Friday, December 20, 2013

On bitcoin

In the last month there has been a lot of discussion about cyber currency and specifically about the bitcoinm which has experienced a meteoric rise in value (relative to the dollar) over this winter season. This has prompted many to suggest that the bitcoin is the currency of the future. This may well be the case at some point.

However, it's important to curtail our expectations about the current possibilities that such a currency offers. In particular, some were quick to suggest that the bitcoin may offer an alternative to the euro for countries such as Cyprus. This is a provocative sound bite, but with no meaningful substance.

Proponents of such schemes may posit that even if not suitable for a whole a country to adopt, the bitcoin offers a way to earn a handsome profit because it is valued so highly. Such assertions neglect to mention that asset prices and currency rates reflect all publicly available information in that the market has already priced in all the publicly available information. In fact, since the internet fastened the speed of the distribution of news and expanded the market, adjustments in prices and rates is almost instantaneous. Hence, a small trader must outsmart the market in order to earn profit through such trades. A nearly impossible task.

But let me return to the claim that it is a good idea to switch your currency of exchange to the bitcoin for a second. Thanks to websites http://www.coindesk.com/price/ and http://epp.eurostat.ec.europa.eu/portal/page/portal/exchange_rates/data/main_tables I was able to find (close) rates of exchange for bitcoin and euro relative to US dollar (that is, how many US dollars a bitcoin and a euro buy at closing rates).

In Figure 1, we see the daily percentage change in value for bitcoin (blue line) and for euro (red line) for the period Aug 1 2013 - Dec 18 2013. The difference in variation is striking. The bitcoin varies greatly in value whereas the euro does not. Hence, holding all your assets in bitcoins might not be such a good idea as the value of your wealth would fluctuate enormously on daily basis. In contrast, the euro exhibited a certain stability which offers a certainty about the value of one's wealth.

Figure 1:


Yet the above comparison might not be fair as the euro has ECB backing it whereas the bitcoin does not. But, the proponents of the bitcoin suggest the absence of a central authority is a plus. Yet the data is clear that bitcoin is not the safest method of storing your wealth.

It could be of course that the bitcoin is fluctuating in such a manner due to the fact that it is new and people do not know much about it. In Figure 2, we see the daily percentage change in value for both the bitcoin (blue) and the euro (red) since their respective inception. It is immediately apparent the euro has never exhibited fluctuations of similar magnitude to those exhibited by the bitcoin.

Figure 2:


It is thus clear that for the time being, the bitcoin is not the safest storage of wealth. But more can be said. In particular, looking at the percentage change in value of the monthly average of each exchange rate we see a similar picture to the earlier. That is, the bitcoin (blue) displays wild fluctuations, while euro (red) does not. Therefore, the bitcoin may not be the safest storage even for longer horizons.

Figure 3:


Yet, in spite of the noted fluctuations in value, it might be possible that for an investor with mean-variance utility to use the bitcoin as part of a diversified portfolio. Specifically, if we look at the changes in daily value (note: traders gain by changes in value), since bitcoin's inception the mean change for bitcoin was .418 dollars with standard deviation 16.86, whereas for euro the mean change was .000279 with standard deviation .008. Hence, neither dominates the other. Moreover, as seen below the two changes seem uncorrelated.

 Figure 4:


 Hence, a portfolio divided between w percent bitcoin and 1-w percent euro would have variance

where DB is change in bitcoin value and DE is change in euro value. In fact, a portfolio which would have consisted a proportion 0<w<0.000000469069 of bitcoin would have had a smaller variance than a portfolio with just euros, and also would have had a higher expected return.