Question

Assume that a stock's price was $15 in 2010, $20 in 2011, $24 in 2012, $21 in 2013, and $28 in 2014.

Find the following:

a) The return of the stock in each year

b) The (arithmetic) average of returns

c) The Geometric average of returns

d) The variance and standard deviation of returns

Answer 1

a

Return year 2010-2011=(Price year 2011+ Dividend year 2011)/Price year 2010-1

=(20+)/15-1

=33.33%

Return year 2011-2012=(Price year 2012+ Dividend year 2012)/Price year 2011-1

=(24+)/20-1

=20%

Return year 2012-2013=(Price year 2013+ Dividend year 2013)/Price year 2012-1

=(21+)/24-1

=-12.5%

Return year 2013-2014=(Price year 2014+ Dividend year 2014)/Price year 2013-1

=(28+)/21-1

=33.33%

b

Arithmetic return = (Return year 2010-2011 + Return year 2011-2012 + Return year 2012-2013 + Return year 2013-2014)/4

=(+0.3333+0.2-0.125+0.3333)/4

=18.54%

c

Geometric return = ((1+Return year 2010-2011)*(1 + Return year 2011-2012)*(1 + Return year 2012-2013)*(1 + Return year 2013-2014))^(1/4)-1

= ((1+0.3333)*(1+0.2)*(1-0.125)*(1+0.3333))^(1/4)-1

=16.89%

d

Year	Stock
2010	33.33%
2011	20.00%
2012	-12.50%
2013	33.33%
Standard dev=	21.63%
Variance=	0.04677

Sample Standard deviation =((∑k=1 to N (observationk – average))/(N-1))^(1/2)

Variance = standard deviation^2