Talk to the City Monetary Group.

I am expecting something of a revolution, over the next few years, in the assumptions that are made about the returns on equity investment. The results of this will, I assume, have a major impact on share prices. They are currently extremely over-priced and this has always been followed, in the past, by a period of marked under-pricing. A revolution in pension fund policy has a high chance of being the key transmission mechanism this time around.

It has been the habit of pension consultants to estimate the required rate of pension fund contributions by reference to the returns they expect on equity investment. There are, as I see it, two problems with this. First they don't need to and shouldn't do it and secondly they have done it almost unbelievably badly.

Unless the consultants' reports that I have encountered are all exceptional, the typical approach of pensions' consultants has been to misuse the Dividend Discount Model, by assuming that dividends per share grow in line with GDP. It follows that the expected return on equities is then, more or less, the sum of the current dividend yield plus the assumed growth of GDP.

There is absolutely no justification whatever for doing this, as even the smallest acquaintance with history will show. Over the past 100 years UK dividends per share have grown at 0.4% p.a. and US ones at 0.6% p.a. (The US divergence is illustrated in Chart 1.)

The way that dividends have grown more slowly than GDP is not just a feature of the UK and US markets but is, as Table 1 shows, general.

It is also a myth to believe that the failure of dividends to grow in line with GDP is the result of a change in policy whereby buy-backs have replaced dividends as the preferred way of distributing returns to shareholders. This can be seen in Chart 2, which shows "cash flow" dividends, which are the total cash paid out to shareholders including money from buy-backs and takeovers, net of new issues.

The fact that equity returns have been badly forecast does not mean that the job is impossible. A rational approach to forecasting equity returns is possible, provided that three basic points are understood:-

• Equities appear to give a stable long-term real return of around 5.5 to 6.5%, before expenses.

• Values are mean reverting, so that real returns exhibit negative serial correlation. It is thus incorrect to assume that this rate of 5.5 to 6.5% will be the return on equities bought today. Even over the very long-term the current value of the stock market will affect the return.

• The volatility of returns is high, even over long periods.

If these points were understood, the current forecasts being made for equity returns would be very low indeed and companies with large pension deficits would be downgraded by credit agencies far more fiercely than is currently the case.

Chart 3 shows one way of illustrating the fact that equity returns exhibit negative serial correlation. If they did not, their long-term volatility would be determined by their short-term volatility. It isn't. Equity investment is much less risky than it would be if returns followed a random walk.

An element of predictability is the counterpart of this comparative safety, as both points arise from the mean reversion. If returns followed a random walk, then the most probable return in the future would simply be the past long-term return. As it is, the most probable return is a function of both the long-term return and the extent to which medium-term returns have diverged from the long-term: in other words, the extent to which shares are currently over- or under-valued.

The high probability of poor equity returns in the future is illustrated by Chart 4. Even today, after the market is 40% or so off its peak, the returns for investors who have owned stock for the previous 10 to 30 years, have been way above average.

There are two fundamental ways in which the value of equities can be approached based on two basic points about them.

• Equities are financial assets. Their value must therefore represent the present, i.e. discounted, value of all future economic benefits that their owners will receive.

• Equities represent a title to the ownership of real assets. As long as the economy is reasonably competitive the value of these assets cannot for long deviate from the cost of their production.

If we assume that the stability of real returns shown in the past will continue, then we know that the long-term P/E will remain around its average. Provided we adjust current profits to their cyclical level using, for example, Professor Shiller's approach of averaging 10 year data, we can then use P/Es to value the stock market.

The fact that equities are financial assets thus leads to the cyclically adjusted P/E; while the "q" ratio of course follows from the fact that shares represent real assets.

These possible approaches can then be tested. The resulting values must be mean reverting and the reversion must be "Granger Caused" by changes in share prices rather than by changes in net worth at replacement cost or earnings. Both q and the cyclically adjusted P/E meet these tests. Valid measures must also of course produce consistent answers. Chart 5 shows they do and that the US market today is more than 60% over-valued.

Armed with this information, the most likely returns in the future can be calculated. For example a market which is over-valued by 60% and has a long-term real return of 6.5% will give an expected future return of around 4%, before expenses, if you have an infinite time horizon and will most likely produce a negative real return over the next 7 years.

The same approach to the UK stock market produces similar answers. The data are not so good, so there is more doubt about the answer, but they suggest that the London stock market is at least 40% over-valued. Again we get consistent answers by either using the cyclically adjusted P/E or q, as shown in Chart 6.

The volatility of markets is such that the actual result is likely to differ quite a lot, even over 7 years, from the most probable return. But the chances of doing even worse are equal to those of doing better.

Investing in an over-valued stock market has many similarities with playing roulette. The chances of making money in the short-term are not far from evens, but the longer you play, the more certain you are to do badly.

One difference is that when roulette analysts correctly forecast a spin of the wheel, they are not subsequently applauded for their judgment.

The prospect of poor returns is not the only or even yet the main reason why fashion seems to be turning against holding equities in pension funds. Changes in tax and accountancy are also having their impact.

Sponsoring companies must see that promised pensions are paid and these promises do not vary with the return achieved by the pension fund. Investing in equities is thus a form of gearing, but it's a most inefficient one in terms of tax. If companies invested in debt assets in their pension funds, they would reduce their leverage. They could replace it by putting the debt on their balance sheet. The net effect, shown in Table 2, would have great tax benefits.

The tax benefit is not the only difference. The systematic risk of having pension funds invest in equities is more or less the same as having the pension funds invest in debt assets while sponsoring companies leverage their balance sheets. Fund managers, who have diversified portfolios, should thus welcome the change. Companies' management, faced with increases in specific risk, may feel differently. It seems to me, however, that they are already at least adequately rewarded.

Another important change is likely to be in accounting. There is growing recognition that companies take much or all of the equity risk that arises from having a defined benefits pension scheme. As the results of such risk-taking are shown annually in company results, the appetite for it will sicken.

As I know from personal experience, the assumption that equities will give better returns than debt has led some pension consultants to require lower contributions to funds that run the highest risks. When the FTSE 100 was at 6,000 I insisted that the company of which I was then Chairman should recommend to the Trustees of its Pension Fund that they sold all the shares in the portfolio. We eventually got out at 5,400 rather than 6,000 because, according to the company secretary, the pension consultants threatened to require an increase in the rate of funding "to compensate for the lower returns than would come from being out of equities."

This type of lunacy will, I feel sure, have fewer adherents as accountancy rules improve.

If markets were fairly valued it would be reasonable to expect equities to give good returns. It is equally reasonable to assume that companies will, in the operation of their own businesses, be rewarded for taking risk. It is not, however, sensible to book the assumed profits from risk-taking either in companies or pension funds before they have been earned.

Accounting rules should change and I think a change is likely. In time, the same principles will apply to returns from risk taken off balance sheet, as are currently applied to those taken on it.

At the moment, CEOs are encouraged to take risks with pension fund investment because the assumed benefits of higher returns come as lower costs today. In addition, they can reasonably hope that if the benefits do not arise, then it will be their successors who have to deal with the situation.