October is traditionally a bad time for stockmarkets. The crashes of 1929 and 1987 both happened in that month. This year could be different, says The Economist. In the four days to October 15th, many of the world’s main stockmarkets saw their biggest four-day gains, in percentage terms, in over a decade. America’s Dow Jones Industrial Average rose by 13%, Germany’s DAX by 17%.

Worries about profits had helped to drive shares to their recent lows. So desperate have investors been for good news that sentiment seems to have been helped by better-than-expected results in the third quarter from Yahoo!, hardly the workhorse of the American economy, and Citigroup, even though tussles with regulators mean an uncertain future for the bank. Those results may have helped the Dow up by 5% on October 15th alone. Then dismaying profit figures from Motorola, Intel and J.P. Morgan Chase dampened spirits once again. Not, however, before investors had begun to wonder if the long bear market might at last be over.

A crucial question, for it is often in the first few months after a bear market ends that the most money is made. America’s S&P 500 index took only six months to rise by 40% from its low in late 1974, and three months from its trough in early 1982. London share prices doubled in only two months after the bear market ended in early 1975. Some investors fancy themselves to be on the cusp of similar gains. Abby Joseph Cohen, Goldman Sachs’s chief equity strategist, predicts that the S&P 500 will rise, over the next year, by almost 50% from its low.

One popular argument for why the bear market may be over is that, by last week, the S&P 500 had fallen by almost 50% from its peak, a slightly bigger decline than during the bear market of 1973-74—indeed, the biggest since the Depression of the 1930s. The end of 1974 turned out to be an excellent time to buy shares (see chart). Moreover, the argument goes, global economic conditions are now healthier than in the 1970s, when economies were in the grip of stagflation. If share prices recovered strongly then, they can surely do so again now.

Remember, however, that the 1970s saw double-digit inflation. Measured in real terms, share prices have fallen by less from their peak this time. Low inflation implies that prices may have to fall by more in absolute terms to return to fair value. Adjusted for the rise in consumer prices, the rebound in share prices in the 1970s was also a lot less impressive. After an initial bounce in 1975, share prices stagnated. In real terms, the S&P 500 did not regain its level of January 1973 until as late as 1987.

A second argument to support a recovery in share prices is that they are now close to fair value. As always, it depends which measure you pick. The S&P 500 stands at just under 30 times historical reported profits. This is down from over 40 at the peak, but well above the 50-year average of 15. Still, this exaggerates the overvaluation, since profits will presumably recover from today’s depressed levels.

To correct for this distortion, Eric Lonergan at Cazenove calculates a cyclically adjusted price/earnings (p/e) ratio, using an estimate of trend profits. At its low point last week, this p/e ratio had fallen to 17, the average during the pre-bubble years of 1990-95. Yet in previous bear markets prices have undershot: in both 1974 and 1982 the p/e ratio dipped below 8. So American shares may yet have further to fall. Using the same measure, Lonergan finds that British shares are cheap, with a p/e of 12; the rest of Europe has a ratio of 14.

Relative to bonds, on the other hand, American shares now look cheap. The dividend yield from shares is historically high, compared with government-bond yields. Yet this is partly because bond yields have tumbled on fears of sluggish growth and deflation. If these fears prove right, future profits will be severely dented. Even without deflation, analysts’ average forecast of 18% growth in American corporate profits over the next year seems unrealistic, given that the growth in nominal GDP is unlikely to be more than 4-5%.