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

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%**

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.
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