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#T1 Shannon's demon: making money from a price that goes nowhere
This page explains an idea and what our tests found when we tried it.
Last checked: 16 October 2026.
Where it comes from
- Claude Shannon (1916–2001) founded information theory, the maths behind digital communication, in a 1948 paper at Bell Labs. He later taught at MIT.
- In the 1960s he gave a talk at MIT about investing, by William Poundstone's account in his book Fortune's Formula (2005). Shannon never published it. The idea was a way to profit from a price that swings up and down but ends where it started.
- "Demon" points to Maxwell's demon, a thought experiment the physicist James Clerk Maxwell first described in 1867: an imaginary creature that seems to get something for nothing by sorting fast molecules from slow ones. Shannon's trick seems to do the same with price swings. The name came later. We couldn't confirm who first used it.
- Close relatives:
- John Kelly, a colleague of Shannon's at Bell Labs, published the Kelly formula for sizing bets in 1956.
- Thomas Cover's "universal portfolios" (1991) build on rebalanced portfolios.
- David Luenberger's textbook Investment Science calls the effect "volatility pumping".
- Robert Fernholz's stochastic portfolio theory calls the extra growth the "excess growth rate".
The idea in plain words
Keep a fixed split, say half in a coin and half in cash. After every move, trade back to half and half.
- When the coin rises, its share grows past half, so you sell some.
- When it falls, its share shrinks, so you buy some.
If the price keeps swinging back and forth, this sells after rises and buys after falls, over and over. The pot grows even if the coin ends where it started. It is also called volatility harvesting.
The maths, step by step
1. One round trip. Start with 0.5 in the coin and 0.5 in cash.
- The price doubles: the coin is worth 1.0 and the cash 0.5, so the pot is 1.5. Back to half and half: 0.75 and 0.75.
- The price halves, back to where it began: the coin is worth 0.375 and the cash 0.75, so the pot is 1.125. Back to half and half: 0.5625 and 0.5625.
- The pot is 1.125. The coin is back where it started, and the same half-and-half left alone is back to 1.0. The extra 12.5% came from selling high and buying back low.
2. Why the coin alone goes nowhere. Say each step the coin doubles or halves, with even odds.
- The average step looks great: (+100% − 50%) ÷ 2 = +25%.
- But one double and one halving bring you back to the start: 2 × 0.5 = 1. The typical growth per step is 0%.
- That gap between the average step and the growth you actually get is the key to the whole idea. Big swings drag growth down.
3. Why the rebalanced pot grows. Half in the coin turns each step into:
- a double: 0.5 × 2 + 0.5 = 1.5;
- a halving: 0.5 × 0.5 + 0.5 = 0.75.
One of each gives 1.5 × 0.75 = 1.125, which is √1.125 = 1.0607, or +6.07% a step. Same coin, same swings, but steady growth.
4. A rule of thumb. Fernholz's "excess growth rate" puts the extra growth at about share in coin × share in cash × (size of the swings)² ÷ 2.
- With half and half, and a double-or-halve swing (0.693 in the log terms this rule uses): 0.5 × 0.5 × 0.693² ÷ 2 = 0.060.
- The exact answer, in the same terms, is 0.059. The rule is close.
- The bonus grows with the square of the swing. Big swings give a lot, and small swings give almost nothing.
5. When the price trends instead. The price doubles, then doubles again.
- Rebalanced: 1.5 × 1.5 = 2.25.
- Left alone: half in the coin is now worth 0.5 × 4 = 2.0, plus 0.5 cash = 2.5.
- Rebalancing kept selling a coin that kept rising. It lost 10% against doing nothing.
6. What fees do. Each trade pays a fee, here 0.1%.
- A 1% move and back earns about 0.0025% of the pot and pays about 0.0005% in fees. It is worth doing, just.
- A 0.2% move and back earns about as much as it pays.
- Anything smaller loses money. The break-even swing is about twice the fee.
This is why real rebalancing waits for a big enough move (a band) instead of trading on every tick.
What others found
This section is other people's work, not ours.
