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Summary

The presented content discusses the portfolio optimization of top cryptocurrencies using Modern Portfolio Theory (MPT) to achieve the maximal Sharpe Ratio over a specific period, allowing for a balance between expected returns and volatility.

Abstract

The article deals with the application of the Modern Portfolio Theory for optimizing a cryptocurrency portfolio, focusing specifically on the top ten most significant cryptocurrencies from January 2, 2023, to May 19, 2024. By adopting a Monte Carlo simulation approach, the post illustrates the process of constructing a portfolio based on the maximum Sharpe Ratio, which involves calculating the covariance matrix of daily returns and simulating numerous combinations of asset weights to explore the efficient frontier – the set of portfolios that offer the most return for a given level of risk. The culmination of this effort is a portfolio that presumably provides the highest possible rate of return for its relative risk, with the outstanding weights suggesting a significant portion in Solana (SOL) and Bitcoin (BTC). The proposed portfolio is not only designed to maximize returns for a given risk level but also to serve as an example of how investors might apply quantitative methods to improve their investment strategies.

Opinions

  • The author advocates for the use of MPT in the cryptocurrency market as a means of achieving optimal portfolio diversification and risk-adjusted returns.
  • By emphasizing the importance of the Sharpe Ratio, the author suggests that investors should not only chase high returns but also pay close attention to the amount of risk they are taking on.
  • The article implies that a diversified portfolio, as informed by the MPT and Monte Carlo simulations, can lead to better investment outcomes in the volatile cryptocurrency market.
  • The author's presentation of the efficient frontier and the max Sharpe Ratio portfolio indicates a preference for a quantitatively driven investment strategy, which relies on statistical analysis rather than speculative decision-making.
  • The inclusion of numerous visualizations, such as the correlation matrix and pie chart of portfolio weights, demonstrates the author's belief in the effectiveness of data visualization to convey complex financial concepts.
  • The conclusion, which highlights the top assets in the optimal portfolio (SOL and BTC), suggests that these two cryptocurrencies should be considered as core components of a well-structured crypto investment portfolio based on the analysis period's performance.

Max Sharpe Portfolio of Top 10 Cryptos with Risk-Adjusted Weights

Image template via Canva.
  • This post is about crypto portfolio optimization using Modern Portfolio Theory (MPT) and its practical applications in the digital currency world.
  • Specifically, we consider the max Sharpe Ratio portfolio (aka tangency portfolio) to calculate risk-adjusted returns on the efficient side of the mean-variance frontier, focusing on ten major cryptocurrencies from 2023–01–03 to 2024–05–19.
  • Our objective is to create a diversified crypto portfolio and evaluate its performance. By adjusting and analyzing portfolio weights, we can make informed decisions that maximize the Return/Risk ratio.

Let’s delve into the details of the crypto portfolio optimization approach.

  • Setting the working directory YOURPATH, importing libraries and reading the historical data of top 10 cryptos
import os
os.chdir('YOURPATH')    # Set working directory
os. getcwd() 

mport yfinance as yf
import numpy as np
import pandas as pd 
import os
import seaborn as sns

data = yf.download("BTC-USD ETH-USD USDT-USD USDC-USD BNB-USD BUSD-USD XRP-USD ADA-USD SOL-USD DOGE-USD", start="2023-01-03", end="2024-05-19")

data.tail()

Price Adj Close ... Volume
Ticker ADA-USD BNB-USD BTC-USD BUSD-USD DOGE-USD ETH-USD SOL-USD USDC-USD USDT-USD XRP-USD ... ADA-USD BNB-USD BTC-USD BUSD-USD DOGE-USD ETH-USD SOL-USD USDC-USD USDT-USD XRP-USD
Date                     
2024-05-15 0.452988 582.074341 66267.492188 1.000666 0.155526 3037.056641 158.186829 1.000128 1.000547 0.519004 ... 357450532 1895100260 39815167074 10177577 1767635344 14666902956 3585715674 8085028154 70663923975 1118098628
2024-05-16 0.459695 569.190247 65231.582031 1.000313 0.149637 2945.131104 159.116455 0.999971 1.000098 0.515698 ... 367462393 1911862000 31573077994 8840931 1374063837 13035465176 3498272951 6684369918 62000126842 1152212983
2024-05-17 0.482000 581.178345 67051.875000 1.000663 0.155563 3094.118652 169.530548 1.000018 1.000400 0.523804 ... 447612110 1557134929 28031279310 5423233 1112782871 14449438097 3371355809 6590780561 56249728895 1015239692
2024-05-18 0.482408 580.481140 66940.804688 1.000472 0.153077 3122.948975 172.539139 1.000082 1.000206 0.521390 ... 240076401 1358737176 16712277406 5423109 771261615 9407051320 2479657643 3748984171 39091871989 496850725
2024-05-19 0.467602 574.631653 66278.367188 1.000103 0.149107 3071.843018 170.091354 0.999953 0.999912 0.509661 ... 250323995 1298887094 19249094538 6368433 786457296 8747800800 2300080451 3531934053 38312293613 562911149
5 rows × 60 columns
  • Getting general info about the dataset
data.shape
(503, 60)

