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For 15 years we have attributed the following quote to late economist Paul Samuelson, though, admittedly, we can’t find a trace of it now. We remember him saying near the height of the technology bubble of 1999–2000, when stock prices were at astronomical highs, something along the lines of, “Market timing is an investing sin, and for once I recommend that you sin a little.” He meant — if he ever actually said it — that things were so obviously wrong at that time that even a lifelong proselytizer of buy-and-hold would recommend some judicious selling. In attempting to confirm this quote, one of us checked in with Vanguard Group founder Jack Bogle, who could not help us with attribution but admitted to lightening up on stocks himself somewhere near the high. (We can confirm that he did indeed make very prescient and public forecasts of lower than normal expected long-term stock returns at the time.)

If market timing is a sin, then there are times when even the saints can be tempted into sinning a little. We are going to argue that market timing isn’t really a sin except, as for so many things, if done to excess. But the results and logic behind the two simple strategies that govern so much of the investing world — basic value, or contrarian, investing and basic momentum, or trend-following, investing — imply that when it comes to market timing, one should indeed sin a little and do so as a matter of course, not just at extremes.

Today’s high stock prices, and for that matter low bond yields and concomitant low expected future returns (at least in our opinion), naturally bring the timing discussion back to the forefront, leading many investors to wonder if they should get out now. The answer to this question is almost certainly not. “Getting out now” is a very extreme action yet oddly often how people think about market timing (an approach to timing that we will soon label binary, immodest and asymmetric). If, on the other hand, investors wonder whether they should own somewhat fewer stocks and bonds than usual right now — well, that’s a much harder and much more interesting question. Overall, for those who think market timing is infeasible, we give hope. At the other extreme, some observers oversell market timing as easy and reliable. It ain’t.

Some of the strongest evidence seemingly in favor of timing the market comes from studies of long-term “predictability” of stock market returns using valuation measures (like the dividend yield or price-earnings ratio of the market). Perhaps the best-known approach uses Yale University professor Robert Shiller’s version of the P/E ratio for the entire S&P 500 (the cyclically adjusted price-earnings ratio, or CAPE). We’ve been using this method ourselves since the technology bubble. This measure compares the current market price with the average inflation-adjusted earnings per share over the past decade (so as to smooth excessive fluctuations in annual earnings). Currently, the ratio (about 25) shows that equities are very expensive compared with historical levels but not very close to record highs (the CAPE peaked in the 40s in early 2000). Expensive valuations can be bearish timing signals if we expect valuations to revert to their long-run averages. Furthermore, even without this expectation, buying at a higher CAPE is similar to simply buying at a lower yield where all-else-equal you make less even in the steady state.

Let’s look historically at what happened to returns over the next decade when starting from different Shiller P/Es (from now on, when we say P/E or Shiller P/E, we always mean Shiller’s CAPE). Incidentally, we focus on the CAPE for exposition, but many measures of price divided by fundamentals for the market give similar results to what we find in this article. In Exhibit 1 we bucket each ten-year period since 1900 by starting CAPE (looking at it every month) and see what happened, on average, from there.

We see a clear and strong relationship. Decades that started with low P/Es had, on average, subsequently higher average excess (over cash) returns, and decades that started with very high P/Es experienced the opposite: very low average excess returns by historical standards. Of course, like all averages, a lot of variation is obscured by only looking at this summary. There was quite a range around the average decadelong return in each of these buckets. Still, in general, even with such a range, averages count a lot, and other performance measures tell a similar story. For instance, worst cases (if you actually picked the worst of all possible decades among all those in the same bucket) get steadily worse after buying at higher prices. Best cases, while never very bad in any of these buckets, get steadily less good after you buy at higher prices.

So we’re done, right? Market timing is easy! Simply measure the CAPE and act as a contrarian, buying when the P/E is low and selling when it’s high.

Not so fast.

