Question

2005 Use the following historical stock returns for GAF, Inc. to answer questions 19 and 20: Year Annual Stock Return 13% 2006 1% 2007 -6% 2008 19% 2009 39% 46% 2011 6% 2012 -4% 2013 14% 2014 -6% 2015 8% 2016 0% 2017 16% 2018 22% 2010 19. What was the average annual historical return for GAF, Inc. over the 14 year period? 20. What was the standard deviation of returns for GAF, Inc. stock over the 14 year time period? (Compute the standard deviation assuming this is a population of returns, not a sample - that is, use the procedure described in the textbook for calculating the standard deviation of a series of stock returns).

Answer 1

19) Average annual historical return = (13% + 1% - 6% + 19% + 39% + 46% + 6% - 4% + 14% - 6% + 8% + 0% + 16% + 12%) / 14 years

= 11.285%

20)

Standard deviation

'X' = return of each year

YEAR	X - Avg of return	(X - Avg of return)2
2005	1.715	2.94
2006	- 10.285	105.78
2007	- 17.285	298.77
2008	7.715	59.52
2009	27.715	768.12
2010	34.715	1205.13
2011	- 5.285	27.93
2012	-15.285	233.63
2013	2.715	7.37
2014	-17.285	298.77
2015	-3.285	10.79
2016	-11.285	127.35
2017	4.715	22.23
2018	10.715	114.81
	TOTAL =	3283.14

Variance of stock = 3283.14 /14 years = 234.51

Standard deviation = root of 234.51 = 15.31