he beginning share price for a security over a three-year period was $50. Subsequent year-end prices were $62, $58 and $64. The arithmetic average annual rate of return and the geometric average annual rate of return for this stock were:

Arithmetic average rate of return = 9.30%

geometric average annual rate of return = 8.58%

Explanation:

share price at the beginning = $50

time = 3 year

price at the end of year 1 =  $62

price at the end of year 2 = $58

price at the end of year 3 =  $64

Annual rate of return in year 1 = ($62 / $50 - 1) x 100 = 24%

Annual rate of return in year 2 = ($58 / $62 - 1) x 100 = -6.45%

Annual rate of return in year 3 = \($64 / $58 - 1) x 100  = 10.34%

Arithmetic average rate of return = sum of annual rate of return / 3

Arithmetic average rate of return =  (24% + -6.45% + 10.34%) / 3

Arithmetic average rate of return = 9.30%

geometric average annual rate of return = { (1 + r1) x (1 + r2) x (1 + r3) }^1/3 - 1

= (1.24) x (0.9355) x (1.1034)^1/3 - 1  =  8.58%

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