There once was a man with a red paper clip who wanted to buy a house. He had no money. So one day he traded his paper clip for a pen shaped like a fish. Then he traded his pen for a hand-crafted doorknob. Weeks later he traded the doorknob for a camping stove. Fourteen more trades would follow, until finally he ended up with a two-story farmhouse in Canada. It sounds like a fairy tale, but the story is true, and the man did it all within just one year.

The story is the perfect illustration of the power of compounding: What starts small becomes big, because you're earning growth on top of more growth. Compounding is important because it's critical in understanding the answer to a favorite question among investors: "How fast could you double your money in the stock market?"

## The "rule of 72"

The simplest way to answer this question is with one easy math trick you can perform without even using a calculator. It's called "the rule of 72": Take your estimated annual return and divide by 72. The resulting number represents the number of years it will take to see your investment double. However, this rule assumes the rate of return will be unchanged over the years. This, in reality, is unlikely.

Image source: Getty Images.

Therefore, you should take special care to make reasonable assumptions about what return you can expect. According to research from the Stern School of Business at NYU, the average annual return on the S&P 500 from 1928 to 2016 was 11.42%. So we might reasonably estimate that an investment in the S&P 500 could conceivably double in just over six years (dividing 72 by 11.42 gives a result of 6.3).

However, can past performance serve as an indicator of future returns? Let's look closer.

## Science says: Blame it on the rain

An in-depth study from researchers at Vanguard revealed some interesting facts about the predictability (or unpredictability) of market returns. In reviewing annualized returns of the stock market since 1926, they drew several conclusions. First, they learned that "stock returns are essentially unpredictable at short horizons." They continue, "Quite frankly, this lack of predictability is not surprising given the poor track record of market-timing."

How about predictability over the long term? Here's what they have to say: "[M]any commonly cited signals have had very weak and erratic correlations with realized future returns even at long investment horizons." These "signals" include things like reported corporate profit margins, economic growth, and even past stock returns.

Their startling conclusion? "[M]any popular signals have had a lower correlation with the future real return than rainfall." Even the best predictor of future returns (price-to-earnings ratio) leaves 60% of performance unexplained. Put simply, nobody knows where the broad market is going to go, or why it went where it did.

## Playing the long game

With so much uncertainty, the lesson is clear: There's no way to make a quick buck on the stock market. Smart investors never make this their goal; instead, they play the long game. They anticipate fluctuations in the market, and handle them by investing money they can afford to leave untouched for years.

It's a game of chess, not checkers. Image source: Getty Images.

This is where the power of compounding (and the red paper clip) comes into play. It's only with a long-term horizon that you can weather the inevitable fluctuations of the market. Consider that in 2008 alone, the S&P 500 dropped by 36.55%; the following year it gained 25.94%.

You can take additional steps to manage the unpredictability of the market with strategies like dollar-cost averaging (DCA). You don't know if you're getting into a stock at a high or a low, because you don't know what's coming next. But you can enter the market at multiple times rather than all at once, by purchasing shares in installments. This means your average "basis," what you paid for your shares, smooths out the ups and downs, helping to avoid the problem of buying at a high only to see the lows follow.

Does it work? The answer: sometimes. Depending on market changes, lump-sum investing can outperform dollar-cost averaging. However, DCA might be a suitable approach if you're seeking to make automated, regular contributions to an investment account over the long term, especially if a lump sum is not available.

It would be wise to remember the adage "the long way is the shortcut." Seeking a fast gain in the market is a risky prospect. Keep the focus on the long term. Wait and win.