tldr; $184k, maybe.

The value of Bitcoin is not a complete mystery. The problems that Bitcoin addresses have existed since the dawn of trade. Bitcoin’s value largely comes from presenting a compelling alternative to existing solutions. The value of solving a problem can be quantified with heuristics that puts a number on the the cost the problem or the cost of implementing an existing solution. We can put a number on Bitcoin by summing these values and dividing by the total supply that will ever exist excluding lost coins. Like estimations in physics, the hope is that the final number will be accurate to an order of magnitude.

I start with a few assumptions:

Bitcoin’s primary use case is as a censorship-resistant store of value

Bitcoin will be the premier store of value among cryptocurrencies

Let’s get started.

Censorship-resistant transactions for institutions and government

The United States dollar has a dominant position in global reserves. For that reason the United States can unilaterally impose sanctions against actions performed between different countries. Due to the market size, liquidity, and reliability as a safe haven, opting out of holding US dollars is not really an option (see: dollar trap). The next most dominant is the Euro. With the joint cooperation between the US and the European Union, financial sanctions can be extremely punitive. It is in the interest of any country which has ever been the target of any international financial sanctions to find ways to sidestep the ability of US banks to censor. Burma, Crimea, Cuba, Iran, North Korea, Russia, Sudan, and Syria are all currently affected by international financial sanctions. (source.) Russia has the largest economy of any of these countries listed and I will use Russia as an approximation for the whole.

The first recent round of targeted sanctions against Russia occurred in March, 2014. International sanctions has cost Russia at least $106 billion between then and 2015. (source.) It is worth noting that sanctions have been broader than financial restrictions. For example, sanctions have limited the ability of Russia to import and export goods to other countries, and Bitcoin will not help with this. One of the bigger effects has likely been on direct foreign investment. Especially during periods of economic downturn, new cash cannot come into the country to spur the economy. One estimate for the net impact of financial sanctions from 2014–2017 has been a $280B reduction on gross capital inflow. (source.)

There are so many factors that come into play with sanctions and economies that an estimate is extremely difficult. For example, sanctions create uncertainty which affect foreign investment in a way that censorship-resistant payments would not alleviate. I think the figure of $280 billion is a reasonable estimation provided that (a) sanctions against Russia are not likely to be lifted anytime soon (source); (b) I am not including other countries in this analysis; (c) and Russia appears may incur even harsher financial sanctions in the future (see: 2017 election).

It is also worth noting that Putin seems to have taken an interest in Ethereum much more than Bitcoin, but I am not including that in this analysis.

Conclusion: $280 billion.

Protection from hyperinflation

Hyperinflation is still a problem today in the developing world where governments are frequently corrupt and inept. During periods of hyperinflation, to prevent further destabilization, access to other currencies like the USD is restricted. However, Bitcoin excels at censorship-resistance. What we find is that Bitcoin has a strong business case here; Bitcoin is not held back by the censorship-rich environment; and competitors are held back by this censorship-rich environment.

I’m going to assume that the total addressable market for a store of value here is the size of a country’s M1 money supply. I am just going to quote a definition I found for M1:

M1 is a metric for the money supply of a country and includes physical money — both paper and coin — as well as checking accounts, demand deposits and negotiable order of withdrawal (NOW) accounts.

Inflation is effectively a transfer of wealth from anyone who owns part of the M1 money supply to whoever controls the treasury mint. Under the quantity theory of money, if the monetary supply is doubled within a year (and other factors kept constant), the value of each unit of currency is half of what it was before any inflation.

In 2017, the top 20 countries with the highest inflation rates were Venezuela (650%, 12B M1), South Sudan (180%, no M1 data), Democratic Republic of Congo (41%, $1.2B M1), Libya (33%, $70.5B M1), Angola (31%, $17.9B M1), Sudan (27%, $6.3B M1), Argentina (27%, $60.7B M1), Egypt (24%, $41.7B M1), Suriname (22%, no M1 data), and Yemen (20%, $5.1B M1), Burundi (18%, $0.5B M1), Mozambique (17%, no M1 data), Sierra Leone (17%, $0.3B M1), Nigeria (16%, $34.1B M1), Haiti (15%, no M1 data), Malawi (13%, $0.7B M1), Uzbekistan (13%, $2B M1), Ukraine (13%, $20.6B M1), Liberia (13%, $0.3B M1), Azerbiajan (12%, $5.9B M1). (source, source, source)

Calculating the effective transfer of wealth as (new money created) / (new supply) * (M1 in USD), the numbers come out to:

Venezuela — $10.4B

Democratic Republic of Congo — $0.3B

Libya- $17.5B

Angola- $4.2B

Sudan- $1.3B

Argentina- $11.6B

Egypt- $8B

Yemen $0.9B

Burundi $0.1B

Sierra Leone $0.0B

Nigeria $4.7B

Malawi $0.1B

Uzbekistan $0.2B

Ukraine $2.4B

Liberia $0.0B

Azerbiajan $0.6B

The final number comes out to $62.3 billion. This is the amount of involuntary wealth transfer in the top twenty countries with the most inflation, excluding cases where the M1 data wasn’t available.

