One of the most common tenets of investing holds that the asset with the highest expected return over the long run is virtually certain to provide superior performance. Thus investors are willing to bear the greater short-term risks associated with equities as compared with bonds, say, because they know the equities will eventually outperform the bonds.

But risk doesn’t disappear over time. According to standard analytical models, an equity portfolio is virtually certain to outperform a fixed income portfolio over a long enough period. But 10, or even 30, years may not be “long enough.”

A simple model using standard assumptions about asset volatilities and risk premiums, for example, shows that a stock portfolio has a 32 per cent chance of underperforming a bond portfolio over a 10-year horizon. Even after 30 years, there remains a substantial 21 per cent probability that stocks will fall short of bonds.