There has been much discussion in the past year(s) whether the Fed has inflated (the final) bubble. Sadly, most of it has been misguided. To get some "guided" analysis of what is easily the most important market topic of the day, we go to GMO's Jeremy Grantham and his latest quarterly letter covering just this: "Looking for Bubbles."

First the background:

What is a bubble? Seventeen years ago in 1997, when GMO was already fighting what was to become the biggest equity bubble in U.S. history, we realized that we needed to define bubbles. By mid-1997 the price earnings ratio on the S&P 500 was drawing level to the peaks of 1929 and 1965 – around 21 times earnings – and we had the difficult task of trying to persuade institutional investors that times were pretty dangerous. We wanted to prove that most bubbles had ended badly. In 1997, the data we had seemed to show that all bubbles, major bubbles anyway, had ended very badly: all 28 major bubbles we identified had eventually retreated all the way back to the original trend that had existed prior to each bubble, a very tough standard indeed.

Then, the bullish case, or in other words, what is the maximum the S&P can stretch further, before it all comes crashing down:

So now, to get to the nub, what about today? Well, statistically, Exhibit 3 reveals that we are far off the pace still on both of the two most reliable indicators of value: Tobin’s Q (price to replacement cost) and Shiller P/E (current price to the last 10 years of inflation-adjusted earnings). Both were only about a 1.4-sigma event at the end of March. (This is admittedly because the hurdle has been increased by the recent remarkable Greenspan bubbles of 2000 and a generally overpriced last 16 years.) To get to 2-sigma in our current congenitally overstimulated world would take a move in the S&P 500 to 2,250. And you can guess the next question we should look at: how likely is such a level this time? And this in turn brings me once again to take a look at the driving force behind the recent clutch of bubbles: the Greenspan Put, perhaps better described these days as the “Greenspan-Bernanke-Yellen Put,” because they have all three rowed the same boat so happily and enthusiastically for so many years.

... purist value managers may try to block out the siren call because they don’t wish to be tempted, and some may hear it and do nothing because the gains are never certain and the lack of prudence is painfully obvious in the end. Yet long-term value managers are outnumbered by momentum managers – always were and probably always will be – and momentum managers have no such qualms. Why this time, then, would they not play the game with even more enthusiasm, at least enough to drive the market to its 2-sigma level of 2,250 and perhaps a fair bit beyond? And although nothing is certain in the market, this is exactly what I  believe will happen.

But what if we are already well past the point of no return? Enter Hussman:

Out there in the wilds of the internet along with our free quarterly letter, which always feels like a long painful delivery, there is an equally free letter from John Hussman, who turns out to have the same work ethic as Alexey Stakhanov, that hero of the Soviet Union known for his massive and routine production over quota. Hussman, can you believe, produces a long and well-researched quarterly letter each week! Deplorable. Surely (he says enviously), he must be a workaholic and obviously unlike some of us less industrious types can have no life at all. But I will say this: he grinds some good data. He therefore makes a good representative of the analytical group, all value diehards who believe the market’s demise is imminent. And the data is comprehensive enough that I admit it worries me. Clearly he and the others may be right. Exhibit 7 reproduces – with his kind permission – his version of all of the value measures he deems important. They indicate an overpricing for the U.S. markets that ranges from 75% overpriced to 125% at the end of March. All of the measures have a history of being predictive – much more so than, say, Yellen’s reprehensible choice of current price as a multiple of next year’s estimated earnings. (Either she’s painfully ill-informed or, most implausibly, not too smart, in which case sooner or later we’re scr*w*d, or she knows this measure is a third-rate prediction of true value and is cynically using it to tout the market, in which case we’re doubly scr*w*d! But at least that latter reason would be an ideal proof of her buying into her predecessors’ Put, in case we had any doubt.)

But back to value and Hussman. Not surprisingly, GMO very much agrees with the spirit of this data, but our preferred measure for our 7-Year Forecast has the market slightly less overvalued at 65%. (Although, interestingly, at 2,250 – our 2-sigma target – it would be about 100% overpriced.) Our estimate allows for a very modest improvement in trend line profitability and an even more modest allowance for a slightly higher P/E as a response to probable lower equilibrium interest rates. Still our estimate of overpricing is pretty close to his.

Exhibit 8 shows an equally disturbing Hussman exhibit in which he has collated very bad things that happen to markets. His exhibit suggests that whenever this large collection of troublesome predictions line up like they have recently there has been a very serious and fairly immediate market decline. While I have no quarrel with the eventual outcome and recognize that possibly the bear market’s time may have come, particularly in light of recent market declines (April 13, 2014), I still think it’s less likely than my suggestion of a substantial and quite lengthy last hurrah.

Which brings us to the punchline: Grantham's "Best Guesses for the Next Two Years":

With the repeated caveat that prudent investors should invest exclusively or nearly exclusively on a multi-year value forecast, my guesses are:

1) That this year should continue to be difficult with the February 1 to October 1 period being just as likely to be down as up, perhaps a little more so.

2) But after October 1, the market is likely to be strong, especially through April and by then or in the following 18 months up to the next election (or, horrible possibility, even longer) will have rallied past 2,250, perhaps by a decent margin.

3) And then around the election or soon after, the market bubble will burst, as bubbles always do, and will revert to its trend value, around half of its peak or worse, depending on what new ammunition the Fed can dig up.

Conclusion and Summary

The bull market may come to an end any time, indeed as I write it may already have happened. It could be derailed by disappointing global growth, profits sagging as deficits are cut, a Russian miscalculation, or, perhaps most dangerous and likely, an extreme Chinese slowdown. But I believe it probably (i.e., over 50%) will not end for at least a year or two and probably not before it reaches a level in excess of 2,250 on the S&P 500. Prudent long-term value investors will of course treat all of the above as attempted entertainment (although I believe all statistically accurate) and be prepared once again to prove their discipline and man-hoods (people-hoods) by taking it on the chin.

I am not saying that this time is different (attention Edward Chancellor). I am sure it will end badly. But given this regime of the Federal Reserve and given the levels of excess at other market peaks, I think it would be different to end this bull market just yet