Bartman Industries\' stock prices and dividends along with the Market Index are

Question

Bartman Industries' stock prices and dividends along with the Market Index are shown below. Stock prices are reported for December 31 of each year, and dividends reflect those paid during the year. The market data are adjusted to include dividends Year Bartman Industries Market Index Stock Price Dividend Includes Dividends 2009 2008 2007 2006 2005 2004 $25.88 $22.13 $25.75 $16.13 $17.06 $11.44 $2.58 $2.21 $1.50 $1.43 1.35 $1.28 17,495.97 13,178.55 13,019.97 9,651.05 8,403.42 7,058.96 Estimate the standard deviation of the annual returns for Bartman Industries Select one: a. 23.01% b. 33.39% c. 10.33% d. 13.82% e. 72.38% O O

Explanation / Answer

TO calculate the standard deviation of the annual returns for Bartman Industries, we have first calculated the annual returns.
Annual returns = (Capital gain + Dividend)/Beginning price
capital gain = Ending price - Beginning price
Note: Annual return cannot be calculated for the first year, here 2004.

After calculating Annual returns for all standard deviation is calculated using the excel formula
= STDEV(range of annual returns) or
Calculate the average return = Sum of all the annual returns/5
      = 155.93%/5 = 31.19%
Now subtract the average returns from each of the annual return and then square it as shown in the table.
Squaring and then Summation of annual return - average return is done (44.590%) and then divided by n-1 or 5-1 = 4. (=44.590%/4 = 0.11147).
Next find the square root of 0.11147 = 0.111471/2= 33.39%

Standard deviation of the annual returns is 33.39% for Bartman Industries

Bartman Industries Year Stock Price Dividend Capital gain (ending price - beginning price) Total gain = Dividend +Capital gain Annual Return = Total gain/beginning price Annual Return - Average return (Annual Return - Average return)^2 2009 25.88 2.58 3.75 6.33 28.60% -2.58% 0.07% 2008 22.13 2.21 -3.62 -1.41 -5.48% -36.66% 13.44% 2007 25.75 1.5 9.62 11.12 68.94% 37.75% 14.25% 2006 16.13 1.43 -0.93 0.5 2.93% -28.25% 7.98% 2005 17.06 1.35 5.62 6.97 60.93% 29.74% 8.85% 2004 11.44 1.28 NA NA NA Sum = 44.590%

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