By:

Financial Modeling: Stock Market

Foundation Course-

Department of:

15th May 2016

Section A

A1. Theoretical Assumptions and implications of Capital Asset Model (CAPM)

As stated by Sharpe (1964) and Lintner (1965), Capital Asset Model (CAPM) is a model that describes the relationship between risk and expected return and has a number of assumptions that investors have to be take into consideration while trading in the stock market. These assumptions are as follows:-

CAPM assumes that investors have preference for more returns as compared to less return thus they tend to be risk averse so as to maximize their return output. Investors while trading in the stock market tend to be risk takers as long as the anticipated returns output will be as high as possible (Dempsey 2013).

Investors can always borrow and lend at risk free rate; although this assumptions is unattainable in reality, it is often believed that the rate at which individual investors borrow funds is never prone to any sort of risks (Dempsey 2013).Therefore, the lowest required return tends to be slightly lower than what the model calculates

There are always no market related frictions such as costs for doing transactions, taxes or even restricted short-selling. While trading in the stock market, investors do not take into account other costs associated with the stock trading, for instance, costs such as advertisement expenses, administrative expenses and tax expenses among others are often assumed (Zabarankin, Pavlikov and Uryasev 2014).

It is always assumed that investors have accessibility to all the information related to stock trading, which is, they can easily make decisions as to when to buy and sell their stocks in the market (Zabarankin, Pavlikov and Uryasev 2014).

A2. The Extent to which a breach of the assumptions invalidate the CAPM model

As a result of the failure of CAPM in empirical tests, its application is often considered invalid in the following ways:-

Based on the model’s assumptions of the probability belief that active and potential investors tend to be in agreement with the allocation of returns. However, there is always a conflicting possibility in that active and potential investors’ expectations are biased hence causing the market prices to be inefficient. Therefore, psychological assumption such as overconfidence-based asset pricing model should be used in addition to CAPM (Gospodinov, Kan and Robotti 2014).

CAPM fails to adequately illustrate the variation in the stock market, for instance, according to the empirical studies that have been undertaken, it has been confirmed that low beta stocks may offer absolutely higher returns than the model’s prediction (Elbannan 2015).

With the model’s assumption that given certain level of expected returns, active and potential investors tend to prefer higher risk (high variance) to lower risks and conversely with a given level of risk will be pleasant with higher returns as compared to lower returns, it does not give adequate consideration to those active and potential investors who have no problem with lower returns at high risks (Ruffino 2014).

CAPM’s assumption that all the active and potential investors will take into consideration all their existing assets and optimize them in one portfolio, has an absolutely sharp contradiction to those portfolios that are held by individual investors (Ruffino 2014). This is due to the fact that, traders tend to have fragmented portfolios or even multiple portfolios thus one portfolio may not give the true picture of the expected returns realized by an investor in the stock market.

A3: Empirical test of the CAPM:

Using the excess return model: By:

Test: By: 1

For the regression result for the first model which runs from the year 1980 to 2009 that is a panel data for 30 years. For the manufacturing industry,

Table 1.1: Model Summary (1980-2009)

Manufacturing

Multiple R

0.811292

0.777144

0.658195

0.603952

Adjusted R Square

0.602846

Standard Error

3.881782

Observations

From table 1.1, the r-square for manufacturing is 0.658195 while that for shop is 0.602846 > 0.1 hence the model is fit and good for analysis.

The significance level of the market portfolio using manufacturing and shop industry portfolio are shown in appendix 1 and extract are shown in the table 1.2 below

Table 1.2: Coefficient analysis for manufacturing and shop (1980-2009)

Coefficients

Standard Error

Manufacturing

Intercept

0.189993

0.184692

1.028703

0.304314

1.049882

0.039986

26.25607

1.82E-85

Coefficients

Standard Error

Intercept

0.206011

0.402748

0.687374

1.042133

0.044602

23.36518

5.37E-74

From the results in table 1.2 above, the p-value for manufacturing is 1.82E-85< 0.05 while for shop is 5.37E-74 < 0.05 hence statistically significance and leading to rejection of null hypothesis of Test:By: 2

The market beta for manufacturing is 1.049882 while that for shop 1.042133 from table 1.2 above. Since the market beta is greater than one hence risky portfolio.

