The need for a long-run perspective, and the dangers of focusing just on recent stock market history, are easily demonstrated. Over the last decade of the twentieth century, US equity investors more than trebled their initial stake. In real terms, they achieved a total return (capital gain plus reinvested dividends) of 14.2 per cent per annum.
During the last five years of the 1990s, US equities achieved high returns in every year, varying from a low of twenty- one per cent in 1996 to a high of thirty-six per cent in 1995. Many investors became convinced that high corporate growth rates could be extrapolated into the indefinite future. With steady growth rates, equity risk appeared lower. Simultaneously, there appeared to be a decline in the premium sought by investors to compensate for exposure to equity market risk. This drove stock prices onward and upward. Surveys suggested that, in consequence, many investors expected long-run stock market returns to continue at double-digit percentage rates of return.
Then the technology bubble burst. Growth projections had been unrealistic. High growth expectations were seen to be associated with high risk. Investors demanded a larger reward for equity market risk exposure. Stock prices fell in 2000 and then again in 2001. With markets having fallen, investors started to project lower returns for the future.

The figure hows how US equity returns compared with those in fifteen other countries and the world index. The black bars show annualised equity returns over 2000/01. In most countries, equities suffered negative returns, underperforming bonds everywhere except Ireland, and falling short of bill returns everywhere except Australia, Ireland, and South Africa.

Estimating the expected risk premium from the performance of equities relative to bills or bonds over this period would clearly be nonsense. Investors cannot have required or expected a negative return for assuming risk. Instead, this was simply a very disappointing period for equities.

But while the opening years of the twenty-first century (fortunately) do not provide a basis for generalising about future returns, looking back at the previous decade only confuses the picture.
Indeed, it would be equally misleading to estimate future risk premia from data for 1990 - 99. The light blue bars in Figure 1 show that over this period, equity returns (except in Japan and South Africa) were high. The 1990s was a golden age for stocks, and golden ages, by definition, recur infrequently.

To understand the risk premium we need to examine periods that are much longer than one or two years, or even a decade. This is because stock markets are volatile, with much variation in year-to-year returns. In order to make inferences we thus need long time series that incorporate the bad times as well as the good. The dark blue bars in Figure 1 provide an insight into the perspective that longer periods of history can bring. These show real equity returns over the 102-year period from 1900¡2001. Clearly, these 102-year returns are much less favourable than the returns during the 1990s, but equally, they contrast sharply with the disappointing returns over 2000/01.

Investors' judgements should thus be informed by the full extent of financial market history, and by looking not just at the United States, but at other countries as well.

Financial economists do tend to measure the equity risk premium over quite long periods. Standard practice, however, draws heavily on the United States, with most textbooks citing only the US experience. By far the most widely cited US source prior to the end of the technology bubble was Ibbotson Associates , whose equity premium history starts in 1926.
They estimated an annualised return on equities of 11.3 percent, and a risk-free return of 3.8 percent. This implied a premium relative of 7.5 per cent.

References to other countries are few and far between, but a few textbooks also cite UK evidence. Before the publication of the research that underpins this paper, the most widely cited sources for the United Kingdom were the studies published by Barclays Capital and CSFB , which both started in 1919, and who published equity and risk-free returns of 12.2 and 5.5 percent, implying an annualised risk premium of 6.7 percent.

In citing these estimates, financial economists are generally making the implicit assumption that, provided the data are of sufficient quality, the historical risk premium, measured over many decades will provide an unbiased estimate of the future premium. Yet the twentieth century proved to be a period of remarkable growth in the US economy, and it seems probable that the outcome exceeded the expectations held in 1926 by US investors.
Similar arguments apply to the United Kingdom, and the likely expectations of UK investors in 1919, but additionally, the UK evidence turned out to be based on a retrospectively constructed index whose composition, up to 1955, was tainted by survivor bias and narrow coverage.

In recent years, both practitioners and researchers have grown increasingly uneasy about these widely cited estimates, largely because they seem high. Apart from biases in index construction, the finger of suspicion has pointed mainly at success and survivorship bias.
One influential study by Jorion and Goetzmann , for example, asserted, "the high equity premium obtained for US (and, by implication, UK) equities appears to be the exception rather than the rule" .
It is possible that high US and UK premia are likely to be anomalous, and underlines the need for comparative international evidence. Long-run studies are always of US or UK premia. There were 36 active stock markets in 1900, so why do we only look at two? This is because many of the others don't have a 100-year history, for a variety of reasons.
The long-term average for equity risk premia as shown by a major study has the UK at 4.5 per cent and the US 5.6 per cent.

Whilst a great deal of work has gone into understanding risk premiums, the fact remains that it is a best guess based on

• anticipated market conditions
• anticipated trading conditions for particular companies
• the degree to which individuals making investment decisions see risk - are they risk takers or risk averse.

For the pessimistic use the mean value plus one standard error (the stand deviation divided by the square root of the number of samples, 102). That gives for the UK from the study of long term premia, 4.6 + 1.97. For the optimistic 4.6 - 1.97

Given the annual standard deviation in U.S. stock prices between 1928 and 2000 of 20%, the standard error associated with the risk premium estimate can be estimated as follows for different estimation periods is shown below..