# Problem Set 1 hint…

Problem Set 1 is due at the beginning of class on Tuesday, January 22. Here is a hint for solving the 4th question on problem set 1.

The objective is to determine how big a hospital must be so that the cost per patient-day is minimized. We are not interested in minimizing total cost; if this were the case, there would be no hospital because marginal costs are positive, which implies that total cost is positively related to the number of patient-days.

The cost equation C = 4,700,000 + 0.00013X2 tells you the total cost as a function of the number of patient-days. This is why you are asked in part “a” of the 4th question to derive a formula for the relationship between cost per patient-day and the number of patient days. Once you have that equation, then that is what you minimize, and you’ll be able to answer the question concerning optimal hospital size.

# Volatility, now the whole thing

It just so happens that Hoover Senior Fellow (and former Univ. of Chicago Finance professor) John Cochrane posted an article yesterday entitled “Volatility, now the whole thing” which builds and expands upon today’s implied volatility topic in Finance 4335. Cochrane’s article provides a broader framework for thinking critically about the implications of volatility for future states of the overall economy. This article is well worth everyone’s time and attention, so I highly encourage y’all to read it!

# Lagrangian Multipliers

There is a section in the assigned “Optimization” reading due Thursday, 1/17 on pp. 74-76 entitled “Lagrangian Multipliers” which (as noted in footnote 9 of that reading) may be skipped without loss of continuity. The primary purpose of this chapter is to re-acquaint students with basic calculus and how to use the calculus to solve so-called optimization problems. Since the course only requires solving unconstrained optimization problems, there’s no need for Lagrangian multipliers.

Besides reading the articles entitled “Optimization” and “How long does it take to double (triple/quadruple/n-tuple) your money?” in preparation for this coming Thursday’s meeting of Finance 4366, make sure that you fill out and email the student information form as a file attachment to options@garven.com prior to the beginning of tomorrow’s class. As I explained during today’s class meeting, this assignment counts as a problem set, and your grade is 100 if you turn this assignment in on time (i.e., sometime prior to tomorrow’s class meeting) and 0 otherwise.

# How to know whether you are on track with Finance 4366 assignments

At any given point in time during the upcoming semester, you can ensure that you are on track with Finance 4366 assignments by monitoring due dates which are published on the course website. See http://fin4366.garven.com/readings/ for due dates pertaining to reading assignments, and http://fin4366.garven.com/problem-sets/ for due dates pertaining to problem sets. Also, keep in mind that short quizzes will be administered in class on each of the dates indicated for required readings. As a case in point, since the required readings entitled “Optimization” and ” How long does it take to double (triple/quadruple/n-tuple) your money?” are listed for Thursday, January 11, this means that a quiz based upon these readings will be given in class on that day.

Important assignments due on the second class meeting of Finance 4366 (scheduled for Thursday, January 11) include: 1) filling out and emailing the student information form as a file attachment to options@garven.com, 2) subscribing to the Wall Street Journal, and 3) subscribing to the course blog. A completed Student information form is graded as a problem set and receives 100 points; if you don’t turn in a Student information form, then you will receive a 0 for this “problem set”. Furthermore, tasks 2 and 3 listed above count toward your class participation grade in Finance 4366.

Regarding the student information form, I prefer that you complete this form (by either typing or writing) and email it to options@garven.com prior to the beginning of class on Thursday, January 17.  However, if you prefer, you may turn in a hard copy instead at the beginning of class on that day.

# Khan Academy “Finance and capital markets” videos

Not only are the Khan Academy Calculus and Statistics videos that I referenced in a previous posting quite useful; I am also a big fan of the Khan Academy “Finance and capital markets” videos which are located at https://www.khanacademy.org/economics-finance-domain/core-finance; these videos do a great job of effectively presenting many of the most important concepts which are typically covered in undergraduate and MBA level finance curricula (indeed, the content provided by the “Options, swaps, futures, MBSs, CDOs, and other derivatives” subsection of the “Finance and capital markets” page effectively subsumes most of the Finance 4366 course content!

# On the relationship between the S&P 500 and the CBOE Volatility Index (VIX)

Besides going over the course syllabus during the first day of class on Tuesday, January 15, we will also discuss a particularly important “real world” example of financial risk. Specifically, we will look at the relationship between stock market returns (as indicated by daily percentage changes in the SP500 stock market index) and stock market volatility (as indicated by daily percentage changes in the CBOE Volatility Index (VIX)):

As indicated by this graph from page 21 of the lecture note for the first day of class, daily percentage changes on closing prices for VIX and the SP500 are strongly negatively correlated. In the graph above, the y-axis variable is the daily return on the SP500, whereas the x-axis variable is the daily return on the VIX. The blue points represent 7,311 daily observations on these two variables, spanning the time period from January 2, 1990 through January 7, 2019. When we fit a regression line through this scatter diagram, we obtain the following equation:

${R_{SP500}} = 0.0588 - 0.1139{R_{VIX}}$,

where ${R_{SP500}}$ corresponds to the daily return on the SP500 index and ${R_{VIX}}$ corresponds to the daily return on the VIX index. The slope of this line (-0.1139) indicates that on average, daily VIX returns during this time period were inversely related to the daily return on the SP500; i.e., when volatility as measured by VIX went down (up), then the stock market return as indicated by SP500 typically went up (down). Nearly half of the variation in the stock market return during this time period (specifically, 48.73%) can be statistically “explained” by changes in volatility, and the correlation between ${R_{SP500}}$ and ${R_{VIX}}$ comes out to -0.696. While a correlation of -0.698 does not imply that ${R_{SP500}}$ and ${R_{VIX}}$ will always move in opposite directions, it does indicate that this will be the case more often than not. Indeed, closing daily returns on ${R_{SP500}}$ and ${R_{VIX}}$ during this period moved inversely 78.4% of the time.

