Finance Quiz: Diversification And Correlation
20 questions · exam conditions
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Diversification And CorrelationQuestion 1 of 20

An investor replaces a stock in her two-stock portfolio with a new stock that has the exact same expected return and standard deviation as the original, but a much lower correlation with the other stock in the portfolio. Which of the following describes the effect on the new portfolio's expected return and standard deviation?

The expected return will decrease, and the standard deviation will decrease.
The expected return will be unchanged, and the standard deviation will be unchanged.
The expected return will be unchanged, and the standard deviation will decrease.
The expected return will increase, and the standard deviation will decrease.
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Finance Quiz

Finance Quiz: Diversification And Correlation

Practice Diversification And Correlation in Finance with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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This quiz focuses on Diversification And Correlation, giving you a quick way to practice the rules, question types, and explanations that matter most for Finance.

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Question 1

An investor replaces a stock in her two-stock portfolio with a new stock that has the exact same expected return and standard deviation as the original, but a much lower correlation with the other stock in the portfolio. Which of the following describes the effect on the new portfolio's expected return and standard deviation?

  1. The expected return will decrease, and the standard deviation will decrease.
  2. The expected return will be unchanged, and the standard deviation will be unchanged.
  3. The expected return will be unchanged, and the standard deviation will decrease. (correct answer)
  4. The expected return will increase, and the standard deviation will decrease.
Explanation: The expected return of a portfolio is the weighted average of the expected returns of its component assets. Since the new stock has the same expected return as the one it replaced, the portfolio's expected return will remain unchanged. However, the portfolio's standard deviation is a function of the individual standard deviations, the weights, and the correlation coefficient. A lower correlation coefficient leads to a lower portfolio standard deviation (greater diversification benefit). Therefore, the standard deviation will decrease.

Question 2

Two portfolios, X and Y, are created using assets with identical expected returns and standard deviations. Portfolio X combines assets with a correlation of 0.8. Portfolio Y combines assets with a correlation of -0.4. Both portfolios are equally weighted. Which statement accurately compares the risk and return of these portfolios?

  1. Portfolio Y will have a lower expected return and a lower standard deviation than Portfolio X.
  2. Portfolio X and Portfolio Y will have identical expected returns and identical standard deviations.
  3. Portfolio Y will have the same expected return as Portfolio X but a lower standard deviation. (correct answer)
  4. Portfolio X will have a lower standard deviation than Portfolio Y due to the stronger magnitude of its correlation.
Explanation: The expected return of a portfolio is the weighted average of the individual assets' expected returns. Since the underlying assets and weights are identical for both portfolios, their expected returns will be the same. Portfolio risk (standard deviation), however, is highly dependent on correlation. A lower correlation provides greater risk reduction. Since Portfolio Y's assets have a much lower correlation (-0.4) than Portfolio X's assets (0.8), Portfolio Y will exhibit a lower overall standard deviation.

Question 3

An equally weighted portfolio of two assets has a standard deviation of 18%. Asset A has a standard deviation of 20% and Asset B has a standard deviation of 30%. What is the implied correlation coefficient (ρAB\rho_{AB}) between the two assets?

  1. 0.33
  2. -0.01 (correct answer)
  3. -0.58
  4. 0.85
Explanation: We use the portfolio variance formula: σp2=wA2σA2+wB2σB2+2wAwBρABσAσB\sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_A w_B \rho_{AB} \sigma_A \sigma_B. We are given σp=0.18\sigma_p = 0.18, wA=wB=0.5w_A=w_B=0.5, σA=0.20\sigma_A = 0.20, and σB=0.30\sigma_B = 0.30. Plugging in the values: (0.18)2=(0.5)2(0.20)2+(0.5)2(0.30)2+2(0.5)(0.5)ρAB(0.20)(0.30)(0.18)^2 = (0.5)^2(0.20)^2 + (0.5)^2(0.30)^2 + 2(0.5)(0.5)\rho_{AB}(0.20)(0.30). 0.0324=(0.25)(0.04)+(0.25)(0.09)+0.5ρAB(0.06)0.0324 = (0.25)(0.04) + (0.25)(0.09) + 0.5\rho_{AB}(0.06). 0.0324=0.01+0.0225+0.03ρAB0.0324 = 0.01 + 0.0225 + 0.03\rho_{AB}. 0.0324=0.0325+0.03ρAB0.0324 = 0.0325 + 0.03\rho_{AB}. −0.0001=0.03ρAB-0.0001 = 0.03\rho_{AB}. ρAB=−0.0001/0.03≈−0.0033\rho_{AB} = -0.0001 / 0.03 \approx -0.0033, which is very close to -0.01.

