On the Determinants of Risk Aversion

Several years ago, The Economist published a particularly interesting article about various behavioral determinants of risk aversion, entitled “Risk off: Why some people are more cautious with their finances than others”. Here are some key takeaways from this (somewhat dated, but still quite timely) article:

  1. Economists have long known that people are risk averse, yet the willingness to run risks varies enormously among individuals and over time.
  2. Genetics explains a third of the difference in risk-taking; e.g., a Swedish study of twins finds that identical twins had “… a closer propensity to invest in shares” than fraternal ones.
  3. Upbringing, environment, and experience also matter; e.g., “… the educated and the rich are more daring financially. So are men, but apparently not for genetic reasons.”
  4. People’s financial history has a strong impact on their taste for risk; e.g., “… people who experienced high (low) returns on the stock market earlier in life were, years later, likelier to report a higher (lower) tolerance for risk, to own (not own) shares and to invest a bigger (smaller) slice of their assets in shares.”
  5. “Exposure to economic turmoil appears to dampen people’s appetite for risk irrespective of their personal financial losses.” Furthermore, low tolerance for risk is linked to past emotional trauma.

Some important intuitions from yesterday Finance 4335 class meeting…

  1. The most important concept covered in class yesterday is that people vary in terms of their preferences for bearing risk. Although we focused most of our attention on modeling risk-averse behavior, we also briefly considered examples of risk neutrality (where you only care about expected wealth and are indifferent about the riskiness of wealth) and risk loving (where you prefer to bear risk and are willing to pay money for the opportunity to do so).
  2. Related to point 1: irrespective of whether you are risk averse, risk neutral, or risk loving, the foundation for decision-making under conditions of risk and uncertainty is expected utility. Given a choice among various risky alternatives, one selects the choice that has the highest utility ranking.
  3. If you are risk averse, then E(W) > {W_{CE}} and the difference between E(W) and {W_{CE}} is equal to the risk premium \lambda. Some practical implications — if you are risk averse, then you are okay with buying “expensive” insurance at a price that exceeds the expected value of payment provided by the insurer, since (other things equal) you’d prefer to transfer risk to someone else if it’s not too expensive to do so. On the other hand, you are not willing to pay more than the certainty equivalent for a bet on a sporting event or a game of chance.
  4. If you are risk neutral, then E(W) = {W_{CE}} and \lambda = 0; risk is inconsequential and all you care about is maximizing the expected value of wealth.
  5. If you are risk loving, then E(W) < {W_{CE}} and \lambda < 0; you are quite willing to pay for the opportunity to (on average) lose money.

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/participation grades for the first four class meetings, 2) two quiz grades and a student survey completion grade which counts as a quiz grade, and 3) problem set 1.  Thus, your current (Monday, January 29) 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 then:

(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 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%

 

Problem Set 2 helpful hints

Problem Set 2 is available from the course website at http://fin4335.garven.com/spring2024/ps2.pdf; its due date is Tuesday, January 30.

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/spring2024/lecture4.pdf lecture note for coverage of that topic.

Z Table Extra Credit Assignment (due at the start of class on Tuesday, January 30)

Here’s an extra credit opportunity for Finance 4335. Working on your own (i.e., this is not a group project; I will only give credit for spreadsheets that are uniquely your own), build your own “z” table in Excel (patterned after the table at http://fin4335.garven.com/stdnormal.pdf); the top row should have values ranging from 0.00 to 0.09, and the first column should have z values ranging from -3.0 to +3.0, in increments of 0.1).

Conveniently, Excel has the standard normal distribution function built right in; e.g., if you type “=normsdist(z)”, Excel returns the probability associated with whatever z value you provide. If you type “=normsdist(0)”, .5 is returned, since half of the area under the curve lies to the left of the expected value E(z) = 0. Similarly, if you type “=normsdist(1)”, then .8413 is returned because 84.13% of the area under the curve lies to the left of z = 1. Perhaps you recall from your QBA course that 68.26% of the area under the curve lies between z = -1; this “confidence interval” of +/- 1 standard deviation away from the mean (E(z)=0) is calculated in Excel with the following code: “=normsdist(1)-normsdist(-1)”, and so forth.

The grade you earn on this extra credit assignment will replace your lowest quiz grade; that is if your lowest quiz grade is lower than your extra credit grade. The deadline is the start of class on Tuesday, January 30.

You can turn your spreadsheet for this extra credit assignment in at the link labeled “Z Table Extra Credit Assignment” under the Assignment tab on Canvas.

Gamma Iota Sigma Chapter Meeting

Gamma Iota Sigma (GIS) is an international collegiate professional fraternity established in 1966 at the Ohio State University in Columbus, Ohio. Baylor University’s Alpha Pi chapter of GIS was founded in 2001. GIS aims to promote, encourage, and sustain student interest in insurance, risk management, and actuarial science as professions. Additionally, it seeks to enhance the moral and scholastic achievements of chapter members while fostering interaction between Baylor University and the business community through research activities, scholarship, and networking opportunities.

Join us for the inaugural chapter meeting of the Spring 2024 semester on Thursday, January 25, from 6:30 to 7:30 pm in Foster 322. We look forward to your participation!