Serious Money:The dark days of January are over, not just for the average human being, but also for distressed investors who endured one of the worst new-year hangovers in recorded history, writes Charlie Fell.

The trauma reached Washington DC and spurred officialdom into action. The Federal Reserve responded with an unprecedented 125 basis point reduction in official rates in just eight days, while the Bush administration announced a $150 billion fiscal stimulus programme.

Stock prices responded positively, albeit in a muted fashion, and the bulls returned and declared the aggressive action would return stocks to their upward trajectory and investors should exploit the buying opportunity as stocks have rarely been cheaper.

Of course, such advice should be taken with a pinch of salt as the so-called experts herald from the same constituency that walked you and your money blindly into the current turmoil.

The notion that stocks are cheap is built on quicksand and the turbulence is far from over.

The blue-sky optimists argue that price/earnings multiples have dropped to historically attractive levels.

However, the historical comparisons are null and void as they typically span a period of no more than 20 years. The limited sample is not statistically significant and artificially inflates the average price multiples used for comparison as the data set includes the bubble-era valuations of the late-90s.

It is hardly surprising stocks look cheap when value is assessed relative to the most expensive valuations in US stock market history and using such faulty analysis is unlikely to lead to long-term investment success.

The foolish talk does not end there as the valuation errors are compounded by comparing price multiples on estimated one-year forward earnings to historical averages computed on 12-month trailing earnings.

Once again stocks appear to be trading at attractive levels with a price multiple of less than 14 times forward earnings versus the historical average multiple based on trailing earnings of 17 times.

However, an historic valuation multiple based on realised one-year forward earnings reveals that stocks are not cheap after all trading only slightly below the average price/earnings ratio of 14 times.

Intelligent investors will note that the forward multiples used by the investment community's elite are based on earnings numbers that routinely overestimate the eventual reality by roughly 10 per cent in normal times and the error grows to as much as 30 per cent during economic slowdowns and recessions.

The consensus still calls for double-digit growth in 2008 when a double-digit decline looks far more reasonable. This puts the market on 18 times, which can hardly be described as cheap. Although it is true that price multiples often look high on recessionary earnings, it is worth noting that stocks traded on less than 15 times' realised one-year forward earnings at the end of 1989 just months before an economic recession struck.

It is clear that stocks are not cheap versus their own history but the blue-sky merchants are not done yet and out of their toolbox springs the so-called Fed model, which concludes that stocks have rarely looked cheaper relative to long-term treasury bonds.

US treasury bonds currently offer a yield of less than 4 per cent, while the inverse of the price/earnings multiple or earnings yield of stocks is 6½ per cent. The additional yield relative to treasuries looks compelling but the model's usefulness as a valuation tool is undermined by the fact that it lacks any theoretical underpinning and its performance record is invalidated by historical data.

Use of the Fed model is theoretically invalid as investors are erroneously comparing a real variable with a nominal one.

Stocks are a claim on real assets and the cash flows thereof should appreciate with inflation, while bonds are unambiguously a claim on nominal cash flows. Inflation clearly affects bond yields but it should not affect earnings yields as a change in the discount rate should be offset by an equal change in the growth rate of dividends.

Even if the comparison was theoretically valid the model requires some implausible assumptions but the most damning case against its use is the evidence that it simply doesn't work in practice.

Successful long-term investment requires skill and luck in equal abundance. The use of faulty analysis and "tools for fools" implies that skill is notably absent among the blue-sky optimists. Those that have entrusted their money must believe that the so-called experts are incredibly lucky.

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