MGEC72-Assignment-3
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MGEC72: FINANCIAL ECONOMICS
Assignment-3
1
Deadline (April 4)
CAPM
I. Individual stocks
a)
Estimate the CAPM
model for each of your four stocks. Obtain the parameters
α
and
β
for
each firm. Do the estimates of
β
correspond well with your prior intuition or beliefs? Why or
why not?
Hint:
To do this question you need to follow the regression analysis in
Lecture 7.
Make sure
the risk premium (excess return) of each stock is regressed over the risk premium (excess
return) of the market.
b)
For two of the stocks, make a time plot of the historical risk premium, and risk premium
predicted by the regression model, and the associated residuals. Are there any episodes or
dates that appear to correspond with unusually large residuals? If so, attempt to interpret
them.
c)
For each of the companies, test the null hypothesis that
α
= 0 using a significance level of
95%. Would rejection of this null hypothesis imply that the CAPM
has been invalidated?
d)
Compute the market risk, and the idiosyncratic risk for each stock. According to William
Sharpe ”Uncertainty about the overall market accounts for only 30% of the uncertainty about
the prospects for a typical stock.” Is this statement verified by your results?
MGEC72 – Computer Assignment
Page 2 of 2
Hint
: Use the R-squared of your regressions to find the proportion of market risk and
idiosyncratic risk.
II. Equally weighted portfolio
Now suppose you have formed an equally weighted portfolio of all four stocks.
a)
Calculate the beta and the alpha of your portfolio and interpret them. What is the
idiosyncratic risk? Show the impact of diversification.
b)
Make a time plot of the historical risk premium of your portfolio, and risk premium
predicted by the regression model, and the associated residuals. How close the actual
portfolio premiums correspond with the CAPM predictions?
c)
For your portfolio, test the null hypothesis that
α
= 0 using a significance level of 95%.
Would rejection of this null hypothesis imply that the CAPM
has been invalidated?
Good luck,
1
Make sure you explain your approach/finding in a detail.
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(Econmetrics)
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13. In the simple linear regression model, the regression slope
a.
O a. indicates by how many percent Y increases, given a one percent increase in X.
ut of
O b. represents the elasticity of Y on X.
uestion
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O d. indicates by how many units Y increases, given a one unit increase in X.
nage
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Topic: Regression
Problem 3: A researcher is interested in determining whether there is a relationship between grades and hours studied for statistics.
Hours studied(X)
Grade on final(Y)
1
20
2
30
4
40
7
60
6
70
7
78
8
83
9
98
1- You are given data for Xi (independent variable) and Yi (dependent variable).
2- Calculate the correlation coefficient, r:
r = -1 ≤ r ≤ 1
3- Calculate the coefficient of determination: r2 = =
0 ≤ r2 ≤ 1
This is the proportion of the variation in the dependent variable (Yi) explained by the independent variable (Xi)
4- Calculate the regression coefficient b1 (the slope):
b1 = =
Note that you have already calculated the numerator and the denominator for parts of r. Other than a single division operation, no new calculations are required.
5- Calculate the regression coefficient b0 (the Y-intercept, or constant):…
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8. Which of the following best describes the linear probability model?
The model is the application of the linear multiple regression model to a binary dependent variable
The model is an example of probit estimation
The model is another form of logit estimation
The model is the application of the multiple regression model with a binary variable as at least one of the regressors
OO
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11. Which of the following statements is not true about multicollinearity?
(a) Perfect multicollinearity will prevent you from being able to estimate a linear regression model.
(b) Imperfect mulitcollinearity affects the individual t-statistics of the regressors.
(c) Multicollinearity is defined as a linear relationship between different independent variables.
(d) Imperfect multicollinearity affects model validity of the model.
(e) The least squares estimators are unbiased in the presence of imperfect multicollinearity.
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5. Among important factors that affecting the price of land lot are size, number of mature trees and
distance to the lake. Using data for 60 recently sold land lots are shown below:
B
1 SUMMARY OUTPUT
2
3.
