Shannon's Demon Calculator

It is a portfolio thought experiment credited to Claude Shannon, the mathematician who founded information theory and, by several accounts, used to describe it to colleagues and students as an illustration of how randomness and rebalancing interact. In the classic version, half your money sits in cash and half in a stock that either doubles or is cut in half on each coin flip; rebalanced back to a 50/50 split after every flip, the portfolio compounds upward even though the stock's own long-run growth rate is zero. The name stuck because the result feels like something for nothing: growth appears without either side of the bet actually growing on its own.

Through variance drag. The compounded (geometric) growth rate of an asset runs below its simple average return by roughly half the variance of its returns, so a wildly swinging asset can have a healthy average return and still barely grow, or not grow at all, once compounded. A portfolio rebalanced back to a fixed split trims the volatile asset after it rises and tops it back up after it falls, which lowers the blended portfolio's variance more than it lowers its average return. Since a smaller variance drag eats less of the average return, the rebalanced portfolio's compounded growth rate can exceed what either asset delivers alone, even when one of them is flat.

A version of it does, but smaller and never guaranteed. Historical studies of rebalanced portfolios, stocks and long-term government bonds, or stocks and gold, for example, do show a measurable bonus over long periods, because those pairs have been volatile with a low or negative correlation to each other. The bonus depends on three things holding up: the two assets need reasonably similar long-run returns, meaningful volatility, and low or negative correlation. When one asset simply outperforms the other for a long stretch, as US stocks did against gold for most of the 2010s, buy and hold can beat a rebalanced mix for years at a time, so the bonus is a tendency over long horizons, not a return you can count on every period.

Because rebalancing has an opportunity cost built in: it systematically trims the asset that is currently winning to top up the one that is currently losing. If the winning asset keeps winning, that discipline costs you every time you do it, and buy and hold, which lets the winner run, pulls ahead. Rebalancing pays off when the assets take turns leading, which is exactly the alternating pattern this calculator's volatile asset follows by construction. Real assets do not alternate on schedule, so which approach wins in any given stretch depends on the path returns actually take, not on a rule that favors one side permanently.

No. Rebalancing is primarily a risk-control discipline, keeping your portfolio at the mix of risk you actually chose, rather than letting whichever asset ran hottest take over your allocation. The return bonus is a side effect that shows up under the right conditions, not a strategy to chase on its own: reaching for it by seeking out pairs of assets purely because they are volatile and only weakly correlated adds real risk (concentrated bets, illiquid instruments, trading costs) for a bonus that is modest and not guaranteed in any given period. Treat the extra return as a possible reward for holding a diversified, periodically rebalanced portfolio for reasons of risk management, not as an independent source of guaranteed return.

It runs a deterministic, alternating up-down-up-down sequence for the volatile asset, not a random or historically sampled one, so it cannot show you the range of outcomes a real, unpredictable market would produce; there is no Monte Carlo simulation here. It also leaves out taxes on rebalancing trades, bid-ask spreads and market impact beyond the flat cost you set, and any correlation structure between two risky assets, since the model only pairs one volatile asset against one stable one. Treat the results as an explanation of a mechanism, not as a projection of what a real rebalanced portfolio will return.