A portfolio manager is analyzing the bonds issued by two companies Aqua Inc. and Chroma Inc. He notices that the correlation between the returns of two bonds is 0.23 and variance of two bonds is 48% for Aqua Inc. and 73% for Chroma Inc. He calculates the covariance coefficient for the two bonds. After a few days, he notices that the standard deviation of Aqua Inc. has become 10% and standard deviation of Chroma Inc has become 7%. He calculates the covariance coefficient again keeping the correlation coefficient same. The covariance coefficient that he calculates second time is: Question 37Answera.the same as firstb.Higher than firstc.Lower than first
Question
A portfolio manager is analyzing the bonds issued by two companies Aqua Inc. and Chroma Inc. He notices that the correlation between the returns of two bonds is 0.23 and variance of two bonds is 48% for Aqua Inc. and 73% for Chroma Inc. He calculates the covariance coefficient for the two bonds. After a few days, he notices that the standard deviation of Aqua Inc. has become 10% and standard deviation of Chroma Inc has become 7%. He calculates the covariance coefficient again keeping the correlation coefficient same. The covariance coefficient that he calculates second time is: Question 37Answera.the same as firstb.Higher than firstc.Lower than first
Solution
The answer is c. Lower than first.
Here's why:
The formula for calculating the covariance using correlation is:
Covariance = Correlation * (Standard Deviation of X) * (Standard Deviation of Y)
In the first scenario, the standard deviations are the square roots of the variances, which are √48% for Aqua Inc. and √73% for Chroma Inc.
In the second scenario, the standard deviations are given as 10% for Aqua Inc. and 7% for Chroma Inc.
Since the correlation coefficient remains the same, but the standard deviations in the second scenario are lower than in the first scenario, the covariance (which is a product of the correlation and the standard deviations) will also be lower in the second scenario.
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