For a simple and non-technical way to grasp the concepts of forward and futures contracts, look no further than this delightful video tutorial in which a group of five and six-year-old children explain the fundamentals of investing in corn, equity, and cocoa futures.
Midterm Exam #2 Formula Sheet Modification
I have updated the Midterm Exam #2 Formula Sheet and uploaded the revised version on the course website. It is also listed here for your convenience. The update involves changes to the final item listed on this document, which explains the relationship between the Sharpe Ratio, an investor’s risk tolerance, and the volatility of an asset in determining the ideal proportion of the risk asset in a portfolio, whether for borrowing or lending purposes. This key concept from capital market theory is detailed towards the end of page 7 in my Portfolio and Capital Market Theory teaching note, a required reading for Finance 4335.
Midterm 2 Formula SheetWSJ Page 1: The Small University Endowment That Is Beating the Ivy League
From WSJ: “The more than $200 million Paul and Alejandra Foster Pavilion at Baylor University opened in January, with proceeds from the endowment helping to fund its construction.
WSJ (2/14/2024) Page 1 story about Baylor’s 2 billion dollar endowment, and how it is managed…
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:
- 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, low tolerance for risk is linked to past emotional trauma.
Some important intuitions from yesterday Finance 4335 class meeting…
- 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).
- 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.
- If you are risk averse, then and the difference between and is equal to the risk premium . 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.
- If you are risk neutral, then and ; risk is inconsequential and all you care about is maximizing the expected value of wealth.
- If you are risk loving, then and ; you are quite willing to pay for the opportunity to (on average) lose money.
Finance: Insights into its meanings, etymology, and more from the Oxford English Dictionary
Kudos to my colleague Dr. Seward for bringing to our attention the many fascinating historical perspectives on the word “Finance” which appear in the Oxford English Dictionary:
Finance in the Oxford English DictionaryTo download this PDF document, click here.
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, January 16, 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 the VIX (the x-axis variable) are strongly negatively correlated with each other. The blue dots are based on 8,574 contemporaneous observations of daily returns for both variables, spanning 34 years starting on January 2, 1990, and ending on January 12, 2024. When we fit a regression line through this scatter diagram, we obtain the following equation:
,
where corresponds to the daily return on the SP500 index and 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 period (specifically, 48.87%) can be statistically “explained” by changes in volatility, and the correlation between and during this period is -0.70. While a correlation of -0.70 does not imply that daily closing values for and always move in opposite directions, it does suggest that this will be the case more often than not. Indeed, closing daily values recorded for and 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.