How to value a currency

[Sword Smith]

A currency derives its value from the objects that you can buy with it. The total amount of tangible objects, services and charitable donations being handled in a currency within a year must be equal to the value of the currency (coins) being used for this trade. But each currency denomination can change hands more than once within a year so we must take account for this. If a currency on average changes hands two times a year, the currency needs only be half as much worth as it would have to be if it changed hands once a year to be able to handle the same kind of assets being traded in this currency. Also, if the amount of a currency increases, this would reduce the value of a currency unit since you have more units following the same amount of goods. These relationships are expressed in the equation of exchange which states

nT=M*V (1)

Where nT is the value of goods being traded in this currency, M is the amount of currency units and V is the velocity of the money - i.e., how fast each currency unit on average changes hand.

nT can be further divided into nT=P*Q where P is the price index (inflation is the derivative of P) and Q is the real value (something that is constant despite of inflation/deflation (CPI defined)).

P is inversely proportional to the value of a currency since when inflation rises, the value falls. So P=1/val. We are then left with:

(1) =>

Q/val = M*V (2)

Let's apply this theory to bitcoins! We will measure nT in Bitcoins traded per year, M in number of bitcoins and V in number of times each coin is traded per year. Q, we will value in dollars per year since the dollar can be considered stable compared to BTCs (bare with me Austrians).

So the unit of val becomes $/BTC as we would like.

(2) =>

val=Q/(M*V) (3)

Now, we should estimate these different values: Q, M and V.

M is the easiest factor to evaluate since we know that there are about 11m BTC in circulation but that only 4m of these are currently being traded - the rest are placed in "savings accounts" or may be lost, so we will, for the time being, exclude these from our calculation. M=4m BTC

V is around 1/year for fiat currencies so we will also guess that that is the case here. V=1/year

Q is the dollar value of goods being traded in BTCs. Silk Road has an overturn on about USD 1m per month I have heard, and Bitcoinstore has a revenue of 400k-500k dollars per month, I believe. This is 1.5m dollars per month. Let us assume that these two constitute a tenth of the total bitcoin trade. So the total BTC trade is worth 15m dollars per month that is 180m dollars per year, let us round that up to Q=200m $ per year.

Plugging these numbers into (3) yields:

val=2*10^8$/year / (4*10^6 BTC * 1/year) = 50 $/BTC

which to me sounds reasonable.

Now, the way to increase val is to increase Q since this is the factor in Equation (3) that can span the most order of magnitudes. V will probably be between 10 and 1/2 no matter what you do and M is also hard to change significantly (by destroying BTCs). So the way to increase the value of bitcoins is to increase the amount of goods traded in bitcoins. Only this way can the current and any future hopes of stratospheric prices be sustained.

I would love to see your own estimates on Q, M and V for bitcoins. I definitely believe that Q can become very large in the future since bitcoin is the optimal internet currency and could make many other payment systems obsolete. Maybe Q=USD 300bn/year in the future? USD 300bn is the size size of Denmark's GDP. I see no reason that Q cannot reach this value or a higher value.

[chiropteran]

Q is the dollar value of goods being traded in BTCs. Silk Road has an overturn on about 1m per month I have heard, and Bitcoinstore has a revenue of 400k-500k dollars per month, I believe. This is 1.5m dollars per month. Let us assume that these two constitute a tenth of the total bitcoin trade. So the total BTC trade is worth 30m dollars per month that is 180m dollars per year, let us round that up to Q=200m $ per year.

What about USD?  There are about a trillion dollars in circulation, and you can buy them with bitcoins, so it seems like your Q is off by several orders of magnitude.

[Crazy]

I like this assessment, but still think $50 is too generous. Not by much, but still generous.

[Sword Smith]

Q is the dollar value of goods being traded in BTCs. Silk Road has an overturn on about 1m per month I have heard, and Bitcoinstore has a revenue of 400k-500k dollars per month, I believe. This is 1.5m dollars per month. Let us assume that these two constitute a tenth of the total bitcoin trade. So the total BTC trade is worth 30m dollars per month that is 180m dollars per year, let us round that up to Q=200m $ per year.

What about USD?  There are about a trillion dollars in circulation, and you can buy them with bitcoins, so it seems like your Q is off by several orders of magnitude.

I believe you have misunderstood something... These trillions of dollars are not traded in BTCs.