For the year 1990-1999 the model summary are shown below

Table 1.3: Model summary 1980-1990

Manufacturing

Multiple R

0.823697

0.678477

0.730631

Adjusted R Square

0.675753

0.728349

Standard Error

3.423918

2.939456

Observations

From the analysis, the R-squared showed 0.678477 and 0.730631 for manufacturing and shop respectively. The model is fit since R-square is greater than 0.1 in both cases. For significance level and beta coefficient the results are shown in the table 1.4 below

Table 1.4: regression results (1980-189)

Manufacturing

Coefficients

Standard Error

Intercept

0.069462

0.315867

0.219909

0.826322

1.015103

0.064329

15.77985

7.47E-31

Coefficients

Standard Error

Intercept

-0.07943

0.271174

-0.29291

0.770107

0.988024

0.055227

17.89026

From the results in table 1.4 above, the p-value for manufacturing is 7.47E-31< 0.05 while for shop is 2.1E-35 < 0.05 hence statistically significance and leading to rejection of null hypothesis of Test:By: 3

On the other hand, the market beta for manufacturing is 1.015103 while that for shop 0.988024 from table 1.4 above. Since the market beta is greater than one for the manufacturing, its confirms that the portfolio tends to be risky however for the shop the beta is less than one thus favorable

The third empirical review is analysis of the monthly returns for the next 10 years from the year 1990-1999. The SPSS results are shown in appendix 3.

Table 1.5: Model fit 1990-999

Manufacturing

Multiple R

0.705692

0.523799

0.498001

Adjusted R Square

0.519764

0.493747

Standard Error

3.266003

3.772581

Observations

The r-square shows that manufacturing is 0.523799 and shop is 0.498001 > 0.1 hence model is fit. For significance level, the results are shown below

Table 1.6: Regression results (1990-1999)

Manufacturing

Coefficients

Standard Error

Intercept

0.308635

-0.64252

0.521784

0.854563

0.075009

11.39274

9.81E-21

Coefficients

Standard Error

Intercept

0.356506

-1.35819

0.176993

0.937438

0.086644

10.81944

2.26E-19

From the results the p-value is 9.81E-21<0.05 for manufacturing and shop is 2.26E-19< 0.05 hence statistically significance. The coefficient gives 0.854563 for manufacturing and 0.937438 for shop. Though beta is less than 1 in both cases, it is still risky hence fulfilling CAPM theory that portfolio cannot be free from risk.

Lastly, we empirically analyses the data from the year 2000 to 2009. From the results we have in excel appendix 4

Table 1.7: Model fit 2000-2009

Manufacturing

Multiple R

0.778492

0.870638

Adjusted R Square

0.602712

0.755959

Standard Error

7.005355

3.430541

Observations

From the analysis of the data from 2000-2009, the R-squared showed 0.60605 and 0.75801 for shop and manufacturing respectively. Therefore model is fit since R-square is greater than 0.1 in both cases.

Table: 1.8 Regression output 2000-2009

Coefficients

Standard Error

Intercept

0.961573

0.313311

3.069073

0.002664

0.065384

19.22561

Coefficients

Standard Error

Manufacturing

Intercept

0.832625

0.639798

1.301388

0.195661

1.798919

0.133517

13.47333

1.27E-25

As indicated in table 1.8 above, the p-value for manufacturing is 1.27E-25< 0.05 while for shop is 3.7E-38 < 0.05 hence statistically significance and hence null hypothesis of Test:By: 4
should be rejected

The market beta for manufacturing is 1.798919 whereas that for shop 1.25704 as shown in table 1.8 above. Since the market beta is greater than one, the portfolio is therefore risky.

A4.The background and important features of the Fama French three factor model

As stated by Foye, Mramor and Pahor (2016), The Fama-French three-factor model is model that was designed by Eugene Fama and Kenneth French to illustrate the stock returns in the stock market.

The two scholars came up with the following three factors to describe the stock returns:-

The Company size

The Company Price to Book ratio

The Market Risk

According to Fama and French analysis, two classes of stocks tend to perform better in the stock market than the market itself as a whole. In their in depth analysis they separated stock returns into three different risk factors as indicated below:-

Beta: This states the volatility of stock as compared to the market as a whole, the risks associated with owning stocks or even the sensitivity of investment in the stock market. According to Fama and French, a beta of 1 would imply that the security will sell off as the market expands, Likewise, if the beta associated with a particular investment is higher than the market, then the anticipated volatility will be high as well (Foye, Mramor and Pahor 2016).

