Looking at USD/BTC prices on Mt Gox, from 2011 to present, on a log chart and fitting along the lowest support levels, that prices have risen about 5x annually. That is awesome growth! Five times in one year, 25x  in two years, 125x in three years.

But speculators get ahead of this underlying awesome growth and create bubbles in which prices have double exponential growth doubling in weeks and days!

Suppose that 13.50 in January was a fairly valued pre-bubble price. When will $500 be reached given ideal steady 5x annual growth from there?

13.5 - January 2013
67.5 - January 2014
337.5 - January 2015
1687.5 - January 2016

I believe, based upon the underlying price growth trend that fairly valued $500 bitcoin will be reached in 2015. Probably $500 will be easily exceeded in the next and much bigger bitcoin bubble.

11 days after the April 10 peak

1. Does the recent dramatic recovery from 50 to 136 USD/BTC negate the case for a short term bear market?

Note that 136 is very close to halving the 266 peak. I suggest, based on price action, that the mid 130's is a significant resistance point. Perhaps, if the comparisons with bubble 1 are still valid, price peaks will be generally lower in the weeks and months to come. In the aftermath of bubble 1, prices declined on average 1% daily.

I have been looking for confirming signs that this second bitcoin bubble has peaked and is declining.

• Google Trends for 'bitcoin' now shows decline from a peak, when viewed over a 12 month or shorter time frame. This important, because an on-boarding step for new bitcoin investors is to search for information about bitcoins.
• Alexa web site traffic statistics for bitcoin.org show a decline from the April peak
• Wikipedia article traffic statistics for Bitcoin show a decline from the April peak here
• Blockchain.info chart for 'My Wallet Number of Transactions per day' appears to have peaked, when viewed on a log scale with 7 day smoothing. This data relates to the underlying bitcoin economy, including gaming.
• Blockchain.info chart for 'Trade Volume vs Transaction Volume Ratio' smoothed values peaked at 12 in early January, and bottomed out April 15 at 1.4.  I was puzzled by this particular chart at first, but a post today explains that the ratio is actually transaction volume / trade volume, i.e. as the bubble formed, the relative increase in trade volume caused the ration to diminish, and as the bubble collapses the ratio will likely return to pre-bubble levels.

Is anyone tracking the the number of Bitcoinity chart number of connected users? As of this writing it is 9021. One might reasonably expect this number to decline as less committed investors drop out.

2. What effect do Mt. Gox problems have on the bubble decline?

Back in June 2011, Mt. Gox was very seriously hacked and closed for several tense days. When the exchange reopened for business, prices sunk that day only to recover, and to gently continue the subsequent three-month long decline to the bottom. Compared to the first bubble, current Mt. Gox problems are much less serious. But as of this writing, Mt. Gox has been offline for hours with yet another DDoS attack.

Yes. Perhaps the rate of decline is faster this time because traders have the first bubble as a reference.

Bubble bursting follows a double exponential rate of decay, which is the opposite of what happened in the run up. Post peak, one would expect the price halving time to increase - thus the first halving from 266 down to 133, then the second very quickly down to 66.5. In contrast to your view, I think that the having time to 33.25 will be some weeks away - if the rate of decline slows down as in a typical bubble collapse.

What is your basis for the growth rate of the bitcoin economy? A linear regression of the log closing price on Mt. Gox starting in 2010 to present suggests a bitcoin economy growth rate of 4.8x annually = 580%. That is a fantastic growth rate, but the market gets ahead of that when doubling several times in a few months.

You are saying that, by way of analogy and symmetry, that because the decline is faster this time, then the recovery will be too.  That is plausible, but I think that the bottom will not be reached until people have forgotten about the bubble peak - months away.

7 days after the April 10 peak

How many more seller capitulations before the bottom?

The previous bitcoin bubble that peaked back in June 8, 2011 at 31.90, did not finally reach bottom at 2.20 until 159 days later. It dropped on average about 1% daily and featured six capitulations, the last two reaching the bottom vicinity. The six capitulations on average occurred 31 days apart. In the previous bubble, every one of the six capitulations failed to make new highs.

In this bubble, I count April 12 as the first capitulation, and yesterday April 16 as the second capitulation. These are only 4 days apart and thus for these two, the capitulations in Bitcoin Bubble 2 are occurring 8x faster than in Bitcoin Bubble 1.

If this bubble has the same number of post-peak seller capitulations as the last one, then 3 or 4 remain until the bottom is reached.