We contrast the lure of graphs like Exhibit 1, which make Shiller P/E look like a very useful contrarian predictor of future market returns, with the somewhat disappointing, at least to us, reality of actual contrarian market-timing performance in Exhibit 2. (If you’re too disappointed after looking at Exhibit 2, don’t despair, as we hope to resurrect things, at least somewhat, from there.) This graph compares the cumulative performance of a buy-and-hold strategy in U.S. large-cap stocks (an unchanging passive 100 percent in equities) with that of a contrarian market-timing strategy that invests varying amounts in equity markets (between 50 and 150 percent every month, moving into cash when bearish and borrowing cash when bullish, depending on where the CAPE is at the month’s start versus history) over the 1900–2014 period. (See the companion piece  Inside the Numbers  for the geeky details.) Basically, this system is straight value or contrarian: It owns more stocks when the CAPE is low versus history (as high as 150 percent), stays at precisely buy-and-hold (100 percent) when the CAPE is at its historical median and owns fewer stocks when the CAPE is high versus history (as low as 50 percent).

Exhibit 2 plots the cumulative performance (always versus risk-free cash) of buy-and-hold, this simple contrarian CAPE-based timing system and the difference between the two (the outperformance). Note these are gross returns before trading costs, but very low costs are not unrealistic over the past 30-plus years and going forward. We handicap the timing strategy by focusing on only the most basic signals in an effort to prevent data mining — and, we hope, balancing the neglected trading costs.

So how does contrarian timing do? It earns higher returns than buy-and-hold over the full period (about 80 basis points per year) but has merely treaded water since the 1950s. It has actually been somewhat less risky than buy-and-hold over this latter period, which is hard to see from the graph but certainly counts. We’ll return to risk later. Outperformance lines can sometimes look anemic just from being plotted on the same scale as total performance. Some of that is going on here, but it’s really pretty anemic any way you look at it.

While we think the full 100-plus years is the most relevant period, failing to add value since the 1950s is, we say with some understatement, a really long time. We think that perhaps few proponents of contrarian timing recognize that their favored strategy, if used every month as in Exhibit 2, with real-time data only looking backward, has not on net worked during most of our lifetimes. (Again, we get similar results if we make different but still reasonable choices, like looking back over different-length periods, trading less frequently, using a different mapping of current versus historical CAPEs to stock market positions and using other reasonable valuation measures. Other researchers, notably Goyal and Welch (2008) and Dimson, Marsh and Staunton (2013) have found similarly disappointing results for contrarian timing strategies.)

So we have a puzzle. Exhibit 1 suggests contrarian market timing using valuation is a very good idea, and many, including us, have shared results of this type. However, Exhibit 2 is, if not outright depressing, hardly a commercial for market timing. And yet both are just using Shiller P/Es and the S&P 500. What’s going on?

Well, there are a few reasons for the difference. We first delve into explaining this for just contrarian, CAPE-based stock market timing before moving on to somewhat redeem more-general market timing. This partial redemption will come from availing ourselves of the two most well-known systematic investing strategies (hint, contrarian investing is only one of them) and the two most well-known asset classes (hint, the stock market is just one of them).

We expect many investors are explicitly or implicitly puzzled by the seeming contradiction between the popularly cited long-term results (Exhibit 1) and their own intuition or evidence that such timing doesn’t help much (Exhibit 2), and we hope to help reconcile these. So why does Exhibit 2 disappoint versus Exhibit 1?

First, put bluntly, Exhibit 1 cheats while Exhibit 2 doesn’t. Hindsight is indeed 20-20. Too often we analyze historical opportunities with the benefit of hindsight, assuming that investors of the past knew more about the future than they could have. (Indeed, simply knowing about the Shiller P/E is a type of hindsight bias, as neither the CAPE nor even Shiller himself has been around this whole period.) For example, the CAPE of the U.S. equity market averaged 13.5 in the first half of the 20th century, 17.0 in the second half and 25.3 from 2000 to the present. Should we assume that our grandparents anticipated this richening trend? More important, such hindsight analysis implicitly assumes that investors knew the boundaries. Did investors know that when the CAPE was in the top or bottom quintile, it never soared beyond or fell below the highest and lowest observed historical values? It is this type of hindsight that we implicitly incorporate when we examine the average or quintile buckets of the whole 1900–2014 period, as in Exhibit 1. The noncheating approach, as employed in the trading rule behind Exhibit 2, involves making forecasts using only data that was available to investors at the time of investing. That is, if an investor was standing in January 1930 and trying to determine if the CAPE was high or low, that investor could only compare the current value with historical values from before 1930.

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