**The setup**

- You invest in 2 coins every week for the next 1000 weeks (19.2 yrs)
- These coins pay a return each week
- Every 4 weeks, you rebalance wealth equally between the 2 coins
- Coins have an expected edge of 10%
- Simulation is run 10,000x
- Assume no transaction costs

Individual Coin Payouts

Coin | Win Payout | Loss Payout | Expected Annual Return | Expected Annual Volatility |

A(Low Vol) | 2.75% | 2.50% | 6.70% | 18% |

B (High Vol) | 8.25% | 7.50% | 21.5% | 54% |

**Results of the 2 Coin Portfolio**^{1}

^{1}

Strategy | CAGR | Volatility | Median Return | Max Drawdown |

Theoretical |
14.1% |
28.5% |
10%^{2} |
– |

Un-rebalanced simulated | 17.9% | 32% | 6% | 68% |

Rebalanced simulated | 13.9% | 30% | 9% | 64% |

**Observations from many simulations like the one described**

- The higher the portfolio volatility, the more the mean and median diverge
- Rebalancing pushes median returns closer to the theoretical mean
- The rebalancing benefit is positively correlated to the difference of volatility between the coins

- Metrics are an average of 10,000 trials of 1000 week simulations
- The median expected return: [ mean return – .5 * (volatility)
^{2}]. In this case: 14.1% – .5*.285^{2}=10%. Option traders will note this is the median of the lognormal distribution where the mean is the stock price adjusted by its expected carry until expiration