[chiropteran]

I believe you have misunderstood something... These trillions of dollars are not traded in BTCs.

How do you separate the dollars that are traded for bitcoin with the dollars that are not?  Just curious what the methodology is.

[fimp]

Q is the dollar value of goods being traded in BTCs. Silk Road has an overturn on about 1m per month I have heard, and Bitcoinstore has a revenue of 400k-500k dollars per month, I believe. This is 1.5m dollars per month. Let us assume that these two constitute a tenth of the total bitcoin trade. So the total BTC trade is worth 30m dollars per month that is 180m dollars per year, let us round that up to Q=200m $ per year.

What about USD?  There are about a trillion dollars in circulation, and you can buy them with bitcoins, so it seems like your Q is off by several orders of magnitude.

I believe you have misunderstood something... These trillions of dollars are not traded in BTCs.

But 100 million dollars per month on MtGox is.

[Sword Smith]

But 100 million dollars per month on MtGox is.

And that would make Q=1.2bn $ + 40 %(?) ~ 1.7 bn $ and thus val = 420 $/BTC all other factors held constant. Interesting. But the other factors have very large uncertainties though.

Edit: 40 % to take into account all those BTCs that are not traded on Mt. Gox.

[Sword Smith]

Q is the dollar value of goods being traded in BTCs. Silk Road has an overturn on about 1m per month I have heard, and Bitcoinstore has a revenue of 400k-500k dollars per month, I believe. This is 1.5m dollars per month. Let us assume that these two constitute a tenth of the total bitcoin trade. So the total BTC trade is worth 30m dollars per month that is 180m dollars per year, let us round that up to Q=200m $ per year.

What about USD?  There are about a trillion dollars in circulation, and you can buy them with bitcoins, so it seems like your Q is off by several orders of magnitude.

I believe you have misunderstood something... These trillions of dollars are not traded in BTCs.

But 100 million dollars per month on MtGox is.

These USD 100m should not all count in Q since many of them may be speculative and the result of daytrading and do thus not count as currency transactions. As others have pointed out, it is supply/demand that determines the value but the above calculations try to seek a more fundamental valuation than just the last traded price.

[myrkul]

A currency derives its value from the objects that you can buy with it.

I'm afraid you're wrong, here. Since the rest of your formula hinges off this flawed premise, it's interesting, but futile, maths.

A currency derives it's value from the desire of it's users to accept it. If the users of a currency really want that currency, it's value will be high, and you can purchase large amounts of other things for small amounts of the currency. If the users of a currency do not want that currency, it's value will be low, and you will require large amounts of currency to buy small amounts of other things.

[Crazy]

A currency derives it's value from the desire of it's users to accept it. If the users of a currency really want that currency, it's value will be high, and you can purchase large amounts of other things for small amounts of the currency. If the users of a currency do not want that currency, it's value will be low, and you will require large amounts of currency to buy small amounts of other things.

How is this different than "from the objects that you can buy with it?" Should he have qualified it with the "quantity" of objects, or the "amount of different" and "quantity" of objects? In either case, it's in the same vein, and entirely sound.

[myrkul]

A currency derives it's value from the desire of it's users to accept it.

How is this different than "from the objects that you can buy with it?"

He is trying to quantify value, and I am pointing out that it is subjective.

[Sword Smith]

A currency derives its value from the objects that you can buy with it.

A currency derives it's value from the desire of it's users to accept it. If the users of a currency really want that currency, it's value will be high, and you can purchase large amounts of other things for small amounts of the currency. If the users of a currency do not want that currency, it's value will be low, and you will require large amounts of currency to buy small amounts of other things.

Yes. Demand/supply is by definition what determines the price since the price is defined as the last traded deal on a major exchange. But my willingness to accept a currency depends on how other people value it (that is my use of it) and thus on what I can get for said currency which is what the formula QP=MV describes. I think you are presenting the Austrian counter argument of my monetarist argument. My own understanding of this monetarist argument is that it describes a natural level for a currency around which the price can deviate due to speculative effects. And what you are describing is merely the definition of the price (a descriptive argument) and not some kind of fundamnetal analysis (a normative argument).

[myrkul]

I think you are presenting the Austrian counter argument of my monetarist argument.

Indeed I am. Value is subjective, and each user of the currency values it differently. To see this quite clearly, look at the other threads here in Speculation. Some bitcoin users value it quite highly, and laugh at people who sold. Others value it less, and laugh at people who bought.

[smoothie]

People give something value, not a set of formulas.

[Sword Smith]

I think you are presenting the Austrian counter argument of my monetarist argument.

Indeed I am. Value is subjective, and each user of the currency values it differently. To see this quite clearly, look at the other threads here in Speculation. Some bitcoin users value it quite highly, and laugh at people who sold. Others value it less, and laugh at people who bought.

I am stating that this prescribes a fundamental analysis. Just like you can analyse stocks from a P/E perspective, Net Present Value or intrinsic value, you can analyse a currency from the equation of exchange. This may not give the full picture but just like a stock is unlikely to be traded below, say, 50 % of intrinsic value, so is a currency also unlikely to deviate too much from this equation although I realise that speculation is very to account.

According to your claims, the price of a currency is totally arbitrary and has nothing to do with the for instance M. Well, what is the problem of printing money then?

[Sword Smith]

People give something value, not a set of formulas.

I don't even know where to start responding to this nonsense. Too much unreflected Austrian theory in here.

[myrkul]

I think you are presenting the Austrian counter argument of my monetarist argument.

Indeed I am. Value is subjective, and each user of the currency values it differently. To see this quite clearly, look at the other threads here in Speculation. Some bitcoin users value it quite highly, and laugh at people who sold. Others value it less, and laugh at people who bought.

I am stating that this prescribes a fundamental analysis. Just like you can analyse stocks from a P/E perspective, Net Present Value or intrinsic value, you can analyse a currency from the equation of exchange. This may not give the full picture but just like a stock is unlikely to be traded below, say, 50 % of intrinsic value, so is a currency also unlikely to deviate too much from this equation although I realise that speculation is very to account.

So, what is the "intrinsic value" of a bitcoin? You give the number of $50/BTC up there in your OP. Would you care to explain, then, why it's currently trading at $92.45? And why it started at less than a dollar?

People give something value, not a set of formulas.

I don't even know where to start responding to this nonsense. Too much unreflected Austrian theory in here.

You should listen to Smoothie. For that matter, you should listen to the Austrians. They both have a track record of being correct in their predictions.

[wachtwoord]

So, what is the "intrinsic value" of a bitcoin? You give the number of $50/BTC up there in your OP. Would you care to explain, then, why it's currently trading at $92.45? And why it started at less than a dollar?

Mr. Market can be crazy at times

Additionally it was also at less than a Dollar because Q changes over time.

I'm not saying $50 is the correct valuation. I have no clue how to value a currency. But stating that something is incorrect because a (by definition) speculative market trades it at a different price is just silly.

[Sword Smith]

I think you are presenting the Austrian counter argument of my monetarist argument.

Indeed I am. Value is subjective, and each user of the currency values it differently. To see this quite clearly, look at the other threads here in Speculation. Some bitcoin users value it quite highly, and laugh at people who sold. Others value it less, and laugh at people who bought.

I am stating that this prescribes a fundamental analysis. Just like you can analyse stocks from a P/E perspective, Net Present Value or intrinsic value, you can analyse a currency from the equation of exchange. This may not give the full picture but just like a stock is unlikely to be traded below, say, 50 % of intrinsic value, so is a currency also unlikely to deviate too much from this equation although I realise that speculation is very hard to account for.

So, what is the "intrinsic value" of a bitcoin? You give the number of $50/BTC up there in your OP. Would you care to explain, then, why it's currently trading at $92.45? And why it started at less than a dollar?

It started at less than a dollar since no one was trading anything in bitcoins. Q = 0 for 2009 as far as I have understood. I already stated that the uncertainties on all values are huge and that speculation also plays a roll and that speculation is hard to contain in the equation of exchange.

People give something value, not a set of formulas.

I don't even know where to start responding to this nonsense. Too much unreflected Austrian theory in here.

You should listen to Smoothie. For that matter, you should listen to the Austrians. They both have a track record of being correct in their predictions.

Maybe so but you will have to come up with some better arguments than what you have come up with so far. From what you two are saying, the price is completely arbitrary other than what people demand and from your perspective it might as well be 1 cent as 1m dollars. At least my estimate is in the correct order of magnitude. And since I was able to recognize your argument as Austrian you should also recognize that I am not completely ignorant to their arguments and ideas.

[Sword Smith]

What drives the speculative valuation of $/BTC is an expectation that Q will become large, that M is contained and that V is also relatively stable.