History suggests the misery suffered by stock investors this summer should end soon, even if relying on precedent seems risky in this year of surprises.

Based purely on averages, the fourth quarter of any year tends to be far better for equities than the third, the one in which investors are now mired.

Over the past 40 years, MSCI's world index of developed stocks <.MIWO00000PUS> has gained an average of 3.7 percent in the fourth quarter compared with a loss of 0.2 percent in the third.

That might be some consolation for investors who have seen the index fall around 10 percent since the start of July.

Given that a number of analysts reckon that this summer's tumble has made stocks a bargain -- the price-to-forward- earnings ratio for the index is 11.7 versus a 22-year average of 16.4 -- some may also feel that the time has come to buy.

Falls, indeed, have been steep enough on various stock indexes that moves need to be made reasonably soon to make sure that the year as a whole is not a loss.

But even with returns on many traditional safe-haven assets continuing to shrink, investors might want to wait a while longer before jumping into shares, partly because the global economic climate is so fragile but also because historical precedent says they should.

Although the final third of the year, beginning in a fortnight, is on average better than the second, since 1971 the MSCI index has fallen an average of 0.7 percent in September -- the worst reading for any month.

The reason that the end of the year numbers look better than the rest is in large part down to December -- the Santa Claus rally. It is the best month for stocks, with average gains of 2.2 percent over the 40 years.

Only April comes close with 2 percent. This year, the MSCI index rose around 4 percent in April.

RALLY NOW ...

So how does all this number-crunching bode for stock investors in the months to come?

These are averages, which means that they level out some pretty major events.

In the fourth quarter of 2008, rather than rise the average 3.7 percent, the index crashed 22 percent when the collapse of Lehman Brothers accelerated a market rout that lasted well into the new year.

This year it would not take too much for equities to get back into the black by the end of December.

For all the volatility, developed market stocks still have four and a half months to gain less than 7 percent for the year to be a wash. A couple of 4 percent months like April and it is a gain.

Some clearly see that as do-able.

Russell Investments cut its end-year target for the U.S. S&P 500 <.SPX> index this week to 1300 from a previous 1372.

But from Wednesday's close that would still imply a 9 percent rise and a roughly 3.5 percent gain for the year -- which with dividends added would not be stunning but would probably do for investors who have been worried about sinking into an abyss.

Russell sees the gain coming from investors looking for a relatively safe haven in U.S. assets and from good company performances.

Corporations are doing great. In the U.S. they are doing very well, Stephen Wood, Russell's chief market strategist, said from New York.

Similarly, Bank of America-Merrill Lynch reckons investor activity is now giving a buy signal.

This is based its monthly fund manager survey, which showed recession fears jumping with corporate profit expectations and equity allocations collapsing.

Specifically, the cash holdings held by participants in the survey hit the low levels the bank has noted in the past are more often than not followed by gains.

Equities normally rally 6 percent in the 4 weeks that follow such a trigger, the bank said.

...OR LATER?

The extent to which investors take advantage of such a situation, however, will also depend on how strongly the headwinds that have been facing them continue to blow.

Japan's economy is bouncing back from the earthquake and tsunami at a faster pace than predicted.

But the U.S. economy remains in the doldrums, albeit with better than expected industrial production in July, and the euro zone debt crisis shows no signs of easing.

So the historical patterns may not repeat. But they are there for guidance, regardless.

(Additional reporting and graphics by Scott Barber. Reporting by Jeremy Gaunt; Editing by John Stonestreet)

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