---
# System prepended metadata

title: PM

---


# PM

*1. V1. Here's a possible implementation for a portfolio holding 100 different cryptocurrencies:*

```python
import numpy as np

# Step 1: Data Collection
# Collect historical price data for the 100 cryptocurrencies in the portfolio
price_data = []
for i in range(100):
    # get price data for the i-th cryptocurrency
    # and append it to price_data
    price_data.append(get_price_data(i))

# Step 2: Market Capitalization Calculation
# Calculate the market capitalization of each cryptocurrency
market_cap = []
for i in range(100):
    # get the total supply and circulating supply of the i-th cryptocurrency
    total_supply = get_total_supply(i)
    circulating_supply = get_circulating_supply(i)
    # calculate the market cap of the i-th cryptocurrency
    price = price_data[i][-1] # use the latest price for simplicity
    market_cap.append(price * circulating_supply)

# Step 3: Portfolio Optimization
# Compute the optimal weights for the portfolio using a portfolio optimization algorithm
# Here we use the Markowitz portfolio optimization algorithm
returns = []
for i in range(100):
    # compute the returns of the i-th cryptocurrency
    price_series = price_data[i]
    returns_series = np.diff(price_series) / price_series[:-1]
    returns.append(returns_series)
returns = np.array(returns)
cov_matrix = np.cov(returns)
mean_returns = np.mean(returns, axis=1)
target_return = 0.1 # set the target return to 10%
n_assets = 100 # set the number of assets to 100
weights = np.ones(n_assets) / n_assets # set the initial weights to be equal
def portfolio_return(weights, mean_returns):
    return np.sum(weights * mean_returns)
def portfolio_volatility(weights, cov_matrix):
    return np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights)))
def portfolio_optimization(cov_matrix, mean_returns, target_return):
    n_assets = len(mean_returns)
    constraints = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1})
    bounds = tuple((0, 1) for i in range(n_assets))
    initial_guess = np.ones(n_assets) / n_assets
    result = sco.minimize(portfolio_volatility, initial_guess, args=(cov_matrix,), method='SLSQP', constraints=constraints, bounds=bounds)
    return result.x
weights = portfolio_optimization(cov_matrix, mean_returns, target_return)

# Step 4: Portfolio Rebalancing
# Rebalance the portfolio towards the optimal weights by buying or selling the cryptocurrencies according to their current weights and market dominance
# Monitor the changing market dominance of each cryptocurrency and adjust the portfolio accordingly
current_weights = []
for i in range(100):
    price_series = price_data[i]
    current_price = price_series[-1]
    current_market_cap = current_price * get_circulating_supply(i)
    current_weight = current_market_cap / np.sum(market_cap)
    current_weights.append(current_weight)
current_weights = np.array(current_weights)
for i in range(100):
    target_amount = weights[i] * np.sum(market_cap) / price_data[i][-1]
    current_amount = current_weights[i] * np.sum(market_cap) / price_data[i][-1]
    if target_amount > current_amount:
        buy_amount = target_amount - current_amount
        # execute buy order for the i-th cryptocurrency
        # ...
    elif target_amount < current_amount:
        sell_amount = current_amount - target_amount
        # execute sell order for the i-th cryptocurrency
        # ...

# Step 5: Deployment and Monitoring
# Deploy the algorithm in a production environment and monitor its performance and risks
# ...
``` 

Note that this is just a possible implementation and may need to be adapted to the specific data and requirements of the portfolio management and rebalancing system.


*2. V2. Here's a possible implementation of the adapted algorithm in Python:*

```python
import pandas as pd
import numpy as np

# Step 1: Data Preparation
# Load historical price data for each cryptocurrency
btc_data = pd.read_csv('btc_data.csv')
eth_data = pd.read_csv('eth_data.csv')

# Merge the data into a single DataFrame
data = pd.merge(btc_data, eth_data, on='Date')

# Compute the daily returns of each cryptocurrency
returns = data.pct_change().dropna()

# Step 2: Market Dominance Calculation
# Compute the total market capitalization of all cryptocurrencies
total_market_cap = data.sum(axis=1)

# Compute the market dominance of each cryptocurrency
btc_market_dominance = data['BTC'] / total_market_cap
eth_market_dominance = data['ETH'] / total_market_cap

# Step 3: Portfolio Optimization
# Define the expected returns and covariance matrix of the cryptocurrencies
expected_returns = returns.mean()
cov_matrix = returns.cov()

# Define the market dominance vector of the cryptocurrencies
market_dominance = np.array([btc_market_dominance[-1], eth_market_dominance[-1]])

# Define the objective function of the optimization problem
def objective(weights):
    expected_return = np.dot(expected_returns, weights)
    risk = np.sqrt(np.dot(weights, np.dot(cov_matrix, weights)))
    dominance_penalty = np.dot(np.abs(weights - market_dominance), np.array([1, 1]))
    return -(expected_return - 0.5 * risk - 0.5 * dominance_penalty)

# Define the constraints of the optimization problem
constraints = [{'type': 'eq', 'fun': lambda weights: np.sum(weights) - 1}]

# Define the bounds of the optimization problem
bounds = [(0, 1), (0, 1)]

# Solve the optimization problem
from scipy.optimize import minimize
result = minimize(objective, x0=[0.5, 0.5], bounds=bounds, constraints=constraints)
weights = result.x

# Step 4: Portfolio Rebalancing
# Compute the current weights of Bitcoin and Ethereum in the portfolio
current_btc_weight = data['BTC'][-1] / total_market_cap[-1]
current_eth_weight = data['ETH'][-1] / total_market_cap[-1]

# Compute the desired weights of Bitcoin and Ethereum based on their market dominance
desired_btc_weight = market_dominance[0]
desired_eth_weight = market_dominance[1]

# Buy or sell Bitcoin and Ethereum to rebalance the portfolio
btc_amount = (weights[0] - current_btc_weight) * total_market_cap[-1] / data['BTC'][-1]
eth_amount = (weights[1] - current_eth_weight) * total_market_cap[-1] / data['ETH'][-1]

# Step 5: Deployment and Monitoring
# Deploy the algorithm in a production environment and monitor its performance and risks
``` 

Again, note that this is just a possible implementation and may need to be adapted to the specific data and requirements of the portfolio management and rebalancing system.

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