Bitcoin price, gold, and nonsense – how not to value bitcoins

Every few days I hear the argument “If x% of the money in gold (or other asset class) moved into bitcoin, a single bitcoin should be worth $y”.  This article explains why this argument is utter nonsense.

The (flawed) reasoning is as follows: the total value of gold in circulation is estimated at US$8 trillion.  If some small fraction of the people holding gold (say, 5%) sold their gold for US Dollars (releasing $400 bn), and the USD proceeds were used to buy bitcoins, the total value of bitcoins (commonly referred to as “market capitalisation”) would increase by that amount of dollars ($400bn), and because we know the total number of bitcoins in circulation, we can derive a price per bitcoin. 

 

Market cap

Market cap = price per bitcoin x total number of bitcoins

The bitcoin industry uses the term “market capitalisation” or “market cap” to mean the total value of all bitcoins in circulation, ie price per bitcoin x number of bitcoins.  This terminology is borrowed from equities, where the market cap of a company is the price per share x number of shares outstanding.

At time of writing, the average price of bitcoin on various exchanges is about USD $11,000 per BTC, and 16.7 million BTC have been mined (though some proportion of these is lost and therefore no longer economically relevant).

This puts the market cap of bitcoin at about $185bn ($11,000/BTC x 16.7 million BTC).

The argument goes, if you add the $400bn of money coming from gold to the market cap of bitcoin, the new bitcoin market cap must be $185bn + $400bn = $585bn.  So, you divide by the number of bitcoins (16.7m BTC) to get a price per BTC:

$585bn / 16.7m = $35,000 per bitcoin!!!  Price target!!!

But this argument is wrong.  That’s not how it works.  That’s not how financial markets work at all!  The “money going into bitcoin” doesn’t simply drop into the “market cap”.  To understand this, let’s explore the fundamentals of how markets work.

 

Order books

The marketplace for financial assets including bitcoin can be described by an order book: a list of prices at which people are prepared to buy and sell an asset.  Traders use order books for price discovery and for executing trades – you can see the cheapest price someone is willing to sell bitcoins for, and the highest price someone is willing to pay for bitcoins.  And you can “hit” the prices to make a trade.

Let’s build an order book from scratch so we can understand how they work.

Let’s say you and a few friends own both bitcoins (BTC) and US Dollars (USD), and you get together to create a marketplace.  And let’s say, for the sake of easy maths, that only 1,000 BTC exist in the whole world (this is so we can derive a market-cap).  The order book currently looks blank, like this:

Bids          |         Offers

Last trade: (none)

What’s the market cap?  Well, since there are no prices and no bitcoins have changed hands, the market cap is undefined at the moment.

Now, say, you want to buy a bitcoin from one of your friends.  You want to buy up to 1 BTC and you’re prepared to pay $20 for it.  You tell the world by submitting an order to buy 1 BTC at $20/BTC.  You are bidding to buy bitcoins, so your order sits in the “Bids” column of the order book.  The order book now looks like this:

Bids          |         Offers
1 BTC @ $20   |

Last trade: (none)

Right now, if any of your friends wants to immediately sell up to 1 BTC, the best price they can achieve is $20.  If they want to sell more than 1 BTC, then they are out of luck: they can sell 1 for $20, then there is no market left – there is no one else willing to buy.

What is the price of Bitcoin?  Well, you could say $20, as that is the only price on the table.

So a market cap of bitcoin, based on the bid price is:

Market cap (bid):  $20k (1k BTC x $20/BTC)

Now let’s say that a participant is willing to sell 5 BTC for $200.  They are offering to sell bitcoins to the market, so their order goes in the “Offers” (sometimes called “Ask”) column of the order book.  The order book now looks like this:

Bids          |         Offers
1 BTC @ $20   |   5 BTC @ $200

Last trade: (none)

So, now what’s the price of Bitcoin?  Well, for someone who needs to sell bitcoins, the best (highest) price they can sell it for is still $20 (and they can only sell up to 1 BTC), and for someone who needs to to buy it, the best (cheapest) price they can buy it for is $200.

So the price of bitcoin is either $20 (best bid), $200 (best offer), or a theoretical mid-market price of $110 (half way between $20 and $200).  Note that there is no way of achieving $110.  No one can either buy or sell a bitcoin at $110 – it’s an entirely theoretical price.

