Net Unrealised Profit And Loss -Median vs average

[fillippone]

One of the most exciting features of the blockchain, as we currently know it _{(something could change in the future, via Taproot)}, is the possibility of knowing when a particular coin was moved, or more precisely, when a specific UTXO was created.
Associating this knowledge with the prevalent market price, we can understand how much an on-chain trade performs.

Glassnode, for example, has a series of measures of that.
One of the most interesting is the Net Unrealized Profit/Loss

Net Unrealized Profit/Loss is the difference between Relative Unrealized Profit and Relative Unrealized Loss. For more information see this article. This metric can also be calculated by subtracting realised cap from the market cap and dividing the result by the market cap as described in this article.

One intuitive way of thinking of it is the second way they exposed it: subtracting the realised market capitalisation from the realised market.

This is the average P&L of every UTXO.

A positive (negative) value means the average UTXO is in profit (loss) of the corresponding amount.
If NUPL is positive 20%, the average UTXO is now in-the-money, in profit, of the 20%.

Please note that the base metric is the current market capitalisation, not the original one.
This has two main effects:

• THe measure is not numerically distorted by deep in the money UTXO from the very beginning, which is several thousand percentage points in the money, having been moved at very low levels
• The measure can get to values. below-100% as the denominator is the CURRENT market calculation. A UTXO last moved at 60,000 USD, when the market is trading at 20,000 USD, has a UNPL of -200%.

So the NUPL is not numerically distorted, but to best capture the nature of the market is better to look at median values rather than an average value.

The average is the total quantity we want to measure, divided by the instances of the distribution: average wealth is the total wealth of the population, divided by the number of people in the population.

The median is the instance of the population that sits in the "middle" when we order the population from the smallest value to the largest one. The median wealth is the wealth we can expect to see when we randomly pick someone in the street.

There are cases when the two values diverge by much: think of a very poor African country of 60 million very poor people where the dictator is Elon Musk (a famous African-American dictator, after all): the average wealth of this African country would probably be quite high: is the wealth of Elon Musk divided by the 60 millions of people. (3,500 USD).
What would be the median wealth? 0 USD.
If we randomly pick a citizen of that county, he would probably have zero wealth.

While reading an essay comparing average and median wealth for a series of nations, I had the idea of this indicator.


Where is the median wealth of the United States?


So I think it would also be nice to have such a measure of "median" wealth in the Case of NUPL.

I think it would be helpful to calculate the NUMPL Net Unrealised Profit and Loss.

Net Unrealized Median Profit/Loss is the difference between Relative Median Unrealized Profit and Relative Median Unrealized Loss.

where:

Median Unrealized Profit is defined as the profit (in USD) of the median coin in existence whose price at realisation time was lower than the current price, normalised by the market price.


Median Unrealized Loss is defined as the loss (in USD) of the median coin in existence whose price at realisation time was higher than the current price, normalised by the market price.

As I expect the distribution of UTXO to be somewhat skewed by many high-value, highly profitable coins, maybe this measure will "correct" the estimate by the "random" factor: how profitable is the "random" investor in Bitcoin?

For all those reasons, I suspect this measure has a way more negative outcome than NUPL.

What do you think? Is it easy to compute?
Cany we propose the idea to Glassnode and or to Tuur Demeester?

[bitmover]

As I expect the distribution of UTXO to be somewhat skewed by many high-value, highly profitable coins, maybe this measure will "correct" the estimate by the "random" factor: how profitable is the "random" investor in Bitcoin?

as all coins are "born" from miners, and most UTXO have a very long history and changed hands a lot, this is a problematic metric to track a "random" bitcoin investor.

A much simpler approach would be to just look at addresses balances. Total value when received x total value for current balance.

You can see that in blockchair.com, just like this. Check this example:

https://blockchair.com/bitcoin/address/bc1q8jjqfldhtu247hewmwy9a9gy7rx0g79y3hxnm0


He received 12k and has now about 20.9k

Ofc you would need some filters, removing addresses which have a lot of reuses and some other problems which can make this metric problematic. But it is a start i guess.

[fillippone]

Bringing back this thread as the user @gbianchi implemented the idea:

There is his graph:

The idea is the following:

• NUMPL<NUPL bullish
• NUMPL>NUPL: bearish

We are just starting to notice a bearish divergence.

