[discount_rates_problem] [long_term] [riskpremia_likelihood]

As pointed out by Shiller ("Irrational Exuberance", 2000), equity risk premia won't always be positive. However, that is only a straw man; nobody actually claims that.

The figures below use the 2018a random numbers used later. Based upon compound UK return differences over 15 years, between equities v long conventional gilts, the risk premium would be negative 28.4% of the time.

Of the 71.6% positive cases, the risk premium (% pa) would be higher than 1% 66.6% of the time, higher than 2% 61.5% of the time and higher than 3% 56.1% of the time. These seem pretty good odds.