Question 4

Consider the formula for the variance of a two-asset portfolio: σp2=w12σ12+w22σ22+2w1w2ρ12σ1σ2\sigma_p^2 = w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\rho_{12}\sigma_1\sigma_2. Which component of this formula captures the primary source of risk reduction from diversification?

  1. The sum of the first two terms, w12σ12+w22σ22w_1^2\sigma_1^2 + w_2^2\sigma_2^2, which represents the weighted individual asset risks.
  2. The individual asset variances, σ12\sigma_1^2 and σ22\sigma_2^2, as selecting low-variance assets is the goal.
  3. The interaction term, 2w1w2ρ12σ1σ22w_1w_2\rho_{12}\sigma_1\sigma_2, because its value depends on the correlation. (correct answer)
  4. The interaction term, which must always be positive and therefore must be minimized to reduce risk.
Explanation: The first two terms represent the weighted contribution of each asset's individual variance. The third term, which is equivalent to 2w1w2Cov(1,2)2w_1w_2\text{Cov}(1,2), captures how the assets move together. The diversification benefit comes from this interaction. When the correlation (ρ12\rho_{12}) is less than 1, this term is smaller than it would otherwise be, reducing the total variance. If correlation is negative, this term becomes negative, actively reducing the portfolio variance below the weighted sum of individual variances. Therefore, this term is the source of the diversification benefit.

Question 5

A portfolio is constructed with a 60% allocation to Asset A and a 40% allocation to Asset B. Asset A has a standard deviation of 20% and Asset B has a standard deviation of 30%. The returns of the two assets are uncorrelated (ρ=0\rho = 0). What is the standard deviation of this portfolio?

  1. 24.0%
  2. 4.3%
  3. 25.0%
  4. 16.9% (correct answer)
Explanation: The formula for the variance of a two-asset portfolio is σp2=wA2σA2+wB2σB2+2wAwBρABσAσB\sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_A w_B \rho_{AB} \sigma_A \sigma_B. Since correlation (ρ\rho) is 0, the last term drops out. σp2=(0.60)2(0.20)2+(0.40)2(0.30)2=(0.36)(0.04)+(0.16)(0.09)=0.0144+0.0144=0.0288\sigma_p^2 = (0.60)^2(0.20)^2 + (0.40)^2(0.30)^2 = (0.36)(0.04) + (0.16)(0.09) = 0.0144 + 0.0144 = 0.0288. The portfolio standard deviation is the square root of the variance: σp=0.0288≈0.1697\sigma_p = \sqrt{0.0288} \approx 0.1697, or 16.97%. Distractor A is the weighted average of the standard deviations, which is only correct if ρ=1\rho = 1. Distractor B is the weighted average of the variances. Distractor C is the simple average of the standard deviations.

Question 6

An investor has a well-diversified portfolio of global equities. A financial crisis begins, causing a market downturn. Historically, the investor's portfolio has benefited from low correlations among its holdings. Which of the following is the most likely effect of the crisis on her portfolio's risk profile?

