# Quantitative methods used in CAPM theory

CAPM Theory and Related Literature

Capital Assets Pricing Model which is commonly referred to as CAPM is used to describe the relationship between methodological risk and the expected return for assets, especially stock. CAPM is used for setting prices of risky securities and producing the expected returns for assets given the risk involved the said assets and the cost of capital (Campbell et al., 2012). CAPM is calculated based on the formula ERi=Rf+Bi(ERm-Rf)

ERi represents the expected amount of income from an investment, Rf represents the Risk-free rate, Bi denotes the beta of the investment, ERm represents the assumed amount in the market that is to go back to business, and (ERm-Rf) is a representation of market risk premium. CAPM aims at a more practical approach as used by investors.

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Investors have the aim of getting their money in the required time in which the money is operational. The risk-free rate present in the CAPM computational formula is used to account for the value of the money

The investor has the goal of using fully the utility that is accompanied by wealth, not considering the wealth or rerun. The individual preferences are taken into account in the utility concept. While the beta of the potential investor is a way of looking at how risky the investment is as compared to the market prices. If a stock is riskier as compared to the market it will have a beta greater than one if the stock contains a beta lower than one the formula assumes it will reduce the risk of the portfolio. The main aim of the CAPM formula is to evaluate whether a stock is fairly valued when there are more risks over a particular time looking at the return in the market.

For the CAPM to hold there are some of the assumptions observed like the Investors have the same expectations of Risk and Return. This agreement helps the investors to have a similar forecast based on the results obtained in the market in terms of mean and variance. The other assumption is that the decision of investors is based on a rationale that depends on the risk and returns, the risk involved is measured by mean and variance. The investors will also get free access to the available information at no cost, and there is no loss of time. If it turns that the required information is not there on that required time the investor will get into a conclusion based on the expected return. The investors should have identical time horizons, which on common grounds is not applicable. However, there are developed models that give independent results that do not depend on the previous outcome in the years. In CAPM, the whole assets are fixed quantitatively, and all assets are can be sold and subdivided, this assumption implies that the rate at which assets can be converted into cash and the investors are not considered and there will be no issues which are not practical. For the proper computation of the Capital Assets Pricing Model, the following requirements should be met; the risk which is measured in terms of variance of returns. The risk has the components which include systems that are non-diversifiable and diversifiable, which is commonly referred to as unsystematic. The investor makes ensures that the assets are well distributed to reduce the risk, and for non-diversifiable, the investor uses the relevant market determinants to adjust their preferences. Under the state of equilibrium, which is achieved by assuming away all taxes and divisibility transactions are also assumed away.

Report of the Four Companies

The data which was obtained run from 1st October 2018-1stOctober 2019. The Beta value for national Grid Plc was -0.103 which means it has reduced risk in the portfolio. The t value for the same company is -1.640, and taking the significance level 0.05 the data implies that the risk the investors are taking is not such riskier this agrees with the beta value. The R squared of the same company is 0.007 which implies 0.7% of the returns which is not the best return. The company is categorized as an energy company.

For Royal Dutch Shell plc, the Beta value is -0.148 which means it has reduced risk in the portfolio. The t value for the same company is -2.361, and taking the significance level 0.05 the data implies that the risk the investors are taking is not such riskier this agrees with the beta value. The R squared of the same company is 0.022 which suggests 2.2% of the returns which is not the best return. The company is categorized as an energy company.

The same period which was considered for the energy industry was also taken by the financial industries. The first to be taken into consideration is Barclays Plc, and the Beta value is 0.32 which means it has reduced risk in the portfolio. The t value for the same company is 0.514, and taking the significance level 0.05, the data implies that the risk the investors are taking is somehow riskier and the investors can expect better returns. The R squared of the same company is 0.001 which sums up to 0.1% of the returns which is not the best return. Looking at this data there can be some of the assumptions that have been over-ruled since the t value is good. Looking into Morgan Stanley (MS), the Beta value is -0.87 which means it has reduced risk in the portfolio. The t value for the same company is -1.375, and taking the significance level 0.05 the data implies that the risk the investors are taking is not such riskier this agrees with the beta value. The R squared of the same company is 0.008 which adds up to 0.8% of the returns which is not the best return.

Even though the results have shown that some of the sectors are no good to venture into, the assumptions which hold for CAPM sometimes can be over-ruled thus further analysis has to be done.

Panel Data Regression

The fixed-effects model and random-effects model depend on the nature of the variables and their distributions. To categorize a variable as fixed or random, check the omitted variable in the model if one believes that no variable has been omitted or the variables are uncorrelated then the random effect is probably best. This will produce unbiased estimators and the standard error produced is minimum. If the model has omitted variables that are correlated, the result for fixed effects is the provision of bias for the omitted variable. The other way to determine is to look into the variability that exists between the subjects. The other factor that is considered is how often the data have to be looked into for the given period, considering the possibility of changing it over time. The fixed effects refer to the assumptions about the independent variables and that error distribution for the variables, the researcher is interested in only generalizing the results to experimental values used in the study.

When a researcher wants to draw into a conclusion beyond the particular values of the independent variable used in the study, a random model effect is used. Random effects not reliable since they produce large errors. The levels of independent variables are considered to be subsets of the possible values one wishes to generalize. The random-effects use ANOVA and regression as the statistical methods to test the random variable. The fixed effects are considered to be independent, and they take the effect of analysis using ANOVA and regression. The fixed effect produces smaller errors, which makes it more powerful (Bosker et al., 2012).

There was a statistically important variation between groups determined by one-way ANOVA (F(4,2722) = 3461.385, p = .0001). Panel data obtained had a relationship with one another having the value of Ys which rely on the value of Xs. Y=aX1+bX2+cX3+dX4 which resulted Y=0.949X1-0.024X2+0.017X3+0.014X4. The value of t is given as -1.267, and therefore considering the value is less than 0.05 the significance level, the panel data concludes that the constant value Y is dependent. The value for R squared obtained was 0.836 which means the model is 83.6%…

References

Campbell, J., Lo, A., MacKinlay, C., 2012. The Econometrics of financial markets. Princeton University Press, pp. 28 – 632.

T.A.B., & Bosker, R.J., 2012. Multilevel analysis: An introduction to basic and advanced multilevel modeling (2nd Edition). London: Sage.