Question

In: Finance

You have the following historical annual total returns on Terlingua Oil & Gas Exploration: Year Annual...

You have the following historical annual total returns on Terlingua Oil & Gas Exploration:

Year Annual total return (%)
2001 8%
2002 -8%
2003 17%
2004 20%
2005 13%
2006 4%
2007 -4%
2008 5%
2009 -5%
2010 5%

Calculate the sample standard deviation of annual return.

Do not round at intermediate steps in your calculation. Express your answer in percent. Round to two decimal places. Do not type the % symbol.

Solutions

Expert Solution

Solution:
The sample standard deviation of annual return (%) = 9.37
Working Notes:
a b = a - 5.5% b^2
Year Annual total return (%) (R-r) (R-r)^2
2001 8 2.5 6.250
2002 -8 -13.5 182.250
2003 17 11.5 132.250
2004 20 14.5 210.250
2005 13 7.5 56.250
2006 4 -1.5 2.250
2007 -4 -9.5 90.250
2008 5 -0.5 0.250
2009 -5 -10.5 110.250
2010 5 -0.5 0.250
Sum of annual return 55 Sum of (R-r)^2 790.500
Mean (r) = sum of returns / no of returns
Mean (r) = 55/10
Mean (r) =5.5%
standard deviation (s.d.) = Square root of (Sum of (R-r)^2 /(n-1))
Where n = no of return considered = 10
standard deviation (s.d.) = Square root of (790.50/(10-1))
standard deviation (s.d.) = Square root of (790.50 /9)
standard deviation (s.d.) = Square root of (87.8333333)
standard deviation (s.d.) = (87.8333333)^(1/2)
standard deviation (s.d.) = 9.371943946 %
standard deviation (s.d.) = 9.37 %
Please feel free to ask if anything about above solution in comment section of the question.

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