Volare, oh, oh! (I)

My wife left this photo on my flash drive.

Flying to Monterrey, Mexico is an ever-worsening trip from Mexico City, as the airport’s saturation problem grows. On top of that, I decided to fly home on Sunday, December 22! After a 4-hour wait, I had a terrible time running from gate 7 to gate 28 because [insert a typical airline justification]. Finally, my wife and I made it on board and, finally, we took off.

I cannot help but think of the new airport project that was cancelled by President Lopez-Obrador’s administration. In October 2018, president Lopez-Obrador (then president-elect) decided unilaterally to cancel the construction of the New International Airport of Mexico (NAIM), under the allegations that the funding for the project represented a substantial diversion of resources from the federal budget — one that a country dealing with poverty cannot afford. Although the decision was taken after the result to a ‘referendum’, I think it is safe to claim that the decision was unilateral due to the referendum’s lack of seriousness.

This decision echoed in several ways in the Mexican society. Some see it as a manifestation of true change for good; to some, this is an announcement of the terrible times that await Mexico in the future. I have my particular views on this, but I am not discussing them here. Rather than that, this article is about measuring volatility in the Mexican Stock Exchange (BMV). Stock markets are a source of information about investor’s views on social phenomena and, as such, we can analyze stock market information to compare the impact of different events.

Back to the airport, while I was waiting for my flight, I was reading an interesting paper (Christos Floros’ paper, which is cited below in the references) on volatility measures and the use of the High, Low, Open and Closing prices that are made public after market closure for all quotes. The basic use of that information is that you compute some statistics (first and second central moments) using the closing price, and that helps you manage a portfolio.

Still, when one downloads data on a stock (or index) from sites such as Yahoo! Finance, there is a lot more of information provided: open, high, and low prices, and the volume traded for a given day. I wondered what purpose could all that information serve. So, I decided to combine my curiosity with my frustration for the delayed flight and came up with this article. I hope you find it useful.

The analysis is organized in three parts: in part I, I provide a definition for the volatility measures that we will use; part II will present the data and explore the volatility time series; and part III will perform the Structural Break analysis and discuss the results. Do note, however, that in no way am I cheering for, nor criticizing, president Lopez-Obrador’s decision to cancel the airport. This is a Finance, not Politics, discussion.

Defining and measuring volatility

In early December I attended a masterclass by a former trader who defined volatility as follows:

Imagine I get home at 04:00 AM. What my wife’s reaction will be is unknown. That’s what we call high volatility. Now, after a few months of jewelry, cars, clothing, and other fancy presents, her behavior will be what we call low volatility.

I hope the explanation illustrates the point of volatility. According to the Merriam-Webster online dictionary, volatility is the tendency to change quickly and unpredictably. In economics, we refer to volatility when discussing the range and speed of price movements. Volatility is either high (prices fluctuate within a wide range at a high speed) or low (there is little change in the price of a financial security, a good or a service, or it takes long for change to happen).

By studying volatility, we get to understand how investors (overall) feel towards current events, phenomena happening at a given time. For example, if there are political tensions or failure to pass a free trade agreement between two neighboring countries, most likely we will notice financial unrest in the markets that are related to that particular phenomenon (more precisely, the stocks of the firms that do business in both countries).

The paper by Christian Floros compares 4 measures of volatility. Their purpose is to identify the circumstances under which a measure is better than the others, but we will use them all here.

Let O_t, C_t, H_t, and L_t be the opening, closing, high, and low prices, at day t, associated to a security. For example:

if the price of UBER stock at 09h00 (when the market opens) was $30.00, then O = $30.00; during the day, the price reaches a maximum of $32.50, a minimum of $29.00, and closes at $31.00, then: L = $29.00, H = $32.50, and C = $31.00.

Then we have the following measures of volatility:

i. Simple volatility measure:

ii. Parkinson volatility:

iii. Garman-Klass volatility:

iv. Rogers-Satchell volatility:

In the references below, you will find the link to the whole discussion. In this article I ask you to take the above equation for granted.

See you in part II!


Floros, Christos. (2009). Modelling Volatility Using High, Low, Open and Closing Prices: Evidence from Four S&P Indices. International Research Journal of Finance and Economics. Link to Research Gate

The exercise presented in this article is only intended to illustrate one way in which I would analyze the impact of policy decisions on financial markets’ volatility. It is neither an exhaustive nor a serious analysis. I am not criticizing President Lopez-Obrador’s policy, nor am I praising him. The opinions expressed in this article are exclusively my own, and represent nothing other than my own views.




Economics & Machine Learning enthusiast | UANL & UT1-Capitole (BA Econ, MX-FR intl. degree); El Colegio de México (M. Econ, 2022) | Opinions STRICTLY personal.

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Oscar Carreón-Cerda

Oscar Carreón-Cerda

Economics & Machine Learning enthusiast | UANL & UT1-Capitole (BA Econ, MX-FR intl. degree); El Colegio de México (M. Econ, 2022) | Opinions STRICTLY personal.

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