But in reality, the whole idea of the risk premium is that it is uncertain. It’s the concept of chasing the two in the bush instead of the one bird in the hand. But, clearly, sometimes that risk doesn’t pay off; the historical, realised risk premium should fluctuate wildly and sometimes be negative even over long periods.
What is indisputable is that over the very long term – 100 years, say – equities have spectacularly outperformed bonds. Between 1900 and 2011, the UK was hit by the Great Depression, nearly bankrupted by two world wars, lost the Empire, and was then again struck by the recent recession; yet according to the Barclays Equity-Gilt Study focusing on that period, the equity markets still showed a realised inflation-adjusted risk reward of 300bps. This is equivalent over the period to a factor of 26. For the US (from 1926), the figure was 4.54%.
However, using simple historical data to estimate the equity risk premium has two serious drawbacks. The first is that it depends enormously on which time period one chooses. Even over long periods (10+ years), there is substantial variation. See below.
The reason for this substantial variation is the domination of a few extreme results within the equity return data. So five good years and one bad day can create a bad five years of returns. To put this in context, Javier Estrada finds that “Outliers have a massive impact on long-term performance. On average across all 15 markets [considered], missing the best 10 days resulted in portfolios 50.8% less valuable than a passive investment; and avoiding the worst 10 days resulted in portfolios 150.4% more valuable”.
The second problem is that using historical data means that any estimate of the equity risk premium would be highest just before a market crash, and lowest before a rally. If one were to use the estimate to make investment decisions, bad news would follow; and given how dependent returns are on single days, this could become very bad news. The investor would be underweight for all the good days and overweight for all the bad days, losing a lot of money as a result.
So it is unlikely that complicated models based on historical data could estimate the equity risk premium with more accuracy than one would get by simply using a fixed value. Either way, any estimate is unlikely to be a reliable indicator of future returns.
In the long term, equities seem likely to outperform bonds. As an investor, one may well feel they are worth the risk. But to any individual or fund depending on earning that premium, the question becomes this: “how reliant can you afford to be on an estimate that you expect to be highly uncertain?” Where a point estimate needs to be made for forecasting purposes, this argues for a more conservative estimate such that undue reliance is not placed on such an uncertain source of returns.
 Barclays Equity-Gilt Study, 2012, 57th edition, p6
 http://web.iese.edu/jestrada/PDF/Research/Refereed/BlackSwans.pdf; on average in this data set, ten days represent less than 0.1% of the days considered.