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 Portfolio1
| 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*.2852=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