Q11. Stock A has a standard deviation of 4.1% and Stock B has a standard deviation of 5.8%. If the stocks are perfectly positively correlated, which portfolio weights minimize the portfolio’s standard deviation?

          Stock A                               Stock B

A)   63%                                       37%

B)   100%                                     0%

C)   0%                                         100%

Q12. An investor calculates the following statistics on her two-stock (A and B) portfolio.

• σ_A = 20%

• σ_B = 15%

• r_A,B = 0.32

• W_A = 70%

• W_B = 30%

The portfolio's standard deviation is closest to:

A)   0.1832.

B)   0.0256.

C)   0.1600.

Q13. Two assets are perfectly positively correlated. If 30% of an investor's funds were put in the asset with a standard deviation of 0.3 and 70% were invested in an asset with a standard deviation of 0.4, what is the standard deviation of the portfolio?

A)   0.151.

B)   0.370.

C)   0.426.

Q14. Which one of the following statements about correlation is FALSE?

A)   If the correlation coefficient were 0, a zero variance portfolio could be constructed.

B)   Potential benefits from diversification arise when correlation is less than +1.

C)   If the correlation coefficient were -1, a zero variance portfolio could be constructed.

Q15. There are benefits to diversification as long as:

A)   there is perfect positive correlation between the assets.

B)   the correlation coefficient between the assets is less than 1.

C)   there must be perfect negative correlation between the assets.

答案和详解如下：

Q11. Stock A has a standard deviation of 4.1% and Stock B has a standard deviation of 5.8%. If the stocks are perfectly positively correlated, which portfolio weights minimize the portfolio’s standard deviation?

          Stock A                               Stock B

A)   63%                                       37%

B)   100%                                     0%

C)   0%                                         100%

Correct answer is B)         

Because there is a perfectly positive correlation, there is no benefit to diversification. Therefore, the investor should put all his money into Stock A (with the lowest standard deviation) to minimize the risk (standard deviation) of the portfolio.

Q12. An investor calculates the following statistics on her two-stock (A and B) portfolio.

• σ_A = 20%

• σ_B = 15%

• r_A,B = 0.32

• W_A = 70%

• W_B = 30%

The portfolio's standard deviation is closest to:

A)   0.1832.

B)   0.0256.

C)   0.1600.

Correct answer is C)

The formula for the standard deviation of a 2-stock portfolio is:

s = [W_A²s_A² + W_B²s_B² + 2W_AW_Bs_As_Br_A,B]^1/2

s = [(0.7² × 0.2²) + (0.3² × 0.15²) +( 2 × 0.7 × 0.3 × 2.0 )23.0 × 51.0 ×]^1/2 = [0.0196 + 0.002025 + 0.004032]^1/2 = 0.0256570^1/2 = 0.1602, or approximately 16.0%.

Q13. Two assets are perfectly positively correlated. If 30% of an investor's funds were put in the asset with a standard deviation of 0.3 and 70% were invested in an asset with a standard deviation of 0.4, what is the standard deviation of the portfolio?

A)   0.151.

B)   0.370.

C)   0.426.

Correct answer is B)

σ portfolio = [W₁²σ₁² + W₂²σ₂² + 2W₁W₂σ₁σ₂r_1,2]^1/2 given r_1,2 = +1

σ = [W₁²σ₁² + W₂²σ₂² + 2W₁W₂σ₁σ₂]^1/2 = (W₁σ₁ + W₂σ₂)²]^1/2

σ = (W₁σ₁ + W₂σ₂) = (0.3)(0.3) + (0.7)(0.4) = 0.09 + 0.28 = 0.37

Q14. Which one of the following statements about correlation is FALSE?

A)   If the correlation coefficient were 0, a zero variance portfolio could be constructed.

B)   Potential benefits from diversification arise when correlation is less than +1.

C)   If the correlation coefficient were -1, a zero variance portfolio could be constructed.

Correct answer is

A correlation coefficient of zero means that there is no relationship between the stock's returns. The other statements are true.

Q15. There are benefits to diversification as long as:

A)   there is perfect positive correlation between the assets.

B)   the correlation coefficient between the assets is less than 1.

C)   there must be perfect negative correlation between the assets.

Correct answer is B)

There are benefits to diversification as long as the correlation coefficient between the assets is less than 1.

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