[HelliumZ]

Today Bitcoin price $100450 at the time of writing  and when I invested market was bullish at $116000

Net Unrealized Profit and loss (NUPL)= 100450- 116000 = -$15550
I invested 300 dollar at Bitcoin then NUPL = 15550×300  ÷116000 = ~40 dollar

[abhiseshakana]

Thank you for reminding me that averages can be deceiving and that the NUPL (Number of Points) can mislead market perception. Initially, I felt this discussion would be too technical, but it's quite interesting to discuss the intersection of statistics and digital economics by discussing NUPL and NUMPL. On-chain analysis focuses more on aggregates (capitalization, average, and total profit) without considering the distribution of wealth and profit on-chain. It would be very interesting if the discussion could be linked to wealth distribution, market behavior and sentiment, and the well-being of the digital economy, with the initial premise that GDP per capita figures do not always reflect the true well-being of society. GDP per capita may be high because there are a handful of super-rich individuals, but that doesn't necessarily mean the population is prosperous. So, with NUMPL, it's hoped to answer the curiosity: is this bull market felt by everyone, or only elite whales?

NUPL only calculates the average unrealized profit, without considering the distribution of coin holders. When the UTXO distribution is highly skewed, NUPL can mislead market perception. So, NUMPL attempts to address distributional issues, similar to those faced by ordinary investors. However, in the blockchain context, the NUMPL concept has several weaknesses, including the vague definition of the median (UTXO, wallet, address, value-weighted?). The median only takes a single midpoint, not the entire distribution, and ignores skewness and kurtosis.

If I'm not mistaken, your ultimate goal is to understand how balanced profits are among Bitcoin investors. Starting from the premise that the economy and markets are distributed phenomena, not single points, and that NUMPL only answers the typical investor's profit, I believe another macroeconomic approach is needed that can be paralleled on-chain to be more informative.

The logic of NUMPL can be expressed as:
GDP per capita = mean output per person
Median income = middle income of the population
In fact, we don't stop at the median; we continue to measure the overall wealth distribution to understand the structure of inequality. Perhaps you could consider some more accurate options for analyzing market stability, sentiment, and wealth inequality.

Gini Coefficient-Based PDI
In macroeconomics, we measure income inequality with the Gini coefficient (Gini), and on-chain profit inequality with the PDI. If the Gini profit increases, it means the market is becoming more concentrated in the hands of whales.

Learning from banking stress testing, I believe we need an approach that combines risk statistics and market behavior. By using an on-chain VAR (Value at Risk) model, we can try to determine the number of investors who will lose if prices fall.

Is it possible to gain a deeper understanding of market structure by applying the on-chain version of the Lorenz curve, not just a single number (mean/median)?

What if we use a richer statistical variation (Weighted Percentile Profit Index) and combine it with the median (NUMPL) to determine the extent of inequality and the evenness of profits?
Everything is still in the conceptual stage for the technical calculations; let me try to figure it out.

https://en.wikipedia.org/wiki/Skewness
https://en.wikipedia.org/wiki/Kurtosis
https://en.wikipedia.org/wiki/Quantile
https://www.investopedia.com/terms/w/weightedaverage.asp

We are just starting to notice a bearish divergence.

In my country, there's a saying, "mendung tidak selalu hujan" (clouds don't always rain). Bearish divergence is only an early warning sign of weakening momentum, not a guarantee of an immediate market decline. This is similar to the difference between a still-high GDP per capita and a stagnant median income, a signal of inequality and a potential economic slowdown. In the real economy, GDP can still grow, but median income is declining, indicating that the welfare of the majority has deteriorated, even though the headline data still looks good. From a digital economic perspective, in the late stages of a bull market, microeconomic indicators (such as NUPL and realized profit) usually begin to decline before prices fall. So, bearish divergence is a signal of asymmetric welfare distribution in the crypto market. Some whales are still strong, but the majority of retail investors are starting to weaken as profit distribution becomes increasingly unequal and selling pressure increases. We may not be in a crash yet, but the market is starting to run out of steam.

CMIIW, perhaps I misread and misinterpreted your chart.

[fillippone]

NUPL only calculates the average unrealized profit, without considering the distribution of coin holders. When the UTXO distribution is highly skewed, NUPL can mislead market perception. So, NUMPL attempts to address distributional issues, similar to those faced by ordinary investors. However, in the blockchain context, the NUMPL concept has several weaknesses, including the vague definition of the median (UTXO, wallet, address, value-weighted?). The median only takes a single midpoint, not the entire distribution, and ignores skewness and kurtosis.

Congrats on the good explanation of the graph.
Yes, the point is the one you pointed out, trying to "smooth" out the effect of the very in the money first initial holders, that could displace the mean of the P&Ls, also knowing that those holders probably won't move their coins anytime soon!
The only thing I can say about the specific point highlighted above: mean and median both don't account for higher moments of the distribution, like the one you mentioned.