… are available at http://fin4335.garven.com/fall2023/ps2solutions.pdf.

### Risk Pooling Class Problem and Solutions

The risk pooling class problem is available at http://fin4335.garven.com/fall2023/Risk_Pooling_Class_Problem.pdf. Solutions are at http://fin4335.garven.com/fall2023/Risk_Pooling_Class_Problem_Solution.pdf.

### Finance 4335 Grades on Canvas

Here is a “heads-up” about the Finance 4335 grade book on Canvas. There, you will find grade averages that reflect 1) attendance grades for the 4 class meetings that have occurred to date, 2) quizzes 1-2, and 3) problem set 1 plus the student survey. Thus, your current (September 4) course numeric grade in Finance 4335 is based on the following equation:

**(1) Current Course Numeric Grade** = (.10(Attendance and Participation) +.10(Quizzes) +.20(Problem Sets))/.4

Note that equation (1) is a special case of the final course numeric grade equation (equation (2) below) which also appears in the “Grade Determination” section of the course syllabus:

**(2) Final Course Numeric Grade** =.10(Attendance and Participation) +.10(Quizzes) +.20(Problem Sets) + Max{.20(Midterm Exam 1) +.20(Midterm Exam 2) +.20(Final Exam), .20(Midterm Exam 1) +.40(Final Exam), .20(Midterm Exam 2) +.40(Final Exam)}

My goal going forward is for the Finance 4335 grade book to dynamically incorporate new grade information on a timely basis for each student, consistent with the final course numeric grade equation. For example, after midterm 1 grading is complete, equation (3) will be used to determine your numeric course grade:

**(3) Course Numeric Grade**** after Midterm 1 **= (.10(Attendance and Participation) +.10(Quizzes) +.20(Problem Sets) +.20(Midterm 1))/.6

After midterm 2 grades are recorded, equation (4) will be used to determine your numeric course grade at that point in time:

**(4) Course Numeric Grade** **after Midterm 2 **= (.10(Attendance and Participation) +.10(Quizzes) +.20(Problem Sets) +.20(Midterm 1) +.20(Midterm 2))/.8

After the fall semester and the final exam period are over, all Finance 4335-related grades will have been collected, and I will use equation 2 above to calculate your final course numeric grade. At that time, your final course *letter* grade will be based on the following schedule (which appears in the “Grade Determination” section of the course syllabus):

A | 93-100% | C | 73-77% |

A- | 90-93% | C- | 70-73% |

B+ | 87-90% | D+ | 67-70% |

B | 83-87% | D | 63-67% |

B- | 80-83% | D- | 60-63% |

C+ | 77-80% | F | <60% |

### Problem Set 2 (2nd of 2) helpful hints)

The first set of problem set 2 hints appears at http://risk.garven.com/2023/09/03/problem-set-2-helpful-hints/.

Here’s the second problem set 2 hint, based on the following questions:

**Finance 4335 Student Question**: “I am in the process of completing Problem Set 2, but I am getting stumped, are there any class notes that can help me with 1E and question 2? I am having trouble finding the correct formulas. Thank you.”

**Dr. Garven’s Answer (for question 2)****:** Yesterday, I provided some hints about problem set #2 @ http://risk.garven.com/2023/09/03/problem-set-2-helpful-hints/. Regarding question #2, here is what I wrote there: “The second problem involves using the standard normal probability distribution to calculate the probabilities of earning various levels of return by investing in risky securities and portfolios; see pp. 13-19 of the http://fin4335.garven.com/fall2023/lecture4.pdf lecture note for coverage of that topic.”

The inputs for this problem are all specified in parts A and B; in part A, the expected return is 10% and the standard deviation is 20%, whereas in part B, the expected return is 6.5% and the standard deviation is 10%. The probability of losing money in parts A and B requires calculating the z statistics for both cases. In part A, the z stat is z = (0-mu)/sigma= (0-10)/20, and in part B it is z = (0-mu)/sigma= (0-6.5)/10. Once you have the z stats, you can obtain probabilities of losing money in Parts A and B by using the z table from the course website.