  1. The diversification benefits will increase as investors seek out unique, uncorrelated assets during the crisis.
  2. The risk-reducing benefits of her portfolio's diversification will likely diminish as asset correlations increase. (correct answer)
  3. Systematic risk will be diversified away, leaving only unsystematic risk which increases during the crisis.
  4. The correlations between assets in the portfolio will likely move towards -1.0, minimizing the portfolio's risk.
Explanation: Empirical evidence shows that during periods of market stress and financial crises, the correlation between asset classes and individual securities tends to increase and move towards +1.0. This phenomenon is sometimes called 'correlation breakdown.' As correlations rise, the benefits of diversification are reduced because assets begin to move in the same direction. Therefore, the portfolio's standard deviation will not be reduced as much as it was in normal market conditions.

Question 7

A portfolio consists of two stocks, A and B, which have a correlation of 0.7. A portfolio manager considers adding a third stock, C. The correlation between C and A is -0.5, and the correlation between C and B is -0.6. Which of the following is the most likely impact of adding Stock C to the portfolio?

  1. The portfolio's standard deviation will increase because a third source of risk is being added.
  2. The portfolio's expected return will remain unchanged, but its systematic risk will decrease.
  3. The overall correlation structure of the portfolio will become more positive, increasing its risk.
  4. The portfolio's standard deviation will decrease due to the negative correlations of the new asset. (correct answer)
Explanation: The initial portfolio of A and B is not well-diversified because of the high positive correlation (0.7). Stock C is negatively correlated with both existing components. Adding an asset that is negatively correlated with the existing portfolio provides significant diversification benefits. The negative covariance terms involving stock C will help offset the positive covariance between A and B and the individual variances, leading to a reduction in the overall portfolio standard deviation.

Question 8

An analyst is constructing an efficient frontier using two assets with positive expected returns. If the correlation coefficient between the two assets decreases from +0.5 to -0.5, how will the investment opportunity set change?

  1. The entire curve will shift to the right, indicating higher risk for any given level of return.
  2. The curve will become more bowed to the left, expanding the set of low-risk portfolio opportunities. (correct answer)
  3. The curve will not change its shape, but the minimum variance portfolio will have a higher return.
  4. The curve will become a straight line connecting the two assets, indicating no benefit from diversification.
Explanation: The curvature of the investment opportunity set (and the efficient frontier) is determined by the correlation between the assets. A correlation of +1.0 results in a straight line. As the correlation decreases, the curve bends or bows more to the left (towards the y-axis of returns). This indicates that for any given level of expected return, a portfolio with lower risk (standard deviation) can be formed. A decrease in correlation from +0.5 to -0.5 will therefore make the curve more bowed, expanding the set of attainable low-risk portfolios.

Question 9

A portfolio manager oversees a well-diversified fund containing 100 different stocks. The manager is considering adding one more stock to the fund. Four candidates are being evaluated. Which stock would provide the greatest marginal diversification benefit?

  1. The stock with the highest expected return.
  2. The stock with the lowest standalone standard deviation.
  3. The stock with the lowest correlation with the existing fund. (correct answer)
  4. The stock with the highest beta.
Explanation: For a well-diversified portfolio, the total risk is dominated by systematic (market) risk. The diversification benefit of adding a new asset is determined by how that asset's returns move in relation to the existing portfolio. An asset with a low (or negative) correlation will provide the greatest reduction in portfolio risk for a given level of expected return. Standalone risk (standard deviation) and expected return are less important than the correlation effect in this context. A high beta stock would add more systematic risk, which is counterproductive to diversification.

Question 10

The covariance of returns between Stock X and Stock Y is 0.0108. The standard deviation of Stock X is 20% and the standard deviation of Stock Y is 30%. Based on this information, an investor combining these two stocks should expect:

  1. Negative diversification effects, as the assets' returns tend to strongly offset each other.
  2. Minimal diversification effects, as the assets' returns are highly positively correlated.
  3. No diversification effects, as the covariance proves the returns are independent.
  4. Positive diversification effects, as the assets' returns have a low positive correlation. (correct answer)
Explanation: First, calculate the correlation coefficient using the formula ρXY=Cov(X,Y)/(σXσY)\rho_{XY} = \text{Cov}(X,Y) / (\sigma_X \sigma_Y). ρXY=0.0108/(0.20×0.30)=0.0108/0.06=0.18\rho_{XY} = 0.0108 / (0.20 \times 0.30) = 0.0108 / 0.06 = 0.18. A correlation of +0.18 is a low positive correlation. Since the correlation is less than +1.0, combining the assets will provide diversification benefits, reducing the portfolio's unsystematic risk. The effect is positive (i.e., beneficial), although not as strong as it would be with a negative correlation.

