Introduction To Econometrics And CAPM Model Estimation
CAPM Model Formula and Concept
- I. What is an econometric (empirical) study?
Econometrics empirical study can be described as the process of running data through a set of mathematics and statistical models in order to develop a qualitative analysis. The goals are to test the hypothesis or an observed trend is to determine if the model is economically viable or not. The other but equally fundamental objective of the study is to provide a deep insight into a certain case (Mairesse, and Mohnen, 2010 pp. 1141).However the outcomes should not be considered as absolute. This is due to the fact that econometrics too has its set of limitations. The totality of the results has a direct relation to the authenticity of the data. This implies that the lesser the errors in the data collected, the more realistic and reliable would the result be. The CAPM formula is :RA=RrF + [BA X (Rm-RrF)] whereby Ra is the expected return on investment, (Rrf) is the risk-free plan, Ba is the Beta of the stocks and Rm is the expected return on the market.
ECONOMETRIC MODEL: The above relationship can be represented in a simple linear form q= β0 + β1c. It is important to keep in mind that β0 = A 2 and β1 = − B 2). However, other unpredictable instances might influence the investment decision and therefore the terms for disturbance is q = β0 + β1c + ε
Brooks, (2014 pp.37) points out that “the reconciliation of critical linear models using econometrics, while it can be applied in a deductive approach.” However, it can also be effective in the Keynesian frameworks between agents. The distinction between the cases in this paper and the Keynesian approach is the spacious distinction and that the models used can be justified, thus forming a legitimate and important tool for various analysis (Mairesse, and Mohnen, 2010).The expected return on the investment using the CAPM formula can be broken down as:
Expected returns: Risk-free investment + (Beta x Market Return.). By definition Beta of the stock market is equal to 1. The investments with more than an average risk will have a higher beta than 1, while the less risky investment will have less than 1. In this cases, the beta for the lower risk investment will be zero. Such an investment would provide less risk (r) to the investor.
- Explain the intuition of the CAPM model
First, we use CAPM, and put the hypothesis of the two investment options which would give us:
Stock A= r+Ba [E (Rm) − r]
Econometric Model and Linear Equations
Stock B=r+ [E (Rm) + r]
In order to solve the equation, r = β0 and E (Rm) = β1c + ε. Therefore
.A= β0+.1*(β0 – β1c + ε), .B= β0 + (β1c + ε) +1*
In this case, CAPM requires that in equilibrium total marks for every student must be equal to the total marks of all the students (De Giorgi, Hens, and Levy, 2011).This can be shown using the formula below. There are only three groups A, B, and C. If we assume that the target portfolio is wT = (WA, wB, WC) then WA ≤ wB and SA < σΒ or if WA>wB while SA ≤σB. The two combinations ultimately depend on the utility function of the individual students which is w and σ. Group A, B, and C correspond to the maximum amount marks that the students can get (Lucas, 1976 pp.49).
2) Explain the OLS estimation method.
Let C= {1….j] Where j denotes the highest marks that the students can get, Therefore, we can have three sets 1A,1B and 1C with components that are one for the elements of A, B, C. Let’s also assume that the indirect utility of i can be written. Then (1j – 1A +1B+1C) 3. This would give us the method to find j. The next issue is concerned with the quality of this estimation. How good is ij at predicting 1A, 1B, and 1C? As a rule, it is important to make further assumptions in order to come up with specific probability statements regarding the accuracy of the established estimates. Therefore, it is important to conduct a number of diagnostics that can be conducted without the application of any theory (Wooldridge, 2010).It is important to note that we are after an investigation of the functional relationship (1j – 1A +1B+1C) 3. When an OLS estimation is applied we have assumed that C= {1….j] is a linear functions of (1j – 1A +1B+1C ) 3 .
There are two way of investigating the accuracy of this assumption through simple means . Given the OLS estimate 1j, these values can be used to compare the fit of the predicted results of 1A,1B and 1C. The standard diagnostic of any model is to analyze the difference between the three groups using the fitted parameters. It is usually the cases with analyzing such sets might reveal various problems in the assumptions that have been made (Shmueli, 2010 pp.296).
- Present the OLS estimates for all coefficients and interpret them.
Understanding OLS Estimation Method
Variable | Category Orbs Mean [90% Intermission]
————-+———————————————————-
A | Arithmetic 1A abc/3 β0+β1×A
B | Arithmetic 1B abc/3 β0+β1×A
C | Arithmetic 1C abc/3 β0+β1×A
It can be written as: (level-level regression) Write=β0+β1×A+β2× (B) +β3×(C).
It is important to note that other variables in a regression model influence the coefficients of the three groups. Since predictor variables are almost always related, two or more variable will be used to explain the variation in β (Blanchard, Amighini, and Giavazzi,2012).As a result, each coefficient does not measure the total impact on Y of its corresponding variable, as it would the only variable in the model (Bali, and Engle, 2010 pp.386).Every coefficient is an additional effect of adding the corresponding marks in A, B, and C because all the variable in the model are accounted for. Neither the repressor 1A, 1B and 1c is significant at a certain level of the simulated data set.
Students marks in the individual areas have a positive linear correlation with their collective results . However, the strong collinearity of the predictor’s results to each of the variables to fails a t-test in the model (Abbas, Ayub, Sargana, and Saeed, 2011). This implies that there should be enough variation in 1A, 1B. And 1C. More variability in the three sets are used to determine the impact of (1j – 1A +1B+1C) 3 on YY. To sum it up 1j, are the sample counterparts of 1A, 1B, and 1C. It is possible to evaluate the three sets for a given sample, but the estimates can change for each set. However, they can also be fixed but unknown (Bertrand, Duflo, and Mullainathan, 2004 pp.296).
Bibliography
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De Giorgi, E.G., Hens, T. and Levy, H., (ed.) 2011. CAPM equilibria with prospect theory preferences.
Lucas, R.E. (1976). Macroeconomic policy evaluation: a critique. Journal of Monetary Economics, 1, 19?46.
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