Claude Shannon described a way to make money off a volatile random walk even if the underlying asset is slowly losing value on average. He asked an audience to consider a stock whose price jitters up and down violently. Put half your capital into the stock and half into a “cash” account. Each day, the price of the stock changes. At noon each day, you “rebalance” the portfolio. That means you figure out what the whole portfolio (stock plus cash account) is presently worth, then shift assets from stock to cash account or vice versa in order to recover the original 50–50 proportions of stock and cash. To make this clear:

Imagine you start with $1,000, $500 in stock and $500 in cash. Suppose the stock halves in price the first day. (It’s a really volatile stock.) This gives you a $750 portfolio with $250 in stock and $500 in cash. That is now lopsided in favor of cash. You rebalance by withdrawing $125 from the cash account to buy stock. This leaves you with a newly balanced mix of $375 in stock and $375 cash.

Now repeat. The next day, let’s say the stock doubles in price. The $375 in stock jumps to $750. With the $375 in the cash account, you have $1,125. This time you sell some stock, ending up with $562.50 each in stock and cash. Look at what Shannon’s scheme has achieved so far. After a dramatic plunge, the stock’s price is back to where it began. A buy-and-hold (or in Bitcoin case "hodl" investor would have no profit at all. Shannon’s investor has made $125.

William Poundstone describes this “Shannon’s demon" in the book Fortune's Formula.

Comments, questions or E-mails welcome: ajbrenninkmeijer@gmail.com

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