Author: Dr. James Garven

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Actuarially Fair Value For an Insurance Policy

A Finance 4335 student asked me the following question via email earlier today:

Q: “How do you find the actuarially fair value for an insurance policy?”

Here’s my answer to this question:

A: The actuarially fair value corresponds to the expected value of the insurance indemnity; the indemnity is the amount of coverage offered by an insurance policy. Under “full coverage”, 100% of the loss is indemnified, and in such a case, the actuarially fair premium is equal to the expected value of the loss distribution.

The concept of “actuarially fair” insurance prices/premiums, along with implications for the demand for insurance, is explained in two previously assigned readings (italics added for emphasis):,

  1. on page 4 of the Supply of Insurance assigned reading (just prior to the section entitled “Example 2: Correlated Identically Distributed Losses), the following sentence appears, “A premium that is equal to the expected outcome is called an actuarially fair premium”;
  2. on page 30 of the Basic Economics: How Individuals Deal with Risk (Doherty, Chapter 2) assigned reading, consider the following excerpt: “Ignoring transaction costs, an insurer charging a premium equal to expected loss would break even if it held a large portfolio of such policies. This premium could be called a fair premium or an actuarially fair premium, denoting that the premium is equal to the expected value of loss (sometimes called the actuarial value of the policy). The term fair is not construed in a normative sense; rather it is simply a reference point”; and
  3. on page 43 of the Basic Economics: How Individuals Deal with Risk (Doherty, Chapter 2) assigned reading, in the first sentence of the first full paragraph: “We know from the Bernoulli principle that a risk averter will choose to fully insure at an actuarially fair premium.”
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Extra credit opportunity – Insurance Economics Class Problem – due at the beginning of class on Tuesday, 2/28

We will begin class on Tuesday by going over the solutions for the Insurance Economics Class Problem which I handed out on Thursday (also available at http://fin4335.garven.com/spring2023/Insurance_Economics_Class_Problem.pdf).

Since we didn’t get very far on Thursday’s class problem, I decided to turn it into an extra credit problem set for Finance 4335. It will be due at the beginning of class on Tuesday, and the grade you earn will replace your lowest problem set grade in Finance 4335 (that is, if your extra credit grade is higher than your lowest problem set grade).

As I promised on Thursday, I also now provide some helpful hints for the Insurance Economics Class Problem in the PDF file linked below (Insurance_Economics_Class_Problem_Solutions (Helpful Hints). This class problem is primarily based on the “Demand for Insurance: Full vs. Partial Coverage” reading that was assigned for last Thursday’s class meeting.

Insurance_Economics_Class_Problem (Helpful Hints).pdf

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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 12 class meetings which have occurred to date, 2) quizzes 1-5, and 3) problem sets 1-4.  Thus, your current (February 25) course numeric grade in Finance 4335 is based on the following equation:

(1) Current Course Numeric Grade = (.10(Class Attendance) +.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(Class Attendance) +.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)}

Going forward, my goal is for the Finance 4335 grade book to dynamically incorporate new grade information on a timely basis for each student, in a manner 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(Class Attendance) +.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(Class Attendance) +.10(Quizzes) +.20(Problem Sets) +.20(Midterm 1) +.20(Midterm 2))/.8

After the spring 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%

 

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Brief Student and Professor Q&A about the Midterm 1 exam in Finance 4335

Student Query:  Hello Dr. Garven, I had a quick question regarding the upcoming exam. Will questions only be pulled from information pertaining to problem sets 3 & 4? Or will there be questions about the math and stat review portion as well?

Dr. Garven’s Response:  Students will find the study guide to be very helpful in preparing for tomorrow’s midterm exam in Finance 4335. The exam covers topics from the January 31 and February 9 assigned readings, the four-part Decision-Making under Risk and Uncertainty lecture series (see item 5 on the lecture notes page), Problem Set 3 and Problem Set 4, and the Risk Aversion and Stochastic Dominance class problems. I also recommend reviewing the various PDFs linked from the Problem Set Solutions page.

Math and stat principles also play important roles in the theory of risk aversion (e.g., the math behind the Arrow-Pratt framework helps explain differences in the degree to which decision-makers are risk averse), and the application of Taylor series math to expected utility indicates that variance is an inadequate risk measure if risks are skewed or fat-tailed.

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Commercial real estate scholarship opportunity

Subject: Trepp’s 2023 Education Scholarship – Those interested in Commercial Real Estate – Apply Now!: Department of Finance Insurance and Real Estate

We are pleased to announce the opening of the application period for the inaugural Trepp Inc. Education Segment Scholarship. The scholarship period is open from February 10-April 7, 2023. Scholarship(s) up to $10,000 USD for tuition will be awarded based on merit.

Please see the application, including all eligibility criteria, learnor visiting www.trepp.com/scholarship2023. Partial or incomplete submissions will not be accepted or reviewed.

Students must have a minimum GPA of 3.4 (4.0 scale), be a citizen of the U.S., be a full-time junior, senior, or graduate student (2023 – 2024 academic year), enrolled at an accredited college or university and have the intent to pursue a career in CRE with a focus of study from one of the following commercial real estate fields. Award winner(s) will be notified via email and will be announced via Trepp social channels by May 18, 2023.

Should you have any questions regarding the application process, please feel free to contact me at (212) 329-6298.

Best,
Erin

Erin M. Liberatore-Timko | Director, Academic & Industry Relations | Trepp, Inc.
600 Fifth Avenue, 7th Floor, New York, NY 10020
Phone: +1 212 329 6298 | Email: erin_timko