So the market cap of bitcoin could be described as any of:

Market cap (bid):   $20k (1k BTC x $20/BTC)
Market cap (mid):   $110k (1k BTC x $110/BTC)
Market cap (offer): $200k (1k BTC x $200/BTC)

These are wildly different numbers!  But as the order books fill up (ie more liquidity is available), the best bids and best offers start to converge.  The best (highest) bids and best (lowest) offers are called “top of book”.

Now let’s say that one of your friends wants to buy three bitcoins and is prepared to pay a bit more than you are, but she isn’t prepared to pay $200 for it.  She submits an order to buy 3 BTC at $50 and the order rests there at the top of the bids.

Bids          |         Offers
3 BTC @ $50   |   5 BTC @ $200
1 BTC @ $20   |

Last trade: (none)

So now, the theoretical mid-market price is $125 (half way between $50 and $200).  But remember, that’s not a tradeable price.  You can’t buy or sell anything at $125.

Also, no trades have happened yet at all, and you and your friends are just suggesting prices you are willing to trade at.

And now the market cap of bitcoin could be described as:

Market cap (bid):   $50k  (1k BTC x $50/BTC)
Market cap (mid):   $125k (1k BTC x $125/BTC)
Market cap (offer): $200k (1k BTC x $200/BTC)

We can continue to build up this order book, and the best bid price and best offer price will converge.  Here is the order book a few minutes later:

Bids          |         Offers
1 BTC @ $95   |  20 BTC @ $105
3 BTC @ $50   |   1 BTC @ $150
1 BTC @ $20   |   5 BTC @ $200

Last trade: (none)

So now, the price of Bitcoin could be described as $95 (best bid), $105 (best offer), or $100 (mid-market).  And the market cap of bitcoin could be described as any of:

Market cap (bid):   $95k  (1k BTC x $95/BTC)
Market cap (mid):   $100k (1k BTC x $100/BTC)
Market cap (offer): $105k (1k BTC x $105/BTC)

Note that these are different to the previous market caps when the order book was emptier.  So the market cap(s) can change even without any trades taking place.

 

Pumping money into bitcoin

The gold argument says that money could flow out of gold and pumped into bitcoin, increasing its market cap, and therefore increasing the target value of a bitcoin.

But let’s look what actually happens when we make a trade.

Let’s say you want 8 bitcoins so much that you “pay the offer” and buy 8 BTC for $105/BTC at a total cost of (8 x $105 = $840).  You “pumped” $840 into Bitcoin to buy 8 BTC.

The “20 BTC @ $105” offer is reduced to 12 BTC @ $105, and the order book now looks like this:

Bids          |         Offers
1 BTC @ $95   |  12 BTC @ $105
3 BTC @ $50   |   1 BTC @ $150
1 BTC @ $20   |   5 BTC @ $200

Last trade: $105 paid.

So now we have an actual traded price!  Some (eight) bitcoins changed hands at $105 when you “paid the offer”.  $105/BTC is now arguably the best estimate for the price of bitcoin, based on transaction activity, even though the mid-market price is still $100.

And the market cap of bitcoin could be best described using the last actual traded price instead of theoretical prices:

Market cap (last): $105k (1k x $105/BTC)

But wait… Where did the $840 that we pumped in go?  Why hasn’t the market cap increased by $840?  Because that’s not how it works!  You can’t just add the money being “pumped in” to the market cap then divide to get a price…  You can’t do this:

Market cap was: $105k
Plus $840 "pumped in” = $105,840
Therefore bitcoin price must be: $105,840 / 1k = $105.84

But that’s not the price of a bitcoin!  You can’t do that!

 

Money in = money out

But why?  Why didn’t your “pumping money into bitcoin” affect the market cap?

Because when you pumped in $840 , think about the other side of the trade – the person you bought the 8 BTC from…  They sold 8 BTC and received $840.  They got out of Bitcoin – they pumped $840 right out of bitcoin!

The amount of money you pumped in… is exactly the same amount of money that “left bitcoin” when your counterparty sold their bitcoins to you!  You pumped in $840, and they pumped out $840! (I’m excluding fees charged by the exchange to keep things simple).

