Oh, Bitcoin. It has people more divided than our commander-in-chief. On one side, we have the aspiring (or closet) millionaires — the Bitcoin enthusiasts — preaching the good word of cryptocurrencies. And on the other side of the aisle, we have the finance millionaires — or the financial establishment — waiting somewhat patiently for Bitcoin’s inevitable expiry.

Taken from Bitcoin.com

In any case, the predicted demise is not keeping people from making incredible amounts of money on the rapid changes in price, or volatility. Volatility is the main concern for not only financial investors, but for everyone. It affects how risky we perceive different activities to be. In the same vein, activities that are risky, tend to be volatile.

Brushing your teeth is not considered to be that risky, simply because there’s not much volatility. It’s likely you can predict how that activity is going to turn out each morning. But, driving your car to work becomes much riskier (though we often forget) because of the volatile nature of dealing with traffic and a whole slew of other unexpected events that can happen in the commute.

Volatility is how many traders make their money in the finance game. They attempt to predict the changes in price, using sophisticated statistical magic, and decide when to buy or sell assets — stocks, bonds, mortgage-backed securities, tulips, Bitcoin, etc.

The “Tulip Bubble” similar to the “Bitcoin Bubble”. There’s nothing new under the sun.

Robert Engle III is the wizard that came up with this money-making magic called autoregressive conditional heteroskedasticity, or ARCH, for short (thank God). The Sveriges Riksbank (the central bank of Sweden) thought it worked well enough to award him the Nobel Prize in economics in 2003. The ARCH model has had such an impact in econometrics and statistics, that it is virtually the standard for measuring changes in the real world, from medicine and health to sports and finance.

Robert Engle III in his office at the Stern School of Business at NYU

It’s not as complicated to explain than it is to do the math. So, we’ll stick to just explaining this sorcery.

Before Engle III, the models used to predict changes in price were limited in that they didn’t really account for the variation of prices in the past. Though I’m kind of hand-wavy right now, the models didn’t really have a good way to incorporate that things change in different ways, particularly prices. So, the models would assume that the changes of the changes in prices were homoskedastic versus heteroskedastic. Oh, screw it. Here’s a picture:

Stolen from a slideshow on statistics. Other people have asked this question too!

In this picture, the line is the mean — or average — change in price, if the x-axes were time and the y-axes were price. If you notice, the dots in the homoskedastic plot have a similar variation from the mean (the red line). In the heteroskedastic one, the dots have a different variation from the mean.

This makes sense. We know that everything is constantly changing. But most importantly, everything is constantly changing in different ways.

This is what Engle’s statistical model attempts to capture. It puts more weight on the variances nearer to the time period you’re trying to predict, while taking into account the differences in past variances as well.

So, back to Bitcoin. This model predicts the changes in price with a bit more accuracy. Here’s another picture of the variance of Bitcoin in one day.

Vavrinec Cermac has been analyzing Bitcoin’s volatility using Engle’s model.

Ah…clearly we see that the variance is not uniform throughout the day. It looks much more heteroskedastic (refer to the first picture). Further, we see that the fluctuations are extremely volatile and tend to cluster, which is another aspect that Engle’s ARCH model captured as well.

In his Nobel lecture, Engle uses a pretty simple example to explain this phenomenon. During the `90s, there was low volatility and a steady increase in asset prices in the stock market. But, as the stock prices got higher and higher, the stock market became rather risky, and volatility shot through the roof. This made the stock market even riskier! His ARCH model is able to predict the increase in volatility and prices with a bit more accuracy than before.

We see this today with Bitcoin. As the price of the cryptocurrency rises higher and higher, we’ll see a ridiculous amount of volatility. One minute it’s at $19,000 and the next minute it plummets to $17,000. That’s like an 11 percent decrease in price in just one minute! (I’m exaggerating a little, but not really. It’s crazy.)

Now, you would be hard-pressed to find ARCH models trying to predict these prices right now. There’s simply not enough time to really have any solid prediction of which direction the price of Bitcoin is heading in the next minute. So, for the time being, making money trading Bitcoin is all just pure speculation and praying to the crypto gods. Godspeed to the enthusiasts.

I mean, you can try to run an ARCH model to see when you should invest in Bitcoin, but you’d be several minutes late, every time. To the financial establishment’s credit, this model and its many variations have worked pretty darn well measuring volatility and prices in the stock market. If you’re like most people and would rather stay on the safer side, perhaps giving the stock market a chance is the better bet.

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