The compounded rate of return is always higher than the sum, because you earn interest on interest. The annualized rate of return is lower than the average rate of return, again because you earn interest on the interest. For example, an investment of $100 that turns into an investment of $200 in 2 years has a total holding rate of return of 100%—which is an average rate of return of 100%/2 = 50% and an annualized rate of return of

√

(1 + 100%) − 1 ≈ 41.42%. Investing $100 at 41% per annum would yield $200, which is higher than 50% per annum.