Question 1

As the number of individual stocks in a portfolio increases, the portfolio standard deviation:
A)increases at a constant rate.
B)remains unchanged.
C)decreases at a constant rate.
D)decreases at a diminishing rate.
E)decreases at an increasing rate.

Accepted Answer

As the number of individual stocks in a portfolio increases, the portfolio standard deviation initially decreases at a diminishing rate because adding more stocks reduces the overall risk of the portfolio by diversification. However, eventually adding more stocks to the portfolio will have a diminishing impact on reducing the portfolio's risk as the portfolio becomes more diversified. Therefore, the rate of decrease in the portfolio standard deviation will decrease over time, resulting in a decreasing rate.

Question 2

Which one of the following is eliminated, or at least greatly reduced, by increasing the number of individual securities held in a portfolio?
A)number of economic states
B)various expected returns caused by changing economic states
C)market risk
D)diversifiable risk
E)nondiversifiable risk

Accepted Answer

Diversifiable risk, also known as unsystematic risk, is the risk specific to individual securities or companies. By increasing the number of individual securities held in a portfolio, the impact of any one security's performance on the overall portfolio is reduced. This means that any specific risk of one security can be diversified away, resulting in a reduction of overall portfolio risk. The other answer choices are not eliminated or greatly reduced by increasing the number of individual securities held in a portfolio.

Question 3

You are graphing the investment opportunity set for a portfolio of two securities with the expected return on the vertical axis and the standard deviation on the horizontal axis. If the correlation coefficient of the two securities is +1, the opportunity set will appear as which one of the following shapes?
A)conical shape
B)linear with an upward slope
C)combination of two straight lines
D)hyperbole
E)horizontal line

Accepted Answer

If the correlation coefficient of the two securities is +1, then the opportunity set will be a linear combination of the two securities without any diversification benefits. The portfolio of the two securities will have a standard deviation equal to the weighted average of the standard deviation of the two assets, and the expected return will be the weighted average of their expected returns. Therefore, the opportunity set will be a straight line with an upward slope.

Question 4

Which one of the following statements is correct concerning asset allocation?
A)Because there is an ideal mix, all investors should use the same asset allocation for their portfolios.
B)The minimum variance portfolio will have a 50/50 asset allocation between stocks and bonds.
C)Asset allocation affects the expected return but not the risk level of a portfolio.
D)There is an ideal asset allocation between stocks and bonds given a specified level of risk.
E)Asset allocation should play a minor role in portfolio construction.

Accepted Answer

Asset allocation is a key aspect of portfolio construction and involves dividing investments between different asset classes, such as stocks, bonds, and cash. The ideal asset allocation will depend on the individual's risk tolerance, investment goals, and time horizon. A well-designed asset allocation strategy can help to reduce risk and increase returns. Therefore, choice D is correct as it highlights the importance of finding the ideal asset allocation based on a specified level of risk. The other options are incorrect as they either suggest a one-size-fits-all approach (A), make incorrect assumptions about asset allocation (B and C), or downplay its significance in portfolio construction (E).

Question 5

Which one of the following statements about efficient portfolios is correct?
A)Any efficient portfolio will lie below the minimum variance portfolio when the expected portfolio return is plotted against the portfolio standard deviation.
B)An efficient portfolio will have the lowest standard deviation of any portfolio consisting of the same two securities.
C)There are multiple efficient portfolios that can be constructed using the same two securities.
D)Any portfolio mix consisting of only two securities will be an efficient portfolio.
E)There is only one efficient portfolio that can be constructed using two securities.

Accepted Answer

Efficient portfolios are those portfolios that provide the highest level of expected return for a given level of risk, or the lowest level of risk for a given level of expected return. There can be multiple efficient portfolios that can be constructed using the same two securities, because the efficient frontier (which represents all efficient portfolios) is typically curved and not a straight line. Therefore, choice A, B, D, and E are incorrect statements about efficient portfolios.

Question 6

To reduce risk as much as possible, you should combine assets which have one of the following correlation relationships?
A)strong positive
B)slightly positive
C)slightly negative
D)strongly negative
E)zero

Accepted Answer

To minimize risk in a portfolio, combining assets with a strongly negative correlation is most effective because their prices move in opposite directions, reducing the overall volatility of the portfolio.

Question 7

Which one of the following correlation coefficients must apply to two assets if the equally weighted portfolio of those assets creates a minimum variance portfolio that has a standard deviation of zero?
A)−1.0
B)−.5
C)0
D).5
E)1.0

Accepted Answer

A correlation coefficient of -1.0 between two assets means they move perfectly inversely to each other. When combined in an equally weighted portfolio, this perfect negative correlation can offset each asset's volatility, potentially reducing the portfolio's standard deviation to zero, thus creating a minimum variance portfolio.

Question 8

What is the correlation coefficient of two assets that are uncorrelated?
A)−100
B)−1
C)0
D)1
E)100

Accepted Answer

The correlation coefficient ranges from -1 to 1, representing a perfect negative correlation and perfect positive correlation, respectively. A coefficient of 0 indicates no correlation, which is the case for two uncorrelated assets.

Question 9

You currently have a portfolio comprised of 70% stocks and 30% bonds. Which one of the following must be true if you change the asset allocation?
A)The expected return will remain constant.
B)The revised portfolio will be perfectly negatively correlated with the initial portfolio.
C)The two portfolios could have significantly different standard deviations.
D)The portfolio variance will be unaffected.
E)The portfolio variance will most likely decrease in value.

Accepted Answer

If you change the asset allocation, the standard deviations of the two portfolios could be significantly different depending on the specific assets you select. The expected return may change depending on the new asset allocation. The portfolios are unlikely to be perfectly negatively correlated, and the portfolio variance is likely to be affected by the change in asset allocation. While it is possible that the portfolio variance may decrease, this is not necessarily true as it depends on the specific assets selected.

Question 10

You are graphing the portfolio expected return against the portfolio standard deviation for a portfolio consisting of two securities. Which one of the following statements is correct regarding this graph?
A)Risk-taking investors should select the minimum variance portfolio.
B)Risk-averse investors should select the portfolio with the lowest rate of return.
C)Some portfolios will be efficient while others will not.
D)The minimum variance portfolio will have the lowest portfolio expected return of any of the possible portfolios.
E)All possible portfolios will graph as efficient portfolios.

Accepted Answer

The graph of the portfolio expected return against the portfolio standard deviation will result in a graph where some of the portfolios are efficient, i.e., they offer the highest expected return for a given level of risk. The minimum variance portfolio will not necessarily have the lowest portfolio expected return of any of the possible portfolios, and it may not be the best choice for risk-taking investors. The portfolio with the lowest rate of return may not necessarily be the best choice for risk-averse investors either. Therefore, option C is the correct choice.

Question 11

Which one of the following distinguishes a minimum variance portfolio?
A)lowest risk portfolio of any possible portfolio given the same securities but in differing proportions
B)lowest risk portfolio possible given any specified expected rate of return
C)the zero risk portfolio created by maximizing the asset allocation mix
D)any portfolio with an expected standard deviation of 9% or less
E)any portfolio created with securities that are evenly weighted in respect to the asset allocation mix

Accepted Answer

A minimum variance portfolio is defined as the portfolio with the lowest possible risk (measured by standard deviation) out of all possible portfolios that can be constructed from a given set of securities. Therefore, option A correctly distinguishes a minimum variance portfolio. Option B is incorrect because it implies that there is a minimum variance portfolio for every expected rate of return, which is not true. Option C is incorrect because a zero risk portfolio does not exist in practice. Option D is incorrect because it puts a specific limit on the standard deviation that is not always true. Option E is incorrect because the allocation mix is not specified and evenly weighting the securities does not necessarily create a minimum variance portfolio.

Question 12

Assume the returns on Stock X were positive in January, February, April, July, and November. During the other months, the returns on Stock X were negative. The returns on Stock Y were positive in January, April, May, July, August, and October, and negative the remaining months. Which one of the following correlation coefficients best describes the relationship between Stock X and Stock Y?
A)−1.0
B)−.5
C)0
D).5
E)1.0

Accepted Answer

The answer of Assume the returns on Stock X were...

Question 13

Where does the minimum variance portfolio lie in respect to the investment opportunity set?
A)lowest point
B)highest point
C)most leftward point
D)most rightward point
E)exact center

Accepted Answer

The minimum variance portfolio lies at the most leftward point on the efficient frontier of the investment opportunity set. This point represents the portfolio with the lowest level of risk (variance).

Question 14

Which one of the following statements is correct?
A)A portfolio variance is a weighted average of the variances of the individual securities which comprise the portfolio.
B)A portfolio variance is dependent upon the portfolio's asset allocation.
C)A portfolio variance is unaffected by the correlations between the individual securities held in the portfolio.
D)The portfolio variance must be greater than the lowest variance of any of the securities held in the portfolio.
E)The portfolio variance must be less than the lowest variance of any of the securities held in the portfolio.

Accepted Answer

The portfolio variance is dependent upon the portfolio's asset allocation. The more diversified a portfolio is, the lower the variance will be due to the effects of correlation. Therefore, choice A is false because the portfolio variance takes into account the correlations between the individual securities. Choice C is false for the same reason. Choice D is false because it is possible for the portfolio variance to be lower than the lowest variance of any of the securities held in the portfolio if those securities are negatively correlated with each other. Choice E is also false for the same reason.

