Why difficulty DOES affect price

[SgtSpike]

Many people here claim that price affects difficulty, not the other way around.  I would argue that each affects the other, though price is still the stronger influence.

As an investor, any sensible person would look at all possible ways to invest in bitcoins.  Investing in mining equipment can be considered an indirect investment into bitcoins.  At a low difficulty/price ratio (what we experienced a month ago), it makes more sense to invest in mining equipment because the payback period is so fast.  At a high difficulty/price ratio (what we are experiencing now), it makes more sense to invest in bitcoins directly.

It boils down to this:
As the difficulty increases, more potential investors will invest into bitcoins directly instead of mining, thus increasing the price.
Also as the difficulty increases, miners will begin to sell their mining equipment, usually in exchange for bitcoins.  This increase in demand for bitcoins helps drive the price up further.

Therefore, difficulty drives price, though not with as much influence as much as price drives difficulty.

I believe the rush about a month ago from $1.XX to $8.00 was a slight bubble, driven by speculation.  The following decline in value was due to more investors investing in mining equipment than bitcoins directly, compared with historical values.  They did this because the profitability of mining was so high.  Now, as the difficulty level is catching up, and investors realize that profitability in mining may not remain for much longer, they have switched back to investing in bitcoins directly, driving the price back up.

Who cares?

Any investor should care.  If difficulty drives price, even to a small extent, then price can be predicted, on average, to go up as difficulty goes up.


Thoughts?  Comments?

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[nazgulnarsil]

yes, supply affects demand.  this is a known economic principle.  I honestly don't know why the economics forum even exists when less than 1% of the posters have a grasp of the basics.

[tomcollins]

As the difficulty increases, more potential investors will invest into bitcoins directly instead of mining, thus increasing the price.
Also as the difficulty increases, miners will begin to sell their mining equipment, usually in exchange for bitcoins.  This increase in demand for bitcoins helps drive the price up further.

This would be true if people were trying to get a certain amount of bitcoins.  If I wanted to get 50 bitcoins, I could mine or buy them.  But I'm not aware of anyone who actually thinks this way.  Anything that is priced in Bitcoins tends to fluctuate in BTC price based on the trade rate.

I cannot speak for those who don't do their homework.  There are a lot of miners who don't like risking money, but have the equipment, so they will go after free money.  There are a few people who calculate between buying mining equipment and buying coins.  

What matters more is the difficulty/price ratio.  If the price is very high compared to the difficulty, people will mine rather than buy.  If the ratio is the other way, less will mine and more might invest.

What happens when the difficulty rises?  It does what you describe and makes mining less profitable and might make someone invest in coins.  Anyone investing in coins for this reason is making a pure speculation play, since they anticipate the price of coins to rise.

Therefore, difficulty drives price, though not with as much influence as much as price drives difficulty.

I believe the rush about a month ago from $1.XX to $8.00 was a slight bubble, driven by speculation.  The following decline in value was due to more investors investing in mining equipment than bitcoins directly, compared with historical values.  Now, as the difficulty level is catching up, and investors realize that profitability in mining may not remain for much longer, they have switched back to investing in bitcoins directly, driving the price back up.

Who cares?

Any investor should care.  If difficulty drives price, even to a small extent, then price can be predicted, on average, to go up as difficulty goes up.


Thoughts?  Comments?

It's a decent theory, although we need to look at the ratio of price to difficulty.  When I did the calculation, difficulty was at 60k and price was $3.50.  At that point, the difficulty was considerably less than the expected price.  I wish I still had my spreadsheet, but it was quite a bit off (I think the expected price would have been $1.80).

I think you are right in another regard- difficulty increases tend to correspond greatly with increased interest in BTC.  So while not cause and affect, but if there is more interest, either that interest is going to increase the difficulty or increase the price, or both.  If a lot goes toward increasing difficulty, the next wave may decide going for the coins themselves is a better approach.  So we see that increased interest and investment leads to one of the two or some combination of both increasing.  If one goes up too fast, you see a swing to the other one in the next batch of investment.

