Consider the yearend prices for Google Inc over the last fiv

Consider the year-end prices for Google, Inc. over the last five years. Google did not pay a dividend over the last five years.

Calculate the standard deviation in the returns.

Solution

Standard deviation is the square root of the Variance and Variance is the average of the squared differences from the Mean.

YEAR   PRICE
2012   $576.65
2011   $605.10
2010   $525.13
2009   $341.19
2008   $566.83
2007   $500.35

So, Calculating the mean first, we get

Mean=($576.65+$605.10+$525.13+$341.19+$566.83+$500.35)/6
=$519.233

Therefore, Variance is
Variance (in $) =(576.65-519.233)²+(605.10-519.233)²+(525.13-519.233)²+(341.19-519.233)²+(566.83-519.233)²+(500.35-519.233)²
=3296.711+7373.141+34.774+31699.309+2265.474+356.567
=45025.976
Standard Deviation(in $)=sqrt(Variance)
   =sqrt(45025.976)
   =212.193