William B. Vogt ECON 4750 (37-419) Homework 4
Homework 4
Assigned: Sep 03, 2018
Due: On ELC, Sep 21, 2018
Problems
1. (10 points) Bailey: Read chapter 3. On your assignment paper, just
write \Done" for this problem to acknowledge that you did it.
2. (10 points each subpart) We will investigate the e ects of chicken
prices, corn prices, and soybean prices on the operating pro ts and
stock price of Sanderson Farms (ticker symbol SAFM), a large, pub-
licly traded, producer of chickens in the US. Our investigation will be
similar to our investigation in class of the petroleum re ner, Valero
Energy (VLO).
Recall that for VLO, we calcuated a 3:2:1 crack spread to understand
how commodity prices in uenced pro tability and stock price for re-
ners. For SAFM, we are going to do something similar. From other
sources, suppose we have determined that, roughly, it takes 1.8 lbs of
corn and 0.6 lbs of soy meal to manufacture each pound of chicken. We
are rst going to calculate a \chicken crack spread" from information
on the prices of chicken, soy, and corn.
You will nd three datasets included with this homework assignment.
These are daily, monthly, and quarterly datasets. Some of the data
(corn, soy, and SAFM stock prices) are available daily because they
trade on US nancial markets. These are in the daily dataset.
Unfortunately, because there is no commodity futures market for chicken,
there is no daily data on chicken prices. Instead, we will settle for
monthly data from the USDA (If I were slightly less lazy, we could
use weekly data collected by Georgia’s Dept of Agriculture). In the
Terry College 1 of 3 UGA
William B. Vogt ECON 4750 (37-419) Homework 4
monthly dataset are the monthly chicken broiler prices. Also in that
dataset are monthly averages of the variables in the daily data.
Finally, SAFM’s operating income is available quarterly. This vari-
able, along with quarterly averages of the daily and monthly data, is
available in the quarterly dataset. It should not a ect what you do,
but SAFM’s scal year is a little odd|the rst quarter of its scal
2016, for example, was November and December of 2015 along with
January of 2016. The second quarter of scal 2016 was Feb, Mar, and
Apr of 2016. Etc.
Each of the three important prices, of corn, of soy, and of broilers (i.e.
whole chickens), is expressed in dollars per lb in the data. SAFM’s
(adjusted) stock price is expressed in dollars per share. SAFM’s oper-
ating income is expressed in millions of dollars.
Where possible, use the data with the highest temporal resolution (i.e.
with the smallest time increments). For example, only use quarterly
data for analyses where you need SAFM’s income. Use monthly or
daily data where you don’t need SAFM’s income.
In making line plots over time, it is useful to have the data sorted by
date. To do this, use the order command to sort the data by date like
this: monthlySAFM <- monthlySAFM[order(monthlySAFM$Date),].
(a) Please calculate a chicken crack spread for SAFM|it should mea-
sure how much pro t there is to be had, per pound, re ning soy
and corn into chicken. In addition, calculate and report summary
statistics for the crack spread and for the prices of soy, corn, and
broilers.
(b) Please calculate the covariance and correlation between SAFM
stock price and the chicken crack spread. Please calculate the
covariance and correlation between SAFM operating income and
chicken crack spread. What do they mean? Are they as you
would expect?
(c) Please make a scatterplot of SAFM stock price against chicken
crack spread. Also, please make a line plot showing both SAFM
stock price and chicken crack spread over time|you will likely
need to express the crack spread in cents per pound, rather than
dollars for the plot to \look right." Do the plots look as you
would expect them to? What do they show?
Terry College 2 of 3 UGA
William B. Vogt ECON 4750 (37-419) Homework 4
When we made the scatterplots in class, we left the plot title
blank and the axis titles looking ugly. Please don’t do that here.
You can use options to the plot command to control these things.
For example putting main=\Crack Spreads A ect Pro t?" as an
option to plot will put that sentence as the title of the graph.
Similarly, xlab and ylab options will allow you to put better axis
titles. When the x-axis is a date, it does not need a title, and you
can put xlab=\" to eliminate it.
3. (15 points) Please formulate and write down a Classical Linear Re-
gression Model embodying the theory that SAFM stock price is caused
by chicken crack spread. Please interpret each term of the equation.
Interpret the terms of the equation in general in the context of this
particular example.
4. (15 points) Please calculate, by hand using the formula we discussed
in class, the OLS estimator of the slope of the relationship between
SAFM stock price and chicken crack spread. Verify that your calcula-
tion was correct using R’s lm() function. Interpret your result.
5. (30 points) Bailey, Exercise 1 in chapter 3 on page 86.
Terry College 3 of 3 UGA