Click here for the PDF: The Monthly November 2024

With this commentary, we plan to communicate with you every month about our thoughts on the markets, some snapshots of metrics, a section on behavioral investing and finally an update on MacNicol & Associates Asset Management (MAAM). We hope you enjoy this information, and it allows you to better understand what we see going on in the marketplace.

“The three most harmful addictions are heroin, carbohydrates, and a monthly salary.”

Black Swan author Nassim Nicholas Taleb

 

 

Negative convexity…and other stuff from the world of mathematics that you probably didn’t know or care about…until you got your hands on some money…

Convexity is the state of being convex. The state of being convex is the state of being curved. In fact, the word convex is the word mathematicians use to describe something that has a curve in it, and it really is as simple as that. Not nearly as simple is why the investment industry insists on borrowing complex mathematical jargon to make investors feel like they are complete morons. For the record, we do not think you are a moron, not even slightly. But we thought it would be useful for us to dive into convexity a bit more and explain how we are using it to protect all that money you have, nevertheless. When Portfolio Managers [or mathematicians] speak of a convex relationship, they are essentially communicating a relationship that is non-linear. To really nail down the concept of a non-linear relationship – let us first review what a linear relationship is with an example. Suppose you are a worker who gets paid a fixed hourly rate. The amount of money you make (known as the dependent variable) is directly related to the number of hours you work (known as the independent variable) since no overtime or “special” rates of payment kicks in at any point. Linear relationships exist in the labor market, but they also exist in other areas such as molecular biology. There is a linear relationship between the amount of guanine and cytosine that a DNA molecule has, and it is known as the “GC” factor. The “GC” factor governs the ambient temperature at which the DNA double helix will denature, and this is arguably the most arcane or irrelevant fact to everyone included in an investment newsletter.

Non-linear relationships describe a situation where there is not a simple, straight-line link between an independent variable and a dependent variable. In a nonlinear relationship, changes in the output do not change in direct proportion to changes in any of the inputs because the relationship has a curve in it. The best example of a nonlinear relationship that we can think of is one that impacts all of us: gravity. The gravitational influence of two bodies is not linear, which means you cannot just assume that the gravitational pull [of the planet Mars] is 225 million times less than that of the Earth just because Mars happens to be 225 million kilometers away while the Earth can be found under your feet. One additional dimension of convexity that merits mention is its direction. Convexity can be positive, such as when stocks go “parabolic” or negative, such as when mortgage amortizations decline due to changes in interest rates. In the world of stock options, individual contracts who derive their own value from the value of an underlying stock or stock index, the direction [and severity] of convexity can be dramatic. And all this dramatic curvature is most important to you as an investor whenever something bad happens in the stock market. Of course, bad years in the stock market are something most investors can understand: a weak economy, lousy corporate profit growth or persistent inflation can truly “grind” stock prices down over time, and this is why Portfolio Managers log hundreds of hours each year carefully separating the good stocks from the bad and building investors diversified portfolios that do not rely on a small handful of bets. But what about sudden, unpredictable plunges in stock prices that take investors by surprise? They can and do happen, and the table below from Money Morning illustrates some specific examples of this from history.