Regression Statistics
4 Multiple R
5 R Square
6 Adjusted R Square
7 Standard Error
0.4924
0.2425
0.2019
40.24
8 Observations
60
9.
10 ANOVA
Significance F
5.97
11
df
S
MS
9676.6
0.0013
12 Regression
13 Residual
3
29,030
90,694
56
1619.5
14 Total
59
119,724
15
16
Coefficients Standard Error
t Stat
P-value
0.0331
0.2156
17 Intercept
51.39
23.52
2.19
18 Lot size
0.700
0.559
1.25
19 Trees
0.679
0.229
2.96
0.0045
20 Distance
-0.378
0.195
-1.94
0.0577
a) Write the regression equation
b) What is the standard error of estimate? Interpret its value.
c) What is the coefficient of determination? Interpret its value.
d) What is the adjusted coefficient of determination? Interpret its value.
e) Test the validity of the model.
f) Interpret each of the coefficients.
g) Test at 5% level of…
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Question 2 B ..
Full explain this question and text typing work only We should answer our question within 2 hours takes more time then we will reduce Rating Dont ignore this line
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Image attached
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d. If the director used these 4 weeks of data to create a linear regression, what does that linear regression
formula suggest for this week's forecast of employee appointments? What does the regression analysis
suggest in general about employee appointments for Director Very Busy?
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Kindly provide a correct answer and a detailed explanation; otherwise, I will have to give multiple downvotes. Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism.
Answer completely and accurate answer.
Rest assured, you will receive an upvote if the answer is accurate.
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Question 9
Regression analysis was applied between demand for a product (Y) and the price of the product (X), and the
following estimated regression equation was obtained.
Y = 120 - 15 X
Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected
to:
O Increase by 120 units
Decease by 30 units
O Increase by 2Q units
Next
« Previous
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No new data to save. Last checked at 9:51pm
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1. Suppose that you have following data:
Variable
Description
CEO salary measured in thousands of $
Firm's sale measure in millions ofS
Return on equity in percent
Salary
sales
roe
*Return on equity is a measure of financial performance calculated by dividing net
income by shareholders' equity.
Your estimated regression is given by
log (salary) = 4.322 + 0.276 log(sale) + 0.0215roe - 0.0008roe?, R = 282, n = 209.
(324) (0.033)
(0.0129)
(0.00026)
a) Is the effect of all independent variables statistically equal to 0?
b) Interpret the coefficient on log(sale).
c) Interpret the effect of roe on log(salary).
• Without more information, your interpretation of the effect of roe on
log(salary) should include answers to these sub-question.
Should the roe be included in this model?
il.
Comment on relationship between roe and log(salary): is it U-shaped or inverse
U-shaped?
What is the turning point? How would you interpret this point?
Plot log(salary) vs roe.
v.
ii.
iv.
Compute predicted value…
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Styles
6. The following two regression models are Probit and Logit respectively:
Pr(Y=1|X)=(Bo+Bi xXr+Bzx X2)
Pr(Y=1|X)=F(Bu + B₁ × Xs + B₂ × X2)
(a) what functions do and F represent?
(b) How do Probit, and Logit ensure that the predicted probabilities are always between 0 and 1?
(c) Sketch a graph of the Y= $(Z) function. (Z on the horizontal axis, Y on the vertical axis)
(d) What estimation method is used to estimate the coefficients in a Probit/Logit model?
(e) What are the two measures of fit for models with binary dependent variables?
Focus
88
B
E
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X
270
360
520
780
The fixed costs are $.
(Round to the nearest dollar as needed.)
ITTI
y =
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Use the linear regression equation found in the previous step to estimate the fixed costs and variable costs per projector.
The variable costs are $ per projector.
(Round to the nearest dollar as needed.)
