Question

In: Finance

Using the following returns, calculate the arithmetic average returns, the standard deviations, and the geometric average...

  1. Using the following returns, calculate the arithmetic average returns, the standard deviations, and the geometric average returns for the stock A, B, and C. Assume the returns of stocks are normally distributed. If Mr. WENG owns a stock C, based on the historical return data, there is only a 2.5 percent chance that the stock C will produce a return less than _____ percent in any one year.   If Mr. WENG owns a stock B, which range of returns would Mr. WENG expect to see approximately two-thirds of the time?

    Year

    A %

    B %

    C %

    1

    2.54

    4.84

    1.5

    2

    -3.27

    -0.97

    -1.97

    3

    -4.54

    -2.24

    -2.4

    4

    2.28

    -4.58

    1.38

    5

    -1.54

    1.76

    -2.44

    6

    4.54

    6.84

    4.84

    7

    -2.54

    -1.24

    -4.44

    8

    2.35

    4.65

    1.45

    9

    2.94

    6.24

    7.24

Solutions

Expert Solution

Arithmetic average return

Stock A = (2.54-3.27-4.54+2.28-1.54+4.54-2.54+2.35+2.94)/9 = 0.306

Stock B = (4.84-0.97-2.24-4.58+1.76+6.84-1.24+4.65+6.24)/9 = 1.7

Stock C = (1.5-1.97-2.4+1.38-2.44+4.84-4.44+1.45+7.24)/9 = 0.573

Standard deviation

Stock A = square root of [ { (2.54-0.306)^2 + (-3.27-0.306)^2 + (-4.4-0.306)^2 + (2.28-0.306)^2 + (-1.54-0.306)^2 + (4.54-0.306)^2 + (-2.54-0.306)^2 + (2.35-0.306)^2 + (2.94-0.306)^2 }/8 ] = 3.273

Stock B = square root of [ { (4.84-1.7)^2 + (-0.97-1.7)^2 + (-2.24-1.7)^2 + (-4.58-1.7)^2 + (1.76-1.7)^2 + (6.84-1.7)^2 + (-1.24-1.7)^2 + (4.65-1.7)^2 + (6.24-1.7)^2 }/8 ] = 4.128

Stock C = square root of [ { (1.5-0.573)^2 + (-1.97-0.573)^2 + (-2.4-0.573)^2 + (1.38-0.573)^2 + (-2.44-0.573)^2 + (4.84-0.573)^2 + (-4.44-0.573)^2 + (1.45-0.573)^2 + (7.24-0.573)^2 }/8 ] = 3.782

Geometric return

Stock A = (1.0254*0.9673*0.9546*1.0228*0.9846*1.0454*0.9746*1.0235*1.0294)^(1/9) - 1 = 0.26%

Stock B = (1.0484*0.9903*0.9776*0.9542*1.0176*1.0684*0.9876*1.0465*1.0624)^(1/9) - 1 = 1.625%

Stock C = (1.015*0.9803*0.976*1.0138*0.9756*1.0484*0.9556*1.0145*1.0724)^(1/9) - 1 = 0.511%

The confidence interval of 2.5% is = Arithmetic mean - 3*(std deviation)

For Stock C it would be = 0.573 - 3*3.782 = -10.773%

Two third of the time means confidence interval of 68% for Stock B ranges from :

Arithmetic mean - (std deviation) to Arithmetic mean + (std deviation) = 1.7 - 4.128 to 1.7 + 4.128 = -2.428% to 5.828


Related Solutions

Using the following returns, calculate the arithmetic average returns, the standard deviations, and the geometric average...
Using the following returns, calculate the arithmetic average returns, the standard deviations, and the geometric average returns for the stock A, B, and C. Assume the returns of stocks are normally distributed. If Mr. Wong owns a stock C, based on the historical return data, there is only a 2.5 percent chance that the stock C will produce a return less than _____ percent in any one year.   If Mr. Wong owns a stock B, which range of returns would...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. Returns Year X Y 1 11 % 23 % 2 29 44 3 18 -11 4 -19 -25 5 20 52 Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.    Returns Year X Y 1 11 %     23 %     2 29         44         3 18         -11...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. Returns Year X Y 1 11 % 23 % 2 29 44 3 18 -11 4 -19 -25 5 20 52 Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.    Returns Year X Y 1 11 %     23 %     2 29         44         3 18         -11...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.    Returns Year X Y 1 15 %     22 %     2 33         43         3 22         -9         4 -23         -23         5 24         51    Calculate the arithmetic average return for X.     Calculate the arithmetic average return for Y.    Calculate the variance for X.     Calculate the variance for Y.    Calculate...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. Returns Year X Y 1 11 % 20 % 2 29 41 3 18 -12 4 -19 -26 5 20 49 Requirement 1: (a) Calculate the arithmetic average return for X. (b) Calculate the arithmetic average return for Y. Requirement 2: (a) Calculate the variance for X. (Do not round intermediate calculations.) (b) Calculate the variance for Y. (Do not round...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.    Returns Year X Y 1 11 %     20 %     2 29         41         3 18         -12         4 -19         -26         5 20         49             Requirement 1: (a) Calculate the arithmetic average return for X.     (b) Calculate the arithmetic average return for Y.    Requirement 2: (a) Calculate the variance for X....
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. Returns Year X Y 1   13% 23% 2   31      44   3   20     -10 4 - 21   - 24 5   22      52
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.    Returns Year X Y 1 12 %     21 %     2 30         42         3 19         -8         4 -20         -22         5 21         50             Requirement 1: (a) Calculate the arithmetic average return for X. (Click to select)10.04%12.40%15.13%14.01%15.50%     (b) Calculate the arithmetic average return for Y. (Click to select)16.60%20.75%13.45%20.25%18.76%    Requirement 2:...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. Calculate the arithmetic average return for both stocks. (5 points) Calculate the variance and standard deviation. (5 points) Compare and contrast the standard deviations of the two stocks. What do the numbers tell you? Which stock is riskier based on your calculation? (5 points) Year Return of stock: You-Be, Inc. Zee Corp. 1 12% 25% 2 28% -34% 3 9% 13%...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for...
Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.    Returns Year X Y 1 10 %     23 %     2 28         44         3 17         -11         4 -18         -25         5 19         52             Requirement 1: (a) Calculate the arithmetic average return for X. (Click to select)13.66%14.00%11.20%12.66%9.07%     (b) Calculate the arithmetic average return for Y. (Click to select)16.60%13.45%18.76%20.25%20.75%    Requirement 2:...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT