Stock market returns over the next 10 years or so are set to be very poor.

The stock market resembles roulette in several ways. In both cases the accuracy of sensible forecasts rises over time. The longer you play roulette the more certain you are of losing. Over time forecasts of stock market returns also become more reliable. If this were not in each case largely ignored, no one would play roulette and share prices today would be much lower.

After sustained periods of high real returns, the chances of poor equity returns become very high. As Chart 1 shows, over the past 10 to 30 years returns have been persistently above average in both the US and UK markets. As a result we know, without certainty but with a high degree of probability, that returns over the next 10 years or so will be very poor.

We can show that markets' returns are not random by looking at their volatility. As Chart 2 shows, this falls over time, by more than time alone would justify. (If returns could not be predicted, the green line would not fall over time as it does, but remain flat, crossing the Chart at 1 on the right-hand scale.) I have found that this is not just true for the US, but for all the other markets where I have tested the data - France, Germany, Japan and the UK.

Just how bad the returns are likely to be is of course uncertain; we simply know that they are likely to be poor. Investors can also, like roulette players, assume that they will win in the short-term, even though the longer-term returns will be bad. They can prefer their unreliable opinions about the short-term to the reliable information about the medium-term. Short-term opinions are bound to be unreliable, as the chances of losing are almost 50/50. Of course, a series of near but just above 50/50 chances becomes a high probability over time.

Playing roulette or investing in the stock market today are each financially irrational. The only rational reasons for doing so are to have fun or because you can thereby benefit from the irrationality of others.

Fund managers, of course, come into the second category, but pension consultants don't appear to do so, and it therefore seems odd that both in the US and the UK pension funds are heavily invested in equities. The standard justification for this is that equity returns will invariably be higher than if the funds were invested in cash or bonds. While this could happen, the evidence is clear that it is not a rational expectation today. It is therefore interesting to consider why the view has been so widely held and what the likely consequences are.

The evidence that stock market returns are not random seems to be little understood, or at least seldom used. This may reflect the training of those who make forecasts of equity returns, or simply the fact that it would render them extremely unpopular with their clients if they did so.

I have encountered two different and equally invalid approaches to forecasting future returns. One is to assume that dividends per share rise in line with GDP and the other is to assume that returns from any level of the stock market will equal the long-term average.

The assumption that dividends per share will rise in line with GDP is held in the teeth of hard evidence to the contrary and in the absence of any theoretical reason why they should. Over the past 100 years, the real dividends per share have risen in the US by 0.6% p.a. and in the UK by 0.4% p.a., which in each case is far less than GDP.

Another approach assumes that equities will give high returns because they have done so over the very long-term. This would only be justified if returns followed a random walk - an idea which is, in academia at least, more than 30 years out of date.

Bad forecasts are very dangerous, because the power of compound interest is so strong. If, for example, a portfolio fails to grow in value while the liabilities that it is designed to match grow at 7% p.a., there will after 5 years be a shortfall equivalent to 40% of the initial value. As many funds start with deficits and returns could easily be negative, the potential problem for pension funds is far worse than the current estimated level of deficits suggests.

Stock markets today are thus much more risky than they have been in the past. Expectations of equity returns are irrationally high. If, as must be probable, they fail to meet these expectations, pension deficits will balloon and the value of companies will fall in a vicious self-reinforcing circle. When this occurs investors, including pension funds, will probably panic. When markets start to look bad investors are usually advised not to panic.

They would be better advised to panic now rather than later.