honeycfa

A portfolio currently holds Randy Co. and the portfolio manager is thinking of adding either XYZ Co. or Branton Co. to the portfolio. All three stocks offer the same expected return and total risk. The covariance of returns between Randy Co. and XYZ is +0.5 and the covariance between Randy Co. and Branton Co. is -0.5. The portfolio's risk would decrease:

A) more if she bought Branton Co.

B) most if she put half your money in XYZ Co. and half in Branton Co.

C) more if she bought XYZ Co.

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In portfolio composition questions, return and standard deviation are the key variables. Here you are told that both returns and standard deviations are equal. Thus, you just want to pick the companies with the lowest covariance, because that would mean you picked the ones with the lowest correlation coefficient.

σ_portfolio = [W₁² σ₁² + W₂² σ₂² + 2W₁ W₂ σ₁ σ₂ r_1,2]^? where σ_Randy = Υ_Branton = σ_XYZ so you want to pick the lowest covariance which is between Randy and Branton.

honeycfa

Stock A has a standard deviation of 10%. Stock B has a standard deviation of 15%. The covariance between A and B is 0.0105. The correlation between A and B is:

A) 0.55.

B) 0.25.

C) 0.70.

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Cov_A,B = (r_A,B)(SD_A)(SD_B), where r = correlation coefficient and SD_x = standard deviation of stock x

Then, (r_A,B) = Cov_A,B / (SD_A × SD_B) = 0.0105 / (0.10 × 0.15) = 0.700

honeycfa

The standard deviation of the rates of return is 0.25 for Stock J and 0.30 for Stock K. The covariance between the returns of J and K is 0.025. The correlation of the rates of return between J and K is:

A) 0.33.

B) 0.10.

C) 0.20.

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Cov_J,K = (r_J,K)(SD_J)(SD_K), where r = correlation coefficient and SD_x = standard deviation of stock x

Then, (r_J,K) = Cov_J,K / (SD_J × SD_K) = 0.025 / (0.25 × 0.30) = 0.333

honeycfa

Which of the following statements regarding the covariance of rates of return is least accurate?

A) If the covariance is negative, the rates of return on two investments will always move in different directions relative to their means.

B) It is a measure of the degree to which two variables move together over time.

C) It is not a very useful measure of the strength of the relationship, there is absent information about the volatility of the two variables.

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Negative covariance means rates of return will tend to move in opposite directions on average. For the returns to always move in opposite directions, they would have to be perfectly negatively correlated. Negative covariance by itself does not imply anything about the strength of the negative correlation.

honeycfa

If the standard deviation of stock A is 10.6%, the standard deviation of stock B is 14.6%, and the covariance between the two is 0.015476, what is the correlation coefficient?

A) +1.

B) 0.0002.

C) 0.

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The formula is: (Covariance of A and B) / [(Standard deviation of A)(Standard Deviation of B)] = (Correlation Coefficient of A and B) = (0.015476) / [(0.106)(0.146)] = 1.

honeycfa

If the standard deviation of stock A is 13.2 percent, the standard deviation of stock B is 17.6 percent, and the covariance between the two is 0, what is the correlation coefficient?

A) +1.

B) 0.31.

C) 0.

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Since covariance is zero, the correlation coefficient must be zero.

honeycfa

If the standard deviation of stock A is 7.2%, the standard deviation of stock B is 5.4%, and the covariance between the two is -0.0031, what is the correlation coefficient?

A) -0.80.

B) -0.19.

C) -0.64.

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The formula is: (Covariance of A and B)/[(Standard deviation of A)(Standard Deviation of B)] = (Correlation Coefficient of A and B) = (-0.0031)/[(0.072)(0.054)] = -0.797.

honeycfa

If the standard deviation of returns for stock A is 0.60 and for stock B is 0.40 and the covariance between the returns of the two stocks is 0.009 what is the correlation between stocks A and B?

A) 0.0375.

B) 0.0020.

C) 26.6670.

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Cov_A,B = (r_A,B)(SD_A)(SD_B), where r = correlation coefficient and SD_x = standard deviation of stock x

Then,  (r_A,B) = Cov_A,B / (SD_A × SD_B) = 0.009 / (0.600 × 0.400) = 0.0375