Question

Given the end-of-month prices for stock X for January 2020 through June 2020,

Month End-of-Month Price

January 2020 15.25

February 2020 16.10

March 2020 16.20

April 2020 15.80

May 2020 15.85

June 2020 16.30

calculate

a.        Monthly holding-period return

b.              Average Return

c.               Standard Deviation

Answer 1

(b) We shall calculate the average return bybthe formula

Average return $=\frac{average \hspace{0.1cm}investment}{initial \hspace{0.1cm}investment}$

The average investment from January through to June is given by

$=\frac{95.5}{6}$

$=15.92$

Now,

$Average \hspace{0.1cm}return=\frac{15.92}{15.25}$

$=1.04$

(C) To calculate the standard deviation

$S.D=\sqrt{\frac{\sum(x-\bar{x})²}{n}}$

Where $\bar{x}$ Is the average value (the mean) in question (b) which is

$\bar{x}=15.92$

$\sum({x-\bar{x}})²=(15.25-15.92)² +(16.10-15.92)²+(16.20-15.92)²+(15.80-15.92)²+(15.85-15.92)²+(16.30-15.92)²$

$\sum({x-\bar{x}})=0.4489+0.0324+0.0729+0.0144+0.0049+0.1444$

$\sum({x-\bar{x}})²=0.7179$

Therefore,

$S.D=\sqrt{\frac{\sum(x-\bar{x})²}{n}}$

$S.D=\sqrt{\frac{0.7179}{6}}$

$S.D=\sqrt{0.11965}\\S.D=0.3459$

HENCE,

(a)the monthly holding -period return is

0.06%

(b)the average return is

1.04%

(c)the standard deviation is

0.3459