data.info()

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 503 entries, 2023-01-03 to 2024-05-19
Data columns (total 60 columns):
 #   Column                 Non-Null Count  Dtype  
---  ------                 --------------  -----  
 0   (Adj Close, ADA-USD)   503 non-null    float64
 1   (Adj Close, BNB-USD)   503 non-null    float64
 2   (Adj Close, BTC-USD)   503 non-null    float64
 3   (Adj Close, BUSD-USD)  503 non-null    float64
 4   (Adj Close, DOGE-USD)  503 non-null    float64
 5   (Adj Close, ETH-USD)   503 non-null    float64
 6   (Adj Close, SOL-USD)   503 non-null    float64
 7   (Adj Close, USDC-USD)  503 non-null    float64
 8   (Adj Close, USDT-USD)  503 non-null    float64
 9   (Adj Close, XRP-USD)   503 non-null    float64
 10  (Close, ADA-USD)       503 non-null    float64
 11  (Close, BNB-USD)       503 non-null    float64
 12  (Close, BTC-USD)       503 non-null    float64
 13  (Close, BUSD-USD)      503 non-null    float64
 14  (Close, DOGE-USD)      503 non-null    float64
 15  (Close, ETH-USD)       503 non-null    float64
 16  (Close, SOL-USD)       503 non-null    float64
 17  (Close, USDC-USD)      503 non-null    float64
 18  (Close, USDT-USD)      503 non-null    float64
 19  (Close, XRP-USD)       503 non-null    float64
 20  (High, ADA-USD)        503 non-null    float64
 21  (High, BNB-USD)        503 non-null    float64
 22  (High, BTC-USD)        503 non-null    float64
 23  (High, BUSD-USD)       503 non-null    float64
 24  (High, DOGE-USD)       503 non-null    float64
 25  (High, ETH-USD)        503 non-null    float64
 26  (High, SOL-USD)        503 non-null    float64
 27  (High, USDC-USD)       503 non-null    float64
 28  (High, USDT-USD)       503 non-null    float64
 29  (High, XRP-USD)        503 non-null    float64
 30  (Low, ADA-USD)         503 non-null    float64
 31  (Low, BNB-USD)         503 non-null    float64
 32  (Low, BTC-USD)         503 non-null    float64
 33  (Low, BUSD-USD)        503 non-null    float64
 34  (Low, DOGE-USD)        503 non-null    float64
 35  (Low, ETH-USD)         503 non-null    float64
 36  (Low, SOL-USD)         503 non-null    float64
 37  (Low, USDC-USD)        503 non-null    float64
 38  (Low, USDT-USD)        503 non-null    float64
 39  (Low, XRP-USD)         503 non-null    float64
 40  (Open, ADA-USD)        503 non-null    float64
 41  (Open, BNB-USD)        503 non-null    float64
 42  (Open, BTC-USD)        503 non-null    float64
 43  (Open, BUSD-USD)       503 non-null    float64
 44  (Open, DOGE-USD)       503 non-null    float64
 45  (Open, ETH-USD)        503 non-null    float64
 46  (Open, SOL-USD)        503 non-null    float64
 47  (Open, USDC-USD)       503 non-null    float64
 48  (Open, USDT-USD)       503 non-null    float64
 49  (Open, XRP-USD)        503 non-null    float64
 50  (Volume, ADA-USD)      503 non-null    int64  
 51  (Volume, BNB-USD)      503 non-null    int64  
 52  (Volume, BTC-USD)      503 non-null    int64  
 53  (Volume, BUSD-USD)     503 non-null    int64  
 54  (Volume, DOGE-USD)     503 non-null    int64  
 55  (Volume, ETH-USD)      503 non-null    int64  
 56  (Volume, SOL-USD)      503 non-null    int64  
 57  (Volume, USDC-USD)     503 non-null    int64  
 58  (Volume, USDT-USD)     503 non-null    int64  
 59  (Volume, XRP-USD)      503 non-null    int64  
dtypes: float64(50), int64(10)
memory usage: 239.7 KB
  • Examining the summary statistics
data.describe().T

count mean std min 25% 50% 75% max
Price Ticker        
Adj Close 
ADA-USD 503.0 4.065172e-01 1.293618e-01 2.418730e-01 2.963965e-01 3.776930e-01 4.858075e-01 7.741900e-01
BNB-USD 503.0 3.208171e+02 1.150505e+02 2.052294e+02 2.402693e+02 3.023846e+02 3.249082e+02 6.328028e+02
BTC-USD 503.0 3.687814e+04 1.483931e+04 1.667986e+04 2.673656e+04 2.977180e+04 4.323705e+04 7.308350e+04
BUSD-USD 503.0 1.000826e+00 2.851725e-03 9.986540e-01 1.000009e+00 1.000249e+00 1.000627e+00 1.040575e+00
DOGE-USD 503.0 9.006512e-02 3.432984e-02 5.789700e-02 7.026600e-02 7.880600e-02 9.015200e-02 2.200640e-01
ETH-USD 503.0 2.133607e+03 6.274484e+02 1.214779e+03 1.670317e+03 1.873076e+03 2.337104e+03 4.066445e+03
SOL-USD 503.0 5.861475e+01 5.290410e+01 1.309227e+01 2.091821e+01 2.431775e+01 9.786334e+01 2.028741e+02
USDC-USD 503.0 9.999469e-01 1.334716e-03 9.715000e-01 9.999540e-01 1.000028e+00 1.000109e+00 1.000751e+00
USDT-USD 503.0 1.000231e+00 7.462615e-04 9.983820e-01 9.999810e-01 1.000159e+00 1.000396e+00 1.007690e+00
XRP-USD 503.0 5.272819e-01 9.217840e-02 3.380390e-01 4.742055e-01 5.189530e-01 6.059070e-01 8.206940e-01
Close ADA-USD 503.0 4.065172e-01 1.293618e-01 2.418730e-01 2.963965e-01 3.776930e-01 4.858075e-01 7.741900e-01
BNB-USD 503.0 3.208171e+02 1.150505e+02 2.052294e+02 2.402693e+02 3.023846e+02 3.249082e+02 6.328028e+02
BTC-USD 503.0 3.687814e+04 1.483931e+04 1.667986e+04 2.673656e+04 2.977180e+04 4.323705e+04 7.308350e+04
BUSD-USD 503.0 1.000826e+00 2.851725e-03 9.986540e-01 1.000009e+00 1.000249e+00 1.000627e+00 1.040575e+00
DOGE-USD 503.0 9.006512e-02 3.432984e-02 5.789700e-02 7.026600e-02 7.880600e-02 9.015200e-02 2.200640e-01
ETH-USD 503.0 2.133607e+03 6.274484e+02 1.214779e+03 1.670317e+03 1.873076e+03 2.337104e+03 4.066445e+03
SOL-USD 503.0 5.861475e+01 5.290410e+01 1.309227e+01 2.091821e+01 2.431775e+01 9.786334e+01 2.028741e+02
USDC-USD 503.0 9.999469e-01 1.334716e-03 9.715000e-01 9.999540e-01 1.000028e+00 1.000109e+00 1.000751e+00
USDT-USD 503.0 1.000231e+00 7.462615e-04 9.983820e-01 9.999810e-01 1.000159e+00 1.000396e+00 1.007690e+00
XRP-USD 503.0 5.272819e-01 9.217840e-02 3.380390e-01 4.742055e-01 5.189530e-01 6.059070e-01 8.206940e-01
High ADA-USD 503.0 4.171063e-01 1.350994e-01 2.460640e-01 3.030255e-01 3.855290e-01 5.025745e-01 8.069850e-01
BNB-USD 503.0 3.263815e+02 1.180971e+02 2.066591e+02 2.431490e+02 3.075839e+02 3.320946e+02 6.414811e+02
BTC-USD 503.0 3.748839e+04 1.521415e+04 1.676045e+04 2.705069e+04 3.018418e+04 4.389223e+04 7.375007e+04
BUSD-USD 503.0 1.001762e+00 3.708004e-03 9.995340e-01 1.000615e+00 1.000965e+00 1.001542e+00 1.040831e+00
DOGE-USD 503.0 9.287642e-02 3.682136e-02 5.849500e-02 7.195150e-02 8.057200e-02 9.286950e-02 2.265810e-01
ETH-USD 503.0 2.173278e+03 6.490980e+02 1.219095e+03 1.702185e+03 1.904483e+03 2.378740e+03 4.092284e+03
SOL-USD 503.0 6.066713e+01 5.484261e+01 1.350027e+01 2.136893e+01 2.511195e+01 1.015043e+02 2.096961e+02
USDC-USD 503.0 1.000608e+00 4.242147e-04 9.954250e-01 1.000373e+00 1.000540e+00 1.000789e+00 1.002967e+00
USDT-USD 503.0 1.000962e+00 1.701064e-03 9.992290e-01 1.000409e+00 1.000768e+00 1.001099e+00 1.029628e+00
XRP-USD 503.0 5.385720e-01 9.670605e-02 3.454690e-01 4.824155e-01 5.263280e-01 6.167330e-01 8.875110e-01