Conclusion: $62 billion.

A better reserve asset for institutions

One business case for banks or governments holding reserve assets is collateral for loans. National currencies have no intrinsic value and are tied to economies. In uncertain economic circumstances, the government may not be able to pay back loans with their national or reserve currency, so reserve commodities provide an additional measure for reducing the likelihood of defaulting. This makes it easier for governments to borrow money (e.g. sell bonds).

Bitcoin has some interesting properties which make it advantageous as a reserve asset:

Low transportation costs (only a transaction fee)

Trust-less nature (no banks intermediate so none can censor)

Easily quantified supply at any point in time

Transparent and predictable emission schedule (mining rewards)

Low storage costs (just secure the keys)

Simple and cheap to secure from theft compared to physical assets

Easy to prove solvency / ownership of assets (sign an arbitrary message with the private key)

Each of the above points is a non-trivial property with real value. National currencies can provide most of the properties that come with digital assets, but require banks to facilitate transactions. Durable commodities like gold do not require a bank to facilitate transactions, but are expensive to secure and transport, and are unwieldy in the digital age. Gold certificates are much easier to secure and transport but require third parties like banks. Bitcoin acts like a digital commodity in that it is a scarce, mostly-fungible digital-asset which does not require a bank to use or store. Digital gold.

The world’s gold reserves are estimated to be 33,791 metric tonnes (source), which at prices of $1317 per troy ounce comes out to about $1431 billion. Gold doesn’t need to move that often, and due to institutional inertia gold will probably not be sold off for cryptocurrencies anytime soon. That said, cryptocurrencies can provide diversification among reserve assets like gold and foreign currencies. The whole point of these reserves is to guarantee solvency even in economic downturns, and diversification provides a safety net. If Bitcoin ends up functioning as a premier store of value, it wouldn’t be out of the question to see it take up non-trivial amounts of allocation in a reserve.

conclusion: $1431 billion

A new asset class included in portfolios for diversification

Cryptocurrencies have properties that are differentiated from every other kind of asset I am aware of. Bitcoin is so easy to transfer in arbitrary amounts that its convenience rivals paper notes acting as redeemable proxies for their underlying asset. The business case for money as we know it emerged as a means of facilitating trade by pegging an asset to a very flexible medium of exchange with a third-party. Cryptocurrencies are natively so flexible that they do not need to be exchanged through proxies and because of it are much more secure than national currencies, bonds, and redeemable notes.

I am going to estimate investing in Bitcoin similarly to investing in gold. The amount of gold held by the major gold-backed ETFs is about 2400 metric tons. (source.). Let’s assume that mutual funds of gold hold a similar amount. At prices of $1317 per troy ounce of gold, that comes out to $102B. Even though part of gold’s value comes from uses as jewelry and for industrial applications, I am including the whole because if someone were interested specifically in jewelry or industrial applications, it would be trivial to buy ETFs in those categories instead. I get the impression that gold ETFs are largely for people investing in gold as a store-of-value, perhaps in part to reduce volatility of their portfolio.

conclusion: $102 billion

Alternative payments, focusing on cross-border payments (not remittances)

For the first time we can send money to anyone in the world at the speed of information any time we want. Traditionally sending national currencies across jurisdictions has been a large pain point due to legacy infrastructure, regulation around capital controls, etc. Having customers from across the world can make payment processing a huge pain point for merchants. Steam, a gaming company, deals with customers worldwide and at one point accepted Bitcoin. I am going to use their accepted payments as a proxy for the major systems in place today. They are: credit/debit, Paypal, WebMoney, iDeal, paysafecard, Moneybookers, DIRECTebanking.com, Russian terminals, and Wallet / in-game transactions.

Paypal has a market cap of $93B. Moneybookers was re-branded to Skrill and acquired by Paysafe Group. Paysafecard is also owned by Paysafe Group. Paysafe Group was sold for $3B in 2017. The others appear to become increasingly more niche and probably do not contribute much to the total market cap.

conclusion: $96 billion.

A hedge against uncertainty for individuals

At first I was skeptical that gold was owned in significant quantities as a sort of insurance policy. Maybe it is a generational thing, because nobody in my demographic (urban, educated, tech sector) seems to take an interest in gold. Looking into it, the demographic of gold bars and bullion buyers seems to be between 40–65 years old (source.) Anyway, it turns out that in periods of political uncertainty, like Brexit, regional gold sales spike. (source.) People do appear to be buying gold and some bigger motivators here seems to be fear-based. For example, gold can be viewed as an insurance policy based on distrust of national currencies backed by nothing and debt-based government spending.

