- You are working as an analyst in an investment bank, and you have been directed to prepare
a report for an S&P 500 company’s performance during 2012 - 2013.
Part A [6 marks]
(A.1) Download the daily close S&P500 index and daily close price (not adjusted close
price) of your assigned company’s stock for the period of 03 January 2012 – 31 December
2013 (via Yahoo Finance).
(A.2) Compute descriptive statistics for S&P 500 index and for your company’s daily prices,
respectively.
(A.3) Construct the frequency distributions (including relative frequency and cumulative
frequency) for S&P 500 index and your company’s stock prices respectively.
Use 30 intervals.
(A.4) Calculate continuous returns for the daily S&P 500 index and your company’s daily
stock prices, respectively.
Note: please use the data you downloaded and computed in Part A to complete the following
questions:
Part B [11 marks]
(B.1) what are the median and the first quartile of S&P 500 index returns and you
company’s stock returns, respectively.
(B.2) Obtain the percentage of values that are within one and two standard deviations of the
mean returns of your company’s stock prices.
(B.3) Calculate the semivariances of daily returns for S&P 500 index and your company’s
stock returns, respectively.
(B.4) What is the probability that your company’s daily stock returns are below 0.5%?
(B.5) What is the probability that S&P500 returns are between -0.5% and 0.5% with the
Normality assumption?
(B.6) Is the distribution of daily returns of your company’s stock prices different from
standard normal distribution? Provide evidences.
Page 3
Part C [11 marks]
(C.1) Test whether the mean returns of S&P 500 index is significantly different from zero at
1% and 5% level of significance, respectively.
(C.2) Calculate the correlation coefficient between the S&P 500 index returns and your
company’s stock returns in 2012; and also their correlation coefficient in 2013. Are the
correlations obtained statistically significant at 5%?
(C.3) Assuming there is a linear relationship between your company’s stock returns and
S&P 500 index returns. You are asked to run a simple linear regression by using your
company’s stock returns being dependent variable, and S&P 500 index returns being
independent variable.
C.3.1 Show the linear regression model you obtained.
C.3.2 Is the intercept coefficient significant at the 5% level? Is the slope coefficient
significant at the 1% level? Give reason(s).
C.3.3 Show the confidence interval of the intercept coefficient at the 1% level.
C.3.4 Obtain the coefficient of determination, and interpret it.
