FINANCIAL MODELLING coursework

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13Financial Modelling

ACF310 COURSEWORK ~ PART 2

The Name of the School

SECTION A

QA1: Assumption and implication of CAPM

Capital asset pricing model can be describes as the theory of asset price determination of a company (Cremers, Halling and Weinbaum 2015). It is normally based on the theory of portfolio and market model. It has several assumption which include:-

  1. That all market portfolio that establishes Beta is composed of all publicly traded assets

  2. Investors in the market have similar information concerning the market behaviour and beliefs about the distribution of returns (Chang, Christoffersen and Jacobs 2013).

  3. There are very many investors and all of them are price takers. That is to say financial markets are very competitive and the returns provides investors with a summary of investment opportunities (Cremers, Halling and Weinbaum 2015).

  4. No distortionary charges or exchange cost which is an unmistakably a false suppositions that is obligation versus value

  5. All investors can acquire or loan in the business sector at the same hazard free rate. Besides, this is a false suppositions yet one can consider zero-beta adaptation of CAPM with short deals (Chang, Christoffersen and Jacobs 2013).

  6. Investors just think about the normal return like and difference which is abhorrence (Cremers, Halling and Weinbaum 2015).

On these assumption, there are implications of CAPM and the implications includes:-

  1. For all portfolios and assets, security market lines hold for the in the same way that is to say that only three things determines the return on the assets and they include risk free rates, market risk premium and lastly beta.

  1. The mean variance efficient is the market portfolio and that is the one with the highest Sharpe ratio (Cremers, Halling and Weinbaum 2015).

  1. The CAPM show normally determines expected returns that would be utilized as a part of the capital planning assessment and direction (Cremers, Halling and Weinbaum 2015).

QA2: validity of the assumptions and extent to which it does breach the assumptions invalidate the CAPM model

The CAPM antedate that trading in the market will be costless so theories are esteemed to all fall on the capital business area line. If not, a couple endeavours would glide underneath or increasingly the line — with trade costs discouraging clear swaps Be that as it may, we understand that various endeavours for example, securing a little business, incorporate huge trade costs. Possibly the capital business division line is really a band whose width reflects exchanging costs (Chang, Christoffersen and Jacobs 2013). Fischer and Black proved that even if there is no risk-free rate asset in the market, one is capable of deriving a zero beta version of CAPM, where the intercept might be higher than expected under the normal CAPM model(Cremers, Halling and Weinbaum 2015). This further validates the assumption and the expected results of its violation. Lastly, the consumption based CAPM normally allows for the fact that investors horizon are longer than one period and therefore when they choose portfolios they are also thinking of how the present portfolios will hedge risk in future time of assets(Cremers, Halling and Weinbaum 2015). By and large, investors hold very much broadened portfolio and this is done to guarantee that the financial specialists has shed out some risk emerging from the firm. In this manner, we can infer that those given portfolio are having high odds of associating with the CAPM model (Barberis et al., 2015).

QA3: The empirical test for CAPM using data from Ken French’s website

In empirical test of CAPM model, we uses the data from two industries that is from technology industry and manufacturing. Eight regression were done using the excess asset return model

FINANCIAL MODELLING coursework

The hypothesis tested in this case was Test: FINANCIAL MODELLING coursework  1

The first case we run the regression for the two industries separately using the 30 year time period. The results are shown in the Table 1 and Table 2 in appendix 1 in excel file.

For the first industry portfolio manufacturing, in appendix 1 Table 1 in excel file. From Appendix 1 Table 1. R-squared is 0.658195 indicating that model is good as stated by Fama and French (1993) that a R-squared between 0.10-0.15 is enough for marking decision therefore this one is perfect since it is much above 15% mark. The P-value is 1.82E-85< 0.05 meaning that at 95% significance level, the results are statistically significance hence rejecting null hypothesis H0:α=0. The coefficient of regression results for manufacturing gives beta 1.049882 this is further approval of CAPM theory states that the assets cannot be fully diversified from the risk hence high risk from this analysis (Fama &French 2015).

