So what is a good estimate of the U.S. equity risk premium going forward? Unfortunately, nobody can know for sure what investors expect in the future. If history is a guide, the expected U.S. equity risk premium could be 7.2 percent based upon estimates from 19002010. We also should be mindful that the average world equity risk premium was 6.9 percent over this same period. On the other hand, the more recent periods (19262017) suggest higher estimates of the U.S. equity risk premium, and earlier periods going back to 1802 suggest lower estimates. The standard error (SE) helps with the issue of how much confidence we can have in our historical average of 7.2 percent. If we assume that the distribution of returns is normal and that each years return is independent of all the others, we know there is a 95.4 percent probability that the true mean return is within two standard errors of the historical average. More specifically, the 95.4 percent confidence interval for the true equity risk premium is the historical average return (2 standard error). As we have seen from 1900 to 2010, the historical equity risk premium of U.S. stocks was 7.2 percent and the standard deviation was 19.8 percent. Therefore, 95.4 percent of the time, the true equity risk premium should be within 3.44 and 10.96 percent. In other words, we can be 95.4 percent confident that our estimate of the U.S. equity risk premium from historical data is in the range from 3.44 percent to 10.96 percent.

What was the arithmetic average annual return on large-company stocks from 1926 through 2017?

a. In nominal terms?

b. In real terms?