 

More trading

Let’s review the order book:

Bids          |         Offers
1 BTC @ $95   |  12 BTC @ $105
3 BTC @ $50   |   1 BTC @ $150
1 BTC @ $20   |   5 BTC @ $200

Last trade: $105 paid.

Market cap (bid):   $95k  (1k BTC x $95/BTC)
Market cap (mid):   $100k (1k BTC x $100/BTC)
Market cap (offer): $105k (1k BTC x $105/BTC)
Market cap (last):  $105k (1k BTC x $105/BTC)

Now, let’s say that someone was desperate to buy 14 bitcoins.  How much money do they need to spend?

Looking at the offers in the order book, they can buy 12 BTC for $105 each, then the next 1BTC will cost $150, and the final 1 BTC will cost $200.

Total cost to buy 14 BTC:
= (12 x $105) + (1 x $150) + (1 x $200)
= $1,260 + $150 + $200
= $1,610 (money “pumped in” to bitcoin)

And how does the order book look after this trade is executed?  Most of the offers have been matched, leaving 4 BTC still available to be bought at $200/BTC:

Bids          |         Offers
1 BTC @ $95   |   4 BTC @ $200
3 BTC @ $50   |
1 BTC @ $20   |

Last trade: $200 paid.

Market cap (bid):   $95k (1k BTC x $95/BTC)
Market cap (mid):   $147.5k (1k BTC x $147.50/BTC)
Market cap (offer): $200k (1k BTC x $200/BTC)
Market cap (last):  $200k (1k BTC x $200/BTC)

Wait… what?  Let’s compare the market caps before and after this trade:

Before: $95k (bid) / $100k (mid)   / $105k (offer) / $105k (last)
After:  $95k (bid) / $147.5k (mid) / $200k (offer) / $200k (last)

The maket cap increased by almost $100,000 by some measures, when all we did was “pump in” a measly $1,610!

According to the gold argument, what would the expected price of a bitcoin be?  Let’s do the calculation, and let’s use the mid price to define our market cap.

Pre-trade market cap = 1k BTC x $100/BTC = $100k
Add money “pumped in” ($1,610) = $101,610
Then divide by the total number of BTC in circulation (1k BTC)
= $101.61/BTC

But that’s not what the order book is showing us.  The order book is showing that the mid market price for a bitcoin is $147.50.

So clearly you can’t add the money “pumped in” to derive a market cap.

 

Prices can also change without trades taking place

Market prices (and therefore market cap) can also change without any trades taking place.  Let’s reset the order book back to what it was like before:

Bids          |         Offers
1 BTC @ $95   |  12 BTC @ $105
3 BTC @ $50   |   1 BTC @ $150
1 BTC @ $20   |   5 BTC @ $200

Last trade: $105 paid.

Market cap (bid):   $95k (1k BTC x $95/BTC)
Market cap (mid):   $100k (1k BTC x $100/BTC)
Market cap (offer): $105k (1k BTC x $105/BTC)
Market cap (last):  $105k (1k BTC x $105/BTC)

Now, let’s say the person who submitted the 12 BTC @ $105 offer changes her mind, and for whatever reason decides that she doesn’t want to sell 12 BTC at $105 any more.  She cancels the order.

And now let’s say that someone wants to buy 5 bitcoins but won’t pay $150/BTC for them (that’s a little too expensive), but he is prepared to pay $140/BTC for them.  He submits an order to buy 5 BTC at $140/BTC and the order book now looks like this:

Bids          |         Offers
5 BTC @ $140  |   1 BTC @ $150
1 BTC @ $95   |   1 BTC @ $200
3 BTC @ $50   |
1 BTC @ $20   |

Last trade: $105 paid.

What’s the market cap now?

Market cap (bid):   $140k (1k BTC x $140/BTC)
Market cap (mid):   $145k (1k BTC x $145/BTC)
Market cap (offer): $150k (1k BTC x $150/BTC)
Market cap (last):  $105k (1k BTC x $105/BTC)

These market cap numbers are very different to the numbers before those two orders were submitted.  All of the market caps (except last) have changed… without any trading taking place at all!  So the market cap can change without any trades taking place.