I watched the trades in the hours before the peak. It appeared there were a relative lack of bids - so sellers had to take what was there and prices dropped fast on little volume. Then gox lag prevented any new market orders for crucial hours during April 10. That too, restricted volume.

After the high on Wednesday, June 8, 2011, at 31.90, the previous bitcoin bubble dropped to just 2.20. That drop took 159 days and most of the time the rate of decline was about 1% a day.  There were several high volume capitulations along the way.

To the extent that this bubble is typical, this crash is not over - the losses for buyers above 70 are only going to increase.

5 days after the April 10 peak

Issue 1 - Evidence for the Bear Case.

The post-peak negative sentiment shut off the flood of new money that caused the bubble. I define this negative sentiment rather weakly - merely the lack of news about 10x price increases and lack of new significant all-time highs, e.g. 33, 50, 100, 150, 200. Clearly the wave of euphoria on Reddit /r/bitcoin has abated.

Sunday/Monday price action was almost exactly reversed from before the peak. Previously, new deposits at Mt. Gox would propel the price strongly upwards. In contrast, the decline since Sunday has been continuous and brutal.

The most compelling evidence for the bear case is that a new post peak low was recorded this morning. This issue is closed.

Issue 2 - Comparison with Bitcoin Bubble 1.

The second halving of price from the 266 peak is 66.60. This price was reached today, April 16, which is six days after the peak. In the previous bubble, the corresponding point of decline occurred 58 days later. Accordingly, the rate of decline for this bubble is more rapid than the first bubble by a factor of 10.

I suppose that in this bubble, the smart money exited sooner - given what they learned from the first one.

I would not buy now, and in fact have sold bitcoin as high as 255, anticipating this crash in order to buy back cheaper coins in several months.

Bubbles are not common enough that people learn from them.

You left out the choice of selling at market now, then buying back more coins cheaper in three months.

According to observed financial bubbles in the past, and especially with 2011, the lowest point is lower than most people would have guessed beforehand.

The selling pressure today was relentless. I think 120 is gone. Maybe 105 is gone too. Next big bid wall is at 85.

I am getting a whiff of capitulation in that big drop from 94 down to 88.

Lots more of that with the six months to come I think.

No sign yet of the tens of thousands of new Mt. Gox depositors lined up to buy ...

Is it just me, or does it seem like the powerful bids from 7 and 14 days ago are absent? Maybe later in the day they will show up.

Smoothing out the boom and bust of the bitcoin price series suggests an annual growth of approximately 5x, or about 400% APR. I take this as a strong indicator of the relative value of the underlying bitcoin economy. Bubbles are happening in bitcoin because 400% APR is enormous and speculators naturally get way, way ahead of the underlying fundamentals as new people learn about bitcoins and big returns.

Back in January, bitcoin was fairly valued at 13.50 even though it advanced during 2012. I think this is sustainable as a base.

And look there is another relatively large ask wall 1673.7778@ 99.5. 

At what price would you buy back in, and is there a minimum time that you would wait for things to settle down?

Professor,

Please take a close look at the price patterns leading up to Bitcoin Bubble 1 back in 2011. They are similar. Here is my analysis.

Bitcoin Bubble 1 December 2011

The way up ...
 0.498 January 31, 2011 -
 0.997 April 15 2011 - doubling time 74 days
 1.99 April 28, 2011 - doubling time 13 days
 3.98 May 10, 2011 - doubling time 12 days
 7.97 May 13, 2011 - doubling time 3 days
15.95 June 4, 2011 - doubling time 22 days
31.90 The high on Wednesday, June 8, 2011 - doubling time 4 days

The way down ...
31.90 The high on Wednesday, June 8, 2011
15.95 June 11, 2011 halving time 3 days
 7.97 August 5, 2011 halving time 55 days
 3.98 October 7, 2011 halving time 63 days
 2.20 November 14, 2011 halving time 38 days

--------------------

Bitcoin Bubble 2

The way up ...
   4.16 December 19, 2011: 8.31 July 16, 2012
   8.31 July 16, 2012 - doubling time 210 days
  16.62 January 21, 2013 - doubling time 189 days
  33.25 March 1, 2013 - doubling time 59 days
  66.50 March 25, 2013 - doubling time 24 days
 133.00 April 3, 2013 - doubling time 9 days
 266.00 Wednesday, April 10, 2013 - doubling time 7 days