Upon closer inspection, I noticed that my first problem on Problem Set 4 was identical to the Risk Aversion Class Problem that we worked in class last Thursday, so as of 6:15 p.m. this evening, I uploaded a new (replacement) version of Problem Set 4, which is due at the beginning of class on Thursday, 9/20. Therefore, if any of you downloaded this problem set prior to 6:15 p.m. today, be sure to replace it with this new Problem Set 4, which looks like this:
Here’s a screenshot from a spreadsheet that I coded for the risk pooling class problem (linked below) that we discussed during class yesterday. We found in class yesterday (and now find in this spreadsheet today), that if risks are independent and identically distributed, then by increasing the number of policies in the risk pool, the probability that the average loss exceeds $1,500 declines as we add policies. Without risk pooling, the probability of a “large” loss of $1,500 is 30.85%; with 5 policies, it is 13.18%, and with 10 policies it is 5.69%. However, if risks are positively correlated, then both unique and systematic risks influence this calculation. For example, with 10 policies that have .1 correlation, the probability that the average loss exceeds $1,500 is 12.57% (compared with 5.69% when there is zero correlation):
Problem Set 1 is due at the beginning of class tomorrow. Here is a hint for solving the 4th question on this problem set.
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 the total cost of operating a hospital; a sure-fire way to minimize total cost would be to not even have a hospital in the first place. Indeed, if you were to differentiate the total cost function given by C = 4,700,000 + 0.00013X2 with respect to X, this is what the math would tell you.
In part “a” of the 4th question, you are asked to “derive” a formula for the relationship between cost per patient-day and the number of patient days; in other words, what you are interested in determining is what is the most cost-efficient way to scale a hospital facility such that the cost per patient-day is minimized. Once you obtain that equation, then you’ll be able to answer the question concerning optimal hospital size.
There is a section in the assigned “Optimization” reading tomorrow on pp. 74-76 entitled “Lagrangian Multipliers” which (as noted in footnote 9) 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 tomorrow’s meeting of Finance 4335, make sure that you fill out and email the student information form as a file attachment to email@example.com prior to the beginning of tomorrow’s class. As I explained during yesterday’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.
At any given point in time during the upcoming semester, you can ensure that you are on track with Finance 4335 assignments by monitoring due dates which are published on the course website. See http://fin4335.garven.com/readings/ for due dates pertaining to reading assignments, and http://fin4335.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, August 23, 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 4335 (scheduled for Thursday, August 23) include: 1) filling out and emailing the student information form as a file attachment to firstname.lastname@example.org, 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 fail to 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 4335.
Regarding the student information form, I prefer that you complete this form (by either typing or writing) and email it to email@example.com prior to the beginning of class on Thursday. However, if you prefer, you may turn in a hard copy instead at the beginning of class on Thursday.
A course blog has been established for Finance 4335 at the address http://risk.garven.com; it is also linked from the “Course Blog” button located on the course website. I recommend that you follow the risk management course blog regularly via email, RSS, Facebook, and/or Twitter.
The risk management 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 4335.
If you already are familiar with RSS, this is a great way to subscribe to the options, futures, and other derivatives course blog. By going to the http://risk.garven.com/feed webpage, you can subscribe by using Firefox’s Live Bookmarks feature, Internet Explorer’s RSS feed subscription feature, or an RSS reader. 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 4335 Facebook page or by “following” @fin4335 on Twitter. Finally, you can also subscribe via email. The remainder of this blog entry explains how to subscribe to the risk management 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://risk.garven.com and entering your email address in the form provided on the left hand side of that webpage:
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.
Since many of the topics covered in Finance 4335 require a basic knowledge and comfort level with differential calculus and probability & statistics, the second class meeting (August 23) will include a mathematics tutorial, and the third and fourth class meetings (August 28-30) will cover probability & statistics. I know of no better online resource for brushing up on (or learning for the first time) these topics than the Khan Academy.
So here are my suggestions for Khan Academy videos which cover these topics (unless otherwise noted, all sections included in the links which follow are recommended):
- Calculus: Taking derivatives, Optimization with calculus, Visualizing Taylor Series for e^x
- Probability and statistics: Basic probability, Compound, independent events, Permutations, Combinations, probability using combinatorics, Random variables and probability distributions, Binomial distribution, Law of Large Numbers, and Introduction to the Normal Distribution.
Finally, if your algebra is a bit rusty, I would also recommend checking out the Khan Academy’s review of algebra.
A subscription to the Wall Street Journal is required for Finance 4335. In order to subscribe to the Wall Street Journal (WSJ) for the Fall 2018 semester, 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 on the course blog and in class. Finance 4335 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 read 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 4335, but also your other courses and careers: