That GMO's Jeremy Grantham thinks U.S. stocks are approaching bubble territory and says the current bull market will "end badly" isn't at all surprising. Grantham is one of Wall Street's most notable and outspoken bears, and in recent years has warned about resource scarcity that could doom a lot more than your 401(k).

So what's most notable about the hedge fund manager's latest quarter letter, published in Barron's, is that Grantham predicts the current bull run "will not end for at least a year or two and probably not before it reaches a level in excess of 2250 on the S&P 500" (that's a 20% rise for the S&P 500 based on Friday's close).

Grantham offers a specific roadmap for how it's likely to occur:

• 1) This year should continue to be difficult with the Feb. 1 to Oct. 1 period being just as likely to be down as up, perhaps a little more so.

• 2) But after Oct. 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 2250, 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.

Another key element of Grantham's latest letter is his technical explanation of what a "market bubble" is, which is well worth reviewing given the current tendency of some pundits to declare every rising market to be one.

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Based on work he began in 1997 -- "when GMO was already fighting what was to become the biggest equity bubble in U.S. history" -- Grantham concludes that "a two-standard-deviation (or 2-sigma) event might be a useful boundary definition for a bubble." (In statistics, a large variation or deviation from an average is represented by the Greek letter sigma.)

Past market bubbles, including U.S. stocks in 2000, have reached or exceeded 2-sigma before imploding and Grantham notes U.S. housing in 2008 was a 3.5-sigma event, i.e. a bubble even among bubbles.

As for the current market, U.S. stocks are currently at a 1.4-sigma event as of March 31, based on what Grantham calls "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)."

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Thus, Grantham forecasts the current rally has more room to run, based on past bubble moves, the Presidential Cycle, the January Barometer (so goes January, so goes the year) and what he calls "the "Greenspan-Bernanke-Yellen Put," i.e. easy money will keep the market elevated until it reaches extreme levels.

To be clear, Grantham's letter is aimed not at short-term traders but at long-term value investors who "simply [have] no alternative to standing our ground and taking it on the chin when crazy markets get even crazier."

Indeed, if you heeded Grantham's warnings in 1997, you would've missed the most dramatic part of the 1990's bull run -- but you would also have been out of the market (or defensively positioned) when the bust occurred. It appears history may be repeating itself as Grantham has largely been leaning against the stock market in recent years while the S&P and Dow have hit a series of record highs and the Nasdaq climbed back above 4,000 for the first time since 2000.

So here's the rub: Are you really a long-term investor willing sit out the likely final "blow off" phase of the rally or a short-term trader who can't afford to miss it?

Aaron Task is the host of The Daily Ticker and Editor-in-Chief of Yahoo Finance. You can follow him on Twitter at @aarontask or email him at [email protected].