2. The geometric average rate of return or compound interest rate of return rG is the n-th root of all income products minus 1 per year. The mathematical expression is rg = [(1+r1) (1+R2) ... (1+rn)] Legal notice-1. An asset with a geometric average rate of return rG will accumulate (1+rG)n times of initial investment after n years. The geometric average rate of return is about equal to the arithmetic average rate of return minus half of the variance σ2 of last year's rate of return, that is, rG≈rA- σ2.
Investment use method:
Only in the long run can investors expect geometric average returns. The geometric average rate of return is always less than the arithmetic average rate of return, unless the annual rate of return is exactly the same. This difference reflects the fluctuation of annual rate of return.
Use a simple example to illustrate the difference. If a portfolio falls by 50% in the first year and then doubles (rises to the original level) in the second year, the "buy and hold" investor will return to his starting point with a total return of 0. According to the previous definition, the compound interest rate or geometric interest rate is (1–0.5) (1+1)-1,which accurately measures that the total yield in the past two years is zero.
The arithmetic average annual interest rate is (-50%+ 100%)/2 = 25%. For two years, by successfully grasping the market opportunity, the arithmetic average rate of return can gradually approach the compound interest rate or the total rate of return. Especially in the second year, you can increase your investment, and then you can expect the stock price to rebound. However, if the stock market falls again in the second year, this strategy is unsuccessful, resulting in its total income being lower than that of "buy and hold" investors.