9300 ASSIGNMENT 1 MONASH UNIVERSITY.docx

1、9300 ASSIGNMENT 1 MONASH UNIVERSITYLinear Regression Analysis Assignment1. Introduction1.1. Data SettingAccording to the raw source of this assignment, the original data have collected the daily digits of ASX200 index, two industry-portfolios (banking and telecom) and the annual return rate of 90-da

2、ys government bond (1 year consists of 365 days) from 17 October 2001 to 31 January 2012. Before starting this analysis, we assume that the return rate of ASX200 index and 90-days government bond can represent for the return rate of market portfolio (Rmt) and risk free asset (Rft). Based on these ti

3、me serial data, we employ the continuously compounded log return to calculate the return rate of ASX200 index and two industry-portfolios. For example, the return rate of ASX200 index is:Where Rmt is the daily return rate of ASX200 index, ASX200 is the value of ASX200 index at day t, ASX200(-1) is t

4、he digit ASX200 index at day t-1. We can get the daily return rate of telecom portfolio and banking portfolio by running the same process in Eviews, respectively are R1t and R2t. Because the risk free return is annual return rate of 90-days government bond, to employ all factors of CAPM equation at

5、same time frequency, we divide the annual return rate of 90-days government bond by 365 days.1.2. Analysing Equation of CAPMAfter the data reprocession, we establish the equation of simple linear regression analysis following the CAPM theory:Rjt represents the return rate of portfolio j at day t (te

6、lecom j=1, banking j=2), Rft is the risk free rate at day t, Rmt is the return of market portfolio at day t, jt is the error term of portfolio j at day t, j and j are the coefficients which will be estimated.2. Regression Equation2.1. Regression Equation of Telecom PortfolioThe econometric model of

7、CAPM for telecom portfolio is presented as below:Empoly R1t-Rft and Rmt-Rft as the two variables (y1 and x) to estimate the equation in Eviews, the result is expressed as: Table 1 Result of Linear Regression of Telecom PortfolioIf we use a1 and b1 to represent the estimated value of 1 and 1, the fit

8、ted regression equation of telecom portfolio is:It should be noticed that r-square of this equation is 18.37%, which means 18.37% data can be explained by the regression analysis. Since 0b11, the banking portfolio is an aggressive portfolio which has greater volatility than the market portfolio. Sin

9、ce a2= 0.00016, the banking portfolio has extra return beside the risk free asset, but it is almost 0.3. Hypothesis Test of Fitted Regression Equation3.1. Hypothesis Test of 1If we assume the hypothesis about 1 as:H0: 1=0 There are no extra returns over the return of risk free asset which can be mad

10、e from telecom portfolioH1: 10 There are extra returns over the return of risk free asset which can be made from telecom portfolioThen, set up the significant level at 5%. There are two way to process the hypothesis test. The testing procedure is as below:(1) P-value TestP-value is the possibility t

11、hat we get the current estimate when the null hypothesis is true, 1=0. According to Table 1, the p-value of 1 is 17.85%, which is greater than significant level. We fail to reject the null hypothesis under the significant level is 5%.(2) Two-tailed T-statistic TestApply the same hypothesis, we calcu

12、late the t-statistic value of 1 employing the formula as below, which also can be gained from Table 1:Based on the hypothesis H0: 1=0 and H1: 10, two-tailed test will be more suitable for this test rather then one-tailed test. Then, the t-critical value of two-tailed test, |tcritical|=1.960878, whic

13、h can be gained under the condition: 5% significant level, 2.5% on each rejection region, 2600 observations, 2 degree of freedom and 2 variables. It is obvious that |t1|significant level or |tstatistic|tcritical|, the null hypothesis will be failed to reject, H0 can be accpeted (1=0). It indicates t

14、hat the return of telecom portfolio tends to be related to the risk premium of market portfolio significantly, 1 has less contribution on influencing the dependent variable y1. In another word, people have less chance to earn investing return more than the return of risk free asset when the risk pre

15、mium of market portfolio is equal to 0.3.2. Hypothesis Test of 2The hypothesis about 2 is:H0: 2=0 There are no extra returns over the return of risk free asset which can be made from banking portfolioH1: 20 There are extra returns over the return of risk free asset which can be made from banking por

16、tfolioThen, the significant level remains at 5%. (1) P-value TestThe p-value of 2 is 99.19% (See Table 2), which is distinctly greater than significant level. It should accept the null hypothesis when the significant level is 5%.(2) Two-tailed T-statistic TestApply the same hypothesis, we calculate

17、the t-statistic value of 2 employing the formula as below, which is also expressed in Table 2:Compared with t-critical value of two-tailed test under the same condition, |tcritical|=1.960878. Because |t2|tcritical|, we reject the null hypothesis. (2) DiscussionWhen |tstatistic|tcritical|, the null h

18、ypothesis will be rejected. In this two-tailed test, the null hypothesis is 1=1. If we reject that, it means that the telecom portfolio is not tracking portfolio which tracks the market portfolio exactly. 3.4. Hypothesis Test of 2, 21(1) Two-tailed T-statistic TestThe hypothesis about 2 is:H0: 2=1 T

19、he banking portfolio is a tracking portfolio which tracks the market portfolio exactlyH1: 21 The banking portfolio is not a tracking portfolio which tracks the market portfolio exactlyThe t-statistic value of 2 is as below:Becasue tcritical is equal to 1.960878, |t2|tcritical|, we reject the null hy

20、pothesis under the specific condition. (2) DiscussionWe fail to reject the null hypothesis, the banking portfolio is not tracking portfolio which tracks the market portfolio exactly. But there is another issue we should mention, these two-tailed tests about 1 and 2 only conclude that 11 and 21 under

21、 a specific condition as we have expressed before, while the other hypotheses about1 and 2 have not been tested, such as 11, 011, 1=0, -111The hypothesis about 2 is:H0: 2=1 The telecom portfolio is a tracking portfolio which tracks the market portfolio exactlyH1: 21 The telecom portfolio is an aggre

22、ssive portfolio which has greater volatility than the market portfolio(1) One-tailed T-statistic TestAccording to the hypothesis, the testing method prefers to the one-tailed test rather than the two-tailed test. Recall the condition of t-statistic test, the significant level is 5%, instead of 2.5%

23、on each rejection region of two-tailed test, one-tailed test sets 5% on one rejection region. As we have calculated that the t-statistic value of 2 is 4.515676. While the t-critical value of one-tailed test has changed to 1.64544. It is significant that |t2|tcritical|, which means that we can reject of the null hypothesis about 2.(2) Discussion and SummarySince we have rejected the null hypothesis of 2, 21 is acceptable. In the context of CAPM, the banking portfolio is more like an aggressiv