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The stars seemed to be aligned, leading many investors to be concerned about there being a bubble in the stock market. First, we've had one of the greatest rallies ever, with the S&P 500 rising from its low of around 666 on March 6, 2009 to crossing the 1,800 level on November 18, 2013, a price-only increase of about 170 percent. That kind of increase causes investors to be concerned that prices are "too high." You hear phrases like, "the market has gotten ahead of itself." Adding fuel to the fire is the concern that the Federal Reserve's easy monetary policy (both its policy of basically a zero Federal Funds interest rate and its bond buying program) has fueled an asset bubble.

The stars came into further alignment when Professor Robert Shiller, author of "Irrational Exuberance," was recently awarded the Nobel Prize in economics, bringing more attention to the question: Are we in a bubble?

The third factor is that while corporate earnings have been rising rapidly, far more than anyone expected, prices have been rising even faster. Earnings for the S&P 500 stocks rose from about $61 in 2009 to an estimate of about $109 for the full year 2013. In other words, while earnings are likely to be up about 80 percent over the period, stock prices rose at more than double that rate. That pushed the Shiller CAPE 10 (cyclically-adjusted price-to-earnings ratio) to 25.1 on November 20, 2013. Cliff Asness of AQR found that when the P/E 10 was above 25.1, the real return over the following 10 years averaged just 0.5 percent - virtually the same as the long-term real return on the risk-free benchmark, one-month Treasury bills. The best 10-year real return was 6.3 percent (so you can get a good outcome), just 0.5 percent below the historical average. But, the worst 10-year real return was -6.1 percent (that's compound annual return over 10 years).

So the question remains, are we in a bubble? How do we answer that question? Unfortunately, there's not a simple answer. We'll begin with assuming when people state that there's a bubble, they are implying that prices are too high, the bubble is about to burst, and prices will come crashing down. You may recall that in December 1996, Alan Greenspan, then chairman of the Federal Reserve, coined the phrase "irrational exuberance." Defying Greenspan, and many pundits, over the next three years the S&P 500 returned 27.6 percent per annum, producing a total return of about 108 percent.

The problem, as Professor Eugene Fama (another recent Nobel Laureate, and the source of much debate between him and Shiller) points out is that bubbles are always easy to "see" after they have burst. The S&P 500 had closed the prior day at 1552, 236 points below its close on November 19! That's a price-only increase of over 15 percent. Adding in the return from dividends would put the total return of an investment in SPDR S&P 500 Trust ETF (SPY) to above 16 percent.

While keeping the above facts in mind, we can provide some insight into the question by looking at some historical evidence. At year end 1994, just before the market began its rally that saw the S&P 500 return 28.6 percent per year over the following five years, the book-to-market (BtM) ratio of U.S. large growth stocks was 0.4 - large growth stocks were selling at 2.5 times their book value. By the end of the first quarter of 2000 (just before the bubble burst), that ratio had fallen all the way to 0.21. So these stocks were now selling at almost five times their book value. In addition, their price-to-earnings (P/E) ratio almost doubled from their level of 15.8 (about their historical average). At those type levels, it's pretty apparent that there was a great risk that there was a bubble. However, and this is a big however, it's important to remember that the market is not made up of just large growth stocks, the ones that dominate the major market indices like the S&P 500.

Over the same time period, the BtM of large value stocks rose from 0.85 to 1.02. In other words, using this metric, large value stocks actually became about 20 percent cheaper! They went from trading at a 15 percent premium to their book value to a 2 percent discount. Looking at their P/E ratios, they did rise slightly from 10.3 to 11.3. In either case, no one would call these levels bubbly. And we see a similar story when we look at small stocks and small value stocks. For the stocks in the CRSP (Center for Research in Security Prices at the University of Chicago) 9-10 Index (the smallest 20 percent of stocks as ranked by the NYSE deciles), the BtM stayed the same at 0.61, while their P/E ratio actually fell slightly from 14.1 to 13.7. Small value stocks saw their BtM actually rise from 0.93 to 0.98 (making them about 5 percent cheaper relative to their book value), while their P/E ratio was virtually unchanged, falling from 11.7 to 11.6. And the evidence was very similar for international stocks, with large value, small, and small value stocks seeing little change in their metrics, while large growth stocks saw valuations rise sharply.

We can see the impact of the different valuations by looking at the returns over the next three years, a period when the S&P 500 lost 38 percent.

2000-2002

Asset Class

Total Return (%)

MSCI US Prime Market Growth

-59

MSCI US Prime Market Value

-12

MSCI US Small Cap 1750

-8

MSCI US Small Cap Value

28

The important takeaway was that while there was a bubble in U.S. large growth stocks, there were other asset classes in the market that certainly were not in a bubble. In fact, as the table above shows, U.S. small value stocks returned +28 percent over the period. The lesson is that you have to be more definitive when talking about bubbles, and not necessarily apply the term to entire markets.

With that lesson learned, we now turn our attention to current valuations. Perhaps they can provide some insight into the question of whether we're in a bubble or not. We'll use two valuation metrics (P/E and BtM) for the funds of Dimensional Fund Advisors (DFA). (Full Disclosure: My firm Buckingham recommends Dimensional funds in constructing client portfolios.) Note: ETFs or mutual funds were not used because Morningstar data on them uses forward-looking estimates of earnings - estimates which are notoriously optimistic. The data is as of October 31, 2013 and comes from DFA's website. Note that the P/E data excludes companies with negative earnings.

DFA's US Large Company Fund (DFUSX) had a P/E ratio of 16.2 and a BtM of 0.44. The comparable figures for the asset class at year end 1994 (before the market rally began) were 15.8 and 0.40. So far, we don't see any sign of a bubble.

DFA's US Large Value Fund (DFLVX) had a P/E ratio of 13.6 and a BtM of 0.79. The comparable figures at year end 1994 were 10.3 and 0.85. While the P/E is higher, the BtMs are virtually identical. Again, no clear sign of a bubble.

DFA's US Micro Cap Fund (DFSCX) had a P/E ratio of 18.9 and a BtM of 0.53. The comparable figures at year end 1994 were 14.1 and 0.61. The valuations here have risen, especially the P/E ratio. So what we can say is that expected returns are now lower than they were in 1994. And while a P/E of about 19 is high, it's not quite bubble territory.

DFA's US Small Value Fund (DFSVX) had a P/E ratio of 16.3 and a BtM of 0.83. The comparable figures for year end 1994 were 11.7 and 0.93. Again here we see higher valuations, meaning future returns are lower than we would have expected back in 1994. However, it's hard to say that stocks that are selling at only a 17 percent premium to their book value are in a bubble.

When we look at the data for international stocks we certainly don't see any sign of a bubble anywhere. For example, the BtM's of DFA's International Large Cap Fund (DFALX) is 0.6 and the P/E is 14.9. For their International (large) Value Fund (DFIVX) the BtM is 0.96 and the P/E just 12.2. For their International Small Company Fund (DFISX) the BtM is 0.74 and the P/E is 14.8. For their International Small Value Fund (DISVX) the BtM is 1.11 and the P/E 13.0. For their Emerging Markets Fund (DFEMX) the BtM was 0.63 and the P/E 12.9.

What conclusions, if any, can we draw from the data? While valuations are higher than historical averages, there doesn't seem to be any clear sign of a bubble in any of the asset classes we looked at. There doesn't seem to be a reason to expect stock prices to come crashing down as "air" comes out of a bubble in valuations. All we can say is that when it comes to U.S. stocks, investors have bid up prices to levels that forecast somewhat lower than historical returns.

Source: Bubble, Bubble, Toil And Trouble (For The Markets)