Download FIN357 In-class-Work No 5 First Name_________ Last Name

FIN822 In-class-Work No. 1
General rules:
t-statistic=coefficient estimate / standard error of the estimates
If the absolute value of t-statistic >2.00 or equivalently p-value <0.05, the corresponding
coefficient is “significantly different from zero” (for simplicity we just say “significant”.)
To test whether a coefficient is significantly different from a specific value, say, 1.5, we
need to compute t-statistic as (coefficient estimate-1.5) / standard error of the estimates
__________________________________________________________________________
Use the following information to answer the following Two questions.
Superstrong fund has developed a regression model for forecasting stock return. The
model is estimated using a cross-section of 40 firms, and the estimated model is given
below:
R=0.0184 - 0.0018 S
(0.0050) (0.0005)
The numbers in the parentheses are the standard errors for the respective parameter estimates.
where R = Monthly stock return of the firm,
S = Market capitalization of the firm (in millions of dollars),
1. At significance level is 5% , which of the following conclusions is correct?
(a) Only the intercept is statistically significant.
(b) Only the slope is statistically significant.
(c) Both the intercept and the slope are statistically significant.
(d) Neither the intercept nor the slope is statistically significant.
2. Based on the regression results, which of the following
statements is correct?
(a) The returns on small firms are higher than the returns on
large firms.
(b) The returns on small firms are lower than the returns on
large firms.
(c) None of the above.
3. Suppose you are doing research on 4 stocks. You can estimate betas for each stock by
regressing each stock's excess return on the market's excess return.
1
How can you compare the four stocks’ market risk?
a.
b.
c.
d.
Compare the estimated coefficients on market's excess return.
Compare the standard error of residuals.
Compare the adjusted R-squared.
Compare the estimated intercepts.
4. If an estimated coefficient is negative, could it be statistically significant?
A) Yes, it could.
B) No, it cannot.
C) An estimated coefficient can never be negative
5. In the simple linear regression model, where y = beta0 + beta1*x + u, we typically refer to x as
the
A) Independent Variable
B) Right-hand Side Variable
C) Explanatory Variable
D) Repressors
E) All of above
6. Which of the following provides correct matching?
A)
Population
sample
mean
---
sample mean
variance
---
variance
residual
---
error term
standard deviation
---
standard error
true parameter
---
estimated
parameter
B)
Population
sample
mean
---
sample mean
variance
---
sample variance
error term
---
residual
standard deviation
---
standard error
true parameter
---
estimated
parameter
2
C)
Population
sample
mean
---
sample mean
coefficient
---
variance
error term
---
deviation
standard residual
---
true parameter
---
standard
deviation
estimated
parameter
Use the following information to answer the following Three questions.
Regression statistics describing the relationship between the excess returns of a stock and
the excess returns of the Standard & Poor's 500 Index (market index) are estimated using
240 monthly observations and they are given as follows:
(excess return= return - risk free rate)
Stock
Estimated
Intercept
Estimated Slope
(Beta)
R-Square
X
0.69
(0.64)
1.17
(0.17)
0.161
Standard Error
(Assume 5% significance level)
7. Is the Beta of stock X significant different from 0? Explain.
8. Is the Beta of stock X significantly different 1? Explain
9. Is the intercept of stock X significantly different 0? Explain
3
10. I try to regress the daily volatility of Motorola on each previous day’s volatility. More
specifically, the dependant variable (y=volatility) refers to daily volatility in the period of
Jan 3, 2006 to Oct 3, 2006, while the independent variable (x=last_vol) refers to each
previous day’s volatility in the period of Jan 2, 2006 to Oct 2, 2006. An intercept is
included in the regression. Below is the regression output:
Model 1: OLS estimates using the 190 observations 1-190
Dependent variable: volatility
Variable
const
last_vol
Coefficient
0.418641
0.24901
Std. Error
Coffee dirt
0.0691459
t-statistic
Coffee dirt
3.6012
p-value
<0.00001
0.00041
***
***
Mean of dependent variable = 0.556684
Standard deviation of dep. var. = 0.195846
Sum of squared residuals = 6.78141
Standard error of residuals = 0.189924
Unadjusted R2 = 0.0645317
Adjusted R2 = 0.0595558
Based on the result, is there a significant relationship between daily volatility over two
adjacent days?