The supply affects demand, but the total daily new supply tries to remain constant (it doesn't in reality- in a growing hashing power, the beginning of difficulty periods are slower than the end by a lot).

[SgtSpike]

tom, I guess I do not understand what stance you are trying to take.  You seem to disagree with me, but then come back with "What matters more is the difficulty/price ratio," and talk about how a higher ratio would encourage more people to buy instead of mine, which is exactly what my post was about.

It'd be interesting to see a timeline graph of the difficulty/price ratio.

[smooth]

More or less correct analysis, which I've pointed out in reason #5 here:

http://forum.bitcoin.org/index.php?topic=9944.msg142929#msg142929

I will add that expected difficulty increases should not affect price (since they should already be included factored into the price set by speculators) but when difficulty increases unexpectedly that should affect price.

It'd be interesting to see a timeline graph of the difficulty/price ratio.

http://forum.bitcoin.org/?topic=7427

[kjj]

http://en.wikipedia.org/wiki/Lotka–Volterra_equation

[goatpig]

Keep in mind that the majority of miners, as the majority of long term investors, are 2 completely different crowd. While a few might think of swinging between mining and buying depending on the market, most just don't. Miners that see the difficulty skyrocket will stop buying mining gear, true, but their long term planning is more likely to be about selling their hardware and BTC and exit the market altogether.

For the rules of supply and demand to be applied properly, you need an omniscient crowd. When you see the amount of people that are mining in DeepBit, it seems obvious that a good portion of the mining crowd just doesn't think things through about their profitability.

Difficulty may and should slow down the gearing up, but a slow down in the mining race would affect the price more by outright reducing supply rather than encourage swapping around.

[trentzb]

If I wanted to get 50 bitcoins, I could mine or buy them.

or steal them, which seems to be following price as well. I don't mean you tc, just in general...you know what I mean, I hope.

[tomcollins]

tom, I guess I do not understand what stance you are trying to take.  You seem to disagree with me, but then come back with "What matters more is the difficulty/price ratio," and talk about how a higher ratio would encourage more people to buy instead of mine, which is exactly what my post was about.

It'd be interesting to see a timeline graph of the difficulty/price ratio.

I think your position is mostly correct, although your reasoning just was confusing high difficulty with high difficulty to price ratio.  Two different concepts.

Growing interest drives the price up.  Growing interest drives the difficulty up too.  The ratio of price to difficulty determines what mix goes where.

[SgtSpike]

tom, I guess I do not understand what stance you are trying to take.  You seem to disagree with me, but then come back with "What matters more is the difficulty/price ratio," and talk about how a higher ratio would encourage more people to buy instead of mine, which is exactly what my post was about.

It'd be interesting to see a timeline graph of the difficulty/price ratio.

I think your position is mostly correct, although your reasoning just was confusing high difficulty with high difficulty to price ratio.  Two different concepts.

Growing interest drives the price up.  Growing interest drives the difficulty up too.  The ratio of price to difficulty determines what mix goes where.

Ah, makes sense.  When I was talking about high difficulty, I meant high difficulty relative to price, so it sounds like we are in agreement.

[tomcollins]

tom, I guess I do not understand what stance you are trying to take.  You seem to disagree with me, but then come back with "What matters more is the difficulty/price ratio," and talk about how a higher ratio would encourage more people to buy instead of mine, which is exactly what my post was about.

It'd be interesting to see a timeline graph of the difficulty/price ratio.

I think your position is mostly correct, although your reasoning just was confusing high difficulty with high difficulty to price ratio.  Two different concepts.

Growing interest drives the price up.  Growing interest drives the difficulty up too.  The ratio of price to difficulty determines what mix goes where.

Ah, makes sense.  When I was talking about high difficulty, I meant high difficulty relative to price, so it sounds like we are in agreement.

