1.791 2.662 -.031 -.673 .501 -.032 -.039 -.027 .755 1.324

    d4_sector4 6.061 6.846 .037 .885 .377 .049 .052 .036 .921 1.086

    a. Dependent Variable: iporeturn

    c. Multiple Linear RegressionInsignificant variables are excluded

    Model Summaryb

    Model R R Square Adjusted R Square Std. Error of the

    Estimate

    1 .726a .527 .521 19.32410

    a. Predictors: (Constant), roce, con, size, founder Founder

    b. Dependent Variable: iporeturn

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    ANOVAa

    Model Sum of Squares df Mean Square F Sig.

    1

    Regression 122750.220 4 30687.555 82.180 .000b

    Residual 110159.106 295 373.421

    Total 232909.327 299

    a. Dependent Variable: iporeturn

    b. Predictors: (Constant), roce, con, size, founder Founder

    Coefficientsa

    Model Unstandardized

    Coefficients

    Standardized

    Coefficients

    t Sig. Correlations Collinearity

    Statistics

    B Std.

    Error

    Beta Zero-order Partial Part Tolerance VIF

    1

    (Constant) -29.201 3.701 -7.890 .000

    Size .0003774 .000 .130 3.212 .001 .120 .184 .129 .982 1.019

    Con .248 .066 .152 3.770 .000 .136 .214 .151 .990 1.010

    founder 16.004 2.539 .262 6.304 .000 .417 .345 .252 .932 1.073

    Roce .678 .047 .598 14.467 .000 .638 .644 .579 .938 1.066

    a. Dependent Variable: iporeturn

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    Appendix 4 REGRESSION ASSUMPTION TESTS (STATA OUTPUT)

    NORMALITY TESTS OF RESIDUALS

    . predict r, resid

    . kdensity r, normal

    _cons -29.20125 3.700855 -7.89 0.000 -36.48468 -21.91783

    roce .6778655 .0468565 14.47 0.000 .58565 .7700809 founder 16.00441 2.538823 6.30 0.000 11.00791 21.00091

    con .2478889 .0657597 3.77 0.000 .1184714 .3773064

    size .0003774 .0001175 3.21 0.001 .0001462 .0006087

    iporeturn Coef. Std. Err. t P>|t| [95% Conf. Interval]

    Total 232909.325 299 778.960954 Root MSE = 19.324

    Adj R-squared = 0.5206

    Residual 110159.105 295 373.420696 R-squared = 0.5270

    Model 122750.22 4 30687.555 Prob > F = 0.0000

    F( 4, 295) = 82.18

    Source SS df MS Number of obs = 300

    . regress iporeturn size con founder roce

    _cons -36.01547 8.734635 -4.12 0.000 -53.20605 -18.82489

    industry .8097259 .7780957 1.04 0.299 -.7216392 2.341091

    roce .6814775 .0470294 14.49 0.000 .5889192 .7740358

    founder 16.0508 2.544542 6.31 0.000 11.04291 21.0587

    con .2631583 .0696444 3.78 0.000 .1260916 .400225

    size .000387 .000118 3.28 0.001 .0001547 .0006192

    age .2278899 .4263863 0.53 0.593 -.6112783 1.067058

    iporeturn Coef. Std. Err. t P>|t| [95% Conf. Interval]

    Total 232909.325 299 778.960954 Root MSE = 19.349

    Adj R-squared = 0.5194

    Residual 109690.747 293 374.371151 R-squared = 0.5290

    Model 123218.578 6 20536.4297 Prob > F = 0.0000 F( 6, 293) = 54.86

    Source SS df MS Number of obs = 300

    . regress iporeturn age size con founder roce industry

    0

    .005

    .01

    .015

    .02

    .0

    25

    -50 0 50 100Residuals

    Kernel density estimate

    Normal density

    kernel = epanechnikov, bandwidth = 4.9020

    Kernel density estimate

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    . pnorm r

    . qnorm r

    . swilk r

    0.0

    0

    0.2

    5

    0.5

    0

    0.7

    5

    1.0

    0

    0.00 0.25 0.50 0.75 1.00

    Empirical P[i] = i/(N+1)

    -50

    0

    50

    100

    i

    l

    -50 0 50

    Inverse Normal

    r 300 0.98621 2.938 2.529 0.00571

    Variable Obs W V z Prob>z

    Shapiro-Wilk W test for normal data

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    HOMOSCEDASTICITY TESTS

    . rvfplot, yline(0)

