"Ultimate" isn't a term to toss around lightly. But in this case it fits. I believe the investment portfolio I'm about to describe is the absolute best way to achieve long-term growth in the stock markets.

My view is based on the very best academic research of which I'm aware, as well as my own experience working with thousands of investors over the past half century.

Fortunately for you, you don't have to take my word for it. I'll show you the evidence.

I can describe this portfolio briefly: The "ultimate" portfolio starts with the S&P 500 Index, then adds small and equal portions of nine other very carefully selected U.S. and international asset classes, each one being an excellent long-term vehicle for diversifying.

When it's properly done, the result is a low-cost portfolio with massive diversification that will take advantage of market opportunities wherever they are, and at no more risk than that of the S&P 500 SPX, -1.13% .

I'll roll this out in steps rather than all at once. That way, you'll see how it goes together.

The base "ingredient" in this portfolio is the S&P 500 Index, which is a pretty decent investment by itself. For the past 46 calendar years, from 1970 through 2015, the S&P 500 compounded at 9.25%. An initial investment of $100,000 would have grown to $5.86 million.

For the sake of our discussion, think of this index as Portfolio 1. It's not bad, and you could do a whole lot worse than just adopting this simple asset class.

But you can do a whole lot better, too. You take the first small step by adding large-cap value stocks, ones that are regarded as relatively underpriced (hence the term value).

(The links above, and others below, are to specific articles from 2015 that focus on each asset class.)

By moving only 10% of the portfolio from the S&P 500 into large-cap value stocks (thus leaving the other 90% in the S&P 500), you create what I call Portfolio 2.

Although only 10% of the portfolio has changed, the 46-year return changes a lot. Assuming annual rebalancing (an assumption that applies throughout this discussion), the 9.66% compound return of Portfolio 2 was enough to turn $100,000 into $6.95 million.

In dollars, that's an 18.5% increase over the index itself – the result of changing only one-tenth of the investments. The following commission-free ETFs are available at either Vanguard, Fidelity, Schwab or TD Ameritrade: iShares Russell 1000 Value ETF IWD, -0.91% , Vanguard Russell 1000 Value ETF VONV, -1.02% , iShares Core U.S. Value ETF IUSV, -0.79% and Schwab U.S. Large-Cap Value ETF SCHV, -0.74%

In the next step we build Portfolio 3 by putting another 10% into U.S. small-cap blend stocks, decreasing the weight of the S&P 500 to 80%. Small-cap stocks, both in the U.S. and internationally, have a long history of higher returns than the S&P 500. Here are my recommended small-cap blend ETFs: Vanguard S&P Small-Cap 600 ETF VIOO, -0.74% , iShares Core S&P Small-Cap ETF IJR, -0.74% , Schwab U.S. Small-Cap ETF SCHA, -0.64% .

This change boosts the compound return of the portfolio to 9.81%; an initial $100,000 investment would have grown to $7.4 million – an increase of $1.54 million (or 26.3%) compared with Portfolio 1.

Taking one more step, we add 10% in U.S. small-cap value stocks, reducing the influence of the S&P 500 to 70%. Here are my recommended small-cap value ETFs: Vanguard S&P Small-Cap 600 Value ETF Vanguard S&P Small-Cap 600 Value ETF VIOV, -1.05% , iShares S&P Small-Cap 600 Value ETF IJS, -0.71% , iShares Russell 2000 Value ETF IWN, -0.66%

Small-cap value stocks historically have been the most productive of all major U.S. asset classes, and they boost the compound return of Portfolio 4 to 10.23%, enough to turn that initial $100,000 investment into $8.82 million.

Compared with Portfolio 1, that's a dollar increase of about 51%, while still leaving more than two-thirds of the portfolio in the S&P 500. To my mind, that's a mighty fine result.

In the next step, creating Portfolio 5, we invest another 10% of the portfolio in U.S. REITs funds. Result: a compound return of 10.36% and an ending cash value of $9.32 million. Here are my recommended REIT ETFs: Vanguard REIT ETF VNQ, -1.84% , Fidelity MSCI Real Estate Index ETF FREL, -1.98% , Schwab U.S. REIT ETF SCHH, -1.82%

Let's pause for a moment to recap.

First, Portfolio 5's increase in return over Portfolio 4 was less than 0.2%, but over 46 years it produced an additional half a million dollars. This is a lesson I hope you won't ever forget: Small differences in return, given enough time, can add up to huge differences in dollars.

Second, every one of these portfolios, 2 through 5, had a lower standard deviation, thus less risk, than the S&P 500 Index. Higher returns came bundled with lower volatility. I think that has to be seen as a win-win.

Some investors may want to stop here and not invest in international stocks. If that's the limit of your comfort level, that's fine. The combination of asset classes in Portfolio 5 is an excellent one that I expect will do well in the future.

But I believe that any portfolio worth being described as "ultimate" must venture beyond the U.S. borders. And the rewards are definitely there.

Accordingly, in building the ultimate equity portfolio I add four important international asset classes: international large-cap blend stocks, international large-cap value stocks, international small-cap blend stocks and international small-cap value stocks.

Giving each of these a 10% weight reduces the influence of the S&P 500 to 20%. If that sounds frightening, think about this: Over 46 years, that increased the compound return to 11.1%, and the portfolio value to $12.61 million.

That is more than double the payout from the S&P 500 alone. And Portfolio 6 produced that result while reducing risk.

The final step, resulting in Portfolio 7, is to add 10% in emerging markets stocks, representing countries with expanding economies and prospects for rapid growth.

This increases the compound return to 11.28% and the final dollar payout to $13.65 million. It is only this last step that increases volatility above that of the S&P 500. That increase, by the way, is so slight that it would most likely never be noticed.

You'll find these figures and more details in Table 1. Incidentally, all these performance figures assume an investor paid a 1% annual management fee. That assumption is probably more than adequate to cover the expenses of investing in these asset classes through mutual funds or ETFs.

Table 2 shows the percentage makeup of each of these portfolios.

This ultimate combination, Portfolio 7, is a result of my long-standing commitment to find higher expected rates of return without taking additional risk.

Investors who build this portfolio using low-cost index funds, as I recommend, don't have to rely on anybody's ability to choose stocks or make any short-term economic predictions.

The perceptive reader will no doubt have noticed that all these performance statistics are based on the past. I am often asked if I expect returns like these to continue into the future.

Obviously, the only honest answer is that I cannot know.

However, every academic I'm familiar with expects that, over the long term, stocks will continue to have higher returns than bonds, small-cap stocks will continue to have higher returns than large-cap stocks and value stocks will continue to have higher returns than growth stocks.

I believe these are reasonable expectations, and Portfolio 7 is the best way I know to put them to work for you.

For more on this combination of investments, check out my podcast "10 lessons from the ultimate buy and hold portfolio."

Finally, it's important to note that most investors should include fixed-income funds in their portfolios. Just how much is a very important question with an answer that depends on several important factors. I've written about that topic before and I'll tackle it again in the coming weeks.

Richard Buck contributed to this article.