Yeah, I think we are close enough here, just nitpicking.  Either way, mining investors should be smart enough to see that a "fair" ratio will get back fairly quickly (they aren't, though).  They are far too optimistic about difficulty rises and make less profitable (or even unprofitable) investments.  The assumption that if difficulty gets too hard, price will go up to match it, is a bit flawed.

One thing I haven't calculated is based on a fixed amount of investing, and people going optimally, if the ratio changes as the price goes up.  It's MUCH harder to make the price go from 8 to 9 than it was from 7 to 8.  Every increase, it gets harder.  Going from 400,000 in difficulty to 500,000 in difficulty is just as hard as going from 500,000 to 600,000.  So this is something I need to investigate to see if it makes sense.

Say it costs $1M of investment to make the difficulty go up by 100k.  If you divert half of it to buying coins, how much does that move the market instead?  How does that affect that ratio?  My gut tells me that price will move slower as price goes up compared to difficulty.  So it will cut the profitability of mining even if the ratio skews less toward mining.  Just thinking out loud, need to think about it more, but maybe you have some thoughts.  I like the way you think, so maybe it will give you ideas.

[dissipate]

Difficulty does affect price in that it knocks down the amount of Bitcoins being generated for a given period of time, causing a restricted supply to be imposed. If 15 blocks per hour are being generated, that's a lot more Bitcoins being potentially sold in the short term. After the next difficulty increase pushing that back down to 6 blocks per hour, the short term supply goes down from miners who sell their Bitcoins right away.

[SgtSpike]

That's certainly an interesting metric to consider.

Assume a cost of $1/MHash.  Also assume that difficulty relates directly to MHash at a rate of 1 difficulty to every 10 MHash (a more accurate number would be appreciated, I just can't find it atm, so 1:10 is my best guesstimate).

A couple interesting facts we can devise from this ratio:
- There has been roughly $4.3M invested in mining equipment so far.
- All of the bitcoins in existence are worth something like $50M at current market value, but they could not actually be sold for that much.
- I would be curious to know the actual $$$ invested into bitcoins, and whether it exceeds the $$$ invested into mining equipment.

We could assume that a $500,000 infusion into the mining system would therefore cause a 50,000 point increase in difficulty.

Now looking at the current market depth on MtGox, let's see what the same $500,000 would do to price.

Surprisingly, it would take only $275,000 to eat up all of the current asks that MtGox shows.  The price would take an immediate jump to $15/btc.  Of course, more people would jump on the sell train with an immediate price jump like that, so you could expect a reasonable amount of market correction there, but I think it is safe to assume than investing $500,000 into bitcoins would cause a permanent price jump of more than $1/btc.

It's hard to say how much this would change as the value of BTC goes up, because there could be more or fewer asks at a higher price.  But you are right that $500,000 would be a constant chance in difficulty, whereas a direct investment in bitcoins would slow as the purchasing power of USD goes down relative to the value in bitcoins.

Another thing to keep in mind though, is that with difficulty, percentages would be key.  A $500,000 investment in mining equipment wouldn't make as much difference tomorrow as it did today, because it would have a lower overall effect on the percentage of difficulty increase.

[tomcollins]

That's certainly an interesting metric to consider.

Assume a cost of $1/MHash.  Also assume that difficulty relates directly to MHash at a rate of 1 difficulty to every 10 MHash (a more accurate number would be appreciated, I just can't find it atm, so 1:10 is my best guesstimate).

A couple interesting facts we can devise from this ratio:
- There has been roughly $4.3M invested in mining equipment so far.
- All of the bitcoins in existence are worth something like $50M at current market value, but they could not actually be sold for that much.
- I would be curious to know the actual $$$ invested into bitcoins, and whether it exceeds the $$$ invested into mining equipment.

We could assume that a $500,000 infusion into the mining system would therefore cause a 50,000 point increase in difficulty.

Now looking at the current market depth on MtGox, let's see what the same $500,000 would do to price.

