Question

The annual returns on the stock of a firm during the last four years are provided below.

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                                   Year Return

                                    ___________________________________

                                    2016               –0.10 (or –10%)
                                    2017                0.10 (or 10%)
                                    2018                0.15 (or 15%)
                                    2019                0.25 (or 25%)

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a) Find the holding period return of the stock over the four-year period.
b) Compute the arithmetic average return of the stock over the four-year period.
c) Calculate the geometric average return of the stock over the four-year period.
d) Calculate the variance and standard deviation of the returns during this period. Use the arithmetic average return in (b) for your calculations in (d).  Use at least 5 decimal places for the variance computation to avoid rounding errors.

Answer 1

a) Holding period return = Ending value / beginning value - 1 = 1.25 / 0.9 - 1 = 38.89%

b) Arithmetic avergae return = sum of returns / no of returns = ( -10 + 10+ 15+25) / 4 = 10%

c) Geometric average return = [ ( 1 - 0.1) *( 1 +0.1) * ( 1+0.15) * (1 + 0.25) ] ^ 1/4 - 1

=1.0922 - 1 = 9.22%

d)

Returns (x)	x - mean of x	( x- mean of x )^2
-10	-20	400
10	0	0
15	5	25
25	15	225
40		650

Variance = sum of ( x- mean of x)^2 / ( n- 1) considering the data to be sample

= 650 / 3 = 216.66667 %^2

standard deviation = variance ^0.50 = 216.67^0.5 = 14.72%