Bitcoin exchange rate volatility affects everybody who uses Bitcoin as a currency or trades it as an asset. However, the available material about Bitcoin volatility is limited. Therefore it’s time for some investigation. The results are somewhat counter-intuitive. That makes the whole topic even more worthwhile.

1. What is Bitcoin volatility

For any traded currency or asset, volatility is a measure for the dispersion of value changes around the average change. Changes in value are usually looked at on a day to day basis. Value changes are measured as relative or percentage changes. That’s because only relative changes are comparable between different assets and over time. To give an example: if the Bitcoin price goes from USD 100 to USD 101 per Bitcoin from one day to the other, that would be a +1 change. If the price went from USD 1,000 to USD 1,001 the absolute change is the same, but the relative change is only +0.1. Looking at a time series of daily changes, we can calculate the average daily percentage change over this period. The average daily change of BTC vs USD on Mt.Gox between July 2010 and August 2013 was 0.7. This figure is also called the mean or expected daily return on an asset. 0.7 average daily return is quite a lot compared to other assets.Once we have the average daily change over a given period, we can calculate volatility. We do this to get a figure for the average dispersion around the mean. The higher this dispersion (i.e. the volatility), the more uncertainty is attached to the expected return of this asset. Bitcoins had a daily volatility of 7.2 over the mentioned period. We annualize this figure to get an idea of the possible dispersion over one year. The result is 136 annualized return volatility, which also is a lot.So the Bitcoin volatility tells us how much the BTC vs USD exchange rate disperses around the mean over a given period. Let’s look at some more historical data to put the Bitcoin volatility into perspective.

2. Historical Bitcoin volatility

Thinking of historical Bitcoin volatility, it’s no big news that it was going through the roof. However, what does deserve attention is how it evolved. Since volatility is calculated as an arithmetic average, single observations have a high influence on the outcome. Therefore we need to put special emphasis on the most extreme moves. Had I asked “when did the most extreme Bitcoin price changes happen?”, what would you have answered? My personal guess would have been: spring 2013. Absolute changes in that time were massive. But looking at relative figures tells us, that’s not the whole story.Data sources: bitcoincharts.com; own calculationsThe chart shows us that the most dramatic Bitcoin price moves happened in 2011. In fact, 7 out of the 10 largest up moves occured in 2011, only one of them was in 2013. As we can see on the chart, it wasn’t the biggest one. Regarding downside moves the situation is similar. 6 out of the 10 largest downside moves happened in 2011. Only 2 of them occured in 2013. This does not say the ups and downs of spring 2013 were small, it just means that the basis for volatility, daily returns, were even more extreme in 2011.When we talk about figures, they have more meaning if we relate them to other comparables. Only then it is possible to say whether something actually is “big, “small”, “extreme” etc. Therefore we need to take a step out of the Bitcoin ivory tower and have a look at the world outside of it. And we have to make sure we are comparing apples with apples.Before we can compare Bitcoin to something else, we need to know what it is. From a volatility perspective, Bitcoin can be two things. First, Bitcoin is a currency and a form of money. Bitcoin satisfies the three criteria that are generally taken to define money. These are: a medium of exchange, a store of value and a unit of account. So when we think of Bitcoin as a currency, we need to compare it to other currencies.The second way of looking at Bitcoin is to regard it as an asset. Assets represent value. As long as someone is willing to pay something in exchange for Bitcoin (be it other currencies, commodities, services etc.), Bitcoins are assets. Whether they are backed by anything or not, whether they have inherent utility (whatever that is) or not, doesn’t matter. Thus we can also compare Bitcoin to other assets. One obvious thing to do is to compare Bitcoins to other financial assets which are traded on liquid markets. Here prices adjust instantly to supply and demand and price data is publicly available.

Data sources: bitcoincharts.com; Yahoo! Finance; quandl.com; own calculations

The above chart shows the annualized 30 day moving average volatility of Bitcoin vs the US Dollar as traded on Mt.Gox. It is compared with the currency pair EURUSD and the S&P500 stock market index. There are two key messages following from this chart.Comparing Bitcoin volatility with EURUSD we can see, that the EURUSD pair has a much smaller volatility. Only very rarely it crosses the 10 line. On the other hand, the S&P500 volatility is higher and fluctuates more. In 2011 it crosses the 40 line. Back in 2008, at the peak of the financial crisis, S&P500 volatility even went beyond 80 on an annualized basis. The Bitcoin volatility graph looks more like the S&P500 graph than like the EURUSD graph. Therefore, in the last three years Bitcoin prices behaved more like an asset than like a currency. The other thing this chart shows us, is that the Bitcoin volatility has significant second order effects. At many points the volatility jumps from moderate values to values beyond 30. So the change rate of volatility is high. This makes Bitcoin prices even more unpredictable. But looking at the development we also see, that these jumps tend occur less often. And more importantly, the Bitcoin volatility is declining. Slowly but steadily. Despite all the attention and the buzz, when it comes to Bitcoin volatility, the year 2013 so far has not been anything like 2011.

