Bitcoin’s Security Budget is Adequate

"In a few decades when the reward gets too small, the transaction fee will become the main compensation for nodes. I'm sure that in 20 years there will either be very large transaction volume or no volume."
-Satoshi Nakamoto in 2010

In this text, I would like to expand on the thoughts laid out in two articles: Dan Held’s Bitcoin’s Security is Fine and Nic Carter’s It’s the settlement assurances, stupid. Dan explains how Bitcoin will likely overcome the diminishing block subsidy. By the end of his article, Dan aims to estimate likely median transaction fees. While Dan does this calculation in a top-down fashion (starting from the total Bitcoin market cap), I would like to offer an opposite, bottom-up approach, that is very much inspired by Nic Carter’s thoughts. By looking at the past data, I think we already have a simple heuristic at hand to find out how much the Bitcoin miners should be paid as the subsidy diminishes.

But first of all, let’s refresh on some basic Bitcoin security concepts.

Mining reward is the reward miners get for performing proof-of-work and appending a new Bitcoin block to the blockchain. It is composed of 2 parts: block subsidy and transaction fees.

1. Block subsidy are newly minted bitcoins that are awarded to miners who successfully mine a new block. This subsidy is only a temporary measure. As this is how new bitcoins are introduced to the network and the Bitcoin protocol is set to allow a maximum of 21 000 000 bitcoins in existence, we know exactly how the block subsidy tapers off over time.

Source: Bitcoin Wiki.

Let’s take a look what that means in terms of how many bitcoins will be at existence by individual block subsidy halvings and how much bitcoins will be mined on a daily basis, as this is important for our analysis at the end of the article:

One important fact regarding block subsidy: the “coinbase” - term for newly minted bitcoins - is only spendable after 100 confirmations (i.e. miner can spend the reward only after 100 blocks are mined on top of the block he mined). As we’ll see later, this plays an important role in analysing how much miners should receive over the long term.

2. Transaction fees constitute the second component of block reward.
So far, the transaction fee component of block reward has been quite small. We can see an uplift in the share during 2016-2017 bull market, when blocks were full and SegWit was not yet implemented and sufficiently adopted. By 2019-Q3, transaction fees make up only about 3 % of block rewards. For now, miners get almost all of their reward from newly minted bitcoins.

The total mining reward (subsidy + fees) over a period of time constitute the Bitcoin security budget - the incentive assurance of Bitcoin’s immutability. The higher the security budget, the more confident we can be that our transactions are set in an immutable stone after several confirmations.

But how do we actually know, as Dan Held puts it in his article, that “Bitcoin’s security is fine”? How do we know we don’t actually overpay miners, like Nic Carter thinks?

I think we can answer these concerns by looking at the data - first of all, we know exactly how much miners get paid via mining rewards:

In 2018, miners received around $10M daily, while by 2019-Q3 miners get around $20M daily. But what does this security budget actually secure? Dan Held works with the assumption that it’s the total market cap of Bitcoin, since he projects future mining rewards based on the total Bitcoin market cap.

But that actually doesn’t make sense, since reorg attacks endanger only the tip of the blockchain (meaning the last few blocks appended to the blockchain). If a hodler’s last transaction is buried thousands of blocks in the past, he won’t be affected by any reorg attempts (unless something akin to black swan event happens).

Mining rewards ensure the immutability of most recent transactions, shielding them from malicious reorgs such as double-spend attacks. If this is true, we should see a consistent correlation between the short-term value of mining rewards and short-term value of transacted bitcoins.

Please note I am talking about on-chain transactions only - not off-chain transactions like trading on exchanges. Only the on-chain transactions are secured by the mining rewards.

Let's take a look at ratio of mining rewards to onchain transacted value:

Seems like a correlation (actually, R = 0.95). Ever since the first price bubble burst in Q2-2011, mining rewards have been in an ever narrower range when compared to value of daily onchain transactions.

It seems the range has more or less stabilized between 1-2 %, never sinking below 0.7 %; quite interesting is that the range has stabilized in a period of otherwise tumultous 4 years, during which a halving and a major price bubble & bust occurred.

I think we can derive a good theory that explains the observed correlation between mining rewards and onchain transacted value.

