The Math Behind Compounding in Trading Accounts

Compounding is the most powerful force in trading, but most traders don't understand its mechanics — or its dangers. Basic Compounding If you make 1% per day, you don't make 365% per year. You make: (1.01)^252 = 12.24x = 1,124% return (252 trading days per year) Sounds incredible. But here's the catch: consistency. The Reality Check Nobody makes 1% every single day. Real trading has variance: import numpy as np def simulate_compounding ( daily_mean , daily_std , trading_days = 252 , sims = 10000 ): results = [] for _ in range ( sims ): daily_returns = np . random . normal ( daily_mean , daily_std , trading_days ) final = np . prod ( 1 + daily_returns ) results . append ( final ) return np . array ( results ) # Scenario 1: Low variance (consistent) consistent = simulate_compounding ( 0.003 , 0.01 ) # 0.3% avg, 1% std # Scenario 2: Same average, higher variance volatile = simulate_compounding ( 0.003 , 0.03 ) # 0.3% avg, 3% std print ( f " Consistent: median = { np . median ( consistent