You can see how the relationship between the SP500 and VIX evolves prospectively by entering http://finance.yahoo.com/quotes/^GSPC,^VIX into your web browser’s address field.On the relationship between the S&P 500 and the CBOE Volatility Index (VIX)

# The 17 equations that changed the course of history (spoiler alert: we use 4 of these equations in Finance 4366!)

I especially like the fact that Ian Stewart includes the famous Black-Scholes equation (equation #17) on his list of the 17 equations that changed the course of history; Equations (2), (3), (7), and (17) play particularly important roles in Finance 4366!

From Ian Stewart’s book, these 17 math equations changed the course of human history.

# How to obtain a Wall Street Journal subscription

A subscription to the Wall Street Journal is required for Finance 4366. In order to subscribe to the Wall Street Journal (WSJ), go to http://r.wsj.net/j73NM. Your WSJ subscription includes access to print, online, tablet and mobile editions, and only costs \$1 for a 15 week subscription. At your option, you may choose to receive both the digital and paper versions of WSJ or only the WSJ digital version.

Throughout the semester, I will often reference specific WSJ articles in class and on the course blog. Finance 4366 topics (as well as topics in many of your other business school courses) come to life in the world outside the Baylor bubble when you make a habit of reading the WSJ on a regular basis. Furthermore, if you expect to interview for jobs or internships anytime soon, reading the WSJ will give you a leg up on the competition, since you will be better informed and have more compelling ideas and insights to share with recruiters.

In closing, the following (2 minute) video provides a helpful introduction to the WSJ, providing time-saving tips to help you get the most from WSJ and succeed not only in Finance 4366, but also your other courses and careers:

# Instructions for subscribing to the Options, Futures and Other Derivatives Course Blog

A course blog has been established for Finance 4366 at the address http://derivatives.garven.com; it is also linked from the “Course Blog” button located on the course website. I recommend that you follow the options, futures, and other derivatives course blog regularly via email, Facebook, and/or Twitter.

The options, futures, and other derivatives course blog provides me with a convenient means for distributing important announcements to the class. Topics covered on the course blog typically include things like changes in the course schedule, clarifications and hints concerning problem sets, information about upcoming exams, announcements concerning extra credit opportunities, and short blurbs showing how current events relate to many of the topics which we cover in Finance 4366.

If you are either a Facebook or Twitter user, everything that is posted on the options, futures, and other derivatives course blog is automatically posted to Facebook and “tweeted”, so you can also subscribe by “liking” the Finance 4366 Facebook page or by “following” @fin4366 on Twitter. Finally, you can also subscribe via email. The remainder of this blog entry explains how to subscribe to the options, futures, and other derivatives course blog via email.

Email Subscription Instructions:

Email Subscription Instructions: If you would like to receive the risk management course blog via email, you can do this by going to http://derivatives.garven.com and entering your email address in the form provided on the right hand side of that webpage:

After clicking “Subscribe”, the following information will appear on your screen:

Next, check for an email from “Options, Futures, and Other Derivatives <donotreply@wordpress.com>”:

Next, simply click the “Confirm Follow” button. This will cause you to receive the following email:

From that point forward, whenever I post to the course blog, you will immediately receive a nicely formatted version of the blog posting via email. Also, you can opt to change your delivery preferences, or even cancel your subscription.

# Required Text Materials in Finance 4366

The required textbook for the Options, Futures, and Other Derivatives (Finance 4366) course at Baylor University (coincidentally) shares the same title as the course. Authored by University of Toronto finance professor John Hull, the “Options, Futures and Other Derivatives” textbook is now in its 10th edition, and it is quite expensive; on Amazon, it costs around \$220 to \$230 to purchase, and around \$45 to rent.

An important marketing “scheme” (or less charitably, “scam”) in the world of textbook publishing involves frequently publishing “new” editions of textbooks. Often, new editions are not all that different from earlier editions. This is certainly the case with Hull’s textbook. For example, I found that by comparing chapter titles and numbers in tables of contents for the 9th and 10th editions, the 10th edition has a new ninth chapter that I would not cover anyway; furthermore, two chapter titles were slightly renamed but chapter contents in both cases remain completely unchanged.

Although I list the 10th (US) edition as “required” for Finance 4366 in the course syllabus, you are welcome to rely upon earlier (and considerably less expensive) editions of this book; e.g., the 7th, 8th, and 9th (US and international) editions are completely acceptable substitutes, since the chapters that we cover in Finance 4366 are virtually identical across the 7th through 10th editions. For example, if you go to http://www.ebay.com/bhp/options-futures-and-other-derivatives, you will find an array of various editions of Hull’s textbooks priced at a small fraction of what Amazon charges (make sure you are buying the textbook, not the solutions.pdf manual). Perhaps you may be able to find even better deals elsewhere; just make sure that the book author (John C. Hull) and title (Options, Futures, and Other Derivatives) are the same, and that the edition of the book is no earlier than the 7th edition.

Finally, don’t worry about whether the book you buy has the CD; the software on the CD (called “Derivagem”) is a rather simple Excel spreadsheet which you can download from the following address: http://fin4366.garven.com/spring2019/DG300.xls.