The results for technology industry R-squared is given as 0.5764 indicating that over 57% of the total variables were included in the analysis and the model is fit to make decision, furthermore the p-value of the technology is 9.23E-69 < 0.05 therefore at significance level of 95%, the model is statistically significance hence rejecting null hypothesis. The coefficient that is alpha (FINANCIAL MODELLING coursework  2) = 14837 while betaFINANCIAL MODELLING coursework  3. This further supports initial findings with Beta greater than 0 indicating that it is high risk portfolio (Chang, Christoffersen and Jacobs 2013).

The second regression output is the analysis of data for 10 year period and we started with data from 1980 to 1989. The first part is the manufacturing industry portfolio followed by technology industry portfolio. Both models are valid with high R-square and p value for manufacturing and technology industry are 7.47E-31 and 2E-33 respectively. The beta coefficient for the two industry portfolios are 1.015103 and 1.278496 for manufacturing and technology respectively. Both beta are greater than 1 hence very risky (Fama &French 2015).

The third analysis is data for another 10 years from 1990-1999. From the result, the R-square for the two industries are 0.523799 and 0.462999 for manufacturing and Technology industry respectively. This results are shown in appendix 3 table 1 and 2 for manufacturing and technology respectively. The p-value for manufacturing is 9.81E-21. And that for technology is
2.26E-19 both are < 0.05 hence rejecting null hypothesis. The beta coefficient are 0.854563 and 0.937438 for manufacturing and technology respectively, though less than 1, both are still risky portfolio.

The last part is from the year 2000 to 2009. The regression output are in appendix 4 table 1 for manufacturing and table 2 for technology. The beta coefficient for manufacturing and technology are 1.25704 and 1.798919 respectively.

We can conclude from the results that all the models supports the CAPM model showing high risk portfolio of the two industry sectors hence achieving risk free portfolio is next to impossible.

QA4. Background and important features of the Fama French three factor model

The Fama-French Three-Factor Model can be described as a methodology for expounding on the risks and return of stocks (Fama &French 2015). It was discover by Nobel Laureate Eugene Fama and well-known scientist Kenneth French when both were professors at the University of Chicago. As a result of poor performance of CAPM, Fama and French created three factor model to help in filling the gap left by CAPM (Fama and French 2015). They stated in their study that the irregularities which are associated with CAPM are caught by the three element model. The three component model were created on the premise of the way that normal excess portfolio returns are ordinarily sensible to the three factor model in specific (Jondeau & Zhang 2013). Features of the Fama and French three factor model are;

  1. The value in owning out-of-support stocks that have alluring valuations. Esteem stocks are organizations that have a tendency to have lower income development rates, higher profits and lower costs contrasted with their book esteem (Jondeau & Zhang 2013). Over the long haul, esteem stocks have produced higher returns than development stocks, which have higher stock costs and income, but in light of the fact that esteem stocks have higher risk

  2. Beta: a measure of unpredictability of a stock in contrast with the business sector overall; the risk of owning stocks when all is said in done; or a venture’s affectability to the business sector (Jondeau & Zhang 2013). A beta of 1 implies that the security will move with the business sector. On the off chance that the beta of any speculation is higher than the business sector, then the normal instability is likewise higher and the other way around (Jondeau & Zhang 2013).

  3. Portfolio Size: The additional risk in little organization stocks. Little organization stocks (little top) tend to act uniquely in contrast to huge organization stocks (huge top). Over the long pull, little top stocks have produced higher returns than substantial top stocks; be that as it may, the additional arrival is not free since they have higher risk (Sharifi, Ohadi & Monjazeb, 2014).

QA5. Empirical test for Fama and French three factor model

The test is done using excess returns on the stock. The difference between the Excess return on a stock of action of high-book to market stocks and the over excess return on a game plan of low book to market stock. The data used is from 1980 to 2009 that is a thirty year period and from two industries which is still manufacturing and technology. Important three factor model characteristics is the regression equation which is stated as:

FINANCIAL MODELLING coursework  4 The result output of the data is in the appendix 5 in the excel file. For this SMB and HML is added from the initial CAPM model which excludes them. First, for the manufacturing industry, the model fitness is tested by the R-squared. The r-square for the manufacturing industry is 0.821117 and that of technology is
0.828339 indicating high fitness of the model (Fama &French 2015).The three variables that is (Rmt-Rft), SMB and HML has p-value of 3.2E-57, 5.55E-10 and 2.5E-81 respectively. All the p-value is less than 0.05 hence they are statistically significance and we are rejecting null hypothesis. For manufacturing in table 1 appendix 5, the beta coefficient are 0.755554, 0.471694 and 1.057159 for SMB, HML and Mkt-RF respectively (Jondeau & Zhang 2013).

