The data in the accompanying table represent the total rates of return (in perce

Question

The data in the accompanying table represent the total rates of return (in percentages) for three stock exchanges over the four-year period from 2009 to 2012. Calculate the geometric mean rate of return for each of the three stock exchanges a. Compute the geometric mean rate of return per year for the stock indices from 2009 through 2012. For stock exchange A, the geometric mean rate of return for the four-year period 2009.2012 was 10.15 %. For stock exchange B, the geometric mean rate of return for the four-year period 2009-2012 was 17.38 %. b. What conclusions can you reach concerning the geometric mean rates of return per year of the three market indices? A. Stock exchange B had a higher return than exchange O and a much higher return than exchange A.

Explanation / Answer

Geometric mean = (product of numbers)1/n, where n is the number of observations

Geometric mean of A = ((1+0.0716)x(1+0.0522)x(1+0.1)x(1+0.1869))1/4 = 1.1015

So, GM of A = 10.15%

Geometric meanof B,

Here, since 0 is involved, we shall calculate the geometric mean of corresponding decimal value

So, GM of B = (1.1342x1x1.1154x1.2326)1/4 = 1.1175

So,GM can be written as 11.75%

C) GM of C = ((1.1609)x(1-0.0242)x(1.1657)x(1.4376))1/4

= 1.1738

That is, 17.38%

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