How expensive are stocks, and what’s an investor to do about it?

For stock market investors, 2013 was a nice ride: The S&P 500 (INDEXSP:.INX) gained 31% and there was no drawdown worse than 5.6% at any point in the year.

Only three years since 1927 have been better by both metrics: 1954, when the market soared by 52%, with 4.4% maximum drawdown; 1958, which saw a 43% gain in stocks overall, with 4.4% maximum drawdown; and 1995, when the market rose by 38%, with 2.5% maximum drawdown.

Most good years for the stock market are more volatile, like the second-best year 1933, with a 44% positive return but a 29% drawdown during the year. Most low-volatility years are only pretty good, like 1964, with the second-lowest maximum drawdown, 3.5%, and a 16% total positive return for the year. (Four of the last five years have been above median return for the S&P 500, and the fifth (2011 at 2% total return) was positive. The last two years have been much less volatile than average.)

Investors responded to 2013s climate by putting $160 billion of new money into equity mutual funds (investment flow data from ICI ), a dramatic shift in a market that saw five straight years of outflows totaling $536 billion. This continues a long-standing pattern of investors putting money into stocks after three to five good years. Since 2007, equity mutual funds inflows have totaled $440 billion in 40 net positive months, while outflows have been $743 billion in 42 net negative months. Unfortunately, the inflows have been at 16% higher average equity prices than the outflows, because equity mutual fund investors, as a group, buy high and sell low. This cost these investors a staggering $300 billion over the period, as they withdrew a net $303 billion but have $605 billion lower current balances as a result.

There are two competing lessons you might draw from this information. First is that it doesn’t pay to time the market. Just put an adequate fraction of your income into tax-efficient, diversified investments with fair fees every paycheck and don’t spend any energy worrying about ups and downs.

The second potential lesson is that since average investors are putting money into the stock market, and since the market has been up so much recently on only fair economic news, stocks are likely headed for a fall. Wait for the decline, and then think about getting back in at that point.

To see if either of these lessons make sense, let’s take a look at history. An important concept to focus on is Robert Shiller’s Cyclically-Adjusted Price-Earnings ratio (CAPE, click here for more about this measure). This takes the current price of the S&P 500 and divides by average earnings of the constituents over the last 10 years, adjusted for inflation. I think it is the best commonly available measure of whether stocks are cheap or expensive (some financial economists disagree in what has come to be known as the Shiller versus Seigel debate ). Over the last 50 years, its median value is 20, and it has been 13 or below about 25% of the time, and 24 or above about 25% of the time. The S&P 500 CAPE is 26 as of market close on December 24, 2013, suggesting that stocks are moderately expensive, but they have been even more expensive in 97 of the last 600 months, so we’re not at an extreme.

Source: S&P 500 Total Return figures from Bloomberg, CAPE data from Robert Shiller. CPI data from St. Louis Fed from January 1928 to December 2013 .

The chart above shows the S&P 500 monthly real (that is, adjusted for inflation) return versus the beginning of month CAPE back to January 1928. There’s not much pattern here; you get good and bad months with high and low CAPEs. It does seem like the best and worst months for the stock market happen when the CAPE is below 15, but that’s not much use for making investment decisions today. If you want to time the market on a monthly or more frequent basis, you’re going to need better value measures than CAPE.

The chart below shows the S&P 500 total real returns over five years versus the beginning of period CAPE, also going back to January 1928. This shows strong patterns. Of course, we don’t know that the future will be like the past, but at least we can get some sense for the possibilities.

Source: S&P 500 Total Return figures from Bloomberg, CAPE data from Robert Shiller. CPI data from St. Louis Fed from January 1928 to December 2013.

Stocks look pretty attractive if you can buy them at a CAPE less than 15, which last happened in April 2009. In the 422 months with CAPEs under 15, S&P 500 investors made an average of 69% after inflation during the subsequent five years. For only 29 of those 422 months was there a negative real five-year return, and the average loss in those periods was only 8%. This is the stocks for the long run world that a lot of optimistic investment books like to emphasize.

When CAPE gets above 30, things have not been so pleasant in the past. In only seven of the 57 months did S&P 500 investors earn a positive real return over the next five years, and all seven were when CAPE started near 30. On average, investors lost 13% to inflation over five years.

S&P 500 investors who buy at a CAPE between 15 and 30 have made money after inflation two-thirds of the time (323 of 493 months), with an average real gain of 29% over five years. While this is not as much fun as buying when stocks are cheap, I think it’s a reasonable basis for most people to seek financial security through regular investing. Of course, determining the level of equity risk to take is only the beginning of an investment strategy. You should also consider how to take the equity exposure and what non-equity risks (if any) to use for diversification. You have to consider the prospects for international stocks, small-cap stocks, bonds, commodities, real estate, and other investments as well. But when US large-cap equities do well, it’s relatively easy to achieve reasonable investment goals; when US large-cap equities do badly, it’s usually pretty hard for investment portfolios to even match inflation, much less beat it.

