Research Affiliates is a California firm that designs investment strategies for $157 billion in mutual funds and ETFs for such clients as Pimco, Charles Schwab and Invesco. This writer has always considered their market outlook the best in the business because it's so deeply grounded in academic research. Founder Rob Arnott is the former editor of the Financial Analysts Journal, and the RA braintrust boasts ten PhDs. RA ignores what's trendy and glamorous, and dismisses the new-age theory now in vogue that investors in U.S. big caps can reap big returns starting at today's lofty valuations.

Instead, it points to over a century of evidence that what's super-expensive typically underperforms in the decade ahead, and what's beaten-down and relatively cheap shines.

Market outlook for 2021

An excellent guide to the most likely future gains for different categories of equities is RA's "Broad Asset Class Expected Returns" chart. It shows estimated annual percentage gains over the next decade for over 30 classes of stocks, encompassing U.S. large and small caps, broad groupings such as Europe and emerging markets, and individual countries from Russia to South Africa to the U.K.

RA calculates the expected "nominal" return––means those including inflation––two ways. The first assumes that the price-to-earnings ratio remains at today's levels for each basket of stocks. The multiple it uses is the famous Robert Shiller cyclically-adjusted price earnings ratio, or CAPE, that smooths the extreme volatility in earnings per share by using a ten-year average of inflation-adjusted profits. The inverse of the CAPE could be called the "earnings yield," representing the dollars in dividends and reinvested profits for every $100 investors pay for a selection of equities.

RA calls it the "yield and growth" approach. I'll spare you the math, but it simply forecasts that investors will pocket the earnings yield plus projected annual inflation from now through late April of 2031. Hence, the higher the starting Shiller PE, the lower the earnings yield, and the more slender the gains to come, chiefly because big prices mean paltry dividend yields.

But a fat multiple can hammer returns a second way. That happens when an elevated PE by slides back towards the historic benchmark, a reversal witnessed sundry times in the past 150 years.

So RA offers a second tool that also accounts for that probable "reversion to the mean." It still uses "yield and growth" system to predict the dividend yield and expansion in earnings, but adds what it calls the "valuation dependent" overlay." The valuation adjustment is conservative. It posits that the CAPE in 10 years will go not all the way back to its moving average over the last century. Hence, starting at a towering PE both depresses what investors get from dividends, and raises the threat that a falling, get-back-to-normal multiple will erase the capital gains that, if the PE stayed at the original heights, would wax in lock step with the rise in earnings.

A dim outlook for U.S. big caps

Let's examine what the RA calculus says about the future of the S&P 500. At midday on April 26, the index hovered at 4188, just above its all-time record close a week earlier. We'll start with "yield and growth," then layer on "valuation dependent." The S&P's Shiller PE was approximately 37, the number we'll use in this analysis. The earnings yield, the inverse of the CAPE, was an exceptionally slight 2.7%. Add RA's annual inflation forecast of 2.4%, and the expected annual return for the next ten years was 5.1%. That's divided between a 1.5% dividend yield, and 3.6% growth in earnings per share.

That's not a great scenario, certainly nothing like the double-digit future foreseen by most of Wall Street's market strategists. But it still beats the consumer price index by 2.4 points, meaning that gains would beat the increases in your grocery bills and rent.

But the mediocre picture turns dark when you incorporate the probable change in the valuation, or PE. RA puts the average CAPE for the past century 74% below the current 37 at just 21.5. Using its formula estimating that the CAPE will retreat halfway to that mark, RA forecasts that in 2031, the multiple on U.S. big caps will shrink to 27. That's still a formidable number, sitting one-quarter above the one-hundred year moving average.

If the PE indeed retreats from 37 to 27, the shift in valuation will erase 3.2 points of the 3.6% earnings growth that, had the PE stayed at 37, would have contributed 3.6% a year in cap gains. Instead, under the "valuation dependent" test, prices should rise just 0.4% a year. That lowers total return to 1.9%, the 1.5% dividend yield plus the 0.4% capital gain. The S&P return would lag 2.4% inflation by 0.5%. Ten years from now, the index would stand about 4% higher at 4356. That's amounts to a full decade of running in place.

History's on RA's side. When the CAPE reached 37 for the first time ever during a period of strong earnings in April of 1998, a moment recalling today, the S&P hit a then-record 1807. Ten years later, it was 7% lower at 1685.

Stocks to buy now

Amazingly, U.S. big caps promise the worst returns of all the 31 stock groups that RA evaluated. The best deals lie beyond our borders. "Although we've seen markets get more expensive since the March lows of 2020, and that includes both stocks and bonds, there are still great opportunities for investors willing to look outside the U.S.," Jim Masturzo, Research Affiliates' head of multi-asset strategies.

Even a "Global Developed" portfolio that spreads holdings across the major industrial nations offers expected returns of 3.8%, double the figure for the S&P 500. Overall, the best gains should come from the emerging markets. RA shows incredible numbers for the likes of Russia (13.7%), Turkey (12.4%), and Brazil (8.4%). The downside: You'll have a bumpy ride getting those big gains because those individual markets are highly volatile.

By contrast, a diversified group of EM stocks should still deliver 7.7% a year, on a much a smoother trajectory than, say, Russia or Poland alone. That 7.7% is split among a 2.0% dividend yield, 0.5 points better than for U.S. big caps, earnings growth of 5.2% (1.6 points better), and most of all, a PE that should rise by 0.4% a year, instead of dropping at eight-times that rate.

Another good bet is the U.K., recently liberated from the E.U. but still in the tariff and quota free market, and hosting one of the world's quickest recoveries from the global pandemic. RA forecasts Britain's annual gains at 7.7%, same as for EM, but featuring fewer fits and starts. Why is the stately U.K. just at attractive as the go-go emerging markets? Not because it's a world beating economy, though the post-EU outlook is excellent. It's because the U.K. is cheap, plain and simple.

Overall, U.S. big caps are vastly overpriced. Getting back to where they're reasonable will a painful slog that will probably start with a big retreat. But exposure to the roaring U.K. and the EMs may help dull the pain.