The rolling 100 block period is the most endangered period in terms of incentive to reorg the chain; miners have to be incentivized to wait for their reward over this period. I think the observed ratio between the rewards and transacted amounts does exactly that - the lower bound around 1 % ensures that miners have a long-term (of rolling 100 block period) incentive to always accept the reward.

Or as Nic Carter puts it:

Since Bitcoin mining is a heavily competitive environment, I think it is safe to assume that long-term net profit margins are not much higher than 50 % (coming only from operating revenue - we disregard any gains from holding on to the mined bitcoin).

This would mean, as Nic says, that miners have only one attempt to expel the hashrate necessary to mine the block, and two options as to where to direct their hashrate: on mining a new block, or re-orging the previous block. Since the long-term reward for mining new blocks is higher than 1 % of daily transacted amount, miners are incentived to mine new blocks.

Why is the 1 % lower bound of the ratio relevant? Because the potential reward from the reorg equals the transacted amount within a single block: if I’d like to perform a double-spend, I would have to remine (or bribe the miners to re-mine) a past block where my transaction went through. And 1 % of the daily transacted amount is 1 block out of the most vulnerable 100 blocks.

So the fact this ratio is kept over long term ensures the miners are always incentivized to take the mining reward within the 100 block period - and of course after that as well, since it gets more and more expensive the deeper the blocks are.

What about the dip to 0.7 % during Q4-2016? 0.7 % eaquals 1/144, or 1 block out of daily 144 blocks. I think this is the bare minimum miners should earn, while 1 % is the safe minimum, as it corresponds to coinbase maturity.

In other words, I don’t think miners are heavily overpaid for the security they provide - I think the rewards satisfy the role of dynamic security budget that is always more or less in line with how much value the Bitcoin ledger secures.

It is of course true that this ratio by itself is not a sufficient assurance against reorg attempts. Other necessary assurances are: sufficient decentralization of hashrate control (and coordination problems if miners were to collude), competitive mining environment (so that miners are limited by profit margins in their attempts to mine & remine the blocks), long-term price consequences of successful reorgs (especially when miners have to pay for their capex in form of single-purpose ASICs).

But I think these assurances make up only the 2nd tier defense of blockchain immutability; without adequate mining rewards, these can be all overcome, as we’ve already seen when some altcoins were 51% attacked.

If the observation and explanatory theory of adequate mining rewards has any merit, it has some interesting consequences. If we accept the notion that mining reward is already adequate as of today, we can calculate how much the average fees would be if there was no subsidy. Average fees should then equal mining rewards divided by the number of transactions - this data is available as “Cost per Transaction” on blockchain dot info:

Assuming daily transacted amounts stay at least near today’s levels in the future, this is how much we should pay for an average transaction after the subsidy tapers off.

But, of course, subsidy will diminish over time, not disappear overnight. So we can actually model future bitcoin price and average transaction fees based on 2 variables:

Daily transacted amounts have been quite stable at around 1 billion USD daily for the past three years:

Let’s assume three future scenarios regarding daily transacted amounts: they stay the same at 1 billion, they rise to 10 billion a day and the third where they rise to 100 billion a day. For comparison, Visa processes around 20 billion daily.

And as we’ve seen, transaction fees are around 5 % of mining rewards. So let’s work with 3 scenarios regarding the share of fees on the mining rewards: 5 %, 25 % and 50 %.

For simplicity, I assume constant amount of daily transactions of 300k.

Let’s try to model what the situation will be like nine years in the future, after May 2028, when daily block subsidy falls to just 225 bitcoin:

As we can see, higher daily onchain value corresponds with higher price of bitcoin and higher transaction fees. The more the fees take over as a component of mining reward, the higher the average fee should be (and the less the need for high bitcoin price). This should be in line with increasing transaction density - onchain transactions being used mostly for high-value transactions relevant to second layer settlements and channel management.

There are of course many variables we’ve kept constant (such as number of daily transactions or adequate mining reward ratio, which could theoretically be higher when securing 2nd layer economic activity as well) but overall I think this way of looking at things is much more relevant than deriving scenarios off the future market cap. Market cap, in my opinion, is irrelevant, as we can’t know how many coins are going to be really active in the future - and only active coins should be relevant.