Question 15

Which one of the following correlation relationships has the potential to completely eliminate risk?
A)perfectly positive
B)positive
C)negative
D)perfectly negative
E)uncorrelated

Accepted Answer

A perfectly negative correlation means that the two assets move in opposite directions at all times, meaning that when one decreases in value, the other increases in value. This provides a completely hedged portfolio, essentially eliminating all risk.

Question 16

If two assets have a zero correlation, their returns will:
A)always move in the same direction by the same amount.
B)always move in the same direction but not necessarily by the same amount.
C)move randomly and independently of each other.
D)always move in opposite directions but not necessarily by the same amount.
E)always move in opposite directions by the same amount.

Accepted Answer

A zero correlation between two assets indicates that there is no linear relationship between their returns. Therefore, their returns will move randomly and independently of each other.

Question 17

Which one of the following correlation coefficients can provide the greatest diversification benefit?
A)−1.0
B)−.5
C)0
D).5
E)1.0

Accepted Answer

A correlation coefficient of -1.0 indicates a perfect negative correlation, meaning that as one asset increases in value, the other decreases, providing the greatest diversification benefit.

Question 18

How will the returns on two assets react if those returns have a perfect positive correlation?
I. move in the same direction
II. move in opposite directions
III. move by the same amount
IV. move by either equal or unequal amounts
A)I and III only
B)I and IV only
C)II and III only
D)II and IV only
E)III only

Accepted Answer

When two assets have a perfect positive correlation, their returns move in the same direction, which means when one asset's return increases, the other's return also increases, and vice versa. However, moving by the same amount is not guaranteed; they can move by either equal or unequal amounts, depending on the magnitude of their returns.

Question 19

Non-diversifiable risk:
A)can be cut almost in half by investing in 10 stocks provided each stock is in a different industry.
B)can almost be eliminated by investing in 35 diverse securities.
C)remains constant regardless of the number of securities held in a portfolio.
D)has little, if any, impact on the actual realized returns for a diversified portfolio.
E)should be ignored by investors.

Accepted Answer

Non-diversifiable risk, also known as systematic risk, is the risk that cannot be eliminated by diversification, as it is inherent in the entire market or economy. This risk remains constant regardless of the number of securities held in a portfolio. Therefore, option C is the correct answer.

Question 20

A portfolio comprised of which one of the following is most apt to be the minimum variance portfolio?
A)100% stocks
B)100% bonds
C)50/50 mix of stocks and bonds
D)30% stocks and 70% bonds
E)30% bonds and 70% stocks

Accepted Answer

The minimum variance portfolio is the portfolio with the lowest possible level of risk or volatility given a certain expected return level. Generally, adding uncorrelated or negatively correlated assets to a portfolio can result in lower overall portfolio volatility. In this case, the 30% stocks and 70% bonds portfolio is likely to have the lowest volatility as stocks and bonds are typically negatively correlated. Therefore, portfolios with a mix of stocks and bonds are likely to have lower volatility than portfolios invested solely in stocks or bonds. A 100% bond portfolio would also have low volatility, but it would likely have a lower expected return than a portfolio with some stocks.

Quiz 11: Diversification and Risky Asset Allocation

As the number of individual stocks in a portfolio increases, the portfolio standard deviation:

Which one of the following is eliminated, or at least greatly reduced, by increasing the number of individual securities held in a portfolio?

Which one of the following statements is correct concerning asset allocation?

Which one of the following statements about efficient portfolios is correct?

To reduce risk as much as possible, you should combine assets which have one of the following correlation relationships?

Which one of the following correlation coefficients must apply to two assets if the equally weighted portfolio of those assets creates a minimum variance portfolio that has a standard deviation of zero?

What is the correlation coefficient of two assets that are uncorrelated?

You currently have a portfolio comprised of 70% stocks and 30% bonds. Which one of the following must be true if you change the asset allocation?

You are graphing the portfolio expected return against the portfolio standard deviation for a portfolio consisting of two securities. Which one of the following statements is correct regarding this graph?

Which one of the following distinguishes a minimum variance portfolio?

Where does the minimum variance portfolio lie in respect to the investment opportunity set?

Which one of the following statements is correct?

Which one of the following correlation relationships has the potential to completely eliminate risk?

If two assets have a zero correlation, their returns will:

Which one of the following correlation coefficients can provide the greatest diversification benefit?

How will the returns on two assets react if those returns have a perfect positive correlation? I. move in the same direction II. move in opposite directions III. move by the same amount IV. move by either equal or unequal amounts

Non-diversifiable risk:

A portfolio comprised of which one of the following is most apt to be the minimum variance portfolio?