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Author Topic: Gold collapsing. Bitcoin UP.  (Read 1805440 times)
dree12
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March 28, 2013, 12:50:56 AM
 #4541

another simpler example would be if Bitcoin went from 1 to 1.2.

if i understand your formula, you would say Bitcoin went up 120%.  that's clearly wrong as it only went up 20%.

Indeed, 20% is correct here.

The issue with your method (6% loss + 1400% gain = 1406%) is that it assumes financial yields can be added. This is false. Consider a stock which appreciates 20%, and then appreciates 20% more. How much has the stock appreciated?

Based on your calculations, it would be 40%. However, this is not entirely correct—one can see that the stock actually appreciated 44%. This may seem counterintuitive, but we will consider some other examples to make this more clear.

Example 1: Imagine a stock A, priced at 1 BTC per share. A appreciates 20% on Monday, but then depreciates 20% on Tuesday. How much has A appreciated or depreciated?

Based on a naïve addition, the answer might be:
Code:
yield = 20% − 20%
      = 0%

However, if we take this one step at a time:
Code:
initial price = 1 XBT
Monday close  = 1 XBT + 0.2 XBT = 1.2 XBT
Tuesday close = 1.2 XBT − 0.24 XBT = 0.96 XBT
∴ yield = −4% !!!

Example 2: Imagine a stock B, priced at 1 BTC per share. B depreciates 20% on Monday, but then appreciates 20% on Tuesday. How much has B appreciated or depreciated?

Based on a naïve addition, the answer might be:
Code:
yield = −20% + 20%
      = 0%

However, if we take this one step at a time:
Code:
initial price = 1 XBT
Monday close  = 1 XBT − 0.2 XBT = 0.8 XBT
Tuesday close = 0.8 XBT + 0.16 XBT = 0.96 XBT
∴ yield = −4% !!!

From the above two examples, we can see that the method of calculating the yield is not additive. However, it seems to have a commutative property. We will now revisit the original goal of calculating Bitcoin's yield compared to gold.

We must understand that by comparing two commodities with no direct exchange rate, we need to introduce an intermediate commodity—in an efficient market, what we pick doesn't matter. We will choose the US dollar here.

Bitcoin, as you stated, has gone up by 1400% since the founding of this topic. Gold has gone down by 6%. These values correspond to yields of 1400% and −6%. Our goal is to calculate the difference between yields. However, we have just shown that this difference is not simply additive. So we will need to break up the problem again.

To simplify this problem, we will define a Standard Bitcoin as the value of a bitcoin, in USD, at the time the thread started. Our symbol for this will be SXBT. Similarly, define SXAU as the standard value of a gram of gold. We then know the constancy, but need not calculate directly, the Standard Ratio:
Code:
r = SXBT/SXAU

By the same process as the equations in our examples.
Code:
initial price of XBT = r XAU
after +ve XBT yield = r XAU + 1400%×r XAU = 1.5r XAU
after −ve XAU yield = [1/(1−6%)]×1.5r XAU ≈ 1.596r XAU
∴ yield = 1496%

So your error was because the ratios could not simply be added. Instead, they have to be normalized and then multiplied. We will now come up with a general formula to express this.

First, we will define a normalized yield as follows:
Code:
Yn = ln(yield + 1)

It turns out that normalized yields are addable. This is because a Yn of +q is exactly cancelled out by a Yn of −q (proof left as an exercise for the reader). So the remaining difficulty is converting from a normalized yield back to a regular yield:

Code:
Yn = ln(yield + 1)
e^Yn = yield + 1
yield = e^Yn − 1

Completing the formula:

Code:
total yield = e^[ln(XBT yield + 1) − ln(XAU yield + 1)] − 1
            = e^ln(XBT yield + 1)×e^[−ln(XAU yield + 1)] − 1
            = (XBT yield + 1)/(XAU yield + 1) − 1

Substituting our values (1400% & −6%), we have:

Code:
total yield = (1400% + 1)/(−6% + 1) − 1
            = 15/0.94 − 1
            ≈ 15.96 − 1
            = 1496%

If you need any more clarification, I'm glad to help.
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March 28, 2013, 01:01:14 AM
 #4542

...