For the technology industry and for the manufacturing, Rmt-Rft), SMB and HML are having p-value of 2E-93, 5.78E-14 and 3.43E-46 respectively and they are less than 0.05 hence significance. The coefficient beta for SMB is 1.256517 indicating high volatility hence high risk. For the HML the beta >0 and is -0.43791 indicating risk free portfolio while Mkt-Rf 1.161159 showing high risk market portfolio (Fama &French 2015).Therefore we can conclude that some level of riskless received in analysis, three factor model has not achieved the state of no risk is portfolio diversification

SECTION B: Wage Analysis

B1. Prepare a table of ‘descriptive statistics’

Seven variables were examined in the study, they incorporate Wage, Education, Experience, Gender, Age, Marital status and Union. The scientist completed illustrative investigation in SPSS and the outcomes are appeared to a limited extent 2 Appendix 1 table 1 in the exceed expectations document. From the examination, age is having the most noteworthy mean of 36.811 took after by involvement with 17.8221 union has the least mean of 0.179775. The investigation additionally gives standard deviation of the variables with experience the most astounding with 12.37971 took after by age 11.72657 with 11.72657 then wage with 7.708645. Union then again gives the littlest standard deviation of 0.38436. Least ranges from 0 and greatest is 66.75. This can be shown below

Table 2.0: Descriptive statistics

Descriptive

Education 

Experience 

Gender 

Married 

13.01872659

0.458801

36.83333

0.655431

0.179775

Standard Error

0.333586

0.113178243

0.535722

0.021584

0.507458

0.020584

0.016633

0

0

0

0

Standard Deviation

7.708645

2.615372628

12.37971

0.498767

11.72657

0.475673

Sample Variance

59.42321

6.840173985

153.2572

0.248769

137.5125

0.226265

0.147733

Kurtosis

4.991768

0.840774992

-0.38095

-1.97993

-0.58079

-1.57561

0.800367

Skewness

1.697286

-0.203677595

0.687758

0.165822

0.548297

-0.65598

1.672538

0

0

0

0

7228.275

Confidence Level (95.0%)

0.655304

0.222330138

1.052386

0.996864

0.040436

0.032674

B2. Regression model 1 is:

FINANCIAL MODELLING coursework  5

The regression output is in the Appendix B2

FINANCIAL MODELLING coursework  6

The regression output is in the appendix B2 in excel. From the result, R-squares is 0.14586446 indicating that the model is fit and conclusion on the relationship of the variables can be reached this is shown in the above graph. On the significance level, p-value = 5.47E-20 < 0.05 therefore, it is statistically significance. The coefficient is of education is 1.125691 implying that one more year of education increases an individual salary by 1.125691 and also there is positively relationship between education and individual salary. From the result we can right the predictive equation as

Wages I = -1.11897 +1.125691educ +Ɛ

This is the predictive equation of education on wage of an individual.

B3. Regression model 2 is:

FINANCIAL MODELLING coursework  7

Adding experience to the first model, the researcher intended to know how education and experience influences an individual wages. The model two is written as:

FINANCIAL MODELLING coursework  8 …………………………… (2)

The regression output are presented in the appendix B3 in excel. From the appendix, it can be noticed that the model is perfectly fit since its R-squared is 0.202025 indicating that of 20% of the variables were analysed in the regression analysis. The fit model line can be represented in the figure below;

FINANCIAL MODELLING coursework  9

On the significance level of the study, education has p-estimation of 5.56E-27 while experience p-value is 1.89E-09 the p-value is < 0.05 accordingly at significance level of 95%, the examination is factually critical. The coefficient of the study gives 1.388 and 0.1576 for education and experience respectively. This demonstrate 1 year of training builds compensation by 1.388 and 1 more year for experience expands compensation by 0.1576. Hence the prescient condition can be given as

