Category Archives: Finance

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

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 of 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 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 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 a particularly important risk management topic; i.e., 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.”

Postscript: The scene above depicts the early days of Lloyd’s Coffee House in London, England. According to Wikipedia, Lloyd’s Coffee House was opened by Edward Lloyd in 1686 and quickly became “… a popular place for sailors, merchants and shipowners, and Lloyd catered to them with reliable shipping news. The shipping industry community frequented the place to discuss maritime insurance, shipbroking and foreign trade. The dealing that took place led to the establishment of the insurance market Lloyd’s of London…”

Apple Is a Hedge Fund That Makes Phones

This is a fascinating article in today’s Wall Street Journal about how Apple is, for all intents and purposes, a highly levered hedge fund, thanks to its wholly owned Braeburn Capital subsidiary which accounts for 70% of the book value of Apple’s assets.

Quoting from this article,

“Similar shadow hedge funds abound within S&P 500 industrial companies. Most disclose less information than Apple about their activities… in 2012 these corporations managed a combined portfolio of $1.6 trillion of nonoperating financial assets. Of this amount, almost 40% is held in risky financial assets, such as corporate bonds, mortgage-backed securities, auction-rate securities and equities.”

The (gated) Journal of Finance article upon which this WSJ op-ed is based is available at

Big companies need to disclose more about their investments.

Plans for next week’s Finance 4335 class meetings, along with a preview of future topics

Next week in Finance 4335 will be devoted to tutorials on probability and statistics. These tools are critically important in order to evaluate risk and develop appropriate risk management strategies for individuals and firms alike. Next Tuesday’s class meeting will be devoted to introducing discrete and continuous probability distributions, calculating parameters such as expected value, variance, standard deviation, covariance and correlation, and applying these concepts to measuring expected returns and risks for portfolios consisting of risky assets. Next Thursday will provide a deeper dive into discrete and continuous probability distributions, in which the binomial and normal distributions are showcased.

While I have your attention, let me briefly explain what the main “theme” will initially be in Finance 4335 (up to the first midterm exam, which is scheduled for Thursday, September 27). Starting on Tuesday, September 4, we will begin our discussion of decision theory. Decision theory addresses decision making under risk and uncertainty, and not surprisingly, risk management lies at the very heart of decision theory. Initially, we’ll focus attention on variance as our risk measure. Most basic finance models (e.g., portfolio theory, the capital asset pricing model (CAPM), and option pricing theory) implicitly or explicitly assume that risk = variance. We’ll learn that while this is not necessarily an unreasonable assumption, circumstances can arise where it is not an appropriate assumption. Furthermore, since individuals and firms are typically exposed to multiple sources of risk, we need to take into consideration the portfolio effects of risk. To the extent that risks are not perfectly positively correlated, this implies that risks often “manage” themselves by canceling each other out. Thus the risk of a portfolio is typically less than the sum of the individual risks which comprise the portfolio.

The decision theory provides a particularly useful framework for thinking about concepts such as risk aversion and risk tolerance. The calculus comes in handy by providing an analytic framework for determining how much risk to retain and how much risk to transfer to others. Such decisions occur regularly in daily life, encompassing practical problems such as deciding how to allocate assets in a 401-K or IRA account, determining the extent to which one insures health, life, and property risks, whether to work for a startup or an established business and so forth. There’s also quite a bit of ambiguity when we make decisions without complete information, but this course will at least help you think critically about costs, benefits, and trade-offs related to decision-making whenever you encounter risk and uncertainty.

After the first midterm, the remainder of the semester will be devoted to various other risk management topics, including the demand for insurance, asymmetric information, portfolio theory, capital market theory, option pricing theory, and corporate risk management.

CFA® Information Session on Monday, August 27th @ 4:30-5:00 pm in FOS 143/144

CFA® Information Session

When: Monday, August 27th @ 4:30-5:00 pm

Where: FOS 143/144

Do you want to be an investor or a financial professional?

Do you want to challenge yourself within the field of investment and finance?

Do you want to differentiate yourself in the job market?

The Chartered Financial Analyst (CFA) program is a globally recognized standard for measuring the competence and integrity of financial analysts, and a valued credential by investment firms, banks, and financial institutions around the world.   If you have unanswered questions about the CFA program and want to find out if it is right for you, come discover its advantages from industry professionals with the CFA designation. Topics will include:

  • Who should pursue the CFA designation
  • The CFA charter and your career
  • Who employs CFA charterholders
  • International recognition
  • Requirements for taking the exams and receiving the charter
  • Exam topics and preparation
  • Scholarships

Stop by, enjoy some food, and learn about the CFA designation.  This session is open to all students. If you have questions, please contact

Risk and Uncertainty – on the role of Ambiguity

This March 2017 WSJ article addresses how to measure uncertainty and also explains the subtle, yet important differences between risk and uncertainty. Risk reflects the “known unknowns,” or the uncertainties about which one can make probabilistic inferences. Ambiguity (AKA “Knightian” uncertainty; see reflects the “unknown unknowns,” where the probabilities themselves are a mystery.

A researcher whose work foreshadowed the VIX now has his eye on an entirely different barometer of market uncertainty—ambiguity.

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

Besides going over the course syllabus tomorrow, we will also discuss a “real world” example of financial risk. Specifically, we will look at the relationship between short-term stock market volatility (as indicated by the CBOE Volatility Index (VIX)) and returns (as indicated by the SP500 stock market index).

As indicated by this graph from page 25 of the lecture note for the first day of class, daily percentage changes on closing prices for VIX and the SP500 are strongly negatively correlated. In the graph above, the y-axis variable is the daily return on the SP500, whereas the x-axis variable is the daily return on the VIX. The blue points represent 7,215 daily observations on these two variables, spanning the time period from January 2, 1990 through August 17, 2018. When we fit a regression line through this scatter diagram, we obtain the following equation:

{R_{SP500}} = 0.0587 - 0.1139{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 (-0.1139) indicates that on average, daily VIX returns during this time period were inversely related to the daily return on the SP500; i.e., when volatility as measured by VIX went down (up), then the stock market return as indicated by SP500 typically went up (down). Nearly half of the variation in the stock market return during this time period (specifically, 48.4%) can be statistically “explained” by changes in volatility, and the correlation between {R_{SP500}} and {R_{VIX}} comes out to -0.696. While a correlation of -0.696 does not imply that {R_{SP500}} and {R_{VIX}} will always move in opposite directions, it does indicate 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 78.3% of the time.

You can see how the relationship between the SP500 and VIX evolves prospectively by entering^GSPC,^VIX into your web browser’s address field.

The Finance Industry’s Incredible Ability to Keep the Money Rolling In

Quoting from this article (which appeared in last Saturday’s Wall Street Journal),

“From the era of railroads and the telegraph to that the internet and smartphones, the price charged by the finance industry to turn a dollar of savings into a dollar of investment has mostly remained between 1.5 cents and 2 cents for every dollar that passes through the finance industry.”