NerdWallet looked at the last 40 years of market returns and interest rates to determine how much a 25-year-old who today earns a median annual income for that age ($40,456) and saves 15% would accumulate over the next 40 years, if conditions were similar to those of the past four decades.

We examined our hypothetical investor’s retirement savings across three scenarios:

• Fully invested in stocks
• Deposited in a standard savings account
• Holding all funds in cash, either literally or in a non-interest-bearing account.

To capture the wide range of possible outcomes, we ran thousands of simulations based on historical returns and volatility. For simplicity, this analysis focuses on a portfolio 100% invested in the market, but that allocation may be too aggressive for some millennial investors.

For details on our calculations, see the methodology.

Historical returns don’t promise future returns

It’s unwise to assume that past market returns will dictate future returns. In fact, some analysts have advised investors to expect lower market returns going forward. But the comparison still makes a strong case for the value of investing in stocks — in this case, through an S&P 500 mutual fund — over a long time horizon when compared with savings accounts and cash.

To get a clearer indication of how investors could fare over a 40-year time frame, NerdWallet performed a Monte Carlo analysis, running the historical S&P 500 and Treasury data through 10,000 possible scenarios.

This process uncovers the probability of a range of possible outcomes by considering not just historical returns, but also the volatility of those returns — how far and how frequently the return strayed from the historical average.

While there is no way to predict future market behavior, the simulation found that for the 40-year period analyzed, stock market investors had over a 99% chance of maintaining at least their initial investment — as they would in cash or a savings account — and a 95% chance of accumulating at least $1.67 million, or nearly three times their initial investment. Those who instead chose a savings account had less than a 3% chance of tripling their initial investment. These figures were not adjusted for inflation.  

“In the short run, the ups and downs of the stock market can make investing seem quite risky. But our simulations use historical volatility to show that over the long term, stock market fluctuations can balance out and generate largely positive outcomes a majority of the time,” says Kyle Ramsay, a chartered financial analyst and head of wealth at NerdWallet. “The long-term story is something millennials ignore at their own risk.”

Millennials can embrace their long time horizons

Despite those odds, survey after survey has shown that millennials shy away from the stock market. In addition to the 2016 NerdWallet survey that found 63% of millennials store their retirement savings in a savings account, a 2015 BlackRock report indicates that 46% of millennials believe investing is too risky, holding the highest cash allocation of any age group at 70%. And a Legg Mason survey from this year reported that 85% of millennials define themselves as either “somewhat or very conservative” when investing.

These results aren’t surprising: Millennials came of age during the 2007-08 financial crisis, either investing for the first time during it or watching parents suffer the fallout. But context is key: Our 40-year analysis includes the Great Recession — the market ended 2008 down 37% — as well as the dot-com bubble burst and several other years of significant losses.

Still, the S&P 500 had an average annual return of 10.96% during the 40-year period analyzed, before inflation. By contrast, three-month Treasurys had an average nominal return of 4.61%.

“The biggest force millennials have on their sides is time,” Ramsay says. “Investing over 30 or more years should help young professionals weather the short-term storms in pursuit of long-term goals like retirement.”

In fact, even if someone invested only over the 10-year period ending in 2016 — which includes the Great Recession — the numbers still come out in favor of the stock market by a wide margin: The average annual nominal return of the market was 6.88%, while Treasurys averaged 0.65%.

And in a worst-case scenario, such as a recession that occurs at or near an investor’s planned retirement age? It’s painful to consider the prospect of delaying retirement or retiring with a down investment portfolio, but the analysis found recovery is typically swift: Since 1976, S&P 500 returns including dividends have recovered 90% of their value within three years of a downturn four times out of five — including post-2008. Only in the 2000 downturn did the S&P 500 take longer to recover, taking five years to recover 89% of its value.

Keeping retirement savings out of the market wastes hard-earned dollars

There are good reasons to keep money in a savings account, such as maintaining an emergency fund, which generally should be kept liquid so it can be tapped when needed.

But as the analysis shows, when it comes to far-off goals like retirement, not investing comes with an opportunity cost — in this case, $3.3 million to $4 million — that will dramatically shrink the saver’s eventual nest egg.

Investing also helps cover a range of financial blemishes. The analysis is based on a steady contribution of 15% of income, with annual salary adjustments for inflation. Most long-term investors will find their savings rate fluctuates with various lifestyle changes and milestones, and rarely is income on a constant upward trajectory.

If there are years when you don’t save money, the money you’ve already invested continues to work for you during that time. Funds kept in cash or savings vehicles that can’t match inflation will inevitably lose purchasing power during those periods.

Diversification and appropriate asset allocation significantly reduce risk

It’s worth highlighting that the returns surfaced in NerdWallet’s simulations are not dependent on risky trading behavior, but instead on regular contributions into the kind of broad-based equity mutual funds offered in a 401(k) or individual retirement account.

Mutual funds, specifically low-cost index funds and exchange-traded funds, allow investors to instantly spread their money around a wide range of investments. An S&P 500 index fund, which could have posted average annual returns similar to the findings in our analysis, allows an investor to hold a piece of up to 500 large U.S. companies with a single transaction.

“While consumers have more investment options today, they should still watch out for high fees that could ruin their future returns,” Ramsay warns. “Today, one can easily and cost-effectively achieve diversification via index funds. And if you don’t feel confident managing your investments yourself, there are numerous low-cost robo-advisors who can do it for you.”

Investors should also carefully select an asset allocation that meets their goals and their risk tolerance. An aggressive millennial investor may start out with a 100% equity allocation, as shown in this analysis, then slowly dial that down as retirement approaches. But even young investors may feel more comfortable allocating a percentage of their portfolio to bonds, and an investor who is closer to retirement age may want to hold just 50% to 70% of his or her portfolio in stocks. Investors can use an asset allocation calculator to determine the best investment mix for their needs.