# HW2 2022

```EF3450 Principles of Econometrics
Semester B 2021-2022
Assignment 2 (Total: 15 points)
Note:
1. Due Feb 28 (Mon.), 11:59pm and submit your answers as pdf, doc, or docx
format only on canvas
2. 20% deduction per late day
3. Write down your full name, student ID number and lecture time in the file
5. For R exercises, do not print out all the computer output; just need to report the
necessary results that are explicitly asked for in the questions.
6. Please copy all code in your script and paste it at the end of file.
7. hw2_data.csv is on canvas and HW2 Sample Handout could be used as an
example to work on this assignment.
(R exercise) Simple Regression and Hypothesis Testing
1. (total 15 points)
Data on the monthly stock prices of the Hong Kong Exchanges and Clearing Limited
(Phkex ) , Hang Seng Index (Phsi ) and the risk free rate (r f ) are provided in the file
hw2_data.csv which is available on the class web page.
Calculate the monthly returns of the HK Exchanges and Clearing Limited and the Hang
Seng Index as
Phsi,t − Phsi,t −1
Phkex,t − Phkex,t −1
rhkex,t =
 100%
 100% and rhsi,t =
P
P
hsi,t −1
hkex,t −1
Estimate the CAPM model
(rhkex,t − rf ,t ) = 1 + 2 (rhsi,t − rf ,t ) + et
(a) Report the estimated intercept and slope 垐
1 and  2 . Based on the estimated ̂1 , does
this stock outperform or underperform the market? Based on the estimated ̂2 , how is the
volatility of this stock compared with the volatility of the market portfolio? (6 points)
1
(b) Test the null hypothesis that  2  1 (the stock is a defensive asset), against the
alternative hypothesis that  2  1 (this stock is an aggressive asset) at the 5% level of
significance by comparing the test statistic with the critical values. (3 points)
(Hint: Since the hypothesized value under the null is 1 instead of 0, you cannot
directly take the t-statistic from the computer output to carry out this hypothesis
ˆ − 1
testing. You need to compute the test statistic using the formula t = 2
by
se( ˆ2 )
yourself.)
(c) Test the null hypothesis that 1 is zero (there is zero abnormal return), against the
alternative hypothesis that it is not, at the 5% level of significance using the reported pvalue. What is your conclusion? (3 points)
(d) Test the null hypothesis that 1 is less than or equal to zero, against the alternative
hypothesis that it is positive, at the 5% level of significance using the reported p-value.
What is your conclusion? (3 points)
(Hint: Be careful about how you should use the p-value when you are doing a
one-tailed test)
2
```