If you need any more clarification, I'm glad to help.

Ah yes.  The beauty and magic of the natural log.  Thx for that!


thezerg
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March 28, 2013, 01:19:51 AM
 #4543

another simpler example would be if Bitcoin went from 1 to 1.2.

if i understand your formula, you would say Bitcoin went up 120%.  that's clearly wrong as it only went up 20%.

Well, no... I wouldn't say it "went up" without subtracting 100% from my result.  That's not really the real issue here.  I understand that financial ppl subtract 100% so they can say "went up".  You'd do that with my formula too.  But actually personally i think that that terminology starts to get really confusing once you pass 100%.  

I guess the dry way to say what I'm calculating is: "Change in Purchasing Power: Bitcoin vs. Gold: XXXX%".  Whether you subtract the 100% or not is getting into english not math.  

I think dree12's method and mine are the same, except perhaps around the treatment of "up"...
cypherdoc
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March 28, 2013, 01:31:20 AM
 #4544

another simpler example would be if Bitcoin went from 1 to 1.2.

if i understand your formula, you would say Bitcoin went up 120%.  that's clearly wrong as it only went up 20%.

Indeed, 20% is correct here.

The issue with your method (6% loss + 1400% gain = 1406%) is that it assumes financial yields can be added. This is false. Consider a stock which appreciates 20%, and then appreciates 20% more. How much has the stock appreciated?

Based on your calculations, it would be 40%. However, this is not entirely correct—one can see that the stock actually appreciated 44%. This may seem counterintuitive, but we will consider some other examples to make this more clear.

Example 1: Imagine a stock A, priced at 1 BTC per share. A appreciates 20% on Monday, but then depreciates 20% on Tuesday. How much has A appreciated or depreciated?

Based on a naïve addition, the answer might be:
Code:
yield = 20% − 20%
      = 0%

However, if we take this one step at a time:
Code:
initial price = 1 XBT
Monday close  = 1 XBT + 0.2 XBT = 1.2 XBT
Tuesday close = 1.2 XBT − 0.24 XBT = 0.96 XBT
∴ yield = −4% !!!

Example 2: Imagine a stock B, priced at 1 BTC per share. B depreciates 20% on Monday, but then appreciates 20% on Tuesday. How much has B appreciated or depreciated?

Based on a naïve addition, the answer might be:
Code:
yield = −20% + 20%
      = 0%

However, if we take this one step at a time:
Code:
initial price = 1 XBT
Monday close  = 1 XBT − 0.2 XBT = 0.8 XBT
Tuesday close = 0.8 XBT + 0.16 XBT = 0.96 XBT
∴ yield = −4% !!!

From the above two examples, we can see that the method of calculating the yield is not additive. However, it seems to have a commutative property. We will now revisit the original goal of calculating Bitcoin's yield compared to gold.

We must understand that by comparing two commodities with no direct exchange rate, we need to introduce an intermediate commodity—in an efficient market, what we pick doesn't matter. We will choose the US dollar here.

Bitcoin, as you stated, has gone up by 1400% since the founding of this topic. Gold has gone down by 6%. These values correspond to yields of 1400% and −6%. Our goal is to calculate the difference between yields. However, we have just shown that this difference is not simply additive. So we will need to break up the problem again.

To simplify this problem, we will define a Standard Bitcoin as the value of a bitcoin, in USD, at the time the thread started. Our symbol for this will be SXBT. Similarly, define SXAU as the standard value of a gram of gold. We then know the constancy, but need not calculate directly, the Standard Ratio:
Code:
r = SXBT/SXAU

By the same process as the equations in our examples.
Code:
initial price of XBT = r XAU
after +ve XBT yield = r XAU + 1400%×r XAU = 1.5r XAU
after −ve XAU yield = [1/(1−6%)]×1.5r XAU ≈ 1.596r XAU
∴ yield = 1496%

So your error was because the ratios could not simply be added. Instead, they have to be normalized and then multiplied. We will now come up with a general formula to express this.

