This Atlantic article is well worth reading!
- The most important concept covered in Finance 4335 so far centers around the notion that people vary in terms of their preferences for bearing risk. Although we focused most of our attention in upon modeling risk-averse behavior, we also considered examples of risk neutrality (where you only care about expected wealth and are indifferent about 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).
- 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 amongst various risky alternatives, one selects the choice which 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’re 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.
During last Thursday’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 280 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 considered 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.
Following up on my previous blog posting entitled “The world has not learned the lessons of the financial crisis”, today’s “Heard on the Street” column in the Wall Street Journal entitled “What Will Trigger the Next Crisis?” is required reading! Both articles are motivated by the fact that we are now ten years out from the bankruptcy (on September 15, 2008) of Lehman Brothers. Many commentators mark this day as the seminal event for what is now commonly referred to as the so-called “Global Financial Crisis of 2008” – widely considered to have been the worst financial crisis since the Great Depression of the 1930s.
One year ago this coming Sunday, the article cited below was the cover story for the 9/2/17 issue of The Economist. The points raised by this article (regarding the “moral hazard” associated with mispriced/subsidized insurance coupled with misguided NFIP claims policies) are (unfortunately) as valid today as they were back then.
Quoting from this article,
“Underpricing (of flood insurance) encourages the building of new houses and discourages existing owners from renovating or moving out. According to the Federal Emergency Management Agency, houses that repeatedly flood account for 1% of NFIP’s properties but 25-30% of its claims. Five states, Texas among them, have more than 10,000 such households and, nationwide, their number has been going up by around 5,000 each year. Insurance is meant to provide a signal about risk; in this case, it stifles it.”
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 https://onlinelibrary.wiley.com/doi/abs/10.1111/jofi.12490.
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.
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 https://en.wikipedia.org/wiki/Frank_Knight) reflects the “unknown unknowns,” where the probabilities themselves are a mystery.