Not that anyone is counting, but market volatility today is comparable numerically to market volatility in the depths of the global financial crisis of 2007-2009. Today, the CBOE’s implied volatility index (ticker symbol VIX) closed at 54.46. Putting this into a historical perspective, this level is at the 99.43rd percentile for all 7,557 daily observations on VIX recorded daily during the 30-year period spanning 1/2/1990 – 12/27/2019. The last time that VIX closed at this high of a level occurred on November 5, 2008, when it closed at 54.56.
For more information about the (contemporaneous) relationship between VIX and the overall stock market (as measured by the S&P 500 index), see “On the relationship between the S&P 500 and the CBOE Volatility Index (VIX)“:
Last week, we began a series of five Finance 4335 class meetings (scheduled for January 28 – February 11) devoted to decision-making under risk and uncertainty. We shall study how to measure risk, model consumer and investor risk preferences, and explore implications for the pricing and management of risk. We will 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.
A few 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 article:
- Economists have long known that people are risk-averse, yet the willingness to run risks varies enormously among individuals and over time.
- 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.
- 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.”
- 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.”
- “Exposure to economic turmoil appears to dampen people’s appetite for risk irrespective of their personal financial losses.” Furthermore, a low tolerance for risk is linked to past emotional trauma.
During today’s class meeting, we discussed (among other things) the famous St. Petersburg Paradox. The source for this is Daniel Bernoulli’s famous article entitled “Exposition of a New Theory on the Measurement of Risk“. As was the standard practice in academia at the time, Bernoulli’s article was originally published in Latin in 1738. It was subsequently translated into English in 1954 and published a second time that same year in Econometrica (Volume 22, No. 1): pp. 22–36. Considering that this article was published 282 years ago in an obscure (presumably peer-reviewed) academic journal, it is fairly succinct and surprisingly easy to read.
Also, the Wikipedia article about Bernoulli’s article is worth reading. It provides the mathematics for determining the price at which the apostle Paul would have been indifferent about taking the apostle Peter up on this bet. The original numerical example proposed by Bernoulli focuses attention on Paul’s gamble per se and does not explicitly consider the effect of Paul’s initial wealth on his willingness to pay. However, the quote on page 31 of the article (“… that any reasonable man would sell his chance … for twenty ducats”) implies that Bernoulli may have assumed Paul to be a millionaire, since (as shown in the Wikipedia article) the certainty-equivalent value of this bet to a millionaire who has logarithmic utility comes out to 20.88 ducats.