Question 11

An investor holds two assets, A and B, whose returns are perfectly negatively correlated (ρ=−1.0\rho = -1.0). Asset A has a standard deviation of 10% and Asset B has a standard deviation of 15%. What weight must be placed in Asset A to construct a zero-risk portfolio?

  1. 60% (correct answer)
  2. 50%
  3. 40%
  4. 33%
Explanation: For a two-asset portfolio with ρ=−1.0\rho = -1.0, the standard deviation is σp=∣wAσA−wBσB∣\sigma_p = |w_A\sigma_A - w_B\sigma_B|. To create a zero-risk portfolio (σp=0\sigma_p = 0), the weights must satisfy wAσA=wBσBw_A\sigma_A = w_B\sigma_B. Given wA+wB=1w_A + w_B = 1, we can write wB=1−wAw_B = 1 - w_A. Substituting this gives wAσA=(1−wA)σBw_A\sigma_A = (1 - w_A)\sigma_B. Plugging in the standard deviations: wA(0.10)=(1−wA)(0.15)w_A(0.10) = (1 - w_A)(0.15). Solving for wAw_A: 0.10wA=0.15−0.15wA⇒0.25wA=0.15⇒wA=0.15/0.25=0.600.10w_A = 0.15 - 0.15w_A \Rightarrow 0.25w_A = 0.15 \Rightarrow w_A = 0.15 / 0.25 = 0.60. Therefore, the weight in Asset A must be 60%.

Question 12

A portfolio manager is considering adding either a gold mining stock or a broad market S&P 500 index fund to a portfolio that currently consists primarily of technology and industrial stocks. Historically, gold has performed well during economic downturns when the broader market has fallen. What is the most likely correlation relationship and diversification outcome?

  1. The gold stock is likely to be highly positively correlated with the portfolio, offering poor diversification.
  2. The gold stock is likely to be negatively correlated with the portfolio, offering strong diversification benefits. (correct answer)
  3. The S&P 500 fund will be negatively correlated with the portfolio, offering the best risk reduction.
  4. Both the gold stock and the S&P 500 fund will be perfectly positively correlated with the existing portfolio.
Explanation: Gold is often considered a 'safe-haven' asset. During periods of economic uncertainty or stock market declines, investors often move capital into gold, causing its price to rise. This creates a negative correlation between gold and the general stock market. Since the existing portfolio is composed of market-sensitive stocks, adding the gold stock, with its likely negative correlation, would provide the strongest diversification benefits by hedging against market downturns. The S&P 500 fund would be highly positively correlated with the existing stocks.

Question 13

An analyst is comparing two potential two-asset portfolios, Portfolio X (Stock A and Stock B) and Portfolio Y (Stock A and Stock C). All three stocks have identical expected returns and standard deviations. The correlation between returns for Stocks A and B is 0.8, while the correlation between returns for Stocks A and C is -0.2. Assuming equal weights in both portfolios, which of the following statements is most accurate?

  1. Portfolio X will have a lower standard deviation than Portfolio Y due to its higher correlation.
  2. Portfolio Y will have a lower standard deviation than Portfolio X due to its lower correlation. (correct answer)
  3. Portfolio X and Portfolio Y will have the same standard deviation but Portfolio Y will have a higher expected return.
  4. Portfolio X and Portfolio Y will have the same standard deviation because the individual stock characteristics are identical.
Explanation: The benefit of diversification is inversely related to the correlation between the assets in the portfolio. A lower correlation coefficient leads to greater risk reduction. Since the correlation between A and C (-0.2) is significantly lower than between A and B (0.8), combining A and C will result in a portfolio with a lower standard deviation (less risk), all else being equal. Therefore, Portfolio Y will have a lower standard deviation than Portfolio X.

