test_beta_similarity.py

import numpy as np
import pandas as pd
from scipy import stats
import matplotlib.pyplot as plt
import ccxt
import statsmodels.api as sm

def test_beta_similarity_textbook(beta_i, beta_j, std_error_i, std_error_j, n_i, n_j):
    delta_beta = beta_i - beta_j
    se_delta_beta = np.sqrt(std_error_i**2 + std_error_j**2 )
    t_statistic = delta_beta / se_delta_beta
    df = min(n_i - 1, n_j - 1)
    critical_value = stats.t.ppf(0.8413, df)
    return abs(t_statistic) <= critical_value
  
def calculate_beta(asset_returns, market_returns):
    X = sm.add_constant(market_returns)
    model = sm.OLS(asset_returns, X).fit()
    return model.params.iloc[-1], model.bse.iloc[-1]

def test_beta_similarity_gooder(asset_A_returns, 
                                  asset_B_returns, 
                                  market_returns, 
                                  threshold=.01,
                                  ):
    delta_asset_returns = asset_A_returns - asset_B_returns
    X = sm.add_constant(market_returns/market_returns.std())
    model = sm.OLS(delta_asset_returns, X).fit()
    return abs(model.params.iloc[-1])<threshold
  
def calculate_beta(asset_returns, market_returns):
    X = sm.add_constant(market_returns)
    model = sm.OLS(asset_returns, X).fit()
    return model.params.iloc[-1], model.bse.iloc[-1]
#%%

SYMBOL_A = '1000PEPE/USDT:USDT'
SYMBOL_B = 'ETH/USDT:USDT'
MARKET = 'BTC/USDT:USDT'
NN = 10
THRESHOLD = 0.001


raw_candles = {coin:ccxt.binance().fetch_ohlcv(coin,'1d',limit=NN)
               for coin in [SYMBOL_A, SYMBOL_B, MARKET]}
merged_candles = pd.concat({coin:pd.DataFrame(df).set_index(0)[4] 
                           for coin, df in raw_candles.items()},
                           axis=1)
returns = np.log(merged_candles).diff().dropna()
 
# Calculate betas
beta1, se1 = calculate_beta(returns[SYMBOL_A], returns[MARKET])
beta2, se2 = calculate_beta(returns[SYMBOL_B], returns[MARKET])

print(f"Beta of {SYMBOL_A} wrt {MARKET}: {beta1:.4f} (SE: {se1:.4f})")
print(f"Beta of {SYMBOL_B} wrt {MARKET}: {beta2:.4f} (SE: {se2:.4f})")

# Test beta similarity
n = len(returns)
are_similar = test_beta_similarity_textbook(beta1, beta2, se1, se2, n, n)
print(f"The betas are statistically similar based {NN} days using random textbook formula: {are_similar}")
are_similar_gooder = test_beta_similarity_gooder(returns[SYMBOL_A], 
                                                 returns[SYMBOL_B],  
                                                 returns[MARKET],
                                                 threshold=THRESHOLD)
print(f"The betas are economically similar at threshold {THRESHOLD} based {NN} days using formula stalequant made up that is probably in a different textbook': {are_similar_gooder}")

# Visualize the data
plt.figure(figsize=(10, 6))
plt.scatter(returns[MARKET], returns[SYMBOL_A], alpha=0.5, label=SYMBOL_A)
plt.scatter(returns[MARKET], returns[SYMBOL_B], alpha=0.5, label=SYMBOL_B)
plt.xlabel('Market Returns')
plt.ylabel('Asset Returns')
plt.legend()
plt.title('Asset Returns vs Market Returns')
plt.show()


'''
Beta of BTC/USDT:USDT wrt BTC/USDT: 1.0012 (SE: 0.0005)
Beta of BTC/USD:BTC wrt BTC/USDT: 1.0056 (SE: 0.0010)
The betas are statistically similar based 365 days using random textbook formula: False
The betas are economically similar at threshold 0.001 based 365 days using formula stalequant made up that is probably in a different textbook': True



Beta of 1000PEPE/USDT:USDT wrt BTC/USDT:USDT: 1.2370 (SE: 0.6083)
Beta of ETH/USDT:USDT wrt BTC/USDT:USDT: 0.7194 (SE: 0.1562)
The betas are statistically similar based 10 days using random textbook formula: True
The betas are economically similar at threshold 0.001 based 10 days using formula stalequant made up that is probably in a different textbook': False
'''