“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 for most investors 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.

I’ve been recommending this combination since the 1990s, and it is the basis of the majority of my own investments.

Fortunately for you, you don’t have to take my word for how good this is. I’ll show you the evidence.

I can describe this portfolio briefly: The “ultimate” portfolio starts with the S&P 500 index

SPX, +1.34%

then adds small and equal portions of nine other 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 about the same risk as that of the S&P 500.

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 48 calendar years, from 1970 through 2017, the S&P 500 compounded at 10.5%. An initial investment of $100,000 would have grown to $12.2 million.

(You should realize, of course, that inflation and taxes can significantly eat into these returns. But that is the case with any portfolio. And as long as I’m in “footnotes” mode, I should point out that in past years I made all these computations assuming that, except for the S&P 500, an investor would pay a 1% annual investment management fee. This year, I’ve dropped that assumption, because do-it-yourself investors now have ultra-low-cost access to funds and ETFs that track these asset classes. )

For the sake of our discussion, think of the S&P 500 index as Portfolio 1. It’s not bad, and you could do much 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 48-year return changes a lot. Assuming annual rebalancing (an assumption that applies throughout this discussion), the 10.9% compound return of Portfolio 2 was enough to turn $100,000 into $14.5 million.

In dollars, that’s an 18.7% increase over the index itself — the result of changing only one-tenth of the investments. Very impressive!

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.

This change boosts the 48-year compound return of the portfolio to 11.1%; an initial $100,000 investment would have grown to nearly $15.5 million — an increase of $3.26 million (or 26.6%) compared with Portfolio 1.

Taking one more step, we add 10% in U.S. small-cap value stocks, reducing the weight of the S&P 500 to 70%.

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 11.5%, enough to turn that initial $100,000 investment into just shy of $18.5 million.

With more than two-thirds of the portfolio still in the S&P 500, that seems like a marvelous 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 11.6% and an ending cash value of nearly $19.2 million.

Let’s pause for a moment to recap.

•First, Portfolio 5’s increase in compound return over Portfolio 4 was very small, but over 48 years that tiny step produced an additional $711,000 or so. 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. That has to be a winning combination.

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 excellent, and I expect it will do well in the future.

But I believe 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 48 years, the changes I just described increased the compound return to 12.3%, and the portfolio value to $25.9 million.

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

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

This boosts the compound return slightly, although with rounding it still looks like 12.3%, which we saw in Portfolio 6. But the dollar increase, about $345,000, yields a final portfolio valued at nearly $26.3 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.

That’s the Ultimate Buy and Hold Portfolio, which obviously stood the test of time very well.

As you will see, table 1 includes another column, labeled Portfolio 8. This is my suggested All-Value Portfolio, which includes only five asset classes instead of the 10 in Portfolio 7.

This portfolio simply eliminates REITs and the blend asset classes.

The 48-year performance of Portfolio 8 is simply stunning. The compound return is 13.5%, which might not seem that impressive.

But over nearly half a century those extra percentage points boosted the final portfolio value to $42.8 million, an increase of $30.6 million over that of the S&P 500 index.

For a detailed discussion of what’s behind Portfolio 8, check out my 2017 article “Why you should consider an all-value portfolio.”

Portfolios 7 and 8 are among the results of my longstanding commitment to find higher expected rates of return with little or no additional risk.

Investors who build either of these portfolios using low-cost index funds or ETFs, as I recommend, don’t have to rely on anybody’s ability to choose stocks. They don’t have to make any short-term economic or market 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.

The only honest answer is that I cannot know.

But 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 that value stocks will continue to have higher returns than growth stocks.

I believe these are reasonable expectations, and Portfolios 7 and 8 are the best ways I know to put them to work for you.

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’ll tackle that topic in the coming weeks.

Meanwhile, for more on the Ultimate Buy and Hold portfolio, check out my podcast.

Richard Buck contributed to this article.

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