Question

In: Finance

" Year Stock X Stock Y 1 8.00% 5.00% 2 1.00% 14.00% 3 11.00% 8.00% 4...

"

Year

Stock X

Stock Y

1

8.00%

5.00%

2

1.00%

14.00%

3

11.00%

8.00%

4

4.00%

12.00%

What is the correlation of Stock X and Stock Y?

Round to 4 decimal places please.

Solutions

Expert Solution

   Stock X          
Year   AR    ER = Avg. R   (AR-ER)   (AR-ER)^2
              
1   8%   6.00%   0.0200   0.000400
2   1%   6.00%   -0.0500   0.002500
3   11%   6.00%   0.0500   0.002500
4   4%   6.00%   -0.0200   0.000400
              
              
Average =   6.00%           0.005800

   Stock Y          
Year   AR    ER = Avg. R   (AR-ER)   (AR-ER)^2
              
1   5%   9.75%   -0.0475   0.002256
2   14%   9.75%   0.0425   0.001806
3   8%   9.75%   -0.0175   0.000306
4   12%   9.75%   0.0225   0.000506
              
Average =   9.75%           0.004875

Volatility (Std Dev. Of X) =           SQRT((∑(AR-ER)^2) / (n-1))          
           √(0.0058 / (4-1))=           0.04396968653
Volatility (Std Dev. Of Y) =           √(0.004875 / (4-1))           0.04031128874
  Covariance between stock                  
                  
Year   Stock X (AR - ER)       Stock Y (AR-ER)       Stock A (AR - ER) * Stock B (AR-ER)
                   0
1   0.0200       -0.0475       -0.000950
2   -0.0500       0.0425       -0.002125
3   0.0500       -0.0175       -0.000875
4   -0.0200       0.0225       -0.000450
                  
                  
                   -0.004400
                  
Covariance = -0.0044 / (4-1)                   -0.001466666667

Correlation = Covariance between stock / (Std. dev. Of X * std. dev. Of Y)          
   -0.001466666667 / (0.04396968652* 0.04031128874)      
   -0.8275      
So, Correlation between two stock is -0.8275          


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