Why Bayes?

The Reverend Robert Thomas Bayes developed his ideas about how to update one's expectations back in the 1750s. His logic, often known as Bayesian Inference, is directly applicable to how we can analyze financial markets and economic activity.

Bayes argued that based on the information available and the ways in which one analyzed and processed information, one would form an expectation and hold that expectation with a certain degree of confidence. Then, one would receive new information, and one would revise one's own expections. New information that supported one's previous expectation might inspire greater confidence. New information that did not fit well with the prior expectation might result in a revised expectation as well as holding it with less confidence. That is, Bayes elegantly laid out how one took in new information and revised both expectations and confidence, which is exactly what happens with traders and investors.

US Rate Expectations

Ours views on potential Fed rate changes are presented in the Expectations section. Our analysis starts with the federal funds futures market operated by CME Group. We take the futures prices for contracts with maturities up to 18 months forward and convert them to implied federal funds rates.

We are especially interested in how these expectations evolve over time. Since 2008 and the embrace of forward guidance by the Fed, expectations about the upcoming Federal Open Market Committee (FOMC) meeting tend form a solid consensus about 4 weeks ahead of the meeting. By contrast, further out expecations can be all over the map, reflecting the Fed's bias toward data dependency. We provide several graphics to show how expecations have shifted over time, especially for further out dates, as well as providing our commentary on these shifts in rate expectations.

Confidence, Tail Risk, and Probability Distributions

Significant tail risk is often present in financial market expectations. That is, the risk-return probability distributions in financial markets are often characterized by material risks in the tails or extremes of the distribution. Put another way, if one's risk system is biased toward bell-shaped curves and normal distributions, one is more than likely inviting disaster.

Our analysis of the potential for serious tail risk is anchored in the study of a variety of metrics based on the prices, volumes, open interest, intra-day swings, among others, obtained from how futures and options actually trade. We combine our analysis of the trading metrics to develop a hypothetical, by which we mean unobservable, risk-return probability distribution that can take on any shape -- skewed right, or skewed left, or even with two modes or peaks (bi-modal). The more unusual the shape (i.e., the more different from a normal or bell-shaped distribution, the more tail risk is embedded in risk-return expectations, and the more attention that needs to be paid to risk management.

Fed's Dual Mandate

The Fed has been given a dual mandate by the US Congress to encourage full employment and price stability. Actually, though, the Fed has a third mandate that takes priority over the dual mandate. The Fed was formed back in 1913 to "maintain an elestic currency" by which was meant to prevent banking panics, as they were called back then, which led to recessions, by being willing and able to serve as a lender of last resort to the financial system. In our monitoring of the progress the Fed has achieved toward realizing its "dual mandate", we always keep the objective of financial system stability in mind.

Equities

We examine equity markets for signs of hightened risk, especially in the tails of the risk-return probability distributions. In cases of elevated tail risk, the probabilities of a sharp, abrupt gap up or down in prices is also increased. While the direction of the potential price gap may be unknown, there are still excellent alternatives for effective risk management, often using options strategies.

Commodities

Our commodity research initially focuses on the oil markets. We are keenly interested in using oil market options to identify and quantify how concered market participants are about geo-political risks. Often there is present consideration asymmetry in the hypothetical risk-return probability distributions we construct fro options and futures market metrics. When our probability distrubution are seriously skewed one way or the other, or even showing a bi-modal state inidcating significant event risk, we then attempt to add fundamentl analysis to understand why the asymmetry is occurring and what to watch as risk managers.

Questions & Answers

We try to answer your questions and ours about financial markets in a clear and straightforward manner. We also will delve into controversial market debates and provide our opinions and analysis.

Research Articles

We often present our research as longer-form reports and in some cases we publish in academic journals. This section contains links to PDFs of selected articles from our archives of our longer-form research.

Connect with Us

We are available for financial consulting assignments or for speaking engagements. Our contact information is as follows:

Blu Putnam on Linked-In: www.linkedin.com/in/bluputnam/

Bayesian Edge / P.O. Box 69 / Ridge, MD 20680 USA