You are analyzing the historical performance of a stock. The annual returns for the last ten...
You are analyzing the historical performance of a stock. The annual returns for the last ten years are shown below.
Year Ann Ret
2018 12%
2017 9%
2016 ‐5%
2015 3%
2014 ‐13%
2013 6%
2012 20%
2011 0%
2010 ‐6%
2009 14%
Calculate the average annual return, the variance and standard deviation of this stock over the ten‐year period.
Homework Answers
Avg Ret = Sum [ Ret ] / n
= [ 12%+9%-5%+3%-13%+6%+20%+0%-6%+14% ] / 10
= 40% / 10
= 4%
Variance = sum [ (X -AvgX)^2 ] / n
| Year | X | X - Avg X | (X- Avg X)^2 |
| 2018 | 12.00% | 8.00% | 0.0064 |
| 2017 | 9.00% | 5.00% | 0.0025 |
| 2016 | -5.00% | -9.00% | 0.0081 |
| 2015 | 3.00% | -1.00% | 0.0001 |
| 2014 | -13.00% | -17.00% | 0.0289 |
| 2013 | 6.00% | 2.00% | 0.0004 |
| 2012 | 20.00% | 16.00% | 0.0256 |
| 2011 | 0.00% | -4.00% | 0.0016 |
| 2010 | -6.00% | -10.00% | 0.01 |
| 2009 | 14.00% | 10.00% | 0.01 |
| Sum [ (X- Avg X)^2 ] | 0.0936 | ||
| Variance = Sum [ (X- Avg X)^2 ] / n | 0.00936 | ||
SD = SQRT [ Variance ]
= SQRT [ 0.00936 ]
= 0.0967
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