In: Finance
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.
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. |