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%**

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%)
__________________________________
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