From 1836 to 2011, the average real rate of price change for gold is 1.1% per year, the standard deviation is 13.1%, and the covariance with consumption and GDP growth rates is small in magnitude and statistically insignificantly different from zero.From the conclusions:
. . . over the same period, the covariances of gold’s real rate of price change with consumption and GDP growth rates are small and statistically insignificantly different from zero. These negligible covariances imply that gold should carry a small risk premium; that is, gold’s expected real rate of return—which includes an unobserved dividend yield—should be close to the risk-free rate, estimated from real returns on Treasury Bills to be around 1.1%. Third, the volatility of the growth rate of real gold prices is small under the classical gold standard from 1880 to 1913 but high—comparable to that on stocks—in other periods, including 1975 to 2011.