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 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.

On the ancient origin of the word “algorithm”

The August 29th assigned reading entitled “The New Religion of Risk Management” (by Peter Bernstein, March-April 1996 issue of Harvard Business Review) offers a concise overview of the same author’s 1996 book entitled “Against the Gods: The Remarkable Story of Risk“. An intriguing excerpt from page 33 of “Against the Gods” elucidates the historical roots of the term “algorithm.” An intriguing excerpt from page 33 of “Against the Gods” elucidates the historical roots of the word “algorithm.”

“The earliest known work in Arabic arithmetic was written by al­Khowarizmi, a mathematician who lived around 825, some four hun­dred years before Fibonacci. Although few beneficiaries of his work are likely to have heard of him, most of us know of him indirectly. Try saying “al­Khowarizmi” fast. That’s where we get the word “algo­rithm,” which means rules for computing.”

Note: The book cover shown above is a copy of a 1633 oil-on-canvas painting by the Dutch Golden Age painter Rembrandt van Rijn.

On the relationship between the S&P 500 and the CBOE Volatility Index (VIX)

Besides going over the course syllabus during the first day of class on Tuesday, August 22, we will also discuss a particularly important “real world” example of financial risk. Specifically, we will study the relationship between realized daily stock market returns (as measured by daily percentage changes in the SP500 stock market index) and changes in forward-looking investor expectations of stock market volatility (as indicated by daily percentage changes in the CBOE Volatility Index (VIX)):
As indicated by this graph (which also appears in the lecture note for the first day of class), daily percentage changes in closing prices for the SP500 (the y-axis variable) and for the VIX (the x-axis variable) are strongly negatively correlated with each other. The blue dots are based on 8,470 contemporaneous observations of daily returns for both variables, spanning the 33-2/3-year period of time starting on January 2, 1990, and ending on August 15, 2023. When we fit a regression line through this scatter diagram, we obtain the following equation:

{R_{SP500}} = .00062 - .1147{R_{VIX}},

where {R_{SP500}} corresponds to the daily return on the SP500 index and {R_{VIX}} corresponds to the daily return on the VIX index. The slope of this line (-0.1147) indicates that on average, daily closing SP500 returns are inversely related to daily closing VIX returns.  Furthermore, nearly half of the variation in the stock market return during this time period (specifically, 48.87%) can be statistically “explained” by changes in volatility, and the correlation between {R_{SP500}} and {R_{VIX}} came out to -0.70. While a correlation of -0.70 does not imply that daily closing values for {R_{SP500}} and {R_{VIX}} always move in opposite directions, it does suggest that this will be the case more often than not. Indeed, closing daily values recorded for {R_{SP500}} and {R_{VIX}} during this period moved inversely 78% of the time.

You can also see how the relationship between the SP500 and VIX evolves prospectively by entering http://finance.yahoo.com/quotes/^GSPC,^VIX into your web browser’s address field.