Low ADA-USD 503.0 3.947252e-01 1.227306e-01 2.304200e-01 2.912275e-01 3.674800e-01 4.674805e-01 7.387190e-01
BNB-USD 503.0 3.141947e+02 1.105243e+02 2.036554e+02 2.369456e+02 2.982126e+02 3.208558e+02 6.017775e+02
BTC-USD 503.0 3.612326e+04 1.432895e+04 1.662237e+04 2.634163e+04 2.935759e+04 4.249658e+04 7.133409e+04
BUSD-USD 503.0 9.998290e-01 1.658972e-03 9.920590e-01 9.992990e-01 9.996070e-01 9.999300e-01 1.016569e+00
DOGE-USD 503.0 8.713972e-02 3.164147e-02 5.746600e-02 6.813650e-02 7.739900e-02 8.759850e-02 2.088100e-01
ETH-USD 503.0 2.087295e+03 5.995190e+02 1.207492e+03 1.644105e+03 1.849437e+03 2.271367e+03 3.936627e+03
SOL-USD 503.0 5.620177e+01 5.053955e+01 1.105327e+01 2.034921e+01 2.368367e+01 9.409155e+01 1.948494e+02
USDC-USD 503.0 9.991619e-01 5.956915e-03 8.774000e-01 9.994345e-01 9.996240e-01 9.997625e-01 9.999790e-01
USDT-USD 503.0 9.996476e-01 6.299658e-04 9.957610e-01 9.993520e-01 9.997150e-01 9.999700e-01 1.005939e+00
XRP-USD 503.0 5.140386e-01 8.805498e-02 3.328310e-01 4.651130e-01 5.086380e-01 5.851500e-01 7.743350e-01
Open ADA-USD 503.0 4.061176e-01 1.295002e-01 2.418680e-01 2.962405e-01 3.768950e-01 4.857945e-01 7.741890e-01
BNB-USD 503.0 3.201684e+02 1.145364e+02 2.052258e+02 2.402719e+02 3.023172e+02 3.247115e+02 6.328028e+02
BTC-USD 503.0 3.677923e+04 1.480780e+04 1.668021e+04 2.667813e+04 2.976670e+04 4.315853e+04 7.307938e+04
BUSD-USD 503.0 1.000831e+00 2.851228e-03 9.986660e-01 1.000027e+00 1.000255e+00 1.000640e+00 1.040566e+00
DOGE-USD 503.0 8.990878e-02 3.423723e-02 5.789700e-02 7.025950e-02 7.880600e-02 8.984150e-02 2.200650e-01
ETH-USD 503.0 2.129967e+03 6.273667e+02 1.214719e+03 1.670375e+03 1.872541e+03 2.329792e+03 4.066690e+03
SOL-USD 503.0 5.830041e+01 5.271064e+01 1.127473e+01 2.089992e+01 2.426184e+01 9.782536e+01 2.028744e+02
USDC-USD 503.0 9.999316e-01 1.480148e-03 9.683000e-01 9.999550e-01 1.000022e+00 1.000107e+00 1.000660e+00
USDT-USD 503.0 1.000225e+00 7.536540e-04 9.982950e-01 9.999620e-01 1.000166e+00 1.000404e+00 1.007690e+00
XRP-USD 503.0 5.269487e-01 9.252934e-02 3.380410e-01 4.737680e-01 5.189330e-01 6.058790e-01 8.206450e-01
Volume ADA-USD 503.0 4.025945e+08 3.080341e+08 5.825736e+07 2.077031e+08 3.264808e+08 4.864287e+08 2.566810e+09
BNB-USD 503.0 8.922951e+08 7.770717e+08 2.038465e+08 4.327303e+08 6.501639e+08 1.043809e+09 5.849157e+09
BTC-USD 503.0 2.239700e+10 1.294233e+10 5.331173e+09 1.337728e+10 1.924909e+10 2.719678e+10 1.028029e+11
BUSD-USD 503.0 2.082870e+09 2.935033e+09 5.423109e+06 4.336331e+07 7.729393e+08 2.578215e+09 1.360079e+10
DOGE-USD 503.0 8.071686e+08 1.038233e+09 9.248368e+07 2.591465e+08 4.411213e+08 8.095854e+08 9.368269e+09
ETH-USD 503.0 9.831194e+09 5.965081e+09 2.081626e+09 5.754758e+09 8.356130e+09 1.224025e+10 4.770690e+10
SOL-USD 503.0 1.640902e+09 1.926525e+09 9.737905e+07 3.582352e+08 8.372113e+08 2.464945e+09 1.409335e+10
USDC-USD 503.0 4.729511e+09 2.768864e+09 1.036839e+09 2.914261e+09 3.923554e+09 5.795573e+09 2.668221e+10
USDT-USD 503.0 3.911067e+10 2.368924e+10 9.989859e+09 2.209906e+10 3.285249e+10 4.873294e+10 1.898671e+11
XRP-USD 503.0 1.337810e+09 9.009379e+08 3.215121e+08 8.295855e+08 1.103767e+09 1.578255e+09 1.039734e+10
  • Calculating the kurtosis of Adj Close
data['Adj Close'].kurt()

