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# Question of the Week - Standard Deviation

IllinoisPosts: 68 Sr Associate
edited September 2014
The percentage returns for a stock for a 5-year period are provided below:

2008     12%
2009     9%
2010     -2%
2011     12%
2012     8%

What is the standard deviation of the stock returns?

## Question of the Week - Standard Deviation 40 votes

5.15%
82%
26.56%
5%
7.8%
12%

• São PauloPosts: 3 Associate
5.15%
By my numbers, the correct value would be 5,76% instead of 5,15%. Does anyone achieved this number too?
• Bangalore, IndiaPosts: 29 Associate
5.15%
I got 5.76% as the answer
• 5.15%
My calculations:

 Values x (values - mean) x^2 2008 12% 4.20% 0.18% 2009 9% 1.20% 0.01% 2010 -2% -9.80% 0.96% 2011 12% 4.20% 0.18% 2012 8% 0.20% 0.00% MEAN 7.80% SUM 1.33% Variance SUM / 5 0.27% Std Deviation SQRT(SUM/5) 5.15%
• IllinoisPosts: 68 Sr Associate

Mean return = [12% + 9% -2% + 12% + 8%]/5 = 7.8%

Variance of returns = [(12-7.8)^2 + (9-7.8)^2 + (-2-7.8)^2 + (12-7.8)^2 + (8-7.8)2]/5 = 26.56

Standard deviation is the square root of variance = (26.56)^0.5 = 5.15%

• St. Louis, MOPosts: 72 Sr Associate
5.15%
Woo! I got it right.

• MumbaiPosts: 175 Jr Portfolio Manager
5.15%
You get 5.76% if you consider it a sample rather than a population. I think since it says 5 year period it should be a sample. However 5.76% isn't one of the options so ...
Hope they don't try to confuse us like this in the exam.
• New YorkPosts: 32 Associate
5.15%
this stumped me as well and i decided to go with the assumption that this is a population data set. "the percentage returns for a stock for a 5 year period..." is very similar language to a CFAI mock exam question that I encountered, and the correct answer was based on the logic that it is a sample data set. My view here is that this data set would be considered a sample set due to the language I previously noted.
• New YorkPosts: 32 Associate
5.15%
One more thing to add - if the question stem would say something like, "the percentage returns for a stock since inception..." then I believe one should assume the data set is a population. And my logic is the "since inception" part of the sentence; this implies that the data set is inclusive of ALL the years. I have seen this sort of example on a practice exam and my logic worked fine there.