Surprisingly, it would take only $275,000 to eat up all of the current asks that MtGox shows.  The price would take an immediate jump to $15/btc.  Of course, more people would jump on the sell train with an immediate price jump like that, so you could expect a reasonable amount of market correction there, but I think it is safe to assume than investing $500,000 into bitcoins would cause a permanent price jump of more than $1/btc.

It's hard to say how much this would change as the value of BTC goes up, because there could be more or fewer asks at a higher price.  But you are right that $500,000 would be a constant chance in difficulty, whereas a direct investment in bitcoins would slow as the purchasing power of USD goes down relative to the value in bitcoins.

Another thing to keep in mind though, is that with difficulty, percentages would be key.  A $500,000 investment in mining equipment wouldn't make as much difference tomorrow as it did today, because it would have a lower overall effect on the percentage of difficulty increase.

Here's an easy way to look at it.  Putting $1 into mining increases the difficulty for a LONG time (until the rig comes offline).  Putting $1 into Bitcoin only absorbs the coins mined RIGHT NOW.  Tomorrow, another $1 is needed for tomorrow's coins.  And the next day.

You need $9x10,000 = $90,000 PER DAY going into Bitcoin to match just the mined coins.  If the price goes to $10, you need $100,000 per day.

[SgtSpike]

That's a very good point. 

So, if the price is staying roughly even, then is it a safe assumption to say that $90,000 is being invested daily in bitcoins?  In the last week then, roughly $630,000 has been invested directly into coins, plus whatever covered the market depth for the price increase (assuming another $100,000 or so there).

Also interesting, is that the 3-day difficulty estimate has increased from about 310,000 to about 550,000 in a week.  So that's a rough estimate of $2.4M invested in mining hardware for bitcoins.  Of course, a chunk of that mining increase would be attributable to people with existing hardware starting up on mining.  Even still, unless 3/4 of the new hashing power was from already-existing hardware, which I would find hard to believe, people are investing far more into mining hardware than into coins themselves.  Up to 3 times as much.

Of course, this hardware was likely ordered and paid for 1-2 weeks ago, and it is just now coming online, but interesting nonetheless.

[realnowhereman]

yes, supply affects demand.  this is a known economic principle.  I honestly don't know why the economics forum even exists when less than 1% of the posters have a grasp of the basics.

Maybe I'm in the 1%, but actually I understand it to be that supply always equals demand, with price setting the balance point.

[smooth]

So, if the price is staying roughly even, then is it a safe assumption to say that $90,000 is being invested daily in bitcoins?

Right, either explicitly via exchanges or implicitly.

People can implicitly invest in BTC by mining them and holding them or accepting them in trade and holding them. I would guess that mining and holding is by far the largest component of this, but I don't really know.

[SgtSpike]

So, if the price is staying roughly even, then is it a safe assumption to say that $90,000 is being invested daily in bitcoins?

Right, either explicitly via exchanges or implicitly.

People can implicitly invest in BTC by mining them and holding them or accepting them in trade and holding them. I would guess that mining and holding is by far the largest component of this, but I don't really know.

Good point.

It's actually quite concerning that (potentially) many times more money is invested every day in mining hardware than in bitcoins themselves.  Makes me believe that we ARE in a bubble still.

[bitcoinBull]

OP is spot on.

Price and difficulty are correlated.  Hard to say which is the dog and which is the tail.  In any case, sometimes the tail wags the dog.

They both grow in sync, so the ratio stays more or less constant.  I prefer to use price over difficulty.

We can arbitrarily add a constant factor of 10^5, defining the ratio such that when price was $1.00 and difficulty was 100,000, the ratio was 1:1.  Then when charted, we can see the ratio has oscillated between 1:1 and 3:1.

Here is the latest chart: http://forum.bitcoin.org/index.php?topic=7427.msg142996#msg142996

[SgtSpike]

I do enjoy your charts bitcoinBull, nicely done!  I agree, price/difficulty is a good ratio to use.  Even at $1.00 and difficulty of 100,000, there was still serious profit to be had by mining.  I think if we see the ratio drop to 0.5 or below, that's when we'll really see a good portion of the miners drop out.