Category Archives: Announcements

Spring 2019 Course Announcement – Finance 4366: Options, Futures and Other Derivatives

Here’s the “prospectus” for the Finance 4366 “Options, Futures and Other Derivatives” course that I will be teaching during the upcoming  Spring 2019 semester; if you click on the image, this will bring up a full-page PDF version. If you have been enjoying Finance 4335 this semester, I hope you’ll consider enrolling in Finance 4366 this spring!

Midterm Exam 1 hints and formula sheet

I just posted the formula sheet for the exam at http://fin4335.garven.com/fall2018/formulas_part1.pdf. It is also linked as the first item on the formula sheets page on the course website.  This is identical to the formula sheet which will be attached to the exam booklet.

The exam consists of a total of 4 problems. The first problem is required, and you are also required to work 2 out of the 3 remaining problems on the exam (i.e., select two problems from Problems #2-#4). At your option, you may work all three of Problems #2-#4, in which case I will count the two problems with the highest scores toward your grade on this exam. Each of the graded problems is worth 32 points, so as a “bonus” I’ll add 4 points for including your name on the exam. Thus, the total number of points possible is 100.

Regarding content, the exam is all about stuff that we covered since the beginning of the semester; specifically, risk preferences, expected utility, certainty-equivalent of wealth, risk premiums, and stochastic dominance.

Risk Management: Premium loading Q&A

On 9/24/18, 1:17 PM, "Finance 4335 Student" <Finance4335student@baylor.edu> wrote:

Dr. Garven,

What does the term “premium loading” mean? I’m familiar with many of the concepts in the problem set, but was unable to find this term and how to calculate it in class notes.

– Finance 4335 Student

Here’s my response to "Finance 4335 Student" on the topic of premium loadings:

It corresponds to the markup in the premium relative to the expected value of the claim (also commonly referred to as the expected value of the "indemnity"). In percentage terms, % loading = (premiumE(indemnity))/E(indemnity), and in dollar terms, $ loading = premiumE(indemnity), where E(indemnity) corresponds to the expected value of the indemnity. As we showed in class last Thursday, the expected value of the indemnity corresponds to the expected value of the loss only when full coverage is offered. Under a deductible policy, the indemnity in state s, indemnity(s) = Min(L(s) – Min(L(s), d)), where L(s) corresponds to the state-contingent loss and d corresponds to the dollar value of the deductible. Under a coinsurance policy, the indemnity in state s, indemnity(s) = L(s) – (1-a)L(s), where a corresponds to the coinsurance rate. Under an upper limit policy, indemnity(s) = Min(L(s), u), where u corresponds to the dollar value of the deductible. If you look at the “Insurance Payment Calculations” worksheet tab in the Coinsurance, Deductibles, and Upper Limits Spreadsheet, you’ll see that these are the equations used in order to determine the indemnity schedules under the various contracts listed there.

Assignments for class: Tuesday, September 25

Not surprisingly, the first midterm exam in Finance 4335 (scheduled for Thursday, September 27 in class) will be all about the "Decision Making under Risk and Uncertainty" and “Insurance Economics” topics.

In preparation for next Tuesday’s in-class review session, your assignments are to 1) review the two-page document entitled “Finance 4335 course synopsis for Midterm Exam 1 (also available from the Readings page on the course website as an assigned “optional” reading for Tuesday, September 25), and 2) review Problem Set 3, Problem Set 4, Problem Set 5, and the Sample Midterm 1 Exam Booklet (this is the exam that I gave in Finance 4335 during the Spring 2018 semester). Solutions for the third and fourth problem sets are available now (see http://risk.garven.com/category/problem-set-solutions/), and I will make the solutions for the fifth problem set and the sample Midterm 1 exam available after class on Tuesday.

In closing, I expect that y’all will prepare adequately so that we can have a productive review session next Tuesday. Be sure to come equipped with questions, and I will do my best to provide answers.

Guidelines for completing the first problem on Problem Set 4

During class today, I elaborated further on my blog posting entitled “Hints for solving problem set #4 (Hint #1)”. Specifically, at your option, you may solve the first problem via either calculus or a spreadsheet model.

If you decide to solve the first problem by building your own spreadsheet model, then you must email your spreadsheet model to “risk@garven.com” prior to the start of class on Thursday. In the problem set that you turn in at the beginning of class on Thursday, please reference your spreadsheet when you explain your answers for this problem. However, if you rely upon the calculus for maximizing expected utility, then no spreadsheet is necessary, although you might consider validating the result that you obtain via calculus with a spreadsheet model anyway. Or, you could validate your spreadsheet model with the calculus.

In order to solve this problem via spreadsheet, you’ll need to use the so-called Solver Add-in. The instructions for loading the Solver add-in into Excel are provided at the following webpage:

https://support.office.com/en-us/article/load-the-solver-add-in-in-excel-612926fc-d53b-46b4-872c-e24772f078ca

Hints for solving problem set #4 (Hint #1)

Problem set #4 consists of two problems: 1) an optimal (expected utility maximizing) portfolio problem, and 2) a stochastic dominance problem.  We’ll discuss stochastic dominance tomorrow (and also (hopefully) work a class problem in connection with that concept), but in the meantime allow me to provide you with some hints for setting up  the first problem.

The first problem involves determining how to (optimally) allocate  initial wealth W0 = $100 to (risky) stock and (safe) bond investments for two investors who are identical in all respects except utility. Let \alpha represent the allocation to stock; then the plan is to invest $100\alpha in the stock and $100(1-\alpha) in the bond. The key here is to find the value for \alpha which maximizes expected utility. The problem is based on the following facts:

  • U(W) = W.5; for Investor A and U(W) = ln W for Investor B;
  • W0 = $100 for both investors;
  • Current bond and stock prices are B0 and S0 respectively;
  • End-of-period bond price is B1 = B0(1.05) with probability 1.0; and
  • eEnd-of-period stock price is S1 = S0(1.3) with probability .6 and S1 = S0(.7) with probability .4.

In order to compute expected utility of wealth for either investor, you must first determine state-contingent wealth (Ws). Since there is a 60% chance that the stock increases in value by 30%, a 40% chance that the stock decreases 30%, and a 100% chance that the bond increases in value by 5%, this implies the following:

  • 60% of the time, Ws = \alphaW0(1.3) + (1-\alpha)W0(1.05) = \alpha100(1.30) + (1-\alpha)100(1.05) = \alpha130 + (1-\alpha)105 = 105 + 25\alpha.
  • 40% of the time, Ws = \alphaW0(.7) + (1-\alpha)W0(1.05) = \alpha100(.7) + (1-\alpha)100(1.05) = \alpha70 + (1-\alpha)105 = 105 – 35\alpha.

Therefore, expected utility for Investor A is: E(U(W)) = .6(105 + 25\alpha).5 + .4(105 – 35\alpha).5, and expected utility for Investor B is E(U(W)) = .6ln (105 + 25\alpha) + .4ln(105 – 35\alpha). It is up to you to solve for the optimal value of \alpha for each investor.  There are two ways to do this – via calculus or a spreadsheet model.  Actually, I would encourage y’all to work this problem both ways if time permits because doing so will help you develop an even better grasp of the underlying principles and concepts in Finance 4335.