# Statistics question for

Lecture Notes 2 Exercises

First, read through the lecture note for concepts. Then, go back and execute all the steps I did, with LGF and/or with IBM. Save that work as text and put it into an Appendix at the end of this assignment.

Put all of your graphs, your R work, and your answers to the following questions into a Word document. Submit two documents: (1) that Word document; (2) the Excel file in which you prepared your stock returns, ranges, and log ranges.

Exercise 2.1. State the name of your company, its stock symbol, and tell me something interesting about the company. For motivation, pretend that you are preparing for a job interview with that company, tomorrow. Surely, you would want to demonstrate that you know something of genuine interest about your potential future employer!

Is it interesting that LGF makes movies and TV shows? A little bit interesting, but how about if you could casually mention during the interview that your favorite films made by LGF were the Hunger Games films directed by Francis Lawrence, and that you had been inspired to learn that he started off directing movie videos and that you wanted to work for a company that had the foresight and courage to let a fresh talent like his blossom, particularly given that his Hunger Games films have grossed over one billion dollars.

How long did it take me to come up with that information? Twenty minutes.

Exercise 2.2. For the time period from 1-1-2006 to today, download daily data for your assigned stock as instructed in Section 2, use Excel to compute percentage returns from the Adjusted Close, and import it into R. Delete the first row because of its missing value. Then, show

(a) The time series plot of your closing daily prices, showing proper titles;

(b) The times plot of your daily returns;

(c) Briefly discuss the differences between those two plots. In particular, which looks stable, and which does not?

(d) Is your daily percentage return data coming from a source with a stable population standard deviation?

Exercise 2.3. Show

(a) The R histogram of your closing daily prices with default breaks, show proper titles;

(b) Increase the number of breaks to 300;

(c) Does increasing the number of bins (breaks) show that the data contains stable features or not?

Exercise 2.4. Show

(a) The R histogram of your daily returns with default breaks;

(b) Increase the number of breaks to 300;

(c) Does increasing the number of bins (breaks) show that the data contains stable features? That is, does it seem that the bell-curve is solid and not a phantom?

Exercise 2.5. Stock returns are often modeled in Finance as coming from an underlying Normal distribution. Generate 4000 standard Normal deviates.

(a) Show a time series plot of this series.

(b) Compare that against your time series plot of returns. Does this argue for or against using a Normal distribution as a model for stock returns?

(c) Show a histogram with 300 breaks for this series.

(d) Comparing the shape of your histogram of returns and this new histogram, in what ways does a Normal distribution seem like a good model and in what ways is it not?

Exercise 2.6. A simple measure of variability (or risk) in stocks is the daily range, which is the daily high of Closing Price minus the daily low of Closing Price. You will be using the daily range data that you compute below throughout the rest of the semester, so pay attention!

(a) In R, compute the daily range for your stock and explore its nature using the techniques you have practiced, above. For example, do the points concentrate in a horizontal band? Do you see a stable underlying average? Is the variability stable?

(b) Take the logarithm of the range (R function log) and explore what happens with that, using the techniques and concepts in this lecture note. Does taking the log seem to make time series more manageable? How so?

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