Monthly average USD/bitcoin price & trend

[BitChick]

(I was using natural logrithm (base e) before for rpietilas function, so I got it wrong... now using hopefully correct function with base 10)

If these graphs are correct, or even close, it really puts things into perspective.  $200 per coin is still so low.  And some people are saying we are already into the late adoption phase?  With these graphs it shows how we are still early adopters for sure and even the small amount of coin some of us are holding is still great in the big scheme of things.

[ArticMine]

I agree on your points about the exponential model. What would be another model you would suggest for after we surpass ~5% penetration?

After we surpass about 5% penetration i would suggest something along the lines of a Sigmoid Function http://en.wikipedia.org/wiki/Sigmoid_function
Edit With t=0 to correspond to a time in the future where one expects 50% market penetration. For t << 0 the sigmoid function approximates an exponential function

[phelix]

30 and 90 days graph on http://blockchained.com

"The fit curve is an exponential percentual to the chart least squares fit - in other words: I played around until it looked good."

The factor of increase is about 10 per year.

According to this curve Bitcoins are a little overvalued. My stash is running low and I am looking forward to a nice drop down to ~130 (with panic maybe 110) - as of now I doubt we can sustain prices above $200 for much longer.... 

[ThomasV]

I could not resist:
http://xkcd.com/605/

[rpietila]

This is an excellent analysis; however there some points I wish to make:

1) The data for the BTC/USD exchange rate for 2009, and early 2010. I have managed to research this and found data for November / December 2009 and posted the results in this post https://bitcointalk.org/index.php?topic=308567.msg3309071#msg3309071 The valuation of .005 BTC /USD is way to high. The values ranged from 0.000614866 to 0.00130719 BTC/USD. Also the "pizza valuation" would place the BTC/USD rate at around 0.0028 in May 2010. https://bitcointalk.org/index.php?topic=137.0. The net result of this is to significantly underestimate the current trend and future value.

I am aware of that pricelist, but I discarded it because it is purely theoretical - no actual trade has occurred at those prices (afaik). I have based my estimate on the following nuggests of information that I consider reliable:
- I heard that "Theymos has purchased bitcoins at an all-time Bitcoin-OTC low of 0.003"
- I heard that the pizza incident (at about ~0.0025) was for a significantly cheaper price than commonly prevailing, to induce someone to make the effort
- The Norwegian guy bought BTC5,000 for $27 (0.0054)
- The price 10-doubled when Mt.Gox opened (to 0.08, i.e. from 0.008)

Since I do not have a reliable OTC price history at my disposal, I estimated the whole time to be a flat 0.005. But if someone wants to add to the information, please do!

2) The exponential model works well only when the market penetration is very low say below 5% since it neglects the probability of a newbie attempting to introduce Bticoin to a veteran. Based upon the value of the world M1 money supply approximately 20 trillion USD and the world gold supply approximately 8.2 trillion USD I would say this model will start to break down between 50,000 and 100,000 BTC/USD.

If we were talking about penetration, the above would hold. But now we are talking about price, and very likely the price will overshoot before finding a long-term realistic value. This has happened before with Internet stocks - userbases have grown steadily but price has behaved erratically, first growing really quickly, overshooting, collapsing, and finding stability.

[giszmo]

If we were talking about penetration, the above would hold. But now we are talking about price, and very likely the price will overshoot before finding a long-term realistic value. This has happened before with Internet stocks - userbases have grown steadily but price has behaved erratically, first growing really quickly, overshooting, collapsing, and finding stability.

Why would the new world currency "find stability"? Either the powers that be decide to let bitcoin live and take over which will lead to infinite $/Ƀ or they destroy it which leads to 0$/Ƀ. I see little in between so I also disagree with the trend flattening out at some level. Bitcoin gains utility with every business that accepts it and as soon as I can use Bitcoin for everything, I will just close my bank account and say goodbye to fiat. Why would anybody stay with fiat if bitcoin gains ultimate trust with a large percentage of the global economy?

After we surpass about 5% penetration i would suggest something along the lines of a Sigmoid Function http://en.wikipedia.org/wiki/Sigmoid_function
Edit With t=0 to correspond to a time in the future where one expects 50% market penetration. For t << 0 the sigmoid function approximates an exponential function

No. Why would that happen?

[DoomDumas]

Quick'n'dirty excel job:
Edit: better time scale

+1

+1 very nice quick n dirty excel job..

Exactly what I foresee for Bitcoin future value... even more.. is this Bitcoin getting more valuable and/or Fiat U$ getting less and less valuable as more and more peoples understand the fiat ponzi ?



Welcome to the future of currency !

[DoomDumas]

30 and 90 days graph on http://blockchained.com

"The fit curve is an exponential percentual to the chart least squares fit - in other words: I played around until it looked good."

The factor of increase is about 10 per year.

According to this curve Bitcoins are a little overvalued. My stash is running low and I am looking forward to a nice drop down to ~130 (with panic maybe 110) - as of now I doubt we can sustain prices above $200 for much longer.... 

I bet we'll not see bitcoins under 200 U$ ever !!!

[Wary]

I haven't made up my mind about how large the effect of using least squares in logarithmic space to fit a linear model vs. using least squares in linear space to fit an exponential model is. It might be negligible (or non-existant?), but it might also be large.

In the least squares method only the biggest values matter. So the shape of the curve in linear space would be defined based only on this year data. Which is not what we want. So using least squares in logarifmic space was the right way.