    Prob > chi2 = 0.0000

    chi2(1) = 22.82

    Variables: fitted values of iporeturn

    Ho: Constant variance

    Breusch-Pagan / Cook-Weisberg test for heteroskedasticity

    . estat hettest

    Total 42.94 18 0.0008

    Kurtosis 2.40 1 0.1214

    Skewness 13.58 4 0.0088

    Heteroskedasticity 26.96 13 0.0126

    Source chi2 df p

    Cameron & Trivedi's decomposition of IM-test

    . estat imtest

    -50

    0

    50

    100

    -40 -20 0 20 40 60Fitted values

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    MULTICOLLINEARITY TEST

    MODEL SPECIFICATION TEST

    . linktest

    . ovtest

    _cons -.8786877 1.531233 -0.57 0.567 -3.89213 2.134755

    _hatsq .0092055 .001993 4.62 0.000 .0052834 .0131276

    _hat .6709956 .0888404 7.55 0.000 .4961591 .845832

    iporeturn Coef. Std. Err. t P>|t| [95% Conf. Interval]

    Total 232909.325 299 778.960954 Root MSE = 18.602

    Adj R-squared = 0.5558

    Residual 102776.122 297 346.047549 R-squared = 0.5587

    Model 130133.203 2 65066.6016 Prob > F = 0.0000

    F( 2, 297) = 188.03

    Source SS df MS Number of obs = 300

    Prob > F = 0.0001

    F(3, 292) = 7.23

    Ho: model has no omitted variables

    Ramsey RESET test using powers of the fitted values of iporeturn

    Mean VIF 1.04

    con 1.01 0.989811

    size 1.02 0.981521

    roce 1.07 0.938088

    founder 1.07 0.931615

    Variable VIF 1/VIF

    . vif

    _cons -29.20125 3.700855 -7.89 0.000 -36.48468 -21.91783 roce .6778655 .0468565 14.47 0.000 .58565 .7700809

    founder 16.00441 2.538823 6.30 0.000 11.00791 21.00091

    con .2478889 .0657597 3.77 0.000 .1184714 .3773064

    size .0003774 .0001175 3.21 0.001 .0001462 .0006087

    iporeturn Coef. Std. Err. t P>|t| [95% Conf. Interval]

    Total 232909.325 299 778.960954 Root MSE = 19.324

    Adj R-squared = 0.5206

    Residual 110159.105 295 373.420696 R-squared = 0.5270

    Model 122750.22 4 30687.555 Prob > F = 0.0000

    F( 4, 295) = 82.18

    Source SS df MS Number of obs = 300

    . regress iporeturn size con founder roce

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    .

    Prob > F = 0.0001

    F(3, 290) = 7.29

    Ho: model has no omitted variables

    Ramsey RESET test using powers of the fitted values of iporeturn

    . ovtest

    _cons -.8816762 1.52568 -0.58 0.564 -3.88419 2.120838

    _hatsq .0091313 .0019613 4.66 0.000 .0052716 .0129911

    _hat .6734393 .087824 7.67 0.000 .5006033 .8462754

    iporeturn Coef. Std. Err. t P>|t| [95% Conf. Interval]

    Total 232909.325 299 778.960954 Root MSE = 18.553

    Adj R-squared = 0.5581

    Residual 102229.375 297 344.206649 R-squared = 0.5611

    Model 130679.95 2 65339.9752 Prob > F = 0.0000 F( 2, 297) = 189.83

    Source SS df MS Number of obs = 300

    . linktest

    _cons -36.01547 8.734635 -4.12 0.000 -53.20605 -18.82489

    size .000387 .000118 3.28 0.001 .0001547 .0006192

    roce .6814775 .0470294 14.49 0.000 .5889192 .7740358

    industry .8097259 .7780957 1.04 0.299 -.7216392 2.341091 founder 16.0508 2.544542 6.31 0.000 11.04291 21.0587

    con .2631583 .0696444 3.78 0.000 .1260916 .400225

    age .2278899 .4263863 0.53 0.593 -.6112783 1.067058

    iporeturn Coef. Std. Err. t P>|t| [95% Conf. Interval]

    Total 232909.325 299 778.960954 Root MSE = 19.349

    Adj R-squared = 0.5194

    Residual 109690.747 293 374.371151 R-squared = 0.5290

    Model 123218.578 6 20536.4297 Prob > F = 0.0000

    F( 6, 293) = 54.86

    Source SS df MS Number of obs = 300

    . regress iporeturn age con founder industry roce size