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Financial modeling
Financial Modeling
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Table of Contents
3Assumptions and implication of Capital Asset Pricing Model 1.0
4Validity of the CAPM assumptions and breach of assumption invalidate the CAPM model 1.2
4Empirical test of the CAPM 1.3
6background and important features of the Fama French three factor model 1.4
7Empirical test of the Fama French three factor model 1.5
9Section two: Factors influencing wage
9Descriptive statistics 2.0
92.1: Model 1
102.2 Model two
112.3 Model three
122.5 Model five
132.6 Characteristics of a good model
15Reference
1.0 Assumptions and implication of Capital Asset Pricing Model
The first assumption under CAPM is that 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 (Ai, Croce and Li, 2013).
Second assumption is that it is common that all the investors wants or plan to invest over the same time horizon (Barberis, et al., 2015). That is to say the abstracts from the heterogeneity in investors which are risk averse have distinct time preference than the ones who are risk tolerant. It help in addressing the issue of deviations from the CER model (Dempsey 2013).
The third presumption of the CAPM is that No distortionary charges or exchange cost which is an unmistakably a false suppositions that is obligation versus value (Chang, Christoffersen and Jacobs 2013). Fourth suspicion is that all speculators can acquire or loan in the business sector at the same hazard free rate. Besides, this is a false suppositions yet one can consider zerobeta adaptation of CAPM with short deals. The fifth supposition is that of inclinations. That is speculators just think about the normal return like and difference which is abhorrence (Dempsey 2013).This is in steady with the portfolio hypothesis and the CER model under the typicality.
To start with suggestion is that the financial specialists will utilize Markowitz calculation to decide same arrangement of productive portfolios. Besides, the danger unwilling speculators will put a large portion of their riches in danger free resources. That is to say hazard tolerant speculators will have the capacity to put their riches in unsafe resources and in balance, not net obtaining. Another critical ramifications is that there is an unequivocal risk return exchange off for each individual stocks (Zabarankin, Pavlikov & Uryasev 2014). The CAPM show ordinarily determines anticipated that profits would be utilized as a part of the capital planning assessment and direction. Also, the risk premium on an individual security is typically a component of its deliberate risk, measured by the covariance with the business section. Last implication is that the tangency portfolio = market portfolio and implies positive weights on all assets in tangency portfolio even for the short sales (Chang, Christoffersen and Jacobs 2013).
1.2 Validity of the CAPM assumptions and breach of assumption invalidate the CAPM model
The CAPM anticipate that exchanging will be costless so theories are esteemed to all fall on the capital business area line. If not, a couple endeavors would glide underneath or increasingly the line — with trade costs discouraging clear swaps (Sharifi, Ohadi and Monjazeb 2014). Be that as it may, we understand that various endeavors, (for instance, securing a little business) incorporate gigantic trade costs. Possibly the capital business division line is really a band whose width reflects exchanging costs. By and large, speculators hold very much broadened portfolio and this is done to guarantee that the financial specialists has shed out some danger emerging from the firm. In this manner, we can infer that those given portfolio are having high odds of associating with the CAPM model.
In his study, Brennan showed that even if the investors had distinct individual tax rate, still the new version of CAPM will be held constant (Sharifi, Ohadi & Monjazeb 2014). In another study, Mayer’s showed that a new version of CAPM will be held in situations where investors were allowed to trade in nontraded assets such as human capital.
The CAPM accept investors have the same convictions about expected returns and risks of accessible speculations (Fama & French 2015). However, we realize that there is huge exchanging of stocks and bonds by speculators with various desires. We likewise realize that speculators have diverse risks inclinations. Once more, it might be that the capital business sector line is a fluffy amalgamation of a wide range of financial specialists’ capital business sector lines (Fama & French 2015).
1.3 Empirical test of the CAPM
In circumstances where the return on investments on a given security portfolio is more than the benchmark or the index of a similar risk, it is called excess return (Correa, Sapriza and Suarez 2014). In empirical test of CAPM model, we uses the data from two industries that is from technology industry and shops. Eight regression were done using the excess asset return model
The hypothesis tested in this case was Test: _{}