11. For the constant term (the intercept, the “const”), the Std. Error and t-statistic in the
computer output above are covered by some coffee dirt and not readable. Is the constant term
(the intercept) significant? (Hint: p-value)
12. What happens if we include variables in our specification that don’t belong?
What if we exclude a variable from our specification that does belong?
13. In a regression, the fraction of the total sum of squares (SST, it measures the volatility
of the dependent variable) that is explained by the model is called the ________ of
regression.
A)
B)
C)
D)
E)
R-squared
Rx
Beta
Intercept
Regressor
4
14. An investment strategy has an expected return of 5 percent and a standard deviation of 10
percent. If investment returns are normally distributed, the probability of earning a negative
return is closest to: (See the normal distribution table attached at the end of the test)
A.
B.
C.
D.
E.
10%.
16%.
31%.
84%.
66%
15. X-Y plot is also called
A.
B.
C.
D.
histogram plot
littering plot
scatter plot
Q-Q plot
Below you have 10 mutual funds’ annual returns and expense ratios in 2007:
Company
Name
Return on
Equity
(ROE)
Debt to
asset ratio
Rank of
Debt-to
asset ratio
Lehman Morgan Obama Franklin Pioneer First
Country GF
Sisters
Energy Corp
Afford
0.10
0.15
-0.22
20.3
0.05
-0.07
0.19
0.07
0.02
0.30
0.45
0.48
0.98
0.65
0.37
0.55
0.39
0.40
9
5
4
1
2
8
3
7
6
16. What are the minimum, median, and maximum values of Debt-to-asset ratio in this sample?
A.
B.
C.
D.
0.30, 0.45, 0.98
-0.22, 0.15, 20.3
0.30, 0.65, 0.40
1, 5, 9
17. If you wish to investigate the relationship between debt ratio and ROE, which of the
following measurement may be most helpful?
A. a histogram on ROE observations
B. A Spearman correlation between ROE and Debt-to-asset ratio
C. A time series plot of the data
18. In a simple regression, R-squared is equal to:
A. the intercept
B. the coefficient
C. the squared correlation between the dependent and independent variable
5
D. the correlation between the dependent variable and the fitted value
E. C and D are correct
19. If in a sample the correlation between two variables are zero. Does this necessarily imply that
the two variables are independent?
A) absolutely
B) Not necessarily
6
FIN822 In-class-Work No. 1
Use the following information to answer the following Two questions.
Superstrong fund has developed a regression model for forecasting stock return. The model is
estimated using a cross-section of 40 firms, and the estimated model is given below:
R=0.0184-0.0018 S
(0.0050) (0.0005)
The numbers in the parentheses are the standard errors for the respective parameter estimates.
where R = Monthly stock return of the firm,
S = Market capitalization of the firm (in millions of dollars),
1. At significance level is 5% , which of the following conclusions is correct?
(a) Only the intercept is statistically significant.
(b) Only the slope is statistically significant.
(c) Both the intercept and the slope are statistically significant.
(d) Neither the intercept nor the slope is statistically significant.
t=3.68 and -3.6 respectively, both are bigger than 2 in magnitudes.
0.0184/0.005=3.68, -0.0018/0.0005=-3.6
2. Based on the regression results, which of the following statements
is correct?
(a) The returns on small firms are higher than the returns on large
firms.
(b) The returns on small firms are lower than the returns on large
firms.
(c) None of the above.
Coefficient before S is significantly negative. This implies that bigger firms have lower
returns.
3. Suppose you are doing research on 4 stocks. You can estimate betas for each stock by
regressing each stock's excess return on the market's excess return.
How can you compare the four stocks’ market risk?
a. Compare the estimated coefficients on market's excess return.
b. Compare the standard error of residuals.
c. Compare the adjusted R-squared.
d. Compare the estimated intercepts.
4. If an estimated coefficient is negative, could it be statistically significant?
A) Yes, it could.
B) No, it cannot.
C) An estimated coefficient can never be negative
For example, question 1 above.
