QBA

Question A1

The table is filled as below

	CAGR
	2002-2016	2012-2016
PERTH	3.93%	1.60%
HOBART	5.33%	3.07%
DARWIN	3.99%	0.91%
CANBERRA	3.31%	3.78%
BRISBANE	4.28%	4.36%
ADELAIDE	3.30%	3.25%
SYDNEY	3.30%	12.01%
MELBOURNE	5.00%	7.94%
Eight capital cities	3.84%	7.60%

Question A2

Based on table in A1, the city with the highest growth rate from 2002 to 2016 is Hobart.

The city that has the highest growth rate in the past 5 –years is Sydney

Question A3

The monthly payment is

The remaining mortagage is 625000 * (1-20%) = 500000

The sum is equal to PVIFA(0.5% , 300) = 155.21

Therefore, the monthly payment is 500000/ 155.21= 3221.51

Question A4

The amount of outstanding loan after the payment of third payment is

The amount of interest in the 4th period is

The amount of principal payment is then 3221.51 – 2489.12 = 732.38

The percentage of interest payment in 4th payment = 2489.12/ 3221.51 = 77.3%

The plot is shown as below

Question A5

Total payment made: 3221.51 * 300 = 966452.1

Principal payment: 500000

Interest paid: 966452.1 – 500000 = 466452.1

Question A6

The price of flat after 25 years:

625000 x ( 1+ 12.01%)^25 = 10031901

Price appreciation: 10031902 – 625000 = 9565450

The interest cost is 466452

The price appreciation is sufficient to cover the interest cost.

Question B1

Regression between Return of ANZ and ASX

Line fit plot

Residual plot

Regression between return of AMCOR and ASX

Line plot

Residual plot

Regression output when APNNEWS is regressed with ASX

Line plot

Residual plot

Question B2

OLS regression assumptions include

1) Residuals have constant variance

2) Residuals are not autocorrelated

3) Independent variables are not correlated to each other

4) Residuals should have zero mean

5) Residuals should be normally distributed.

For regression equal between ANZ Bank and ASX, the residuals are random. However, some residuals are serially correlated with difference variances between different groups. Thus, the constant variance assumption is violated. The uncorrelated residual assumption is also violated.

For regression equal between AMCOR and ASX, the residuals are random. However, some residuals are serially correlated with difference variances between different groups. Thus, the constant variance assumption is violated. The uncorrelated residual assumption is also violated.

For regression equal between ABNNEWS and ASX, the residuals are random. However, some residuals are serially correlated with difference variances between different groups. Thus, the constant variance assumption is violated. The uncorrelated residual assumption is also violated.

Question B3

Beta of ANZBank is 1.207

Beta of AMCOR is 0.769

Beta of ABNNEWS : 1.216

All of them are statistically different from zero as indicated by p-values obtained from their regression output.

A stock with beta equal to 1 means when market return goes up by 1%, the expected return of the stock should go up by 1% as well. It is a neutral stock.

A stock with beta equal to 0 means the covariance between the return of the stock and the return of the market is 0. However , it does not mean that the firm does not have risk. The variability of firm’s return cannot be explained by the variability of the market return due to the zero covariance.

Question B4

The R-squared of the regression model for ANZ Bank vs ASX is 0.68

The R-squared of the regression model for AMCOR vs ASX is 0.126

The R-squared of the regression model for ABNNEWS Bank vs ASX is 0.263

This is inline with expectations. ANZ Bank is a major blue chip stocks. It should a high correlation with the market.

The R-squared values of AMCOR and ABNNEWS also agree with prior expectation due to its spread in residuals found from the line plot.

Question B5

Regression output between the equal-weighted portfolio and ASX

Line fit plot

residual plot

Violation of regression assumptions

For regression equal between the equal-weighted portfolio and ASX, the residuals are random. However, some residuals are serially correlated with difference variances between different groups. Thus, the constant variance assumption is violated. The uncorrelated residual assumption is also violated.

The beta of the portfolio is 1.064. The beta is the average beta of the three stocks estimated in B1.

The R-squared value of the regression is 0.44. It is higher than the R-squared value obtained by AMCOR and ABNNEWS. The R-squared value of the portfolio is also higher than the average value of the R-squared values obtained from the three regression models above. It indicates that the diversification effect by investing into a portfolio.

The portfolio diversification is prominent as it can remove the firm-specific risk of stocks in the portfolio.

Question C1

Estimated intercept: 2.763

Estimated slope:0.5612

Question C2

Regression output

the 95% confidence interval of Age is (0.497 , 0.602 ) from the Excel output.

Question C3

The slope coefficient of Age in the first regression (C1) is 0.561. The slope coefficient of Age in the regression of C2 is 0.5491. The corresponding 95% CI is (0.497,0.602) , which contains 0.561. Thus, it can be concluded that the slope coefficients of Age found in these two regression equations are not statistically different.

Question C4

C4
		Alexis	Bob
	Coefficient	Value	Value
Intercept	0.57	1	1
bachelor	8.22	1	0
female	-3.74	1	0
age	0.55	30	26
	Predicted value	21.52	14.84

Question C5

Question C6

For the hypothesis that Bachelor can be removed from the regression equation, a t-test can be performed to test the hypothesis. The t-test of testing the statistical significance of the partial regression coefficient can be performed as below

The test statistic is 53.77 which is found from the regression output in C1.

The p-value of the test statistic is less than 0.001. With 5% significance level, the null hypothesis of zero slope coefficient is rejected. In other words, the regressor Bachelor cannot be removed from the regression model.

To test the joint significance of the model , we apply the following null and alternate hypothesis

We test the hypothesis using the F-test for restricted model . We used the formula below to construct the test statistic

Data of the parameters in the formula above is summarized as below

C6
SSRur	1331450.479
SSRr	1606044.874
q	2
K	3
F	1562.245518
df1	2
df2	15150
P-value	0.000

The test statistic is 1562. The corresponding p-value of the test statistic under F-distribution of 2 and 15147 degrees of freedom is less than 0.0001. Thus, the null hypothesis of no joint significance between Female and Bachelor is rejected at 10% , 5% and 1% significance level.

Question C7

Two conditions of omitted variable bias are

1) omitted variable is determinant of the dependent variable

2) omitted variable is correlated with the included independent variable

These conditions do not seem to hold here. First, none of these three variables are deleted. Condition 2 cannot be known.