Question
In: Finance
The table below shows annual returns for stocks of companies X and Y. Calculate the arithmetic...
| The table below shows annual returns for stocks of companies X and Y. Calculate the arithmetic average returns. In addition, calculate their variances, as well as their standard deviations. |
| Returns | ||
| Year | X | Y |
| 1 | 11 % | 19 % |
| 2 | 29 | 40 |
| 3 | 18 | -9 |
| 4 | -19 | -23 |
| 5 | 20 | 48 |
| Requirement 1: | |
| (a) | The arithmetic average return of company X's stock is: |
| (Click to select) 11.80% 9.56% 13.33% 14.75% 14.40% | |
| (b) |
The arithmetic average return of company Y's stock is: |
| (Click to select) 15.00% 16.95% 18.30% 12.15% 18.75% |
| Requirement 2: | |
| (a) | The variance of company X's stock returns is: (Do not round intermediate calculations.) |
| (Click to select) 0.027354 0.041997 0.033770 0.033597 0.042213 | |
| (b) | The variance of company Y's stock returns is: (Do not round intermediate calculations.) |
| (Click to select) 0.075938 0.117188 0.107043 0.093750 0.085635 |
| Requirement 3: | |
| (a) |
The standard deviation of company X's stock returns is: (Do not round intermediate calculations.) |
| (Click to select) 18.23% 14.89% 20.49% 18.38% 22.97% | |
| (b) |
The standard deviation of company Y's stock returns is: (Do not round intermediate calculations.) |
| (Click to select) 32.72% 29.26% 24.80% 30.62% 38.27% |
rev: 09_20_2012
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Expert Solution
Requirement 1)
Arithmetic Return = Sum of all returns / Number of observations
For Stock X
xbar = (11% + 29% + 18% - 19% + 20%) / 5
xbar = 11.8% -- Average return
For Stock Y
Ybar = (19% + 40% - 9% - 23% + 48%) / 5
Ybar = 15.00% -- Average return
--------------------------------------
Requirement 2)
Variance
For Stock X
| Year | X | X- Xbar | (X - Xbar)^2 | |
| 1 | 11% | -0.80% | 6.4E-05 | |
| 2 | 29% | 17.20% | 0.029584 | |
| 3 | 18% | 6.20% | 0.003844 | |
| 4 | -19% | -30.80% | 0.094864 | |
| 5 | 20% | 8.20% | 0.006724 | |
| Xbar --- > | 11.80% | 0.13508 | Total |
Hence, Variance = 0.13508 / (5 - 1)
Variance = 0.0337700
For Stock Y
| Year | Y | Y- Ybar | (Y - Ybar)^2 | |
| 1 | 19% | 4.00% | 0.001600 | |
| 2 | 40% | 25.00% | 0.062500 | |
| 3 | -9% | -24.00% | 0.057600 | |
| 4 | -23% | -38.00% | 0.144400 | |
| 5 | 48% | 33.00% | 0.108900 | |
| Ybar --- > | 15.00% | 0.375000 | Total |
Hence, Variance = 0.375 / (5 - 1)
Variance = 0.093750
-----------------------------
Requirement 3)
For Stock X
Standard Deviation = Square root (0.033770)
Standard Deviation = 0.183766156 = 18.38%
For Stock Y
Standard Deviation = Square root (0.09375)
Standard Deviation = 0.306186218 = 30.62%
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