First, we will define a normalized yield as follows:
Code:
Yn = ln(yield + 1)

It turns out that normalized yields are addable. This is because a Yn of +q is exactly cancelled out by a Yn of −q (proof left as an exercise for the reader). So the remaining difficulty is converting from a normalized yield back to a regular yield:

Code:
Yn = ln(yield + 1)
e^Yn = yield + 1
yield = e^Yn − 1

Completing the formula:

Code:
total yield = e^[ln(XBT yield + 1) − ln(XAU yield + 1)] − 1
            = e^ln(XBT yield + 1)×e^[−ln(XAU yield + 1)] − 1
            = (XBT yield + 1)/(XAU yield + 1) − 1

Substituting our values (1400% & −6%), we have:

Code:
total yield = (1400% + 1)/(−6% + 1) − 1
            = 15/0.94 − 1
            ≈ 15.96 − 1
            = 1496%

If you need any more clarification, I'm glad to help.

now that was crystal clear.  you're right.  i won't add them anymore.
cypherdoc
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March 28, 2013, 01:37:59 AM
 #4545

do one of you guys want to take over the Update and do the normalization?  zerg or dree?  its time for one...
thezerg
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March 28, 2013, 03:10:05 AM
 #4546

the silverbox update (comparison from the beginning of this thread, March 13th, 2012, gold=1690, Bitcoin=5.4):
Bitcoin is 89.50.  Gold is 1605.80

Bitcoin: 1557.41%

Gold:    -4.98%

Diff:  1644% advantage Bitcoin and Growing








(Here's how I get it, still a WIP to think about whether it differs from dree12's formulation)

def _gcbu(PriceBitcoinToday,PriceGoldToday,N=1):
  goldAmt = N/1690.0
  goldValue = goldAmt*PriceGoldToday
  bitcoinValue = (N/5.4)*PriceBitcoinToday
  ratio = bitcoinValue / goldValue
  print("the silverbox update (comparison from the beginning of this thread, March 13th, 2012, gold=1690, Bitcoin=5.4):")
  print("Bitcoin is %f.  Gold is %f" % (PriceBitcoinToday*100,PriceGoldToday*100))
  print("Bitcoin: %4.0f%%" % (bitcoinValue-1.0)*100)
  print("Gold:    %4.0f%%" % (goldValue-1.0)*100)
  print("Diff:  %4.0f%% advantage Bitcoin and Growing" % ((ratio-1)*100))
  return ratio*100
rpietila
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March 28, 2013, 07:22:49 AM
 #4547

What are the current terms of the paid subscription?

Melbustus
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March 28, 2013, 07:47:38 AM
 #4548

What are the current terms of the paid subscription?

I'm sure cypher will chime in with terms/details, but fwiw, I've been a subscriber for a couple months, and his calls on bitcoin have been spot-on. And even if they weren't, it's interesting reading regardless.

Bitcoin is the first monetary system to credibly offer perfect information to all economic participants.
But Bitcointalk & /r/bitcoin are heavily censored. bitco.in/forum, forum.bitcoin.com, and /r/btc are open.
Best info on Casascius coins: http://spotcoins.com/casascius
thezerg
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March 28, 2013, 03:06:25 PM
 #4549

Gold down today, bitcoin UP  Grin

the silverbox update (comparison from the beginning of this thread, March 13th, 2012, gold=1690, Bitcoin=5.4):

Bitcoin is 95.70.  Gold is 1598.10

Bitcoin: 1672.22%

Gold:    -5.44%


Diff:  1774% advantage Bitcoin and Growing
cypherdoc
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March 28, 2013, 03:56:52 PM
 #4550