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 below. For the first industry which is the technology and the second industry which is Shops. The results for technology industry Rsquared 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 pvalue of the technology is 9.23E69 < 0.05 therefore at significance level of 95%, the model is statistically significance. The coefficient that is alpha (_{}) = 14837 while beta_{}. This is approval of CAPM model that it is not possible to remove all risk in the any portfolio even if you diversify. Beta is greater than 0 indicating that it is high risk portfolio. For the second industry that is shop, in appendix 1 Table 2 in excel file. From Appendix 1 Table 2. Rsquared is 0.603952 indicating that model is good as stated by Fama and French (1993) that a Rsquared between 0.100.15 is enough for marking decision therefore this one is perfect since it is much above 15% mark. The Pvalue is 5.37E74< 0.05 meaning that at 95% significance level, the results are statistically significance. The coefficient of regression results for shops gives alpha to be (_{}) = 0.0829704 while beta 1.0421 this is further approval of CAPM theory states that the assets cannot be fully diversified from the risk hence high risk from this analysis.
In order to investigate the theory of CAPM further, we divided data into 10 years period and run the regression analysis separately for the three periods and for the two industry. For the first 10 years, is in the Appendix 2 and runs from 1980 to 1989 period.
Table 1 in appendix 2 gives regression result of technology industry for the first 10 years. The model is fit since Rsquared is given as 0.709073 while the results are statistically significance at significance level of 95% since Pvalue is 2E33 < 0.05
The beta coefficient is 1.278496 showing high risk portfolio. In table 2 of appendix 2, Rsquared is 0.730631 indicating model which is fit while Pvalue is 2E35 < 0.05 hence statistically significance. The beta value further shows high risk portfolio and only risk averse investors would wish to take chances, it shows beta of 0.988024 though is not as risky as the initial cases since the beta less 1.
The researcher further investigated the second time period of the two industry which is from the year 19901999. This is presented in table 1 & 2 in the appendix 3 in excel file. The two models are fit since they have are square which is greater than 0.15 and that is 0.462999 and 0.498001 for technology and shop respectively. The coefficient beta for technology and shop industry is 1.287678 and 0.937438 respectively. This is an indication of high volatile technology industry compared to shop. It is worth noting that though shop assets are less volatile, they are not free from risk hence still supporting the theory of CAPM which alludes that the diversification of portfolio does not shield us away from risk (Fama & French 1997).
In the last period in appendix 4 and table 1 and 2 contains regression output for technology industry and shop for the period of 2000 to 2009. The two models that is technology and shop are fit with high rsquare of 0.60605 and 0.62482 respectively. The beta of technology industry from table 1 appendix 4 is 1.798919 while for the shop is 1.213195 indicating high risk within the two portfolio. Therefore, we can conclude that the results of the empirical evidence is a proof of CAPM position that in practical sense, there is not diversification which can 100% remove risk from asset (Fama & French 1997).
1.4 background and important features of the Fama French three factor model
The FamaFrench ThreeFactor Model is a technique for clarifying the risks and return of stocks. It was outlined by Nobel Laureate Eugene Fama and eminent scientist Kenneth French when both were educators at the University of Chicago. What makes the FamaFrench ThreeFactor Model so exceptional is that it not just uncovers the essential components that drive stock return additionally gives a methodology to utilizing those elements as a part of your portfolio for a conceivably higher expected long haul return (Fama & French 2015)
Numerous researchers utilizes the CAPM model, the covariance of return portfolio with the business sector portfolio come back to clarify the minor departure from the excess portfolio return. All things considered, in an observational study embraced by Fama and French (1992) demonstrates that the covariance of the arrival portfolio and the business sector return is not ready to completely clarify the progressions on the portfolio over excess returns. They discovered that the covariance have extremely negligible or no force at all as far as clarifying the crosssectional variety in resource/value return.
The three main characteristics is the three risk measurements which include;
Beta: a measure of unpredictability of a stock in contrast with the business sector overall; the danger of owning stocks when all is said in done; or a venture’s affectability to the business sector (Dempsey 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 (Dempsey 2013).
Size: The additional danger in little organization stocks. Little organization stocks (little top) tend to act uniquely in contrast to huge organization stocks (huge top). Over the long haul, 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 danger (Dempsey 2013).
Value: The value in owning outofsupport 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 (Dempsey 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 danger.
1.5 Empirical test of the Fama French three factor model
We can use the excess return model to empirically test the Fama and French three factor model. This data will be from 1980 to 2009 that is a thirty year period and from two industries which is still shop and technology. Important three factor model characteristics is the regression equation which is stated as:
For this SMB and HML is added from the initial CAPM model which excludes them. This is added to ensure that actually the risk aspect of the data and validity is captured. Appendix 5 table 1 and 2 shows the regression results from the data. First, for the technology industry, the model fitness is tested by the Rsquared. The rsquare for the technology industry is 0.828339 and that of shop is 0.780422 indicating high fitness of the model. The three variables that is (RmtRft), SMB and HML has pvalue of 3.2E57, 5.55E10 and 2.5E81 respectively. All the pvalue is less than 0.05 hence they are statistically significance and we are rejecting null hypothesis below;
_{} , _{} ,_{} ,_{}
For the technology industry and for the shop, RmtRft), SMB and HML are having pvalue of 2.6E93, 5.78E14 and 3.43E46 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 MktRf 1.161159 showing high risk market portfolio (Fama &French 2015). And for the shop SMB beta is 0.849885, HML beta 0.422361 while that of MktRF is 1.024926. In conclusion, though there are some level of riskless received in analysis, three factor model has not achieved the state of no risk is portfolio diversification.
Section two: Factors influencing wage
2.0 Descriptive statistics
Seven variables were analyzed in the study, they include Wage, Education, Experience, Gender, Age, Marital status and Union. The researcher carried out descriptive analysis in SPSS and the results are shown in part 2 Appendix 1 table 1 in the excel file. From the analysis, age is having the highest mean of 36.811 followed by experience with 17.8221 union has the lowest mean of 0.179775. The analysis also gives standard deviation of the variables with experience the highest with 12.37971 followed by age 11.72657 with 11.72657 then wage with 7.708645. Union on the other hand gives the smallest standard deviation of 0.38436. Minimum ranges from 0 and maximum is 66.75. The result of descriptive analysis is presented in appendix 1 below.
2.1: Model 1
In the part 2 Appendix 1 table 2 in excel file, the regression output for the first model is give. It investigated the effect of education on an employee wage using the equation;
_{} …………………………………………… (1)
The regression output is in the appendix 2 below.
From the result, Rsquares is 0.14586446 indicating that the model is fit and conclusion on the relationship of the variables can be reached. This can be represented in the graph below
The, Pvalue is 5.47^{E20} < 0.05 meaning the result is statistically significance at the significant level of 95%. From the study, 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
2.2 Model two
If experience is added to the first model, the researcher intended to know how education and experience influences an individual wages. The model two is written as:
_{}…………………………… (2)
The regression result are in the part2 appendix 2. It can be noticed that the model is perfectly fit since its Rsquared is 0.202025 indicating that of 20% of the variables were analyzed in the regression analysis. The fit model line can be represented in the figure below;
On the significance level of the study, education has pvalue of 5.56E27 while experience pvalue is 1.89E09 the pvalue is < 0.05 therefore at significance level of 95%, the analysis is statistically significant. 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
Therefore the predictive equation can be given as
Wage= 7.35672 +1.388 education + 0.1576 experience
2.3 Model three
The third model which includes gender was developed. The model equation is given by,
The regression is in part 2 appendix 3 in excelThe model gives Rsquared of 0.253158 indicating that the model is fit since over 25% of the variables were included in the study.The pvalues of education, experience and gender is gives as 3.28E29, 3.19E11 and 3.19E09 respectively. The pvalue 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 4 with education, experience and gender coefficients as 1.41076, 0.169951 and 3.50645 respectively. Both experience and education positively influence individual wage while gender negatively influence.
2.4 Correlation analysis
The study further investigated the correlation between the factors influencing the individual wage. The correlation results is shown in excel part 2 appendix 4. The researcher intended to investigate the correlation of all of the 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. All these factors in one way or the other influence the wage of an individual the difference is that the magnitude which they influence vary from one variable to another.
2.5 Model five
Lastly we formulated the model including all the variables and the model is given as
(4)
The regression results are shown in appendix 5 in excel part 2. From the regression result in appendix 5, the Rsquare is 0.266 indicating that the model is perfect fit and over 26% of the total variables were included in the analysis. 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 pvalue of 0.625681> 0.05 hence is not statistically significance. Gender on the other hand gives a pvalue of 5.88E08< 0.05 hence is statistically significance at 95% significance level, age pvalue is 0.691697 which is >0.05, not statistically significance, marital status gives a pvalue of 0.259017 >0.05 indicating that it is not statistically significance and lastly union which gives Pvalue of 0.005088 <0.005 indicating that it is statistically significance at 95% significance level. Therefore we develop the new results with significance value and we get
Therefore, the new regression output can be given as
Coefficients 
Standard Error 