Size: The smaller company stocks (small caps) often act differently as compared to larger companies’ stocks (large cap), therefore in the long run, small-cap stocks tend to generate higher returns as compared to large-cap stocks although they are prone to higher risks than large companies (Shi, Dempsey and Irlicht 2015).

Value: There are values stocks associated with companies that have lower earnings growth rate, higher dividends as well as lower prices as compared to their book value (Shi, Dempsey and Irlicht 2015). In the long run, value stocks tend to generate high return output than growth stocks which have higher stock prices and earnings instead. Thus, value stocks are favorable despite having higher risks

Therefore, Fama-French Three-Factor Model as an advancement of the CAPM is an appropriate model that should be used to determine the ideal value of the expected returns.

A5: Empirical evidence for three factor model

Table: 1.9 Regression output

Manufacturing

Multiple R

0.906155

0.883415

0.821117

0.780422

Adjusted R Square

0.778572

Standard Error

2.898465

Observations

From the results of the analysis in table 1.9 above, the R-squared showed 0.821117 and 0.780422 for manufacturing and shop respectively. This therefore confirms that the model is fit since R-square is greater than 0.1 in both cases

Table: 2.0 Regression output

Coefficients

Standard Error

Manufacturing

Intercept

0.362198

0.135627

2.670538

0.755554

0.044437

17.00288

6.97E-48

0.471694

0.046806

10.07773

3.52E-21

1.057159

0.031359

33.71181

7.7E-113

Coefficients

Standard Error

Intercept

-0.17336

0.156371

-1.10863

0.268339

0.849885

0.051233

16.58853

3.43E-46

0.422361

0.053964

7.826651

5.78E-14

1.024926

0.036155

28.34813

As showed in table 0.2 above, the p-value for manufacturing is 7.7E-113< 0.05 while that for shop is 2.6E-93 < 0.05 hence statistically significance and hence null hypothesis of Test:By: 5
should be rejected

The market beta for manufacturing is 1.057159 whereas that for shop 1.024926 as shown in table 2.0 above. Since the market beta is greater than one, the portfolio is therefore risky.

Section B: Wage determination

B1: Descriptive analysis

Descriptive statistic can be described as the analysis of data that assist in describing or summarizing the meaningfulness of the data in way such that it can be easily understood. From the wage data, we have classified the data and summarizes their standard deviation, mean, maximum, Skewness and mode, median among other variables. In Appendix Q3B1, it shows the descriptive output of the data and the summary of the results. From the result age has the highest mean of 36.83333 while the highest maximum value is in wage and is around 66.75.

B2: First Model analysis

The regression result showing the relationship between wages and education is shown in Appendix B2 part 2 in excel. The regression model equation used in analyzing this data is given by;

By: 6

The analysis gives the R-squares is 0.14586446 representing that the model is fit as proposed by XX that R-square above 0.1-0.5 is good for analysis hence the fitness of the model. The resultant fit can also be presented in scattered diagram below.

By: 7

It is important also to investigate the significance level of the data used in the analysis and this has been done using p-value at significance level of 95%. From the results, the, P-value is 5.47E-20 < 0.05 indicating that the result is statistically significance at the significant level of 95% hence null hypothesis is rejected. XX states that if the p-value of a data is statistically significant, then a conclusion or effect can be established between the variables and is good to reject null hypothesis. The coefficient of education is 1.125691 showing that one more year of education increases an individual salary by 1.125691 and also there is positively relationship between education and individual salary, the relationship between the two that is wage and education is positive.

