ACTL 2131/5101 - Assignment 2 (practical)
Submission deadline:
Friday, 19th April, 5 pm sharp via Turnitin on Moodle
This assessment activity aims to reinforce your learning by providing you with an opportunity
to apply the concepts you have learned in the course to practical problems. They will help you
solidify the relevance of the course to the real world.
Instructions:
This assignment is worth 10% of the course mark.
1. Please upload a maximum of 2 pages report which provides answers to all questions.
2. Submit your R code.
3. Please pay attention to plagiarism [Turnitin will pick it up].
Background/Data preparation
You are an investment analyst working for an investment bank. Your manager has requested
you to download, prepare and analyse data concerning financial returns.
1. Access historical S&P 500 ETF prices, which track the S&P 500 index, by visiting Yahoo
Finance at http://finance.yahoo.com. Directly download the needed data from this
https://au.finance.yahoo.com/quote/SPY/history?p=SPY&.tsrc=fin-srch, select-
ing the timeframe from January 1, 2019, to December 31, 2023. This period, covering
about 1250 daily observations, assumes an average of 250 trading days per year, aligning
with typical financial data collection over five years. Use the “Adj.Close” prices, adjusted
for dividends and splits, found in the second last column. [Note: Copying and pasting the
data into a text editor is the most straightforward method to save the time series.]
2. Also through Yahoo Finance, locate historical prices for one stock of your choice, which is
a constituent of S&P 500 index, ensuring it aligns with the same timeframe and approxi-
mately 1250 daily observations as mentioned in the previous point.1 Enter the company’s
name in the “Quote Lookup” search bar and navigate to “Historical Data”. There, select
the identical period as chosen for the S&P 500 ETF analysis. Again, use the ”Adj.Close”
prices, which adjust for dividends and splits, available in the final column.
1For a list of S&P 500 companies, visit Wikipedia?s S&P 500 Companies page: http://en.wikipedia.org/
wiki/List_of_S&P_500_companies
1
Assignment tasks
1. Calculate daily log-returns for the S&P 500 ETF and a chosen stock using Rt = ln(St)−
ln(St−1), where St is the price on day t. Plot these returns over time, with the x-axis
showing the calendar year. Comment on the main characteristics of the data that you
may find interesting considering the selected time frame.
2. Present and compare summary statistics for the S&P 500 ETF and chosen stock’s returns,
including mean, variance, skewness, and kurtosis. Highlight any interesting findings.
3. Create histograms for both the S&P 500 ETF and the selected stock’s returns. Overlay
each histogram with a normal density with the same mean and variance. Discuss any
findings you may find interesting.
4. Examine if the log-returns fit a normal distribution through both numerical methods
and visual tools (beyond the histograms). Suggest an alternative distribution that might
better fit the data, explaining your rationale. [Note: Formal hypothesis testing is not
required.]
5. Explore potential dependencies between the S&P 500 ETF and the selected stock’s returns
using numerical and graphical summaries. Comment on any interesting findings. [Note:
No formal hypothesis testing is needed.]
6. Test if the annualised returns (computed as average daily return from the sample mul-
tiplied by 250) of the S&P 500 ETF and the selected stock are statistically different.
Discuss the chosen test and its underlying assumptions.
Plagiarism awareness
Please ensure that your submission is your own work. Discussion of assignments is allowed,
but submitted material must be independently created (both, the code and the report), which
should be developed on your own without copying from peers. Significant similarities in code,
even with altered variable names or comments, will be flagged by Turnitin as plagiarism. Famil-
iarise yourself with what constitutes plagiarism, as detection is highly likely and not diminished
by collective work or varied assignment markers.