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By mungofitch
October 26, 2009

Posts selected for this feature rarely stand alone. They are usually a part of an ongoing thread, and are out of context when presented here. The material should be read in that light. How are these posts selected? Click here to find out and nominate a post yourself!

A few posts ago... ...kelbon pointed out that my forecast for no returns for the S&P in the next 5-10 years was very much in contradiction of Mr Buffett's forecast. I started a new thread since I thought there might be folks who like me read things in threaded mode and would be interested in the issue but  would otherwise have missed it buried in an aging thread.

I mentioned--- I expect a real total return for the S&P to be slightly negative in the next 10 years as a central estimate based on valuation levels. which kelbon replied... For what it's worth, you're at odds with Buffett's expectations.

Well, to be sure, any time I disagree with Mr Buffett, the odds strongly favor my being wrong. But, FWIW, my position isn't just a gut feel.

Here's my line of reasoning.

The value in the US markets ultimately derives from corporate earnings, which vary over time but have a central trend which can be estimated. After you smooth it just enough to take out the squiggles caused by the business cycle, the real trend line rises only so much per year after inflation. As with all such things regarding value, you never know the exact level of the central trend today, but you can be very sure of the  approximate level. When there is an extreme, it's obvious. So far so good.

The level of valuation (overvaluation or undervaluation) of the market at any given time can be expressed succinctly as the earnings yield on the current price, using the current on-trend real earnings divided by the current real price. From 1871 to 2009 in the US, this has averaged 7.77%. Since 1940 it has averaged 7.49%. This latter is a reasonably good starting point, since it covers two full secular bull markets and two secular bear markets, while being concentrated in the modern era with good data.

So, what's the trend real earnings yield now? That's a bit tricky, since it is very contentious to try to state exactly what the earnings trend line value is right now. But, we can do the exercise backward, and see if it makes sense using reduction ad absurdum. Let's assume that the market is fairly valued today compared with history. If you take the current real price and multiply by the average trend-earnings yield since 1940, you get what the real trend earnings would have to be today **IF** the market were fairly valued at the moment, where "fairly" is defined here as "trend earnings yields is equal to its long run observed average since 1940".

Here's the picture you get.  If the market were fairly valued today, the trend line would have to pass through the orange spot. I have shown two plausible long run trendlines on the graph, one (in grey) based on a minimum-error constant increase in real earnings. This has the problem that things deviate from this trend for very long periods during secular cycles of good and bad earnings.

The other trend line fit (the green line, the one I use) is based on a  smoothing of the observed data with the latest section fit by eye. Other than the last few years, the green line is guaranteed perfect, because we have perfect foresight for most of the past. The smoothing method is a symmetric capped WMA, which is very similar in effect to a Hodrick-Prescott filter. But you can see by eye that it forms a pretty good central trend through most of the history (because it looks into the future as well as the past!). The most recent data  points are my own approximations, gradually falling from all-known down to 50%-known 50%-prediction at today's value. To be as generous as possible to the bulls who I think are wrong, I have chosen recent  values which err if anything a bit to the high side, to join them in  their optimism, so the conclusions below are the consequences of  giving the market a little bit of a benefit of the doubt.

In short, the higher the on-trend real earnings trend line is, the more undervalued the market is today. The lower the trend line, the more overvalued the market is today.

As you can see from the graph, there is no possible way that any plausible long run trend for real earnings can pass as high as the orange spot. Anyone arguing that today's market is undervalued has to explain how the long run sustainable trend real earnings line can pass above the orange point. Therefore, the broad US market is unquestionably overvalued right now. QED. [the orange spot's location might not be precisely right, but it is definitely in the right neighborhood]

What does that tell us? Just because the US market is overvalued doesn't mean that returns can't be positive in the next decade, but it certainly moves the central  expected value quite a lot. There is no other metric which even comes close to the predictive power of the method described here for time frames over five years. (this is similar to, but more sophisticated and accurate than the E10 method).

So, historically, what has happened starting from periods which were at the approximate level of overvaluation that we observe today? Well, if you accept that the green line is a plausible representation of the trend real earnings, then past periods with about the same ratio of then-current price to then-current trend real earnings can be observed. The average real total return in the subsequent decade starting from periods within plus or minus 5 percentile points from today's level of overvaluation was +1.59%/yr. This is a very low figure. Looking forward five years the index-only movement (no inflation adjustment and no dividends) has been an average of +0.07%/year. Bear in mind that this assumes the "green line" trend line is correct; it's quite possibly pretty high/optimistic, in which case future returns should be expected to be correspondingly lower.

So, ultimately I'd have to agree with Mr Buffett that the evidence suggests a probably higher S&P index in 5 or 10 years, but by such a small margin that one should not take comfort in it. The only way that the index is likely to be meaningfully higher is by the amount of inflation. Though in theory one never knows what this will be, a pretty good guess is "extremely low for a few years then probably either a little or a fair bit higher". As far as Berkshire's long-dated puts are concerned, inflation is the magic bullet to be hoped for. It's extremely unlikely that Berkshire will lose money on the puts, but that's principally because of the likely returns on the float. Absent that, I've estimated the odds of the puts expiring in the money at very roughly 1 in 3.

In case anybody is wondering, the TTM real earnings for the S&P were about $6.65. Obviously, this is way below trend, which is why we work so hard to find the trend level. The grey long-run constant-growth trend line suggests today's on-trend  real earnings should be $49.01, rising to $56.77 in ten years' time. If the market were valued at the average historical level at that time, the S&P would be at 758 in ten years plus whatever ten years of inflation comes out at. The "green line" history-plus-recent-approximation line suggests the  trend value should be $56.18 now, rising to $65.34 in ten years' time. If the market were valued at the average historical level at that time, the S&P would be at 872 in ten years plus whatever ten years of inflation comes out at.

And, the "orange spot"---today's real index price multiplied by the since-1940 average trend earnings yield implies that if the market were fairly valued today, the on-trend real earnings today would have to be $77.95. Taken together, bearing in mind their flaws, these figures suggest the broad US market might be 41-59% overvalued right now with the S&P at 1080.

�Here is another interesting graph which arises as a corollary of the reasoning above.  It shows the earnings yield since 1871, calculated as the earnings from  the "green line" trend fit above used as the real trend earnings level,  divided by the then-current real index level. When the line is high, the trend-earnings yield is high, meaning the market prices are low. The average values since 1871 and since 1940 are shown, along with today's point. It's pretty easy to believe we'll be seeing some points on that graph above the horizontal "average" line some time in the next few years. If so, this implies much higher trend earnings yields, implying much lower  multiples of on-trend earnings, meaning much lower market prices to come.

Bottom line: this is a really terrible time to enter a broad-US market position for the purposes of long term buy and hold. Better to sit on cash and wait for better prices for buyers yet to come. Of course, certain individual companies are great deals, but no one should consider buying individual companies unless they know how to  value individual companies with around this much rigor.

Note, all "real" prices in this post are corrected to December 2008. The historical prices, earnings, and inflation data are from Mr Shiller's web site, with the most recent few months from Pinnacle Data & Barron's.