CFA CFA Level 1 Question of the Week – Standard Deviation

Question of the Week – Standard Deviation

  • This topic has 8 replies, 7 voices, and was last updated Jan-18 by jak5189.
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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%
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      4

      Correct Answer:  A

      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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      1

      Woo! I got it right. ­čÖé 

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      I got 5.76% as the answer

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