How easily global equities bounce back from May-June losses is in large part dependent on how much of a bargain shares have become for investors, and that depends on what measure you choose to determine value.

With prices lower and corporate earnings showing little immediate sign of slowing, valuations relative to forecast earnings (price-to-earnings, or P/E) have improved, and so correspondingly has the risk premium on offer to investors.

Based on those measures, major investors have kept faith with equities, retaining positive positions in their portfolios - with some adjustments into more defensive stocks - even as the value of their holdings has fallen.

So new research from investment bank Societe Generale suggesting that many equity markets are overvalued and heading for more falls could give some pause for thought.

SG says judging the value of a stock market by P/E can mislead, and that price-to-book gives a better reading.

The bad news for investors is that price-to-book - the share price relative to the value of corporate assets net of debt - currently paints a gloomier picture than P/E.

Societe Generale looked at performance on 33 equity markets since 1994 and concluded that when price-to-book is below 1.5, the average return in the following 12 months is 23 percent.

When it is above 2.5, however, the average return is minus 3 percent.

The average price-to-book across markets, even after the current setback, is currently 2.5. This does not bode well for equity returns over the coming months, the research noted.

VALUE SEARCH

That would be a blow to many investors. The latest asset allocation polls from Reuters show professional investors holding just under 60 percent of their assets in stocks.

Merrill Lynch's monthly survey of fund managers in June showed 54 percent of respondents were overweight in equities, compared with just 17 percent who were underweight. It also suggested investors were leaning toward raising exposure.

Valuation is a major factor in keeping investors bullish about stocks. German fund giant DWS, for example, reckons losses in Europe have helped make stocks attractive.

In its latest outlook, it says that low share valuations and stable growth in corporate profits are among the factors working in favor of the equity markets at the moment.

SG's research, however, suggests that optimism is misplaced.

Historical P/E ratios may be low not because the equity is cheap but because earnings are above their sustainable trend, but the assumption of continuing growth leads to over-optimistic forward P/E ratios, the market's favorite valuation tool, which are based on expected earnings.

Analysts generally do not forecast declines in earnings per share, Bijal Shah, Societe Generale's chief global strategist, told Reuters.

PRICEY MARKETS

Shah said U.S. markets had a price-to-book ratio of above 2.8, while Britain's was at 2.5, which in the past has preceded an average annual return of minus 3 percent.

Japan and the euro zone are slightly cheaper at 2.1, but still at the higher end of valuations. Within the euro zone Spain is at 3.0 and France at 2.2.

The German market looks relatively cheap, with an average price-to-book ratio of 1.8, as do the Hong Kong and Singapore markets, which are between 1.8 and 1.9.

But Societe Generale notes that price-to-book measures are not that useful for stock-picking investors, as an individual company's performance can be affected by its growth outlook, gearing, and individual risk premium. These are all smoothed out when averaging for a market.

Similarly, for the cross-market investors, it does not take into account alternatives. With global interest rates currently on the up, bonds and other fixed income investments are unlikely to attract much money away from stocks.

DWS, for example, cites a lack of investment alternatives as another reason for liking European stock.

Actual market performance, however, is suggesting that investors are at the very least struggling to re-embrace equities after the May-June fall.

In the month to date, Japan and Europe have made gains of less than half a percent, and the U.S. has shown losses.

The latest data from State Street, meanwhile, shows cross-border demand for equities by institutional investors weakening for emerging markets and at the lowest level this year for developed markets.

Japan Merrill Lynch Investment