Intercept 
14.36573 
0.484336 
29.66065 
9.4E115 
2.85181 
0.658662 
1.79E05 

0.854716 
3.115935 
0.001933 
The conclusion is that change in gender influences age by 2.85181 while union increase wage by 2.66324.
2.6 Characteristics of a good model
A model can be described as a representation of the truth that catches «the substance» of reality. In choosing the model, the following factors should be considered include;

Length or the time frame of panning and division of choice stages in the model

Scenario generation (technique, risk components captured, stretching variable, size of situation tree) Objective measure and the risk function of the model

Application particular prerequisites (requirements)

Conservation of convexity is critical in the linearity best, in any event for imperatives

Model should have fewer assumption as possible as stated in Occam’s razor theory. The theory is a coherent rule credited to the medieval logician William of Occam (or Ockham). The standard expresses that one ought not to make a larger number of suppositions than the base required. This guideline is frequently called the standard of miserliness. It underlies all experimental demonstrating and hypothesis building.
In conclusion, in deciding on the model, it is advisable for us to look over an arrangement of generally equal models of a given wonder the least complex one. In any given model, Occam’s razor helps us to «shave off» those ideas, variables or develops that are not so much expected to clarify the marvel. By doing that, building up the model will turn out to be much less demanding, and there is less risk of presenting irregularities, ambiguities and redundancies.
Reference
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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.4668.
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.93121.
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.577614.
Dempsey, M., 2013. The capital asset pricing model (CAPM): the history of a failed revolutionary idea in finance? Abacus, 49(S1), pp.723.
Fama, E.F. and French, K.R., 1993. Common risk factors in the returns on stocks and bonds. Journal of financial economics, 33(1), pp.356.
Fama, E.F. and French, K.R., 1997. Industry costs of equity. Journal of financial economics, 43(2), pp.153193.
Fama, E.F. and French, K.R., 2015. A fivefactor asset pricing model. Journal of Financial Economics, 116(1), pp.122.
Fama, E.F. and French, K.R., 2015. A fivefactor asset pricing model. Journal of Financial Economics, 116(1), pp.122.
Fama, E.F. and French, K.R., 2015. International Tests of a FiveFactor Asset Pricing Model. FamaMiller Working Paper
Fama, E.F., 2015. CrossSection Versus TimeSeries Tests of Asset Pricing Models. FamaMiller 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 (CCAPM) in the Food and Pharmaceutical Industries. Asian Journal of Research in Banking and Finance, 4(5), pp.90103.
Zabarankin, M., Pavlikov, K. and Uryasev, S., 2014. Capital asset pricing model (CAPM) with drawdown measure. European Journal of Operational Research, 234(2), pp.508517.