Question

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

                                    ___________________________________

                                   Year Return

                                    ___________________________________

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

                                    __________________________________

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

Qa) Holding period return= (1+r1) (1+r2) (1+r3) (1+r4) - 1

= (1-0.10) (1+0.10) (1+0.15) (1+0.25) - 1

= (0.90) (1.10) (1.15) (1.25) - 1

= 1.423125 - 1

= 0.423125 or 42.3125%

QB) Arithmetic mean = sum of return / number of years

= -10 + 10 + 15 +25 / 4

= 40 / 4

= 10%

Qc) Geometric return = [(1+r1) (1+r2) (1+r3) (1+r4)]^1/n - 1

= [(1-0.10) (1+0.10) (1+0.15) (1+0.25)]^1/4 - 1

= [ (0.90) (1.10) (1.15) (1.25)]^1/4 - 1

= (1.423125)^0.25 - 1

= 1.09222 - 1

= 0.09222 or 9.222%

Qd) Variance = sum of (X - mean)^2 / n - 1

= (-0.10 - 0.10)^2 + (0.10 - 0.10)^2 + (0.15 - 0.10)^2 + (0.25 - 0.10)^2 / 4 - 1

= (-0.20)^2 + 0 + (0.05)^2 + (0.15)^2 / 3

= (0.0400) + (0.0025) + (0.0225) / 3

= 0.0650 / 3

= 0.0217

Standard deviation = √variance

= √0.0217

= 0.147196 or 14.7196%