Ticker
ADA-USD      -0.197942
BNB-USD       0.959046
BTC-USD      -0.151112
BUSD-USD     98.241346
DOGE-USD      2.376104
ETH-USD       0.492625
SOL-USD      -0.088051
USDC-USD    415.422489
USDT-USD     36.985199
XRP-USD      -0.116245
dtype: float64
  • Calculating the skewness of Adj Close
data['Adj Close'].skew()
Ticker
ADA-USD      0.816931
BNB-USD      1.454830
BTC-USD      1.055717
BUSD-USD     8.786259
DOGE-USD     1.817589
ETH-USD      1.234688
SOL-USD      1.123322
USDC-USD   -19.782285
USDT-USD     4.460127
XRP-USD      0.238453
dtype: float64
  • Plotting the standard deviation (volatility) of Adj Close
stddata=data['Adj Close'].std()
stddata.plot.bar()
Standard deviation (volatility) of Adj Close
  • Plotting the correlation matrix
corr = data['Adj Close'].corr()
ax = sns.heatmap(
    corr, 
    vmin=-1, vmax=1, center=0,
    cmap=sns.diverging_palette(20, 220, n=200),
    square=True
)
ax.set_xticklabels(
    ax.get_xticklabels(),
    rotation=45,
    horizontalalignment='right'
);
Correlation matrix of Adj Close
  • Plotting daily and cumulative returns
# daily return:
daily_returns = data['Adj Close'].pct_change()

