The following table shows the historical returns for large

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Reference no: EM13382455

The following table shows the historical returns for large company stocks from 1980-1999. Let's find the average return and the standard deviation of the large firm returns.

Data:   Yearly Historical Returns for U. S. Large Company Stocks 1980-1999.





















Year Large Company Stocks  







1980 32.61%

Step 1: Average Return



1981 -4.97%








1982 21.67%

Calculate the historical average return for large co. stocks

1983 22.57%








1984 6.19%

Use the Excel function:  =average(cell range)/100

1985 31.85%

We need to divide by 100 because the values are in per cent.

1986 18.68%








1987 5.22%

A.     In cell J116 enter:  = average(C108:C127)

1988 16.58%





 

1989 31.75%

           

1990 -3.13%

Step 2: Return Distribution



1991 30.53%








1992 7.62%

Calculate the variance and standard deviation of  large firm 

1993 10.07%

historical returns.




1994 1.27%








1995 37.80%

Variance is the average of the squared deviations from the mean.

1996 22.74%

We calculate the deviation of each individual return from the mean (average), square those numbers, sum the squares, and then divide 

1997 33.43%


1998 28.13%

by the number of returns minus one.    

1999 21.03%












The standard deviation is the square root of the variance.  It is in





percentage form and is used to make comparisons.  























Year Large Co. Return Average Return Deviation Squared  Deviation




1 1980 32.61%







2 1981 -4.97%







3 1982 21.67%







4 1983 22.57%



Steps for calculating standard deviation:
5 1984 6.19%







6 1985 31.85%



Hint: range means a row or column of cells
7 1986 18.68%







8 1987 5.22%



A.  Enter the 1980-1999 historical average
9 1988 16.58%



      from J116. Copy from year 1 to 20.
10 1989 31.75%







11 1990 -3.13%



B.  Find the yearly deviation by subtracting
12 1991 30.53%



      the average return from the Lg Co Ret.
13 1992 7.62%



      Copy from year 1 to 20.
14 1993 10.07%







15 1994 1.27%



C.  Find the squared deviation by multiplying
16 1995 37.80%



      the deviation by itself.  Copy.
17 1996 22.74%







18 1997 33.43%



D.  In cell F153 enter:   =sum(range)/(20-1)
19 1998 28.13%







20 1999 21.03%



E.  In cell F154 take the square root of F153

st dev   
variance   
        Enter:   = sqrt(F153)




st dev   



























F. We can use the built-in formula:  in cell C153 enter:   =stdev(range).  C153 should be equal to F154 (13.13%).
                     











Test Your Skills:




















Question 1:   A stock had annual returns of 9 percent, -5 percent, 14 percent, 16 percent, 11 percent, & 12 percent


  each for the past six years.  What is the average return and standard deviation for this


  stock?





















Year Return








1  








2  








3  








4  








5  








6  


















  Average return  







  Standard deviation  




























Question 2: A stock had annual returns of -1 percent, -5 percent, 0 percent, 16 percent,  25 percent, and 50 percent


  each for the past six years.  What is the average return and standard deviation for this stock?














Year Return








1  








2  








3  








4  








5  








6  


















  Average return  







  Standard deviation  





Reference no: EM13382455

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