Imagine that you walk into a bank to open a savings account, and you’re offered a bizarre opportunity instead. Here’s how it works: You make an initial deposit, and each month it sits, the balance gets multiplied by a random number between 0.9 and 1.12. In other words, every month you have a random chance of losing up to 10% of your money, or gaining up to 12% — or anything in between — all with equal chance. Will you participate?

There’s obviously some potential to make a profit. After all, the account is statistically likely to increase in value more often than it loses*. But what if you get served a lot of unlucky random numbers that cause your account to lose value for many months in a row? The opportunity is not without risk.

This weird account is totally fictional, but it bears a striking resemblance to how investing in stock market index funds really works. Actually, by viewing the real stock market through the lens of this model, we’ve been able to get great results and make a lot of money over time.

Of course, this isn’t a perfect model**. The real market isn’t based on a random number generator — it reacts to actual events in the world. But strangely enough, **if you pretend that the stock market behaves like a random number generator, you’re actually likely to become a better investor**. We’ll see how by the end of this article.

*Note: We are not financial advisors. We’re just a couple of bloggers honestly sharing what has worked for us. This article contains personal opinions for your consideration, not professional financial advice. Check out our **Disclosures** page for more information.*

## Testing Our Stock Market Model

Suppose our fictional random number generator really *was* how the stock market works. What would happen if we actually invested in it?

Based on this simulation, it seems like a pretty good value! There’s a clear upward trend, and our $10,000 initial investment turned into $28,146 after 10 years. That’s an annualized return of about 10.9% per year (very close to the actual historical average of the US stock market).

In fact, our simulated stock market chart doesn’t look too dissimilar from a 10-year chunk of the actual US stock market’s history:

So, what should we do with this information?

## Gaming the System

When most beginner investors look at that last graph of the actual US stock market, they typically draw the same conclusion: “It would have been really smart to buy shares during that giant dip in 2009.” It seems obvious — buy shares when they’re cheaper, and make a bigger profit.

But would it make sense to apply the same logic to our stock market simulation chart above? Is it smarter to invest in the dip of month 24 than in month 0, because you could have made a bigger profit?

*Of course not*. Each month’s return was determined by a literal *random* number generator. The likelihood of our account balance increasing or decreasing at any time is always completely unaffected by what happened in previous months. “Buying the dips” makes no sense at all (except in retrospect, which isn’t helpful).

Counter-intuitively, this is actually good advice for the real stock market, too. Timing the market is hard — so hard that the majority of professionals who try, fail. It’s better to just *pretend* that the market’s behavior is as random as the spin of a roulette wheel, rendering market timing completely illogical.

Like our model (but unlike a casino game), the real stock market has an overall upward trend over the long run. It’s always more likely to go up than to go down, so **the best time to invest is always right now**.

## Looking Longer Term

Wait a second though. If the stock market has seemingly random behavior, isn’t it possible to *lose* money if we hit a streak of bad luck? We only looked at one 10-year trial.

I ran my randomized stock market simulation fifteen more times to demonstrate that possibility, and the results were pretty realistic! In the best case, our initial $10,000 investment turned into over $56,000 over a 10-year period, implying an annualized return of about 18.8% per year. In the worst case, the $10k turned into $7,000 after 10 years, giving us an annualized return of -3.5% per year.

You can check out the details of all 15 simulations (PDF, 1 MB) for yourself. As you look through them, you’ll notice that many different outcomes are possible. Although 13 out of 15 simulations were profitable, the returns (and the paths taken to achieve them) vary wildly. The same thing is true of the real stock market.

Coincidentally, the best and worst annualized returns from our fifteen simulation trials were pretty close to the best and worst 10-year annualized total returns of the S&P 500 in history. Knowing those historical “best case” and “worst case” possibilities is helpful for judging risk.

But what if you’re willing to ride out that risk for a *really* long time? Is it possible to eliminate long-term risk altogether and guarantee a profit?

After 50 years, our initial $10,000 investment has turned into about $1.5 million(!), which represents an annualized return of about 10.5% per year. Running the simulation repeatedly over 50-year timespans, I produced many differing returns, but they never once turned out negative.

The same is true of the actual stock market: Over a 50-year period of buy-and-hold index investing in the US stock market, a negative return has never happened a single time in history, and annualized nominal total returns of 10% per year or more have actually been the norm***. Long-term investing works!

## Conclusions About Investing in Stocks

My background is in physics, not finance. This model is, at best, an educational approximation. Nobody should use it to draw direct conclusions about what’s actually going to happen in the real stock market. But one thing that physicists are trained to do well is to create very *simple* models that work okay for drawing broad, *general* conclusions.

Based on our study of the charts above, and the sample of additional trial runs, what investing wisdom might we come away with regarding our “toy stock market?”

- Regardless of recent performance, our investment is more likely to increase in value than to decrease in value at any given time. Therefore,
**investing as early as possible is more logical than trying to invest at some specific “right time**.” - Investing involves risk. It is possible to get unlucky! But bad luck is very unlikely to persist for decades at a time. So,
**we should never invest money that we can’t afford to**.*leave*invested for many years if necessary - Over a lifetime,
**the effects of investing can be breathtaking**. We turned a single $10,000 investment into $1.5 million over 50 years, and that wasn’t even a particularly exceptional result.

Each of these conclusions was drawn from a fictional stock market model based on a random number generator. But every one of these statements is just as applicable to the *real* stock market.

By thinking of the stock market as a random system instead of something we have the power to predict, we’ll be less likely to make emotionally driven investing decisions. Investing less emotionally leads to more consistent actions — and more consistently positive results.

Another benefit of viewing stock market investing through this lens is that it stops us from wasting valuable time trying to outsmart the market. When we think of the stock market as completely random, it becomes apparent that reading Marketwatch articles, watching Jim Cramer, or even poring over earnings reports is futile — and that time can be reclaimed to do useful work that will earn us more money to be invested in the first place.

— Steven

** For the statistics nerds, the expected value of the monthly wealth multiplier associated with this hypothetical account is >1 and given by the following integral:*

*Unsurprisingly, this is just the average of 1.12 and 0.9, since we’re dealing with a continuous uniform probability distribution. The annual wealth multiplier’s expected value is equal to the monthly EV raised to the 12th power: 1.01^12 = 1.127, meaning this account should return 12.7% annually on average — probably a little more than we should expect from the actual stock market, long-term.*

*** A quantitative analyst might laugh at this oversimplified stock market model. It lacks a robust risk profile (a uniform probability distribution of returns with hard limits is definitely not the best choice, but it’s easy for anyone to understand, which was much more important to me). It also lacks any consideration for macroeconomic variables, like current interest rates. But the lesson it teaches — that you can’t outsmart the stock market by jumping in and out of it — is an important one.*

**** Actually, a negative nominal total return has never even happened over a 20-year period in the entire history of the S&P 500! You probably don’t need anywhere near a 50-year time horizon to safely wait out volatility (barring an unprecedented event, like total economic collapse, which almost no asset class would protect against).*