辅导ECON 424、R编程调试、R语言讲解、辅导Return calculations
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ECON 424 Lab 1
Summer 2019
Due: Monday, July 29th at 8pm via Canvas
Part I: Return calculations
Consider the following (actual) monthly adjusted closing price data for
Starbucks stock over the period December 2017 through December 2018
Monthly Price Data for Starbucks Stock
December, 2017 $57.43
January, 2018 $56.81
February, 2018 $57.10
March, 2018 $57.89
April, 2018 $57.57
May, 2018 $56.67
June, 2018 $48.85
July, 2018 $52.39
August, 2018 $53.45
September, 2018 $56.84
October, 2018 $58.27
November, 2018 $66.72
December, 2018 $64.40
1. Using the data in the table, what is the simple monthly return between
December, 2017 and January, 2018? If you invested $10,000 in
Starbucks on Dec, 2017, how much would the investment be worth on
January, 2018?
2. Using the data in the table, what is the continuously compounded
monthly return between December, 2017 and January, 2018? Convert
1this continuously compounded return to a simple return (you should
get the same answer as in part a).
3. Assuming that the simple monthly return you computed in part (1)
is the same for 12 months, what is the annual return with monthly
compounding?
4. Assuming that the continuously compounded monthly return you computed
in part (2) is the same for 12 months, what is the continuously
compounded annual return?
5. Using the data in the table, compute the actual simple annual return
between December 2017 and December 2018. If you invested $10,000
in Starbucks at the end of December 2017, how much would the investment
be worth at the end of December 2018? Compare with your
result in part (3).
6. Using the data in the table, compute the actual annual continuously
compounded return between December 2017 and December 2018. Compare
with your result in part (4). Convert this continuously compounded
return to a simple return (you should get the same answer
as in part 5).
Part II. Excel exercises
Go to http://finance.yahoo.com and download monthly data on Starbucks
(ticker symbol SBUX) over the 15 year period Janurary, 2004 to January,
2019. See the Homework page on the class website for detailed instructions
on how to download data from Yahoo!. (Note, you may need to start
a month earlier in order to obtain the full range; you may also note that
Yahoo designates monthly data with date ”mm/1/yy”, but you may treat
the downloaded data as ”end-of-month”. ) Read the data into Excel and
make sure to re-order the data so that time runs forward. Do your analysis
on the monthly closing price data (which should be adjusted for dividends
and stock splits). Name the spreadsheet tab with the data “data”.
1. Make a time plot (line plot in Excel) of the monthly price data over
the period (end of Jan 2004 through Jan 2019. Please put informative
titles and labels on the graph. Place this graph in a separate tab
(spreadsheet) from the data. Name this tab “graphs”. Briefly comment
2on what you see (e.g. price trends, etc.); you can comment within the
spreadsheet.
(a) If you invested $1,000 in Jan 2004, what would your investment
be worth in Jan 2018?
(b) What is the compound annual rate of return over this period assuming
annual compounding? (Hint: what is the geometric average
annual rate for the 15 year investment?)
2. Make a time plot of the natural logarithm of monthly price data over
the entire and place it in the “graph” tab. Comment on what you see
and compare with the plot of the raw price data.
(a) Why is a plot of the log of prices informative? (Hint: what is the
slope between two time periods?)
3. Using the monthly price data over the period in the “data” tab, compute
simple monthly returns (assume Starbucks did not pay a dividend
over this period). When computing returns, use the convention that
Pt
is the end of month closing price. Make a time plot of the monthly
returns, place it in the “graphs” tab and comment. Keep in mind that
the returns are percent per month and that the annual return on a US
T-bill is about 0.5% right now.
4. Compute simple annual returns for the years 2004 through 2019 (note:
there are easy and hard ways to do this). Make a time plot of the
annual returns, put them in the “graphs” tab and comment. Note: You
may compute annual returns using overlapping data or non-overlapping
data. With overlapping data you get a series of annual returns for every
month. That is, the first month annual return is from Jan, 2004 to Jan,
2005. The second month annual return is from the Feb 2004 to Feb
2015 etc. With non-overlapping data you get a series of 15 annual
returns for the 15 year period 2004:Jan - 2019:Jan. That is, the annual
return for 2004:Jan - 2005:Jan is computed from the data of Jan 2004
through Jan 2005. The second annual return is computed from the Jan
2005 through Jan 2006 etc.
5. Use the monthly data over the full period to compute continuously
compounded (cc) monthly returns and place them in the “data” tab.
3Make a time plot of the monthly cc returns, put them in the ”graphs”
tab and comment.
(a) Briefly compare the continuously compounded returns to the simple
returns. Which ones are bigger?
6. Compute continuously compounded annual returns for the years 2004
through 2019 (Again, there are easy and hard ways to do this). Make
a time plot of the annual returns and comment. Briefly compare the
continuously compounded returns to the simple returns.
Part III. R Exercises - OPTIONAL
[PLEASE TRY THIS PART OF THE HOMEWORK AS MUCH AS YOU
CAN; you do not have to turn it in.]
Go to http://finance.yahoo.com and download monthly data on Starbucks
(ticker symbol SBUX) over the period March, 2003 to March, 2018.
Read the data into Excel and make sure to reorder the data so that time
runs forward. Delete all columns except those containing the dates and the
adjusted closing prices. Save the file as a .csv (comma separated value) file
and call it sbuxPrices.csv. This is important because base R does not have
functions for importing data from an Excel spreadsheet (see the RODBC and
xlsReadWrite packages for functions to read and write directly to Excel files).
Start R and open the file econ424lab1.r. Execute the commands in this
file line by line. Copy and paste your output into a Word (or whatever word
processor you use) document to show that you have done this assignment.
1. Import the data in the file sbuxPrices.csv using the R function read.csv()
into the data.frame object sbux.df. Follow the commands in econ424lab1.r
to manipulate the data.
2. Plot the closing price data using the plot() function. Notice that the
dates do not show up on the x-axis in the line plot. We will learn how
to fix this in future labs.
3. Compute monthly simple and continuously compounded returns. Plot
these returns separately and on the same graph.
44. Finally, the R package dygraphs (rstudio.github.io/dygraphs/) has
functions for creating interactive time series graphs similar to those
on finance.yahoo.com. If you are using R studio then you can view
the graph in the R studio web viewer. Follow the short example at
the end of the code in econ424lab1.r to see how easy it is to create
an interactive web graph using dygraphs within R studio (Besides
installing the package dygraphs, you should also install xts and zoo
for handling time-series data.)
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