Thanks to a huge rally off the market's March 9 low, the S&P 500 and the Dow have just put in their best quarter since 1998. Bulls are coming up with all sorts of reasons to justify the rally-- and to explain why it will continue. Meanwhile, bears have been wringing their hands with increasing intensity. Who's right? To answer that question, let's estimate expected medium-term returns for both indexes.

Forecasting future stock returns
To forecast index returns, I start by breaking down the price return into two components: earnings growth and price-to-earnings multiple expansion (or contraction). The multiple I use here is the cyclically adjusted P/E ratio (CAPE), which is calculated using average inflation-adjusted earnings over the prior 10-year period. The CAPE originated with the father of value investing, Ben Graham; it's since been championed by Professor Robert Shiller of Yale. It's one of the very few consistently predictive indicators of stock market returns.

Index (Segment)

Index Level (Sept. 30, 2009)

CAPE: Cyclically Adjusted P/E

CAPE Long-Term Historical Average

Overvaluation

Dow Jones Industrial Average (Megacap)

9,712.28

19.1

17.7

7.9%

S&P 500 (Broad Market/ Large Cap)

1,057.08

18.8

16.3

14.8%

Source: Author's calculations based on data from Dow Jones and Robert Shiller.

In order to continue, I need to make a couple of assumptions:

The CAPE reverts to its long-term historical average. (There's a wealth of data to back this up.)

I use a reversion period of seven years. (Hat tip to Jeremy Grantham's firm GMO here; this is the period they use in their forecasts.)

With these assumptions, we can calculate the annualized impact on index returns of an index's CAPE returning to its long-term average over seven years. Combine that with an estimate of long-term earnings growth, and you obtain the expected annual price return of the index:

Index (Segment)

Long-term Earnings Growth (Bottom-Up Estimate)*

Expected Annualized Multiple Expansion

Expected Return (Annualized)

Dow Jones Industrial Average (Megacap)

8.3%

(1.1%)

7.2%

S&P 500 (Broad Market/ Large Cap)

10.6%

(2.0%)

8.4%

*This is a bottom-up estimate I calculated from the long-term earnings growth estimates for the index components.
Source: Author's calculations based on data from Capital IQ, a division of Standard & Poor's; Dow Jones; and Robert Shiller.

Don't forget the dividends
What of dividends, you ask? Good point -- you won't leave your income return on the table. No fancy calculations here: I'm simply going to use the current dividend yield as a proxy for the expected dividend return. Combining the estimated price return and the dividend return yields annualized total return estimates over the next seven years:

Index (Segment)

Expected Price Return

Dividend Yield

Total Return (Annualized)

Dow Jones Industrial Average (Megacap)

7.2%

2.8%

9.9%

S&P 500

(Broad Market/ Large Cap)

8.4%

2%

10.5%

Source: Author's calculations based on data from Capital IQ, a division of Standard & Poor's, Dow Jones and Robert Shiller.

What if things don't turn out that well?
Those sort of returns look pretty good – perhaps too good. In fact, I suspect the index earnings growth estimates have introduced an upward bias in the results. I calculated these estimates on a bottom-up basis as a weighted average of the consensus long-term EPS growth estimates of the index components. One should treat the prognostications of sell-side analysts with skepticism at the best of times; during this year's stock rally, I've become particularly concerned that analysts are wearing rose-tinted glasses.

As a counterpoint, let's imagine that things work out more like they have over the last 80 years. Instead of relying on analysts' crystal balls, let's use long-term average earnings growth rates as our forecast of future growth rates (the long-term average growth rates in 10-year average earnings for the S&P 500 and Dow are 6.2% and 3.9%, respectively). Once I give my spreadsheet a whir, this is how the numbers pan out:

Index (Segment)

Expected Price Return

Dividend Yield

Total Return (Annualized)

Dow Jones Industrial Average (Megacap)

5.0%

2.8%

7.8%

S&P 500 (Broad Market/ Large Cap)

1.8%

2%

3.9%

Source: Author's calculations based on data from Capital IQ, a division of Standard & Poor's, Dow Jones and Robert Shiller.

These returns are a lot less enticing, especially for the S&P 500. Furthermore, these are nominal returns -- inflation will be collecting its excise on the purchasing power of your assets along the way. If this scenario came to pass, and assuming current expectations for inflation, the real return on the S&P 500 would be just 2.3%. My hunch is that actual returns will fall somewhere in the range between our "Analyst Estimate" and "Historical Precedent" scenarios (although probably closer to the bottom end of the range):

Index

Expected Annual Total Return – Range*

Dow Jones Industrial Average (Megacap)

8.9% ± 1.1%

S&P 500 (Broad Market/ Large Cap)

7.2% ± 3.3%

*Note that the true range of returns is subject to uncertainty beyond that on the rate of earnings growth. Consequently, it's wider than the range displayed.

For stock pickers, the range of returns for stocks in these indices is bound to be much wider. I've written multiple times that the stocks of high-quality companies appear undervalued right now; in fact, within the blue-chip Dow index, there is only one stock – Coca-Cola (NYSE: KO) -- that trades at a CAPE that is higher than that of the S&P 500. As the following table shows, some of the stock's brethren look very attractive right now:

Company

Cyclically Adjusted P/E Multiple*

Chevron (NYSE: CVX)

6.7

ExxonMobil (NYSE: XOM)

8.1

Pfizer (NYSE: PFE)

9.1

Microsoft (Nasdaq: MSFT)

13.7

Johnson & Johnson (NYSE: JNJ)

13.5

JPMorgan Chase (NYSE: JPM)

12.3

*As of Sept. 30, 2009. Note that the CAPE calculations here aren't exactly consistent with those for the indexes.
Source: Author's calculations, based on data from Capital IQ, a division of Standard & Poor's.

The outlook for the next 12 months
If you are like most investors, seven years may seem like a long time -- you want to know where stocks will be at the end of this quarter. Unfortunately, valuation isn't a good indicator of stock returns in the short or medium term; however, one can certainly make some informed guesses based on the data at hand.

Between the two indexes, the S&P 500 is the riskier proposition in the short term, because of its overvaluation. If the S&P 500 went from being 15% overvalued to 20% undervalued -- for the statistics wonks, that's less than a one standard deviation move -- that would equate to a 30% loss, putting the S&P 500 at 737. I'd estimate the odds of a decline of that magnitude or greater over the next 12 months are better than 1 in 5.

Final recommendations
If you're an index investor, your medium- to long-term prospects aren't bad, but they aren't stellar, either. Expect to earn returns that lag historical averages. In that respect, it is no time to be overweight U.S. equities -- particularly since I think there are good odds that short-term price declines will create more attractive buying opportunities. If you're a stockpicker, the rally hasn't buried all opportunity. Far from it! I recommend heavily favoring "quality" in your search, and avoiding the more speculative names that are highly exposed in this environment.

Morgan Housel has identified three high-quality companies that are still cheap.

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Fool contributor Alex Dumortier, CFA has no beneficial interest in any of the companies mentioned in this article. Coca-Cola, Microsoft, and Pfizer are Motley Fool Inside Value picks. Johnson & Johnson and Coca-Cola are Motley Fool Income Investor recommendations. Try any of our Foolish newsletter services free for 30 days. The Fool's disclosure policy wishes it had a graphing calculator.