CFA CFA Level 1 Question of the Week – Standard Deviation

# Question of the Week – Standard Deviation

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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?

• 5.15%
• 26.56%
• 7.80%
• 4

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%

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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.

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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%
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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.

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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.

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By my numbers, the correct value would be 5,76% instead of 5,15%. Does anyone achieved this number too?

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Woo! I got it right. 🙂

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I got 5.76% as the answer