[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.

These use the 2018a random numbers. Based upon compound UK return differences over 15 years, between equities and 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.