The Money Angle

Lesson from coin flip investing

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

  1. The higher the portfolio volatility, the more the mean and median diverge
  2. Rebalancing pushes median returns closer to the theoretical mean
  3. The rebalancing benefit is positively correlated to the difference of volatility between the coins
If you use options to hedge or invest, check out the moontower.ai option trading analytics platform
  1. Metrics are an average of 10,000 trials of 1000 week simulations
  2. 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
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6 years ago

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