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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.
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Some important intuitions from today’s class meeting of Finance 4335

  1. The most important concept covered in class today 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 actually 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.
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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 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%

 

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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.