Not all power-laws are equal — Why ‘Pareto-like’ investments are bad for you!

People are using “power laws” to justify bad investment practices.

Arslan Shahid
FireBird Technologies
7 min readDec 28, 2024

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Image by Author

By now, most people have heard about the Pareto, or power-law, distribution. It’s the idea that in some situations, only a small percentage of people end up with the majority of the rewards, while the rest get just a little.

This concept is often talked about in the startup world, where it explains venture capital returns. Most VC-funded startups don’t make money, but a few (around 7–8%) generate nearly all the returns, paying off for investors.

Now, with the rise of memecoins, NFTs, and cryptocurrencies, some people are using this idea to justify investing in these risky assets. They argue, “Just like VCs invest in many startups, hoping that one or two will be big successes, I can invest in multiple coins or NFTs, and I only need one big win to come out ahead. That’s the power-law effect!”

This thinking is deeply flawed, this post will tell how most likely following such a strategy you will lose money. You would also very likely go bankrupt without making a single winning investment.

What is the power law?

The probability density function of pareto

The Pareto distribution is a continuous probability distribution. With two parameters alpha and Xm . Alpha determines how the function is sloped and Xm is the minimum possible value for the distribution.

Visualization of different alpha values. With Xm = 1

In simple terms, for a fixed value of Xm, a higher alpha makes the distribution more unequal. Changing Xm adjusts all the values but doesn’t affect the level of inequality. Think of it like this: if rewards follow a Pareto distribution, having a high Xm with a lower alpha is ideal. It makes the system wealthier while keeping things fairer.

Pareto distribution visualized with different alpha & Xm values.

How does this relate to “meme-coins” & other risky investments?

It is hard to prove scientifically that meme-coin returns are exactly Pareto — but there are some characteristics that make it likely or a good assumption to have while modelling. Here are some reason’s why meme-coins exhibit “Pareto-like” behavior:

  1. Ownership Distribution: In many cryptocurrencies, including meme coins, a small number of wallets hold a large proportion of the total supply. For example, “whales” (large holders) dominate the market, leaving the majority of smaller holders with negligible stakes. This matches the Pareto principle (80/20 rule), where ~20% of holders control ~80% of the asset.
  2. Trading Volume and Activity: Pareto-like Behavior: A small fraction of traders or transactions often accounts for the majority of trading volume. This is typical in speculative markets where high-frequency or institutional traders dominate.
  3. Market Capitalization and Gains: Early adopters or insiders (such as project creators or influencers) typically capture the lion’s share of profits, while the majority of latecomers buy during peaks and lose money. This uneven distribution of gains is consistent with Pareto dynamics.

There is an article by Fortune that estimates that only 3% of meme coin projects survive & other estimates place the probability of making any money from meme-coins between 1–10%.

It is harder to estimate how many traders are actually profitable, so we would need to make some assumptions around that & simulate how based on different parameters how likely are you to make money.

Simulation

The simulation is straight forward to run, we assume that returns from trading are pareto-distributed & every player starts with $1 as initial capital in the game. So, if the reward > 1 then the trader is profitable & if less than <1 then the trader lost money.

# Simulate trading outcomes with Pareto distribution
# this function checks out of 10000 simulations for a given alpha & Xm
# what is the frequency of profit.
def simulate_trading_outcomes(n_simulations=1000, alpha=2, xm=1):
"""
Simulate trading outcomes and calculate probability of making any money (return > 0)

Args:
n_traders: Number of traders in each simulation
n_simulations: Number of simulations to run
alpha: Pareto distribution shape parameter
xm: Minimum value parameter
"""
profit_count = 0

# Run simulations
for _ in range(n_simulations):
# Generate random trading outcome from Pareto distribution
my_outcome = np.random.pareto(alpha) * xm

# Check if made any money (outcome > 1 means profit)
# Outcome > 1 means we made more than our initial investment (100% return)
# e.g. if outcome = 1.5, we made 50% profit on our investment
if my_outcome > 1:
profit_count += 1

# Calculate probability
prob = profit_count / n_simulations
return prob

# We will test out different alpha values, while keeping Xm the same.
# Remember we are trying to find out given memecoin returns follow
# pareto like distribution with a certain alpha what is the chance of making
# any money.
alphas = [i for i in range(1, 20)]
xm = 1

results = []
for alpha in alphas:
prob = simulate_trading_outcomes(alpha=alpha, xm=xm)
results.append({
'alpha': alpha,
'probability': prob
})
print(f"Alpha: {alpha}, Probability of making profit: {prob*100:.1f}%")

Plotting the results of the simulation we get

Image by Author — Bar chart shows the probability of making any money in 10000 simulations.

The graph shows that probability of making money diminishes quickly as alpha changes. Beyond a value of 10, less than 1/10000 trades are profitable. A random meme-coin trade in such an environment would likely never make any money, your just donating money.

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Wealth Concentration

You might wonder: if meme-coins are such a bad investment, why do we see headlines like “Crypto Trader Turns $2.2K of SOL to $2.26M Within Eight Hours on Memecoin Trade”?

The answer lies in something called the Pareto effect, which shows how wealth tends to be concentrated. In risky environments like this, the average person is likely to lose money, but for the few who win, the rewards can be massive.

Put simply: if you hit the jackpot, you win big, but most of the time, you’re going to lose.

To make this clearer, let’s compare the huge gains of the top 1% of traders with what the average & median trader typically makes.

# slight changes to the simulation function
def simulate_trading_outcomes(n_traders=100000, n_simulations=10000, alpha=2, xm=1):
"""
Simulate trading outcomes and calculate returns for top 1%, median and average traders

Args:
n_traders: Number of traders in each simulation
n_simulations: Number of simulations to run
alpha: Pareto distribution shape parameter
xm: Minimum value parameter
"""
avg_returns = []
top_returns = []
median_returns = []

# Run simulations
for _ in range(n_simulations):
# Generate random trading outcomes for all traders
outcomes = np.random.pareto(alpha, size=n_traders) * xm

# Calculate average outcome
avg_outcome = np.mean(outcomes)
avg_returns.append(avg_outcome)

# Calculate median outcome
median_outcome = np.median(outcomes)
median_returns.append(median_outcome)

# Calculate average of top 1%
cutoff_index = int(n_traders * 0.99) # Index for top 1%
top_1pct = np.mean(np.sort(outcomes)[cutoff_index:])
top_returns.append(top_1pct)

# Return average values across all simulations
return np.mean(avg_returns), np.mean(median_returns), np.mean(top_returns)

Here is the visualization of the results

Image by Author — Shows the return multiple of the average (blue), median (red) & top1 (green)

When alpha is 1, both the average trader and the top 1% of traders are making huge profits, but the median trader (right in the middle) is just breaking even. Once alpha goes above 1, the average and median traders start losing money. This means that if you don’t have a strong edge, you’re very likely to lose, while the top 1% can still stay profitable — at least until alpha hits 9. At that point, even the top 1% stop making money, and only the top 0.1% end up capturing most of the wealth.

This explains why you often see headlines about traders making outrageous returns — they’re rare exceptions. Whether through luck or insider knowledge, these traders manage to earn massive profits, but for the vast majority (including 99% of traders), losing money is the norm.

Conclusion

Don’t trade high risk investments, you will likely bankrupt yourself trying to get lucky. Gambling in meme-coins is not worth the effort, the more you trade the more likely you will lose money.

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