Method of the Personalized System - Linear Probability Model - Mathematics Assignment Help

Assignment Task :

Question 1
The capital asset pricing model (CAPM) is an important model in the field of finance. It explains variations in the rate of return on a security as a function of the rate of return on a portfolio consisting of all publically traded stocks, which is called market portfolio. Generally the rate of return on any investment is measured relative to its opportunity cost, which is the return on a risk free asset. The resulting difference is called the risk premium, since it is the reward or punishment for making a risky investment. The CAPM says that the risk premium on any security is proportional to the risk premium on the market portfolio. That is,
 1 2 r rf rm rf −=+ − β β ( ) (1)
Where r refers to return on any given asset, rf is the return on risk free assert and rm is the return on the market portfolio. Here β1 is expected to be zero and the stock’s ‘beta’ value (β2) is important to investors since it reveals the stock’s volatility. ‘beta’ measures sensitivity of any stock’s return to variation in the whole stock market. As such, values of β2 less than 1 indicate that the stock market is “defensive” since its variation is less than the market’s. A β2 greater than 1 indicates an “aggressive stock”
The data file HW4_q1.xlsx contains quarterly returns of Ford (r), the rate of return on the market portfolio (rm), the rate of return on the risk free asset (rf) and four quarterly dummies
(Q1 to Q4). The 64 observations cover 2001Q1 to 2016Q4.
(a) Estimate the CAPM model for Ford and report the results. (Hint: Define y=r-rf and x = rm-rf).
(b) It is believed that the Ford asset is an aggressive stock. Test this belief at the 10% level of significance.
(c) How would you modify the equation (1) to capture quarterly seasonal effects (in intercept)? Estimate the modified model. Interpret the regression coefficients.
(d) How would you modify the model in (c) to capture quarterly seasonal effects in intercept and slope? Estimate the modified model. Interpret the regression
coefficients.
(e) Using the model in (c), examine the joint significance of the seasonal effects at the 5% level of significance. Clearly present the restricted model.
(f) Using the model in (d), examine the joint significance of the seasonal effects at the 1% level of significance. Clearly present the restricted model.
(g) Use the model estimated in (c) to predict the return for Ford (r) for the first quarter of 2017 assuming rf = 2.0 and rm =1000. 

(h) Use the model estimated in (d) to predict the return for Ford (r) for the first quarter of 2017 assuming rf = 2.0 and rm =1000.

Question 2
The data file Hw4_q2.xlsx contains information on the factors that could affect the final grades of an Econometrics course.
Variable descriptions:
Grades = 1 if the final grade in Econometrics is “D” or “HD”, = 0 otherwise
GPA = the entering grade-point average
QM = score from Quantitative Methods course
PSI = 1 if the new method of the personalized system of instruction is used, = 0 otherwise

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