All of the above is based on historical averages. Having a plan that would have worked well in the past is no guarantee of success, but I think it’s rarely a good idea to adopt a plan that would have failed in the past, or that can only succeed if unprecedented events occur. Moreover, it’s not enough for a plan to succeed in the average historical case; it is prudent to consider if your finances could survive the bad historical outcomes.

Most of the 5-year periods in which S&P 500 investors lost to inflation, and all of the periods with the largest real losses, occurred as part of four events: the Great Depression, the Stagflation beginning in the late 1960s, the Internet Bubble and the Credit Bubble. Only the Internet Bubble was clearly a result of overvaluation. The Credit Bubble occurred at moderately high S&P 500 valuations, close to current levels. Stagflation occurred with valuations in the second and third quartile relative to history — that is, about average levels. The Great Depression started with very high valuations, but even investors who bought after prices fell suffered some terrible losses (the Great Depression points in the graph above include two periods, one from 1928 to 1930 and one from 1936 to 1937).

So let’s start by assuming we are not in any of those unusual periods. Just look at the blue diamonds for CAPEs between 26 and 30. The 5-year real returns range from 11% to 49%. If history is any guide, this is the most likely result of investing in stocks today. You can hope for a real return above 50% for the next five years, but you are hoping for something that has never happened before when you buy at CAPE above 26. It’s certainly not impossible that it will happen, but it would be foolish to count on it. And while pretty good total real returns of 20% to 50% seem achievable, returns between 0% and 20% also seem possible, even if there is no major stock market crash or other financial disaster.

Now let’s consider the special historical periods, all of which are bad. Are we approaching another Great Depression? The argument for it is that the financial problems revealed in 2007 and 2008 have been papered over, not solved. A sovereign default might take down financial institutions, or a financial institution crash might destroy government credit. Trade barriers could go up, unemployment could soar, and GDPs could collapse — with an extended period of severe global economic pain. I don’t think this is likely, but more to the point, I don’t think there’s much a retail investor can do about it. Stocks, bonds, commodities, real estate, and other assets are likely to lose most of their value. Gold might go up, but governments might take gold and other hard assets away. While people should consider this scenario in their planning, I don’t think it argues for any particular rearrangement of mutual fund allocations.

Are we in a bubble? I dont think we’re in a pure equity-market bubble because current stock prices can be justified by some economic assumptions. But it could be that quantitative easing and other central bank and government policies are keeping asset prices inflated, and that investors are paying up for stocks because they have been going up, and if things turn south, there will be a rapid deflation of prices. Call this a frothy stock market rather than a bubble.

I think this is more likely than a Great Depression, but I also think that we’re nowhere near the extremes of the Internet Bubble or the Credit Bubble. Given that investors made money over five years starting in some of the months of both bubbles, and only starting at the worst times did investors lose a lot, I don’t think a frothy stock market today is an investor’s worst nightmare. Yes, if you knew things were frothy, that is, if you knew CAPE would decline a lot from here, you wouldn’t buy stocks, but a moderate possibility of froth shouldn’t keep you out of the market. If CAPE increases, say to near 30, fear of froth becomes fear of bubble, and investors might want to reconsider this point.

Are we entering a period of inflation and weak government like the 1970s with high marginal tax rates, disordered public finances, growth of intrusive regulations, international tension, and distrust of institutions? That’s possible, too, and perhaps the scariest scenario, because the terrible damage to investor portfolios of that era was inflicted even though investors bought at reasonable or low valuations. Buying at a CAPE of 26 would have made things much worse.

The final thing to think about is, what if we get a scenario unlike any in history? I don’t think it’s useful for individual investors to consider lots of these in detail. There are too many possibilities, and too many unknowns in analyzing them. I think it’s broadly true that a diversified portfolio is your best defense. In almost any scenario there are at least some assets that do well. If we draw a scenario in which all assets do badly, your investment choices today won’t matter much.

In summary, I think equities bought at today’s levels most likely will give a small positive real return (0% to 20%) over the next five years, with some possibility of pretty good (20% to 50%) real returns. The stock market might do better than that (over 50%), but I know of no historical or economic argument that makes a very good outcome likely. There are downside risks (negative real returns), both known and unknown, but I don’t think they’re abnormally large, and I don’t think there’s much retail investors can do about most of them. Therefore I think the likely modest positive real returns are worth a moderate allocation to equity risk.

All of this assumes you can stick with the stock market for at least five years, even if it crashes. I’m pretty confident that there will be some painful drawdowns during the next five years, and if you plan to get out after one of them, you’re probably better off getting out now.

So we’re back to the usual dull advice. Save an adequate fraction of your income. Diversify broadly. Accept a level of risk commensurate with your expected return goals. Stay the course. Look at valuation, but not too closely, and don’t follow daily ups and downs of the market at all. Keep fees fair and taxes low. Hope for good returns, plan for mediocre ones, and prepare to survive terrible ones.

Disclaimer: The information set forth herein has been obtained or derived from sources believed by the author and AQR Capital Management, LLC (AQR) to be reliable. However, the author and AQR do not make any representation or warranty, express or implied, as to the information’s accuracy or completeness, nor does AQR recommend that the attached information serve as the basis of any investment decision. In addition, neither AQR nor the author assumes any duty to update forward looking statements.