## On the Determinants of Risk Aversion

This week, we completed the first two of a series of five Finance 4335 class meetings (scheduled for September 7-21) devoted to decision-making under risk and uncertainty.  Our focus is on measuring risk, modeling consumer and investor risk preferences, and exploring implications for the pricing and management of risk. We focus especially on the concept of risk aversion. Other things equal, risk averse decision-makers prefer less risk to more risk. Risk aversion helps to explain some very basic facts of human behavior; e.g., why investors diversify, why consumers purchase insurance, etc.

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.

## Also featured as one of “50 Things That Made the Modern Economy”: The Index Fund

Besides insurance, Tim Harford also features the index fund in his “Fifty Things That Made the Modern Economy” radio and podcast series. This 9-minute long podcast lays out the history of the development of the index fund in particular and the evolution of so-called passive portfolio strategies in general. Much of the content of this podcast is sourced from Vanguard founder Jack Bogle’s September 2011 WSJ article entitled “How the Index Fund Was Born” (available at https://www.wsj.com/articles/SB10001424053111904583204576544681577401622). Here’s the description of this podcast:

“Warren Buffett is the world’s most successful investor. In a letter he wrote to his wife, advising her how to invest after he dies, he offers some clear advice: put almost everything into “a very low-cost S&P 500 index fund”. Index funds passively track the market as a whole by buying a little of everything, rather than trying to beat the market with clever stock picks – the kind of clever stock picks that Warren Buffett himself has been making for more than half a century. Index funds now seem completely natural. But as recently as 1976 they didn’t exist. And, as Tim Harford explains, they have become very important indeed – and not only to Mrs Buffett.”

Warren Buffett is one of the world’s great investors. His advice? Invest in an index fund

## Insurance featured as one of “50 Things That Made the Modern Economy”

From November 2016 through October 2017, Financial Times writer Tim Harford presented an economic history documentary radio and podcast series called 50 Things That Made the Modern Economy. This same information is available in book form under the title “Fifty Inventions That Shaped the Modern Economy“. While I recommend listening to the entire series of podcasts (as well as reading the book), I would like to call your attention to Mr. Harford’s episode on the topic of insurance, which I link below. This 9-minute long podcast lays out the history of the development of the various institutions which exist today for the sharing and trading of risk, including markets for financial derivatives as well as for insurance.

“Legally and culturally, there’s a clear distinction between gambling and insurance. Economically, the difference is not so easy to see. Both the gambler and the insurer agree that money will change hands depending on what transpires in some unknowable future. Today the biggest insurance market of all – financial derivatives – blurs the line between insuring and gambling more than ever. Tim Harford tells the story of insurance; an idea as old as gambling but one which is fundamental to the way the modern economy works.”

## 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 24, 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 on 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 7,961 contemporaneous observations of daily returns for both variables, spanning the (more than 30-year) time period from January 2, 1990, through August 5, 2021. When we fit a regression line through this scatter diagram, we obtain the following equation:

${R_{SP500}} = .00064 - .11412{R_{SP500}}$,

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 (-0.11412) indicates that on average, daily realized SP500 returns during this time period were inversely related to contemporaneous daily returns on the VIX; i.e., when forward-looking investor expectations of stock market volatility fell (rose), then the stock market return as indicated by SP500 typically rose (fell). Nearly half of the variation in the stock market return during this time period (specifically, 48.68%) can be statistically “explained” by changes in volatility, and the correlation between ${R_{SP500}}$ and ${R_{VIX}}$ comes out to -0.698. While a correlation of -0.698 does not imply that ${R_{SP500}}$ and ${R_{VIX}}$ always move in opposite directions, it does suggest that this will be the case more often than not. Indeed, closing daily returns on ${R_{SP500}}$ and ${R_{VIX}}$ during this period moved inversely 78.66% of the time.