Wage= -7.35672 +1.388 education + 0.1576 experience

B4. Regression model 3 is:

FINANCIAL MODELLING coursework  10

In the regression we add gender as the third variable. The regression output is shown in appendix B4. The model gives R-squared of 0.253158 indicating that the model is fit for the study. The scattered plot is shown below

FINANCIAL MODELLING coursework  11

The p-values of education, experience and gender is gives as 3.28E-29, 3.19E-11 and 3.19 E-09 respectively. The p-value of the three variables are < 0.05 meaning the variables are statistically significance at significance level of 95% and null hypothesis is rejected. The relationship of the three variables are also shown at the appendix B4 with education, experience and gender coefficients as 1.41076, 0.169951 and -3.50645 respectively. It can be seen that both experience and education positively influence individual wage while gender negatively influence.

B5. Correlation matrix

EDUCATION

EXPERIENCE

EDUCATION

0.381922

EXPERIENCE

-0.35268

-0.20537

0.002031

0.176967

-0.15002

0.977961

0.079179

0.100579

-0.03552

0.011225

0.278947

0.161766

-0.02389

0.117926

-0.15703

0.119466

0.093164

The correlation matrix of all of the variables was analysed and results shown above, and use the matrix to discuss the importance of each variable for wages as well as the relationships between the variables. From the above table the relationship between wage and the other variables can be seen clearly with all variables positively related with wage except gender which is negatively related. All variables that is experience, Age, married and union are negatively related with education except gender which is positively related. Experience on the other hand is positively correlated with gender, age, married and union. From the correlation matrix above, gender is positively correlated with age and marital status while negatively related with union. Age on the other hand is positively correlated with marital status and union and lastly married is positively related with being in union (Chang, Christoffersen and Jacobs 2013). These factors influence the wage of an individual the difference is that the scale which they influence vary from one variable to another.

B6. Regression model 4 is

FINANCIAL MODELLING coursework  12(4). The regression results are shown in appendix B5 in excel. From the regression result in appendix 5, the R-square is 0.266 indicating that the model is perfect fit for making conclusion. The p value of the variables include education which is 0.2190 > 0.05 hence education is not statistically significance in explaining the effect of the wage in this model, furthermore, experience gives a p-value of 0.625681> 0.05 hence is not statistically significance. Gender on the other hand gives a p-value of 5.88E-08< 0.05 hence is statistically significance at 95% significance level, age p-value is 0.691697 which is >0.05, not statistically significance, marital status gives a p-value of 0.259017 >0.05 indicating that it is not statistically significance and lastly union which gives P-value of 0.005088 <0.005 indicating that it is statistically significance at 95% significance level. In this case we can re define the model that is when we can make conclusion.

Reference

Barberis, N., Greenwood, R., Jin, L. and Shleifer, A., 2015. X-CAPM: An extrapolative capital asset pricing model. Journal of Financial Economics, 115(1), pp.1-24.

Chang, B.Y., Christoffersen, P. and Jacobs, K., 2013. Market skewness risk and the cross section of stock returns. Journal of Financial Economics, 107(1), pp.46-68.

Correa, R., Lee, K.H., Sapriza, H. and Suarez, G.A., 2014. Sovereign credit risk, banks’ government support, and bank stock returns around the world. Journal of Money, Credit and Banking, 46(s1), pp.93-121.

Cremers, M., Halling, M. and Weinbaum, D., 2015. Aggregate Jump and Volatility Risk in the Cross‐Section of Stock Returns. The Journal of Finance, 70(2), pp.577-614.

Fama, E.F., 2015. Cross-Section Versus Time-Series Tests of Asset Pricing Models. Fama-Miller Working Paper.

Jondeau, E. and Zhang, Q., 2013. The Driving Force for Stock Market Skewness: A Systematic Downside Risk Approach to Forecast Market Movements.

Sharifi, M., Ohadi, F. and Monjazeb, M.R., 2014. The Relationship between Stock Risk and Return Using the Consumption Based Capital Asset Pricing Model (C-CAPM) in the Food and Pharmaceutical Industries. Asian Journal of Research in Banking and Finance, 4(5), pp.90-103.