[Wary]

After we surpass about 5% penetration i would suggest something along the lines of a Sigmoid Function http://en.wikipedia.org/wiki/Sigmoid_function Edit With t=0 to correspond to a time in the future where one expects 50% market penetration. For t << 0 the sigmoid function approximates an exponential function

After 5% a new factor will come: Fiat's market share diminishing > fiat depreciates > everybody dumping it. Positive feedback loop, fiat run. So the jump from 5% to 100% can be very fast.

[bitcoin carpenter]

Remember, even if there were no large holders, only 22 million people could own 1 full bitcoin

In the end it will be worth an unfathomable amount or nothing

[rpietila]

If we were talking about penetration, the above would hold. But now we are talking about price, and very likely the price will overshoot before finding a long-term realistic value. This has happened before with Internet stocks - userbases have grown steadily but price has behaved erratically, first growing really quickly, overshooting, collapsing, and finding stability.

Why would the new world currency "find stability"? Either the powers that be decide to let bitcoin live and take over which will lead to infinite $/Ƀ or they destroy it which leads to 0$/Ƀ. I see little in between so I also disagree with the trend flattening out at some level. Bitcoin gains utility with every business that accepts it and as soon as I can use Bitcoin for everything, I will just close my bank account and say goodbye to fiat. Why would anybody stay with fiat if bitcoin gains ultimate trust with a large percentage of the global economy?

Stability against the USD? Of course not, since the latter will die.

Stability means that wages and prices are denominated in XBT and do not fluctuate so much.

(I have always had the implicit assumption in my theories that "USD" means "2013USD" so as to only account for the bitcoin's rise, and not the USD's demise.)

[rpietila]

Remember, even if there were no large holders, only 22 million people could own 1 full bitcoin

In the end it will be worth an unfathomable amount or nothing

, where "nothing" means "0 <= X < $10,000" per BTC.

[rpietila]

OP updated with chart and methodology!

[Zarathustra]

chart courtesy to oper128

Flattening out?

[molecular]

I haven't made up my mind about how large the effect of using least squares in logarithmic space to fit a linear model vs. using least squares in linear space to fit an exponential model is. It might be negligible (or non-existant?), but it might also be large.

In the least squares method only the biggest values matter. So the shape of the curve in linear space would be defined based only on this year data. Which is not what we want. So using least squares in logarifmic space was the right way.

In that case I'm probably not sure about "what we want" here. Note: I'm not arguing that we shouldn't do it like rpietila did, just that it isn't clear-cut.

[rpietila]

Flattening out?

I will stick to just one trendline, thank you

As outlined in the OP, there are myriads of other methods in drawing trendlines that differ in the following main points from mine:
- Daily exchange data used / this uses monthly volume weighted
- Starting 7/2010 when Gox opened / this starts 1/2009 when Bitcoin started
- Trend drawn by hand / this trend drawn using least squares method.

[stripykitteh]

Interesting analysis.

Something to bear in mind when considering the exchange rate skyrocketing is the possibility (or probability) that not only will bitcoin become more valuable, but fiat will become less valuable. So while an exchange rate of $300,000 in 2016 sounds optimistic, it is less so if the dollar fell significantly. After all, the trend line only compares relative value, not intrinsic value.

Either way, the argument for having some exposure to bitcoin in its infancy is sustained.

[Wary]

In the least squares method only the biggest values matter. So the shape of the curve in linear space would be defined based only on this year data. Which is not what we want. So using least squares in logarifmic space was the right way.

In that case I'm probably not sure about "what we want" here. Note: I'm not arguing that we shouldn't do it like rpietila did, just that it isn't clear-cut.

We are trying to find an exponent curve that matches bitcoin growth for it's whole history. That curve will let us predict bitcoin future growth. But for it to work, some assumptions must hold:

i. Mechanics of bitcoin growth is viral: basically every 3 month each old user "infects" a new user. That causes the exponent.
ii. The rate of infection is constant, whether BTC worth 1c or 10K$, whether is it a crypto-geek infecting his friend or multi-billion hedge fund infecting it's competitor.

This is obviously a big simplification. Any model is simplification. The trick is to get complexity just right, to go between Scylla and Charybda. If the model is too simple, it's predictions will be too far off the mark. If it's too complex, we won't have enough data to setup it's parameters.

1.The simplest model: OP.  IMO, it's too simple (I doubt the assumption ii) and, as result, too optimistic.

2. More complex: Zarathustra's model. Here he discards assumption ii, and draws a 4-segment line instead of 1 line. So the Scylla is better, but there is already a bit of Charybda: he lack enough data to draw the 4-th segment, since he draws by peaks and we don't know where the current peak is going to be. Maybe the better approach would be to use just 2 segments, with joint somwhere in 2011 and match them using least squares technique.

3. Even more complex: Staircase model. Discard both assumption. Instead take others.
i. Growth is viral: but it is not users that are infected, but markets. Geek market infects SR market, SR market infects amator speculators market etc. It causes "staircase" curve. Vertical part is filling up of the market, horysontal part - building of infrastructure for the next market.
ii. The rate of infection is different for each step and depends on relative size of markets, how long it takes to build infrastructure etc.

Unfortunately this model would be practically useless because of Charybda: we don't know all the required parameters.

So I would suggest improving rpietila's model: using least squares method, match (in log scale) either 2-segment line, or a log curve.

Anyone with experience of a proper math package?

[DoomDumas]

Interesting analysis.

Something to bear in mind when considering the exchange rate skyrocketing is the possibility (or probability) that not only will bitcoin become more valuable, but fiat will become less valuable. So while an exchange rate of $300,000 in 2016 sounds optimistic, it is less so if the dollar fell significantly. After all, the trend line only compares relative value, not intrinsic value.

Either way, the argument for having some exposure to bitcoin in its infancy is sustained.

+1

Totally agree.. relative value.. everything is there !