Question 14

A portfolio currently has an expected return of 10% and a standard deviation of 15%. A risk analyst suggests adding a new asset to the portfolio. This new asset has a standard deviation of 25% and a very low correlation with the existing portfolio. A junior analyst objects, stating, 'We cannot add an asset with 25% risk to our 15%-risk portfolio; it will automatically increase the portfolio's total risk.' The risk analyst's suggestion is:

  1. Invalid, because adding a riskier asset will always increase portfolio risk.
  2. Invalid, because the new portfolio's risk will be the weighted average of 15% and 25%, which must be higher than 15%.
  3. Plausible, because the new asset's higher beta could offset its standalone risk.
  4. Plausible, because the diversification effects from the low correlation could outweigh the new asset's higher standalone risk. (correct answer)
Explanation: The junior analyst's reasoning is flawed. The change in a portfolio's risk depends not only on the standalone risk of the added asset but also, crucially, on its correlation with the existing portfolio. If the correlation is sufficiently low (or negative), the risk-reducing diversification effect can be powerful enough to offset the high standalone risk of the new asset, potentially leading to a decrease in the overall portfolio's standard deviation. Therefore, the risk analyst's suggestion is plausible.

Question 15

An analyst is comparing two potential two-asset portfolios, Portfolio X (Stock A and Stock B) and Portfolio Y (Stock A and Stock C). All three stocks have identical expected returns and standard deviations. The correlation between returns for Stocks A and B is 0.8, while the correlation between returns for Stocks A and C is -0.2. Assuming equal weights in both portfolios, which of the following statements is most accurate?

  1. Portfolio X will have a lower standard deviation than Portfolio Y due to its higher correlation.
  2. Portfolio Y will have a lower standard deviation than Portfolio X due to its lower correlation. (correct answer)
  3. Portfolio X and Portfolio Y will have the same standard deviation but Portfolio Y will have a higher expected return.
  4. Portfolio X and Portfolio Y will have the same standard deviation because the individual stock characteristics are identical.
Explanation: The benefit of diversification is inversely related to the correlation between the assets in the portfolio. A lower correlation coefficient leads to greater risk reduction. Since the correlation between A and C (-0.2) is significantly lower than between A and B (0.8), combining A and C will result in a portfolio with a lower standard deviation (less risk), all else being equal. Therefore, Portfolio Y will have a lower standard deviation than Portfolio X.

Question 16

A portfolio manager oversees a well-diversified fund containing 100 different stocks. The manager is considering adding one more stock to the fund. Four candidates are being evaluated. Which stock would provide the greatest marginal diversification benefit?

  1. The stock with the highest expected return.
  2. The stock with the lowest standalone standard deviation.
  3. The stock with the lowest correlation with the existing fund. (correct answer)
  4. The stock with the highest beta.
Explanation: For a well-diversified portfolio, the total risk is dominated by systematic (market) risk. The diversification benefit of adding a new asset is determined by how that asset's returns move in relation to the existing portfolio. An asset with a low (or negative) correlation will provide the greatest reduction in portfolio risk for a given level of expected return. Standalone risk (standard deviation) and expected return are less important than the correlation effect in this context. A high beta stock would add more systematic risk, which is counterproductive to diversification.

