Question

Use the following historical stock returns for GAF, Inc. to answer questions 19 and 20: Annual Stock Return Year 2005 13% 2006 1% 2007 -6% 2008 19% 2009 39% 2010 46% 2011 6% 2012 -4% 2013 14% 2014 -6% 2015 8% 0% 2016 2017 16% 2018 22% 19. What was the average annual historical return for GAF, Inc. over the 14 year period? 20. What was the standard deviation of retuns 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

Annual stock return (X) 13% 1% -6% 19% 39% 46% Year 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 6% X- mean 1% -11% -18% 7% 27% 34% -6% -16% 2% -18% -4% -12% 4% 10% (X-mean) 1% 121% 324% 49% 729% 1156% 36% 256% 4% 324% 16% 144% 16% 100% -4% 14% -6% 8% 0% 16% 22% Total 168% 3276% Average annual historic return for GAF = SX/N = 168%/14 - 12% Mean) Where X = Annual return N = Number of Years b.) Standard deviation of return for GAF = Whole square root of 2 (X - mean) /N = Whole square root of 3276% / 14 = Whole square root of 234% = 15.2971