# calculate cumluative return
cum_returns = np.exp(np.log1p(daily_returns).cumsum())
daily_returns.plot()
plt.grid()
cum_returns.plot()
plt.grid()
Daily returns
Cumulative returns
import matplotlib.pyplot as plt
#calculate percentage change between the current and a prior element - it will be daily returns
daily_returns = data['Adj Close'].pct_change()
num_assets = len(daily_returns.columns)

#calculate covariance matrix
cov_matrix = (daily_returns.cov())*365 # multiply by days in year to get annual covariance 

# run optimization of portfolio weights
dict_portfolios = {"portfolio_std":[],"portfolio_returns":[],"weights":[], "sharpe_ratio":[]}
for i in range(N_iterations):
    
    #get random weights and calculate returns and variance
    weights = np.random.random(num_assets)
    weights = weights/np.sum(weights)
    expected_portfolio_return = np.sum(daily_returns.mean()*weights)
    expected_portfolio_variance = np.dot(weights.T,np.dot(cov_matrix,weights))
    sharpe_ratio = expected_portfolio_return / np.sqrt(expected_portfolio_variance)
    
    # collect all portfolios in the dictionary
    dict_portfolios['portfolio_std'].append(np.sqrt(expected_portfolio_variance)) # get standard deviation instead of variance
    dict_portfolios['portfolio_returns'].append(expected_portfolio_return)
    dict_portfolios['weights'].append(weights)
    dict_portfolios['sharpe_ratio'].append(sharpe_ratio)
    
simulated_portfolios=pd.DataFrame(dict_portfolios)

# Plot returns vs. standard deviation to find optimal portfolio (efficient frontier)
simulated_portfolios.plot.scatter(x='portfolio_std', y='portfolio_returns', marker='o', s=10, alpha=0.3, grid=True, figsize=[10,10])
max_sharpe_ratio = simulated_portfolios.query('sharpe_ratio == sharpe_ratio.max()')

# red dot for max sharpe ratio
plt.plot(max_sharpe_ratio['portfolio_std'],max_sharpe_ratio['portfolio_returns'],'ro',markersize=20)
plt.ylabel('Mean daily returns')
plt.xlabel('Annual volatility (standard deviation)')
plt.show()
Plot returns vs. standard deviation to find max Sharpe efficient frontier (red dot)
  • Checking the portfolio weights
dictionary_of_weights = {}
for i in range(len(daily_returns.columns)):
    dictionary_of_weights [daily_returns.columns[i]] = max_sharpe_ratio['weights'].values[0][i]
print('max sharpe ratio: \n')
efficient_frontier = pd.DataFrame.from_dict(dictionary_of_weights, orient='index').reset_index()
efficient_frontier.columns = ['crypto pair','weights']
display(efficient_frontier)

crypto pair weights
0 ADA-USD 0.028841
1 BNB-USD 0.045777
2 BTC-USD 0.270432
3 BUSD-USD 0.096357
4 DOGE-USD 0.007903
5 ETH-USD 0.022292
6 SOL-USD 0.280154
7 USDC-USD 0.125300
8 USDT-USD 0.103320
9 XRP-USD 0.019625
  • Creating a pie chart of the above weights
labels = efficient_frontier['crypto pair'][0],efficient_frontier['crypto pair'][1],efficient_frontier['crypto pair'][2],efficient_frontier['crypto pair'][3],efficient_frontier['crypto pair'][4],efficient_frontier['crypto pair'][5],efficient_frontier['crypto pair'][6],efficient_frontier['crypto pair'][7],efficient_frontier['crypto pair'][8],efficient_frontier['crypto pair'][9]
print (labels)
sizes = [efficient_frontier['weights'][0],efficient_frontier['weights'][1],efficient_frontier['weights'][2],efficient_frontier['weights'][3],efficient_frontier['weights'][4],efficient_frontier['weights'][5],efficient_frontier['weights'][6],efficient_frontier['weights'][7],efficient_frontier['weights'][8],efficient_frontier['weights'][9]]
print (sizes)
fig, ax = plt.subplots()
ax.pie(sizes, labels=labels, autopct='%1.1f%%')
Max Sharpe crypto portfolio weights

Conclusions

  • Using the simple MPT for Crypto, we have created a diverse crypto portfolio and evaluated its performance.
  • The max Sharpe portfolio yields portfolio_std=0.440951 and portfolio_returns=0.00303 with sharpe_ratio=0.006871 based on mean daily returns and annual volatility (standard deviation).
  • The max Sharpe portfolio is expected to offer the max return per unit of risk, while the minimum volatility portfolio is, in fact, the most optimal portfolio with the lowest amount of risk.
  • Top 2 assets to include in this portfolio are SOL-USD (28%) and BTC-USD (27%).

Explore More

References

Contacts

Python
Cryptocurrency
Portfolio
Risk Management
Diversification
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