- The maths is settled. Rebalancing between assets that swing and don't drift apart adds growth. Kelly's, Cover's and Fernholz's work all rest on it.
- In real portfolios the gain is modest. David Booth and Eugene Fama (1992) measured a "diversification return" from rebalancing: real, but small.
- The cost is just as well known. When one asset grows much faster than the others, rebalancing keeps selling the winner. A portfolio left alone then ends ahead.
What we tested and found
This section is ours. It repeats the known result above on crypto prices; it doesn't discover it.
1. Half-and-half on Bitcoin, Ether and Solana, October 2022 to September 2026, checked every hour, with 0.1% fees. We rebalanced at bands or every day or week.
- Month by month, there was no harvest worth having. Against the same half-and-half left alone, the rebalanced books did −0.33% to +0.03% a month, all close to zero, with no steady sign.
- Over four years, the path decided it.
- Bitcoin mostly rose: rebalanced ×2.29 to ×2.32, left alone ×2.65.
- Ether went up and came back: rebalanced ×1.67 to ×1.76, left alone ×1.51.
- Solana did the same: rebalanced ×2.86 to ×3.10, left alone ×2.30.
That is step 5 of the maths and step 1, played out on real prices.
2. Grid bots are the same machine. A grid buys at each step down and sells at each step up. Each band edge of a rebalance works like a grid rung. Our grid studies found the same thing: a grid follows its coin. It does well in a coin that swings sideways and badly in one that trends.
3. Selling slices high to end with more Bitcoin is a one-sided version of the same idea. On Bitcoin's rising years, most settings ended with less Bitcoin than holding.
The catch
- The demon feeds on swings, and a trend starves it. It beats holding when the price goes up and down and ends near where it started. It loses when the price goes one way. You don't know in advance which you'll get.
- The bonus grows with the square of the swing. Small hourly wiggles pay almost nothing and are easily eaten by fees.
- The "free money" is measured against the coin alone, whose growth the swings drag down. Against the same mix left alone, the result can go either way.
- It needs the coin to survive. Rebalancing into a coin that keeps falling keeps buying it all the way down.
Limits
- The worked examples use clean doubles and halvings. Real prices move in many small, uneven steps.
- Our tests cover three coins over four years: one long path each.
- Fees of 0.1% a trade; no tax.
Update, 18 October 2026: a chart
Steps 3 and 4 drawn out: the rebalanced pot's growth a step at every share kept in the coin, for a coin that doubles or halves with even odds, and for one that moves 10% up or down. Both coins go nowhere on their own.
Rebalancing grows most at half and half (6.07% a step for the double-or-halve coin), and with small swings the bonus almost disappears, before any fee.
Credits
- Claude E. Shannon, "A Mathematical Theory of Communication", Bell System Technical Journal, 1948.
- William Poundstone, Fortune's Formula, Hill and Wang, 2005: the book that made Shannon's idea widely known, and our source for his MIT talk. The idea is Shannon's.
- James Clerk Maxwell, Theory of Heat, 1871: the demon.
- John L. Kelly Jr., "A New Interpretation of Information Rate", Bell System Technical Journal, 1956.
- Thomas M. Cover, "Universal Portfolios", Mathematical Finance, 1991.
- David G. Luenberger, Investment Science, Oxford University Press, 1998: "volatility pumping".
- E. Robert Fernholz, Stochastic Portfolio Theory, Springer, 2002: the excess growth rate, step 4's rule.
- David G. Booth and Eugene F. Fama, "Diversification Returns and Asset Contributions", Financial Analysts Journal, 1992.
- Our tests: "Shannon's demon: does rebalancing 50/50 harvest volatility?", "Grid bots on 14 coins: what 30 months of prices say", and "Ending up with more Bitcoin, without adding money". Prices from Binance's public archives: futures prices for the first two, standing in for spot, and spot prices for the third.
- PerpGremlin and Claude, Shannon's demon: making money from a price that goes nowhere, TerminalGremlin, 2026: the tests, the code and the words.
Educational research from public market data; any trading discussed is paper, never real. Nothing here is advice. The full notice.