B3: Second model adding experience

The experience of people have influence on wage and education also is used to investigate the effect. The regression model used is;

By: 8

The spss output result is shown in appendix B3, it can be seen that the model is perfectly fit since its R-squared is 0.202025 which is a good model. Figure below shows the fit model

By: 9

Using signifance level at 95%, the p-value shows that, education has p-value of 5.56E-27 while experience p-value is 1.89E-09 the p-value is < 0.05 hence rejecting null hypothesis due to statistical significance. The coefficient of the study gives 1.388 and 0.1576 for education and experience respectively. This indicate that 1 year of education increases salary by 1.388 and 1 more year for experience increases wages by 0.1576

The new equation can be given as;

Wage= -7.35672 +1.388 education + 0.1576 experience

B4: Model three adding Gender

To establish the role of gender in individual wage, gender was added. The model equation is given by,

By: 10

The regression output is given appendix B4 in excel. R-squared of 0.253158 indicating that the model is fit since it is more than 0.1 and can be shown in the figure below:

By: 11

From the regression output, the p-values of education, experience and gender is given as 3.28E-29, 3.19E-11 and 3.19E-09 respectively. The p-value of the three variables are < 0.05 indicating that the variables are statistically significance at significance level of 95% and null hypothesis is rejected. The coefficients are 1.41076, 0.169951 and -3.50645 respectively for education, experience and gender. Education and experience is positively related to the wage that increase in either increases wage with proportional amount.

B5 Correlation analysis

Correlation coefficient helps in measuring the linear relationship between variables. In Appendix B5 it shows the results of the correlation analysis of these variables. From the result 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.

B6: Model four: Age, Marital status and Union

Factors like marital status, age and Union influence wage. These are represented in the model below

By: 12

The regression output is shown in appendix B6 in excel. From the regression output result in appendix B6, the R-square is 0.266 indicating that the model is perfect fit and over 26% of the total variables were included in the analysis.

By: 13

The regression result from excel shows that p value of the variables include 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.

B7: Important factors and problems that need to be considered when designing a financial model.

Financial related modeling is one of the zones which needs much consideration since is one zone which helps speculators and nation in general with the best choice to make before focusing on a specific venture. Utilizing the idea of Occam’s razor which expresses that «Substances ought not to be duplicated pointlessly. In like manner the monetary model additionally ought to have particular attributes. They include:

  1. The model being produced must have the capacity to mirror this danger profile of the advantages and the conceivable results of the model being finished

  2. The model ought to be very much archived, it legitimacy must be past any sensible verification and sufficiently thorough.

  3. When one is outlining the model, the technique you will test it with must be considered

  4. When one is outlining the model, the technique you will test it with must be viewed as Model must be basic and straightforward

  5. The standard communicates that one should not to make a bigger number of suppositions than the base required. This rule is every now and again called the standard of niggardliness. It underlies all test exhibiting and theory building

  6. Model must be basic and straightforward

  7. Conservation of convexity is basic in the linearity best, in any occasion for objectives

  8. Model ought to have less presumption as could reasonably be expected as expressed in Occam’s razor hypothesis. The hypothesis is an intelligent guideline credited to the medieval rationalist William of Occam (or Ockham).

  9. When one is outlining the model, the technique you will test it with must be viewed as Model must be basic and straightforward

  10. The standard communicates that one should not to make a bigger number of suppositions than the base required. This rule is every now and again called the standard of niggardliness. It underlies all test exhibiting and theory building.

  11. The model ought to be very much reported, it legitimacy must be past any sensible confirmation and sufficiently thorough.

References

Dempsey, M., 2013. The capital asset pricing model (CAPM): the history of a failed revolutionary idea in finance. Abacus, 49(S1), pp.7-23.

Elbannan, M.A., 2015. The capital asset pricing model: an overview of the theory. International Journal of Economics and Finance, 7(1), p.216.

Foye, J., Mramor, D. and Pahor, M., 2016. A Respecified Fama French Three Factor Model for the Eastern European Transition Nations. Available at SSRN 2742170.

Gospodinov, N., Kan, R. and Robotti, C., 2014. Misspecification-robust inference in linear asset-pricing models with irrelevant risk factors. Review of Financial Studies, 27(7), pp.2139-2170.

Ruffino, D., 2014. A robust capital asset pricing model. Available at SSRN 2355950.

Shi, X., Dempsey, M. and Irlicht, L., 2015. Fundamental indexation and the Fama-French Three Factor Model: Risk assimilation or stock mispricing?. Journal of Investment Management, 13(4), pp.57-70.

Zabarankin, M., Pavlikov, K. and Uryasev, S., 2014. Capital asset pricing model (CAPM) with drawdown measure. European Journal of Operational Research, 234(2), pp.508-517.