It's a special case of the AM-GM inequality, assuming that market returns follow a lognormal distribution.
Consider the simple example of a stock that has a 50% probability of rising and falling 10% every period.
Its arithmetic average is obviously 0: (50% * +10%) + (50% * -10%) = 0
Its geometric average is (1+10%)^0.5*(1-10%)^0.5 -1 = -0.5%
Or a more extreme example the other way. A stock that doubles and halves with equal probability. It's geometric average is obviously 0. In the long-run, there's a doubling for every halving, and vice versa. But the arithmetic average is (50% * +100%) + (50% * -50%) = +25%.
For the full continuous lognormal distribution rather than my discrete examples above, the half variance formula above is derived from calculating its first moment.