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Given the following returns over the past 10 periods from two assets, determine the mean rate of return for each, the standard deviation for each, and the covariance and correlation coefficient between the two stocks. Period 1 2 3 4 5 Asset 1 Return 18% 15% 21% 8% 12% 14% -1% 7% 19% 24% Asset 2 Return 15% 12% 16% 14% 14% 14% 11% 13% 16% 13% 6 7 8 9 10



Answer :

  1. For Asset 1, the mean rate of return is 14.2%.
  2. The standard deviation for Asset 1 is 9.56%.
  3. For Asset 2, the mean rate of return is 14%.
  4. The standard deviation for Asset 2 is 3.16%.
  5. The covariance between the two assets is 19.44.
  6. The correlation coefficient between the two assets is 0.84.

To calculate the covariance between the two assets, you will need to multiply the difference between each period's return for Asset 1 and the mean rate of return for Asset 1 by the difference between each period's return for Asset 2 and the mean rate of return for Asset 2, and sum up all of the products. Then, you will need to divide this sum by the number of periods minus one. To calculate the correlation coefficient between the two assets, you will need to divide the covariance between the two assets by the product of the standard deviations of each asset.

For Asset 1, the mean rate of return is:

(18 + 15 + 21 + 8 + 12 + 14 + -1 + 7 + 19 + 24) / 10 = 14.2%

The variance is:

((18 - 14.2)^2 + (15 - 14.2)^2 + (21 - 14.2)^2 + (8 - 14.2)^2 + (12 - 14.2)^2 + (14 - 14.2)^2 + (-1 - 14.2)^2 + (7 - 14.2)^2 + (19 - 14.2)^2 + (24 - 14.2)^2) / 9 = 91.56

The standard deviation for Asset 1 is:

sqrt(91.56) = 9.56%

For Asset 2, the mean rate of return is:

(15 + 12 + 16 + 14 + 14 + 14 + 11 + 13 + 16 + 13) / 10 = 14.0%

For Asset 2, the variance is:

((15 - 14.0)^2 + (12 - 14.0)^2 + (16 - 14.0)^2 + (14 - 14.0)^2 + (14 - 14.0)^2 + (14 - 14.0)^2 + (11 - 14.0)^2 + (13 - 14.0)^2 + (16 - 14.0)^2 + (13 - 14.0)^2) / 9 = 10.0

The standard deviation for Asset 2 is:

sqrt(10.0) = 3.16%

The covariance between the two assets is:

(((18 - 14.2) * (15 - 14.0)) + ((15 - 14.2) * (12 - 14.0)) + ((21 - 14.2) * (16 - 14.0)) + ((8 - 14.2) * (14 - 14.0)) + ((12 - 14.2) * (14 - 14.0)) + ((14 - 14.2) * (14 - 14.0)) + ((-1 - 14.2) * (11 - 14.0)) + ((7 - 14.2) * (13 - 14.0)) + ((19 - 14.2) * (16 - 14.0)) + ((24 - 14.2) * (13 - 14.0))) / 9 = 19.44

The correlation coefficient between the two assets is:

covariance(Asset 1, Asset 2) / (stddev(Asset 1) * stddev(Asset 2)) = 19.44 / (9.56 * 3.16) = 0.84

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