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I is the average income per household in each outlet’s service area,
ui…
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QUESTION 17
I am trying to figure out how to measure an athlete's productivity. So, I have
run a linear regression of a NBA player's salary (dependent variable) on a
player's statistics including average points, assists, rebounds per game, and
turnovers per game (the independent variables).
The final model is: Salary = 1,000,000 * Points per game + 50,000 * Assists
per game + 20,000 * Rebounds per game - 30,000 * Turnovers per game
%3!
Last year, Lebron James averaged 25 points per game, 8 assists per game, 8
rebounds per game and 4 turnovers per game. What is Lebron's predicted
salary?
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2.9.
Based on price statistics of 26 properties sold (Y
USD/m? ) linear correlation coefficients were
calculated with potential explanatory variables X,,X2,X3, X4 . Vector R, and matrix R are listed
below
0,3
0,6
0,5 1
Ro=
R =
-0,7
0,6 0,6 1
0,4
0,8 0,8 0,7 1]
The critical value of the linear correlation coefficient was assumed to be r* =0, 55. Perform the
selection of explanatory variables for the model using the correlation coefficient analysis method.
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10- What would be the consequences for the OLS estimator if
heteroskedasticity is present in a regression model but ignored?*
a. It will be biased
b. It will be inconsistent
c. It will be inefficient
d. All of (a), (b), and (c) will be true
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6
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When the regression line passes through the origin then:
O The intercept is zero.
O The regression coefficient is zero.
O The correlation is zero.
O The association is zero.
O All of the above.
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In a recent closely contested lawsuit, Apex sued Bpex for patent infringement. The jury came back today with its decision. The rate o
return on Apex was rA = 3.7%. The rate of return on Bpex was only rg = 3.3%. The market today responded to very encouraging new
about the unemployment rate, and M = 3.4%. The historical relationship between returns on these stocks and the market portfolio has
been estimated from index model regressions as:
Apex: A = 0.3% + 1.5PM
Bpex: rg = -0.1% + 0.5rM.
Required:
a. What is the predicted returns for Apex & Bpex?
b. Which company do you think won the lawsuit?
Complete this question by entering your answers in the tabs below.
Required A Required B
What is the predicted returns for Apex & Bpex?
Note: Do not round intermediate calculations. Round your answers to 1 decimal place.
Apex
Врех
Predicted Returns
%
%
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Please provide the correct answer along with the calculation. Do not use ChatGPT, otherwise I will give a downvote.
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1. An analyst from your firm used a linear demand specification to estimate the demand for its product
and sent you a hard copy of the results:
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
ANOVA
Regression
Residual
Total
Intercept
Price of X
Income
0.38
0.14
0.13
20.77
150
df
2
147
149
SS
58.87
-1.64
1.11
10398.87
63408.62
73807.49
Coefficients Standard Error
15.33
0.85
0.24
MS
5199.43
431.35
t Stat
3.84
-1.93
4.63
F
12.05
P-value
0.00
0.06
0.00
Significance F
0
Lower 95%
28.59
-3.31
0.63
Upper 95%
b. Which regression coefficients are statistically significant at the 5 percent level?
a. Based on these estimates, write an equation that summarizes the demand for the firm's product.
89.15
0.04
1.56
C. When price is $10, what is the income elasticity for this product for an income level of 35?
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Econometrics may be defined as the social science in which the tools of economic
theory, mathematics, and statistical inference are applied to the analysis of economic
phenomena.
A. True
B. False
10.
11.
What is/are the objective(s) of regression analysis?
A. To estimate the expected value of the dependent variable only
B. To test hypotheses about the nature of the dependence between the variables only
C. To predit the expected value of the dependent variable, given the value(s) of the
dependent variables beyond the sample range only
D. All of the above
What is the population regression line or PRL?
A. A line derived from the sample collected in a population
B. A line that passes through the conditional means of the independent variable (X)
C. Gives the average value of the dependent variable corresponding to each value of
the independent variable
D. Gives the average value of the independent variable corresponding to each value
of the dependent variable
12.
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