Part C asks a different probability question – What the probability of earning *more* than 6% is, given the investment alternatives described in parts A and B? To solve this, calculate 1-N(z) using the z table, where z = (6-mu)/sigma.

**Dr. Garven’s Answer (for question 1E)****: **Regarding 1E – since returns on C and D are uncorrelated, this means that they are *statistically independent* of each other. Thus, the variance of an equally weighted portfolio consisting of C and D is simply the weighted average of these securities’ variances. See the http://fin4335.garven.com/fall2023/lecture3.pdf lecture note, page 9, the final two bullet points on that page. Also see the portfolio variance equation on page 13, which features two variance terms and one covariance term – Since C and D are statistically independent, the third term there (2w(1)w(2)sigma(12)) equals 0.

### Problem Set 2 helpful hints

Problem Set 2 is available from the course website at http://fin4335.garven.com/fall2023/ps2.pdf; its due date is Tuesday, September 5.

Problem Set 2 consists of two problems. The first problem requires calculating expected value, standard deviation, and correlation, and using this information as inputs into determining expected returns and standard deviations for 2-asset portfolios. The second problem involves using the standard normal probability distribution to calculate the probabilities of earning various levels of return by investing in risky securities and portfolios; see pp. 13-19 of the http://fin4335.garven.com/fall2023/lecture4.pdf lecture note for coverage of that topic.

### On the importance of oversight, financial controls, and risk management in the real world – the case of FTX and Sam Bankman-Fried

I highly recommend that everyone tune in to Season 3, episodes 8 through 14 of the Michael Lewis podcast, “Against the Rules.” These seven episodes, each averaging around 35 minutes, delve into the extensive research conducted by Lewis for his upcoming book on the fascinating story of Sam Bankman-Fried, a 31-year-old entrepreneur who served as the founder and CEO of the cryptocurrency exchange FTX and its associated trading firm, Alameda Research. Both entities made headlines due to their dramatic collapse, culminating in Chapter 11 bankruptcy filings in late 2022. To access the podcast, you can visit Michael Lewis’s podcast homepage at https://omny.fm/shows/against-the-rules-with-michael-lewis/.

This podcast illustrates how a lack of oversight, financial controls, and risk management gave rise to spectacular business failures. The podcast host, Michael Lewis, is a well-known and highly regarded author whose books often become major motion picture productions; e.g., The Blind Side (2009), Moneyball (2011), and The Big Short (2015).

### Formula Sheet for Extra Credit stat problem

I have posted a formula sheet at http://fin4335.garven.com/fall2023/statformulasheet.pdf for the statistics extra credit problem due tomorrow, September 1 at 5 p.m.

### Gamma Iota Sigma Interest Meeting, August 31, 6:30-7:30 in Foster 322

The purpose of the Gamma Iota Sigma (GIS) at Baylor University is to promote, encourage, and sustain student interest in insurance, risk management, and actuarial science as professions, to promote high moral and academic excellence of chapter members, and to facilitate the interaction between Baylor University and the business community by fostering research activities, scholarship, and networking opportunities.

### Erratum: Problem Set 1 solutions

With the help of one of your Finance 4335 classmates, we have discovered, and have corrected an important typo contained in the original solution for problem 5. If you downloaded the PDF for the solutions for problem set 1 prior to 1:30 pm today, please trash that PDF and replace it by re-downloading it from http://fin4335.garven.com/fall2023/ps1solutions.pdf.

### Visualizing Taylor polynomial approximations

On pp. 18-23 of the Mathematics Tutorial, I show how *y = **e*^{x} can be approximated with a Taylor polynomial centered at *x*=0 for values ranging from -2 to +2. In his video lesson entitled “Visualizing Taylor polynomial approximations”, Sal Kahn essentially replicates my work; the only difference between Sal’s numerical example and mine is that Sal approximates *y = **e*^{x} with a Taylor polynomial centered at *x*=3 instead of *x*=0. The important insight provided in both cases is that the accuracy of Taylor polynomial approximations increases as the order of the polynomial increases.