Gold down today, bitcoin UP  Grin

the silverbox update (comparison from the beginning of this thread, March 13th, 2012, gold=1690, Bitcoin=5.4):

Bitcoin is 95.70.  Gold is 1598.10

Bitcoin: 1672.22%

Gold:    -5.44%


Diff:  1774% advantage Bitcoin and Growing

thanks for doing this!  Cheesy
notme
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March 29, 2013, 08:51:20 AM
 #4551



Anybody have a clue wtf those rectangle shaped patterns are?  I've never seen anything like that.

https://www.bitcoin.org/bitcoin.pdf
While no idea is perfect, some ideas are useful.
12jh3odyAAaR2XedPKZNCR4X4sebuotQzN
tvbcof
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March 29, 2013, 06:17:58 PM
 #4552

<graphic snipped>
Anybody have a clue wtf those rectangle shaped patterns are?  I've never seen anything like that.

Hard to know.  I looked at one of my physical Krugerrands and saw no sign of such behavior.  The damn thing weighs a bit over an once just as the day I bought it.


miscreanity
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March 29, 2013, 07:15:02 PM
 #4553

Anybody have a clue wtf those rectangle shaped patterns are?  I've never seen anything like that.

Paper gold dying.
tvbcof
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March 29, 2013, 09:38:27 PM
 #4554

Anybody have a clue wtf those rectangle shaped patterns are?  I've never seen anything like that.

Paper gold dying.

Very cool!  I went through a several months phase of being engrossed with EKGs when I was around 2nd grade age.  Back in the day when these things were printed on paper.  A family friend would bring them back from the hospital for me and taught me various things about the patterns.  All of which I've subsequently forgotten.

Isn't it mind-blowing how there are such interesting matches across (seemingly) diverse systems?  The way computer viruses and biological viruses mimic one another, for instance, is almost spooky to me.


Melbustus
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March 31, 2013, 07:03:58 AM
 #4555


The way computer viruses and biological viruses mimic one another, for instance, is almost spooky to me.



Same principles. It just means physical tangibility is not the presiding factor giving meaning to something. Good for bitcoin, in my opinion.

Bitcoin is the first monetary system to credibly offer perfect information to all economic participants.
But Bitcointalk & /r/bitcoin are heavily censored. bitco.in/forum, forum.bitcoin.com, and /r/btc are open.
Best info on Casascius coins: http://spotcoins.com/casascius
cypherdoc
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April 01, 2013, 02:06:17 PM
 #4556

zerg?!!! Cheesy
cypherdoc
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April 01, 2013, 03:59:40 PM
 #4557

The Daaash for Digital Caaash?!
molecular
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April 01, 2013, 04:02:26 PM
 #4558

The Daaash for Digital Caaash?!

hahahaaa, I've been waiting for this in big letters from you for a long time!

PGP key molecular F9B70769 fingerprint 9CDD C0D3 20F8 279F 6BE0  3F39 FC49 2362 F9B7 0769
thezerg
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April 01, 2013, 04:23:35 PM
 #4559

the silverbox update (comparison from the beginning of this thread, March 13th, 2012, gold=1690, Bitcoin=5.4):

Bitcoin:  yaaaaahoooooo!
Gold:     sitting on its ass doing nothin'...

Bitcoin is 105.99.  Gold is 1600.80
Bitcoin: 1862.78%
Gold:    -5.28%
Diff:  1972% advantage Bitcoin and Growing
cypherdoc
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April 01, 2013, 04:28:25 PM
 #4560

the silverbox update (comparison from the beginning of this thread, March 13th, 2012, gold=1690, Bitcoin=5.4):

Bitcoin:  yaaaaahoooooo!
Gold:     sitting on its ass doing nothin'...

Bitcoin is 105.99.  Gold is 1600.80
Bitcoin: 1862.78%
Gold:    -5.28%
Diff:  1972% advantage Bitcoin and Growing

Bwahahahahaha!

you are going to be worse than I!!!! Cheesy
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