I am going to measure this as the outstanding amount of privately owned gold bars and bullion and not include jewelry. While people do buy gold jewelry in part as a store of wealth (it can be melted down later if needed), it is difficult to differentiate this from displays of wealth, fashion, or cultural customs (see: diamond rings). Bitcoin is a very abstract, unsexy store of value and that is best approximated by gold coins and bars.

Estimates for the amount of privately held coins and bullion are approximately 28,000 metric tonnes. (source, source.) At current prices of $1317 per troy ounce of gold, that comes out to $1186 billion.

conclusion: $1186 billion

Getting a final number

First let’s sum the individual contributions.

$280B + $62B + $1431B + $102B + $96B + $1186B = $3157B.

Furthermore, it is likely that a percentage of Bitcoin owners have lost their private keys with no chance of recovery. Chainanalysis estimates this at around 3.8 million Bitcoins. (source.) Given the total lifetime supply of 21 million coins, about 17.2 million coins are accessible.

Final number: $184k per bitcoin.

Much of this value comes from adoption as a reserve asset. In the case this does not happen, the number comes out to $100k.

Addendum

About some things I don’t include in this analysis

Bitcoin’s lack of privacy is its greatest design flaw, and with the current level of privacy it provides it is currently not appropriate for certain use cases. These include offshore banking, money laundering, darknet markets, and a censorship-resistant store of value for wealthy individuals (e.g. billionaires from authoritarian countries). These use-cases will provide significant amounts of cash in-flow but to only to cryptocurrencies that can provide strong privacy guarantees. There have been a number of developments related to on-chain privacy relevant to Bitcoin that include: CoinJoin, stealth addresses, TumbleBit, CoinShuffle, CoinShuffle++, ZeroLink, ValueShuffle, and more. Because privacy was not baked into the base layer, implementing privacy on Bitcoin is a challenging problem. Darknet markets have already started phasing out Bitcoin for a mature private cryptocurrency. That is the best indicator you can expect that the privacy infrastructure around Bitcoin either not well-developed or adequate.

I do not attempt to include banking the unbanked as part of my analysis because of the difficulty of measurement. But I think that this could be significant given the size of the global unbanked population. For example, there are more than 10 million undocumented immigrants in the US, and there is a reasonable fear of their accounts being frozen, so many are likely unbanked due to fear of censorship. In developing countries, global mobile money is becoming the defacto banking system, MPesa being an example. (source.)

I am not including the money remission services because the reality is unfortunately significantly more complex than “but a BTC transaction is X times cheaper”. (source.) But if lightning networks have global reach, and people in developing countries transact in cryptocurrencies directly, this may change.

I’m not including people who actually want to use and spend cryptocurrencies because today there is not widespread merchant adoption. Accepting cryptocurrencies today seems to act as a novelty. Hopefully this will change when lightning networks mature and the infrastructure around cryptocurrencies evolves, but it is too early to include this in my analysis.

I don’t include domestic payments because it is not clear to me that this is a pressing problem that people desperately want solved. Bitcoin has existed since 2009, and during most of this time it was cheaper to use than credit cards for any amount but it didn’t seem to capture anyone’s attention. I think that convenience will determine the winners of domestic payments, and cryptocurrencies are not particularly convenient in 2018. As an emerging technology, I think cryptocurrencies are at a severe disadvantage for this use-case. Maybe it might make sense to revisit domestic payments in 15–20 years. With crypto you can spend with a card, no age restrictions, and push-only payments, it may eventually make a comeback.

What could really change this analysis in the coming years

The bad:

Ethereum, Monero, a StableCoin, or something yet to be made overtakes Bitcoin as the premier store of value. There is no technical justification for why Bitcoin is inherently the best store of value. Public compute, base-layer privacy, and price stability are all extremely important features which could make or break the winner of store-of-value.

Inertia to transition from gold to Bitcoin is strong. Institutions which have gold may feel that it is good enough to meet their needs and aren’t interested in the improved efficiency of Bitcoin. Or the immediate costs of transitioning are higher than the medium-term cost savings of Bitcoin and no bank wants to pay those upfront costs.

The United States views Bitcoin as a national security risk because it opens up new avenues for economic warfare. They push for central banks to reject cryptocurrencies as reserve assets indefinitely.

Bitcoin’s price and liquidity never rises to what is necessary for central banks to purchase Bitcoin without moving the price significantly. Because of the increased volatility during these buys and sells, central banks and governments find that they cannot use Bitcoin as a reserve asset.

The good: