Question

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

Year	Annual total return (%)
2001	9%
2002	10%
2003	14%
2004	12%
2005	-1%
2006	4%
2007	-1%
2008	8%
2009	-1%
2010	6%

Calculate the sample standard deviation of annual return.

Answer 1

Year	Annual total return (%)
2001	9%
2002	10%
2003	14%
2004	12%
2005	-1%
2006	4%
2007	-1%
2008	8%
2009	-1%
2010	6%

Method 1: Sample standard deviation calculation using formula

Expected Return or Average return = E[R] = (9% + 10%+14%+12%+(-1%)+4%+(-1%)+8%+(-1%)+6%)/10 = 60%/10 = 6%

Expected return of the sample = E[R] = 6%

Sample size = n = 10

Varaince of a sample with sample size n is calculated using the formula:

Sample size = n = 10

n-1 = 9

Variance of the sample = σ² = (1/9)*[(9%-6%)² +(10%-6%)²+(14%-6%)²+(12%-6%)²+(-1%-6%)²+(4%-6%)²+(-1%-6%)²+(8%-6%)²+(-1%-6%)²+(6%-6%)²]

σ² = (1/9)*[0.0009+0.0016+0.0064+0.0036+0.0049+0.0004+0.0049+0.0004+0.0049+0] = 0.028/9 = 0.00311111111111111

Standard deviation of the sample is square root of the sample

So, standard deviation of sample = σ = 0.00311111111111111^1/2 = 0.0557773351022717 = 5.57773351022717%

Answer -> Standard deviation of the sample = σ = 5.57773351022717%

Method 2: Sample standard deviation calculation using Excel

We can use the STDEV.S function in Excel to calculate the standard deviation of the sample as shown below

=STDEV.S(B2:B11) = 5.5777335%

Answer -> Standard deviation of the sample = σ = 5.5777335%