Data: Yearly Historical Returns for U. S. Large Company Stocks 1980-1999. |
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Year |
Large Company Stocks |
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1980 |
32.61% |
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Step 1: Average Return |
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1981 |
-4.97% |
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1982 |
21.67% |
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Calculate the historical average return for large co. stocks |
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1983 |
22.57% |
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1984 |
6.19% |
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Use the Excel function: =average(cell range)/100 |
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1985 |
31.85% |
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We need to divide by 100 because the values are in per cent. |
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1986 |
18.68% |
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1987 |
5.22% |
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A. In cell J116 enter: = average(C108:C127) |
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1988 |
16.58% |
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1989 |
31.75% |
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1990 |
-3.13% |
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Step 2: Return Distribution |
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1991 |
30.53% |
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1992 |
7.62% |
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Calculate the variance and standard deviation of large firm |
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1993 |
10.07% |
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historical returns. |
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1994 |
1.27% |
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1995 |
37.80% |
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Variance is the average of the squared deviations from the mean. |
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1996 |
22.74% |
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We calculate the deviation of each individual return from the mean (average), square those numbers, sum the squares, and then divide |
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1997 |
33.43% |
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1998 |
28.13% |
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by the number of returns minus one. |
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1999 |
21.03% |
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The standard deviation is the square root of the variance. It is in |
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percentage form and is used to make comparisons. |
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Year |
Large Co. Return |
Average Return |
Deviation |
Squared Deviation |
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1 |
1980 |
32.61% |
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2 |
1981 |
-4.97% |
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3 |
1982 |
21.67% |
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4 |
1983 |
22.57% |
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Steps for calculating standard deviation: |
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1984 |
6.19% |
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6 |
1985 |
31.85% |
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Hint: range means a row or column of cells |
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1986 |
18.68% |
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8 |
1987 |
5.22% |
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A. Enter the 1980-1999 historical average |
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1988 |
16.58% |
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from J116. Copy from year 1 to 20. |
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1989 |
31.75% |
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11 |
1990 |
-3.13% |
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B. Find the yearly deviation by subtracting |
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1991 |
30.53% |
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the average return from the Lg Co Ret. |
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1992 |
7.62% |
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Copy from year 1 to 20. |
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14 |
1993 |
10.07% |
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15 |
1994 |
1.27% |
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C. Find the squared deviation by multiplying |
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1995 |
37.80% |
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the deviation by itself. Copy. |
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1996 |
22.74% |
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18 |
1997 |
33.43% |
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D. In cell F153 enter: =sum(range)/(20-1) |
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1998 |
28.13% |
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20 |
1999 |
21.03% |
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E. In cell F154 take the square root of F153 |
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st dev |
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variance |
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Enter: = sqrt(F153) |
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st dev |
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F. We can use the built-in formula: in cell C153 enter: =stdev(range). C153 should be equal to F154 (13.13%). |
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Test Your Skills: |
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Question 1: |
A stock had annual returns of 9 percent, -5 percent, 14 percent, 16 percent, 11 percent, & 12 percent |
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each for the past six years. What is the average return and standard deviation for this |
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stock? |
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Year |
Return |
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1 |
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5 |
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6 |
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Average return |
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Standard deviation |
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Question 2: |
A stock had annual returns of -1 percent, -5 percent, 0 percent, 16 percent, 25 percent, and 50 percent |
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each for the past six years. What is the average return and standard deviation for this stock? |
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Year |
Return |
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1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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Average return |
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Standard deviation |
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