3. Friend or foe?

Now that we have looked at some facts, the question is how we judge them. Is high volatility helpful for Bitcoin or not. This depends on the perspective, from which you look at it. Volatility is also a synonym for risk. And risk usually has a connection to return. There is upside and downside potential. Some might like this, some might not.

Investors

People who invest in assets and derivatives on these assets calculate the risks of their investments. With high volatility, there is also a potential for big returns. Bitcoin has so far delivered outstanding returns. So for those investors who are risk-prone, high Bitcoin volatility is a gift. If investors are risk-averse, they can simply stay out of Bitcoin and invest in other assets. The upside potential outweighs the risk for this group.

Miners

I’m not a mining expert. But if I became a miner, I would want to have a somewhat reliable estimate about the expected return from my hardware investment. Such a calculation gets very difficult when Bitcoin volatility is high. For miners, a high Bitcoin volatility means more risk than opportunity. If prices are on a temporary decline, miners can’t wait forever for a recovery. Mining difficulty could get too high in the meantime.

Merchants

Shops and e-commerce businesses make a living from selling goods and services. They are fully occupied with improving their products and their marketing. Managing exchange rate fluctuations isn’t their field of expertise. It would be bad news for them if their profit margins deteriorated due to foreign exchange risk. And if you have someone managing FX, it costs you money. Merchants need a stable currency.

Average Joe users

People who use Bitcoin simply to pay with it or to transfer money from one place to the other are a comparable to merchants . They use Bitcoin as a means to an end. When you use Bitcoin to send your earned money back home, you wouldn’t like the fact that it lost much of its value before your family could convert Bitcoins to their local currency. Surely, they would be happy about a value appreciation. But probably not at the expense of a high risk that their savings might lose value. For three of the mentioned groups, a high Bitcoin volatility is not desirable. Some might argue, that since Bitcoin is a deflationary currency, it is more likely that these people will profit from a rising Bitcoin value than suffer losses. This might be true in the long term. But if you want to use Bitcoin as a means of payment on a daily basis, you don’t have this long term perspective. You can get badly hurt from short term price swings. So for most of us, high Bitcoin volatility is a foe. And again, appreciation and volatility are not the same thing. If the price went up by 1 every day, then volatility would be 0. Even though the Bitcoin value would skyrocket. Therefore, one condition for Bitcoin to succeed as a widely-used currency is, that its exchange rate volatility keeps declining. And if Bitcoin succeeds as a currency, it will also succeed as an asset.

4. Bitcoin volatility outlook

This article so far has not treated the causes behind the Bitcoin volatility development. Large price swings are the result of either high volume selling or buying. The motivations behind trading activities are complex and only rarely obvious. News are usually one of many factors. But in this regard, if you understand the past, it doesn’t say too much about the future. Unless you can predict news bites. One thing that definitely has a measurable impact on volatility is market volume and liquidity. The last chart of this article shows how many Bitcoins have been traded on Mt.Gox against the US Dollar as a share of total Bitcoins in circulation on a daily basis.Data sources: blockchain.info; own calculationsAs the chart shows, an amount that exceeds 1 of total Bitcoins in circulation is traded frequently just against the US Dollar and just on Mt.Gox. This excludes all other currencies Bitcoin is traded against and all other exchanges where Bitcoins are traded. So if we were to sum up the entire trading volume and related it to the amount of Bitcoins in circulation, the share should be significantly higher. And values above 1 are already quite high if you compare this to a stock for instance. But there is also a development visible. The amount of daily traded Bitcoins as a percentage of total Bitcoins is falling. For one thing, the peak days have diminished since mid 2012.One factor for this fall could be increasing Bitcoin market capitalization. The more all Bitcoins are worth, the less one single trade impacts the market price (ceteris paribus). There is almost a circular reference. As long as Bitcoin volatility is high, new users are less likely to participate. But the more users there are, the easier it gets to convince new users because of a smaller volatility.The three charts we have looked at unveil a tendency of declining Bitcoin volatility. If this is a real trend, I wish it was here to stay. I’m cautiously optimistic about it. With roughly USD 1.5 bn market capitalization Bitcoin is still on a low level. That’s less than the smallest S&P500 company (Intel for instance has a market cap of USD 110 bn) and about one third of the money supply of Uganda. Both, small cap stocks and currencies of small countries are known to be volatile. Exactly because of the impact single trades can have on market prices. My retained optimism comes from the growing Bitcoin user base. Users drive demand and demand increases market cap. In this chain of events volatility declines and Bitcoin can succeed.