Category Archives: Risk

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.

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.