Shannon's Demon

It is easy to think that making money in the stock market means finding a company whose stock price will rise. Many investors buy and sell stocks based on their predictions about which companies will become more valuable. But what if you could make money even when a stock ends up at exactly the same price where it started? To understand how this is possible, we need to look at an idea associated with the American mathematician Claude Shannon. In 1948, Shannon laid the foundations of information theory, a field that studies how information can be measured and transmitted. His work helped shape the development of modern computers, the internet, and digital communication. Shannon was also interested in investing, and an interesting investment concept bears his name. It is known as "Shannon's Demon." To understand Shannon's Demon, we first need to understand what a stock is. A stock represents a small piece of ownership in a company. When investors buy shares of stock, they become partial owners of that company. If people become more optimistic about the company's future, its stock price may rise. However, if the company performs poorly or economic conditions change, its stock price may fall. But is it possible to make money from the movement of stock prices itself? Let's consider a simple experiment. Imagine an investor who has $100. The investor decides to use $50 to buy shares of Company A and keep the remaining $50 in cash. Half of the investor's money is now invested in stocks, while the other half remains in cash. Some time later, Company A's stock price falls by 50%. The shares that were originally worth $50 are now worth only $25. The investor still has $50 in cash, so the total value of the portfolio has fallen to $75. At this point, the investor does something unusual. Instead of simply waiting for the stock price to recover, the investor decides to restore the original balance between stocks and cash. Since the portfolio is now worth $75, the investor wants to hold $37.50 in stocks and $37.50 in cash. To accomplish this, the investor uses $12.50 in cash to buy additional shares of Company A. Now imagine that Company A's stock price eventually returns to its original level. Since the stock price has doubled from its lowest point, the shares held by the investor are now worth $75. The investor also has $37.50 remaining in cash. The total value of the portfolio is now $112.50. The investor started with $100 and ended with $12.50 more. Even though the stock price returned to exactly where it started, the investor earned a 12.5% return. To keep this example simple, we are ignoring trading fees, taxes, and any interest that might have been earned on the cash. What would have happened if the investor had simply held the original shares without making any additional purchases? Because the stock price returned to its starting point, the shares would once again be worth $50. Adding the original $50 in cash would bring the total portfolio value back to $100. The investor would have earned no profit. Why did the two approaches produce different results? The answer is not the stock price itself, but the number of shares the investor owned. The first investor purchased additional shares when the price was lower. When the price recovered, those extra shares increased the value of the portfolio. This process of adjusting investments to maintain a predetermined balance is called "rebalancing." For example, an investor who wants to keep half of a portfolio in stocks and half in cash may sell some shares when stock prices rise and buy additional shares when prices fall. The goal is to restore the original proportions of the portfolio. Shannon's Demon illustrates how this process can sometimes turn price fluctuations into investment gains. Even without correctly predicting whether a stock will rise or fall, an investor may benefit from following a consistent rule as prices move up and down. However, there is an important limitation. Shannon's Demon does not guarantee profits. In our experiment, the stock price fell and then recovered to its original level. In the real stock market, prices do not always recover. A company's stock may continue falling for months or even years. If a company experiences severe financial problems or goes bankrupt, its shares may lose most or all of their value. Buying additional shares of such a company could lead to even greater losses. The opposite situation can also create a disadvantage. Suppose a company's stock price continues rising for a long time. An investor who repeatedly sells shares to maintain a fixed balance may earn less than someone who simply bought the stock and held it. By selling some shares during a strong upward trend, the investor reduces the amount of money benefiting from future price increases. Trading costs are another important factor. Buying and selling investments can involve fees and taxes. Frequent rebalancing may increase these expenses. In some cases, the costs of trading could be greater than the additional returns produced by rebalancing. So what can we learn from Shannon's Demon? The lesson is not that investors can always make money by constantly buying and selling stocks. Instead, it shows that how investors divide and manage their money can influence their investment results. For example, an investor who decides to keep half of a portfolio in stocks and half in cash can use rebalancing to prevent stocks from becoming too large a portion of the portfolio after a major price increase. This can help manage the size of potential losses if stock prices later decline. Of course, holding cash does not eliminate all investment risks. In practice, investors may also spread their money across shares of different companies or different types of investments rather than relying on a single stock. This approach is called diversification. Diversification and rebalancing can help investors avoid depending too heavily on the performance of one company or one type of asset. Ultimately, Shannon's Demon shows that investment returns do not depend only on whether stock prices rise. The path prices take, the way money is divided among investments, and the rules used to maintain those proportions can also influence the final result. There is no real demon in the stock market that can guarantee investors a profit. Nevertheless, the idea behind Shannon's Demon reveals an important principle of investing. Predicting where stock prices will go is not the only thing that matters. How investors divide and manage the money they already have can be just as important.