Since then, the publication of slightly better economic data seems to have convinced investors that the worst of the crisis is over and the markets have regained (in local currency) around 20% (despite that recovery, most of the main indices remain however below their levels at the start of the year).

The recovery of the past few weeks could continue some time yet, especially given that the relatively low level of trading volumes seems to indicate that many investors have not participated in the upturn and may change strategy out of fear of missing out on the rise. However, it would be dangerous to get carried away by the renewed optimism and believe in a sustainable recovery in share prices.

From an economic point of view, despite the numerous recovery plans and the massive sums involved, there is still no sound foundation for sustainable organic growth (see my article 11 March). On the contrary, the deleveraging process in the private sector, which began in 2007, is likely to continue to weigh on economic growth for some time yet. Believing governments can sustainably offset this weakness by increasing public spending (at least without creating other dangerous imbalances) is rather unrealistic. From a financial point of view, there are many uncertainties hovering over the announced rescue plans.

In this environment, a sustainable recovery on the markets would only be possible if equities were strongly undervalued. Compared to the historical average, the stock markets are indeed currently no longer overvalued.
One of the most commonly-used ratios for equity valuations is the Shiller (1) P/E ratio, which divides the share price by the average profit of the last ten years. By taking an average of 10 years rather than only 12 months, the ratio allows profits to be smoothed out to avoid the distortions linked to the economic cycle (abnormally low profits during periods of recession and abnormally high profits in periods of strong growth). Based on the current level of the Standard&Poor's 500 (834), the Shiller P/E is around 14.5, slightly below the long-term average of 16. Analysis of the very long-term changes in this ratio (for which we have figures dating back to 1881) reveals 2 important things however:

1. Stocks rarely trade at the long-term average of 16. The P/E is either above 16 (overvalued stocks) or below (undervalued stocks).

2. Long periods of overvaluation are usually followed by long periods of undervaluation and vice versa.

The Shiller P/E shows that there have been 4 speculative bubbles on the American stock market: 1901, 1929, 1966 and 2000. At the peak of each bubble, the ratio reached or exceeded 25. The bursting of the first three bubbles resulted in the ratio falling below 8. It goes without saying that periods of sharp decline in this ratio are (very) bad for the stock markets. In the best case, the markets stagnate for a long period while waiting for a rise in profits - the denominator - to bring the ratio down again. This is what happened in the period 1966-1982.

The bursting of the fourth bubble, which was by far the most significant (in 2000, the Shiller P/E exceeded 40), has until now only pushed the ratio back to 14.5. One could argue that there is no absolute rule to say that a much overvalued market should automatically give way to a much undervalued market. After all, the decline in valuation multiples in the 1970s was also due to rising inflation and interest rates following the 2 oil crises.

There are a number of reasons nevertheless to explain why we think that share prices will become less expensive:

- Debt reduction in the private sector. As indicated above, the process of deleveraging (and the risk of over-regulation in many industries) will weigh on economic growth in the years to come, just as the process of increasing debt artificially inflated growth. And the share price of a company is equal to the discounted value of its future earnings. The lower the earnings growth (and the higher the volatility of that growth), the lower their present value;

- The valuation of equities is directly linked to the level of investors' risk aversion. The current crisis will lead to increased risk aversion. In his article published in November 2008 (2), Peter Bernstein (3) notes that for most of the period between 1870 and 1958, the dividend yield exceeded the 10-year government bond yield. There was a simple reason for this: as equities were more risky investments than government bonds, the return on equities would naturally have to be higher. This relationship was then inverted and between 1958 and 2008 dividend yields fell below long-dated government bond yields. The reason for this was that coupons on bonds were fixed while economic growth allowed dividends to increase over time. During the fourth quarter 2008, the relationship inverted again;

- The loss of confidence in equities as the best investment solution in the long term. A number of studies show that over a period of 10, 20 and even 40 years, equities have not offered adequate returns for the risks involved by underperforming less risky asset classes such as money-market investments and bonds. The irony is that this underperformance could lead many investors to shun equities whereas the underperformance is actually making the long-term potential for equities much more attractive than at the end of the 1990s when stock market's outperformance compared to other asset classes prompted a craze for equities.

- Demographic trends as the baby-boomers retire.

- The possibility that the current measures implemented to combat the crisis will result in a resurgence in inflation.

Based on currently used earnings in the calculation of this ratio, a Shiller P/E of 8 (the highest previous trough after a bubble) would give a Standard&Poor's level of 460, or 45% under the current level (834). As indicated above, the Shiller P/E could diminish through a fall in the numerator (the share price) and/or an increase in the denominator (increased earnings). We could thus also imagine a scenario in which the market stagnates for 10 years at the current level, while earnings increase at around 6% annually.

The scenarios described in the previous paragraph may seem over-pessimistic, especially when we consider that the markets have already lost more than 50% since their peak. The example of Japan, where some 20 years after the bursting of the bubble the Nikkei index is close to 80% below its December 1989 level, should provide food for thought on the wisdom of a passive investment in equities in the current environment however.

In sum, I think that the current recovery on the markets should be used to reduce exposure to equities. There is currently no sound basis for a sustainable recovery in growth. In the absence of this, it seems premature to conclude that the markets bottomed out in mid-March.

(1) Robert Shiller serves as Professor of Economics at Yale University. He is also the founder and Chief economist of the investment management firm MacroMarkets CCC. He is the author of the bestselling book 'Irrational Exuberance'.

(2) Peter Bernstein: Two little-noted features of the markets and the economy

(3) At 89 years old, Peter Bernstein is President of an investment advisory firm and one of the most respected analysts in the United States. He is author of a number of books.