This happens in practice.  The bid/mid/offer can move to any price, up or down, without a single trade taking place.  This means that the (bid, offer, mid) market caps can change significantly without any trades.  And just one tiny trade to hit a resting order will trigger the last price to change, affecting the market cap (last), and this happens irrespective of how small the trade is that triggers the last price to change, and how much money was “pumped” in or out.

 

A valiant pumping attempt

Now let’s see what can happen if we do try to pump a lot of money into bitcoin.  Let’s reset the order book:

Bids          |         Offers
1 BTC @ $95   |  12 BTC @ $105
3 BTC @ $50   |   1 BTC @ $150
1 BTC @ $20   |   5 BTC @ $200

Last trade: $105 paid.

Market cap (bid):   $95k (1k BTC x $95/BTC)
Market cap (mid):   $100k (1k BTC x $100/BTC)
Market cap (offer): $105k (1k BTC x $105/BTC)
Market cap (last):  $105k (1k BTC x $105/BTC)

Now let’s have someone want to sell 600 BTC (yes, 600 out of the total 1,000 in circulation… they would be considered a “whale”).  And they want to sell them at $100/BTC:

Bids          |         Offers
1 BTC @ $95   | 600 BTC @ $100
3 BTC @ $50   |  12 BTC @ $105
1 BTC @ $20   |   1 BTC @ $150
              |   5 BTC @ $200

Last trade: $105 paid.

Market cap (bid):   $95k (1k BTC x $95/BTC)
Market cap (mid):   $97.5k (1k BTC x $97.5/BTC)
Market cap (offer): $100k (1k BTC x $100/BTC)
Market cap (last):  $105k (1k BTC x $105/BTC)

Note that this order has already changed the mid and offer market caps, even though a trade hasn’t yet taken place.

Ok, now it’s time to pump some money into bitcoin.  You decide to match the offer and buy all of those 600 BTC, at a cost of $100 per BTC.  Your outlay is 600 BTC x $100/BTC = $60,000 to match the offer exactly.

So how does the order book look after your trade?

Bids          |         Offers
1 BTC @ $95   |  12 BTC @ $105
3 BTC @ $50   |   1 BTC @ $150
1 BTC @ $20   |   5 BTC @ $200

Last trade: $100 paid.

Market cap (bid):   $95k (1k BTC x $95/BTC)
Market cap (mid):   $97.5k (1k BTC x $97.5/BTC)
Market cap (offer): $100k (1k BTC x $100/BTC)
Market cap (last):  $100k (1k BTC x $100/BTC)

Wait… What?  We pumped $60k into Bitcoin and the market caps didn’t move at all!  In fact, in this case the market cap (last) has actually gone down from $105k to $100!  Even though you pumped $60k into bitcoin!

The “money from gold” theory would suggest that the market cap should increase by $60k, yet we see from above that this isn’t how it works.

 

Conclusion

So the market cap is derived from the market prices (bid, mid, offer, last), and the market prices can change without any trades happening.  And even a very small trade at a new price can alter the market cap (last).

“Pumping in money” doesn’t necessarily alter the market cap in any deterministic way.

You certainly don’t need to “pump in money” in order to move the markets: traders simply altering their limit orders is enough to change the market cap.

Having said that… yes of course, if there are more buyers with a greater desire to buy and pay whatever it takes to accumulate BTC, then the prices (bid, mid, offer, last) should increase.  But certainly not how the “money from gold” analysts suggest.

So, no, you can’t add money from gold or any other asset class to the market cap of bitcoin and derive a price per bitcoin.

There is no method of establishing a “fair value” price of bitcoin.  Our existing models for valuing securities such as stocks and bonds simply don’t work.  Perhaps that’s why it’s fun, and perhaps that’s why influential hedge funds and social media analysts buy bitcoins and then make outrageously high predictions on the future price of bitcoin: because no one can call them out!

2 thoughts on “Bitcoin price, gold, and nonsense – how not to value bitcoins

  1. A great article and not something most people involved in Bitcoin understand. It’s interesting how little people in this space understand exchanges. It is important to learn that, as otherwise the HFTs and Prop Traders will have full control of the market.

    Like

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s