Question 17

The covariance of returns between Stock X and Stock Y is 0.0108. The standard deviation of Stock X is 20% and the standard deviation of Stock Y is 30%. Based on this information, an investor combining these two stocks should expect:

  1. Negative diversification effects, as the assets' returns tend to strongly offset each other.
  2. Minimal diversification effects, as the assets' returns are highly positively correlated.
  3. No diversification effects, as the covariance proves the returns are independent.
  4. Positive diversification effects, as the assets' returns have a low positive correlation. (correct answer)
Explanation: First, calculate the correlation coefficient using the formula ρXY=Cov(X,Y)/(σXσY)\rho_{XY} = \text{Cov}(X,Y) / (\sigma_X \sigma_Y). ρXY=0.0108/(0.20×0.30)=0.0108/0.06=0.18\rho_{XY} = 0.0108 / (0.20 \times 0.30) = 0.0108 / 0.06 = 0.18. A correlation of +0.18 is a low positive correlation. Since the correlation is less than +1.0, combining the assets will provide diversification benefits, reducing the portfolio's unsystematic risk. The effect is positive (i.e., beneficial), although not as strong as it would be with a negative correlation.

Question 18

An investor replaces a stock in her two-stock portfolio with a new stock that has the exact same expected return and standard deviation as the original, but a much lower correlation with the other stock in the portfolio. Which of the following describes the effect on the new portfolio's expected return and standard deviation?

  1. The expected return will decrease, and the standard deviation will decrease.
  2. The expected return will be unchanged, and the standard deviation will be unchanged.
  3. The expected return will be unchanged, and the standard deviation will decrease. (correct answer)
  4. The expected return will increase, and the standard deviation will decrease.
Explanation: The expected return of a portfolio is the weighted average of the expected returns of its component assets. Since the new stock has the same expected return as the one it replaced, the portfolio's expected return will remain unchanged. However, the portfolio's standard deviation is a function of the individual standard deviations, the weights, and the correlation coefficient. A lower correlation coefficient leads to a lower portfolio standard deviation (greater diversification benefit). Therefore, the standard deviation will decrease.

Question 19

Consider the formula for the variance of a two-asset portfolio: σp2=w12σ12+w22σ22+2w1w2ρ12σ1σ2\sigma_p^2 = w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\rho_{12}\sigma_1\sigma_2. Which component of this formula captures the primary source of risk reduction from diversification?

  1. The sum of the first two terms, w12σ12+w22σ22w_1^2\sigma_1^2 + w_2^2\sigma_2^2, which represents the weighted individual asset risks.
  2. The individual asset variances, σ12\sigma_1^2 and σ22\sigma_2^2, as selecting low-variance assets is the goal.
  3. The interaction term, 2w1w2ρ12σ1σ22w_1w_2\rho_{12}\sigma_1\sigma_2, because its value depends on the correlation. (correct answer)
  4. The interaction term, which must always be positive and therefore must be minimized to reduce risk.
Explanation: The first two terms represent the weighted contribution of each asset's individual variance. The third term, which is equivalent to 2w1w2Cov(1,2)2w_1w_2\text{Cov}(1,2), captures how the assets move together. The diversification benefit comes from this interaction. When the correlation (ρ12\rho_{12}) is less than 1, this term is smaller than it would otherwise be, reducing the total variance. If correlation is negative, this term becomes negative, actively reducing the portfolio variance below the weighted sum of individual variances. Therefore, this term is the source of the diversification benefit.

Question 20

An analyst is constructing an efficient frontier using two assets with positive expected returns. If the correlation coefficient between the two assets decreases from +0.5 to -0.5, how will the investment opportunity set change?

  1. The entire curve will shift to the right, indicating higher risk for any given level of return.
  2. The curve will become more bowed to the left, expanding the set of low-risk portfolio opportunities. (correct answer)
  3. The curve will not change its shape, but the minimum variance portfolio will have a higher return.
  4. The curve will become a straight line connecting the two assets, indicating no benefit from diversification.
Explanation: The curvature of the investment opportunity set (and the efficient frontier) is determined by the correlation between the assets. A correlation of +1.0 results in a straight line. As the correlation decreases, the curve bends or bows more to the left (towards the y-axis of returns). This indicates that for any given level of expected return, a portfolio with lower risk (standard deviation) can be formed. A decrease in correlation from +0.5 to -0.5 will therefore make the curve more bowed, expanding the set of attainable low-risk portfolios.