7
5. In the simple linear regression model, where y = beta0 + beta1*x + u, we typically refer to x as
the
A) Independent Variable
B) Right-hand Side Variable
C) Explanatory Variable
D) Repressors
E) All of above
6. Which of the following provides correct matching?
B)
Population
sample
mean
---
sample mean
variance
---
sample variance
error term
---
residual
standard deviation
---
standard error
true parameter
---
estimated
parameter
Use the following information to answer the following Three questions.
Regression statistics describing the relationship between the excess returns of a stock and
the excess returns of the Standard & Poor's 500 Index (market index) are estimated using
240 monthly observations and they are given as follows: (excess return=return - risk free
rate)
Stock
Estimated
Intercept
Estimated Slope
(Beta)
R-Square
X
0.69
(0.64)
1.17
(0.17)
0.161
Standard Error
Assume 5% significance level
7. Is the Beta of stock X significant different from 0? Explain
t=1.17/0.17=6.88>2, coefficient is significant. That is, significantly different from 0.
8. Is the Beta of stock X significantly different 1? Explain
t=(1.17-1)/0.17=1<2, coefficient is not significantly different from 1. That is, this stock’s
8
market risk is not significantly different from the market risk of an average stock.
9. Is the intercept of stock X significantly different 0? Explain
T=0.69/0.64=1.08<2. So the intercept is not significantly different from 0.
If CAPM holds, we should observe an intercept close to zero. This regression result also implies
that the CAPM model works well in the data.
10. Yes, based on the result the t-statistic=3.6012, larger than 2 in magnitude. From another
perspective, p-value=0.00041, smaller than 0.05. The results imply that, if on one day the
stock price is very volatile, then next day the price likely will be volatile, too.
11. For the constant term (the intercept, the “const”), the Std. Error and t-statistic in the
computer output above are covered by some coffee dirt and not readable. Is the constant term/
the intercept significant? (Hint: p-value)
p-value<0.00001 so the p-value is also <0.05, so the intercept is significant.
12. What happens if we include variables in our specification that don’t belong?
OLS estimators remain unbiased. Our hypothesis test will still be correct, but less powerful
(meaning less likely to detect significant relationship)
What if we exclude a variable from our specification that does belong?
OLS estimators will usually be biased and our hypothesis test is no longer correct.
13. In a regression, the fraction of the total sum of squares (SST) that is explained by the model
is called the ________ of regression.
C)
D)
E)
F)
G)
R-squared
Beta
Intercept
Regressors
Rx
14. An investment strategy has an expected return of 5 percent and a standard deviation of 10
percent. If investment returns are normally distributed, the probability of earning a negative
return is closest to: (See the normal distribution table attached at the end of the test)
A.
B.
C.
D.
10%.
16%.
31%.
84%.
9
E. 66%
15.X-Y plot is also called
A.
B.
C.
D.
histogram plot
littering plot
scatter plot
Q-Q plot
Below you have 10 mutual funds’ annual returns and expense ratios in 2007:
Company
Name
Return on
Equity (ROE)
Lehman Morgan Obama Franklin Pioneer First
Country GF
Sisters
Energy Corp
Afford
0.10
0.15
-0.22
20.3
0.05
-0.07
0.19
0.07
0.02
0.30
0.45
0.48
0.98
0.65
0.37
0.55
0.39
0.40
9
5
4
1
2
8
3
7
6
Debt to asset
ratio
Rank of Debtto asset ratio
16. What are the minimum, median, and maximum values of Debt-to-asset ratio in this sample?
A.
B.
C.
D.
0.30, 0.45, 0.98
-0.22, 0.15, 20.3
0.30, 0.65, 0.40
1, 5, 9
17. If you wish to investigate the relationship between debt ratio and ROE, which of the
following measurement may be most helpful?
A. a histogram on ROE observations
B. A Spearman correlation between ROE and Debt-to-asset ratio
C. A time series plot of the data
18. In a simple regression, R-squared is equal to:
A.
B.
C.
D.
E.
the intercept
the coefficient
the squared correlation between the dependent and independent variable
the squared correlation between the dependent variable and the fitted value
C and D are correct
19. If in a sample the correlation between two variables are zero. Does this necessarily imply that
the two variables are independent?
A) absolutely
B) Not necessarily
10