Entering The Realm
First and foremost, we will, to use one of Richard Feynman's memorable quotes, "Learn by trying to understand simple things in terms of other ideas." The things we will try to understand for the purposes of this article are the following: Do people invest (or trade) at different time horizons? Are there different views of risk among investors? And are there different views of where the same stock's price will be one week, one month or one year from now? These are the questions we will attempt to answer in a direct way. From there we will be able to ask subtler questions that will hopefully illuminate the Realized Volatility Index (RVI).
To the question, "Do people invest (or trade) at different time horizons?" the answer is clearly yes. And though modern portfolio theory (MPT) assumed this fact away, keep in mind that MPT is the grandfather of much of what followed in financial economics and financial mathematics, including steps forward like the RVI. So though grandfather may have gotten some things wrong, he made some terrific pioneering efforts.
It is accepted by many, if not all, practitioners and by a growing number of academics, that different market participants have different time horizons when it comes to their analysis of past events. These different time horizons and resolutions affect their trading or investing goals. The existence of heterogeneous trading behaviors has given rise to the hypothesis that the market itself is fractal. By fractal, we mean there is no single preferred time period or investment horizon in the market. Not one day, two weeks, one month … nothing. Why no one investment horizon? Because the heterogeneous trading behaviors that make up the market can be characterized as different actor groups or components, each with their own frame of reference. In other words, the differing time horizons of investors and traders are a key aspect of the market. To state it another way, it's the variety of time horizons and their interaction that is probably one of the most important factors that make up a market. Given the variety of time scales and frames of reference, each component could be modeled in the form of an intrinsic or individual time for that component (this statement will be key in understanding the RVI later).
The fractal approach to analyzing objects of different kinds, including financial data, can be stated as follows:
Objects are analyzed on different scales, with different degrees of resolution, and the results are compared and interrelated.
Rather sounds like the market as we know it, doesn't it?
As to our next question, "Are there different views of risk among investors?" the answer is also clearly yes. Studies by folks such as Olsen and Associates1 and Lynch and Zumbach2 have demonstrated that this difference in risk is also fractal, meaning that, as we noted in bold above, risk (or volatility) is analyzed at different time scales with different degrees of resolution. An obvious example of this is people who trade volatility on a short-term basis, e.g., over a few days. There are also other actors whose horizons are typically a month, if not more (such as portfolio managers). The sudden movement in the price of a stock could move volatility enough for a short-term trader that he will adjust his position accordingly that day or the next. The portfolio manager, however, will more than likely view a one-day or even a few-day unexpected movement in price as a bump in the road and will probably not adjust her position, or will adjust it minimally. What is also of interest in the work of Lynch and Zumbach is that risk (volatility) can cascade. What the authors mean by this is that when the typical time horizons (or different scales and resolutions) collapse, it is a one-way flow, always from the telescopic to the microscopic. In other words, if enough of those participants with longer-term views of volatility begin to act like those with the shorter-term views, a cascade or a volatility cluster occurs, such as during that period of wretched months for the equity market in late 2008 and early 2009.
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