Question 1

The global minimum variance portfolio formed from two risky securities will be riskless when the correlation coefficient between the two securities is
A) 0.0.
B) 1.0.
C) 0.5.
D) −1.0.
E) any negative number.

Accepted Answer

The global minimum variance portfolio formed from two risky securities will be riskless when the correlation coefficient between the two securities is -1.0. This is because a perfect negative correlation (-1.0) between the two securities means that their returns move exactly in opposite directions, allowing for the elimination of risk through diversification.

Question 2

In a two-security minimum variance portfolio where the correlation between securities is greater than −1.0,
A) the security with the higher standard deviation will be weighted more heavily.
B) the security with the higher standard deviation will be weighted less heavily.
C) the two securities will be equally weighted.
D) the risk will be zero.
E) the return will be zero.

Accepted Answer

In a minimum variance portfolio, the goal is to minimize risk. When the correlation between two securities is greater than -1.0, diversification benefits exist. To minimize risk, the portfolio will weight more heavily the security with the lower standard deviation, as it contributes less to the portfolio's overall risk. Therefore, the security with the higher standard deviation will be weighted less heavily.

Question 3

A two-asset portfolio with a standard deviation of zero can be formed when
A) the assets have a correlation coefficient less than zero.
B) the assets have a correlation coefficient equal to zero.
C) the assets have a correlation coefficient greater than zero.
D) the assets have a correlation coefficient equal to one.
E) the assets have a correlation coefficient equal to negative one.

Accepted Answer

A two-asset portfolio can achieve a standard deviation of zero when the assets have a correlation coefficient of -1. This perfect negative correlation means that the assets move exactly opposite to each other, allowing for the elimination of risk through diversification.

Question 4

Consider the following probability distribution for stocks A and B: $\begin{array}{cccc}
\text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \
1 & 0.15 & 8 \% & 8 \% \
2 & 0.20 & 13\% & 7\% \
3 & 0.15 & 12\%& 6\% \
4 & 0.30 & 14\%& 9\% \
5 & 0.20 & 16\% & 11 \%
\end{array}$
 The expected rates of return of stocks A and B are _____ and _____, respectively.
A) 13.2%; 9%
B) 13%; 8.4%
C) 13.2%; 7.7%
D) 7.7%; 13.2%

Accepted Answer

The answer of Consider the following probability distribution for stocks...

Question 5

As the number of securities in a portfolio is increased, what happens to the average portfolio standard deviation?
A) It increases at an increasing rate.
B) It increases at a decreasing rate.
C) It decreases at an increasing rate.
D) It decreases at a decreasing rate.
E) It first decreases, then starts to increase as more securities are added.

Accepted Answer

The average portfolio standard deviation decreases at a decreasing rate as more securities are added, due to the benefits of diversification. Initially, adding more securities significantly reduces risk, but after a certain point, the marginal benefit of adding more securities diminishes.

Question 6

Consider the following probability distribution for stocks A and B: $\begin{array}{cccc}
\text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \
1 & 0.15 & 8 \% & 8 \% \
2 & 0.20 & 13\% & 7\% \
3 & 0.15 & 12\%& 6\% \
4 & 0.30 & 14\%& 9\% \
5 & 0.20 & 16\% & 11 \%
\end{array}$

The coefficient of correlation between A and B is
A) 0.474.
B) 0.612.
C) 0.590.
D) 1.206.

Accepted Answer

The coefficient of correlation is calculated using the covariance of returns and the standard deviations of the returns of stocks A and B. After calculating these values, the correlation coefficient is found to be approximately 0.590.

Question 7

When borrowing and lending at a risk-free rate are allowed, which capital allocation line (CAL) should the investor choose to combine with the efficient frontier?I) The one with the highest reward-to-variability ratio.II) The one that will maximize his utility.III) The one with the steepest slope.IV) The one with the lowest slope.
A) I and III
B) I and IV
C) II and IV
D) I only
E) I, II, and III

Accepted Answer

The correct choices are I, II, and III. The CAL with the highest reward-to-variability ratio (I) is equivalent to the one with the steepest slope (III), as both indicate the highest return per unit of risk, which is desirable for investors. Additionally, investors should choose the CAL that maximizes their utility (II), as this aligns with their risk tolerance and investment goals. The one with the lowest slope (IV) would not be preferred because it offers lower returns for a given level of risk.

Question 8

When two risky securities that are positively correlated but not perfectly correlated are held in a portfolio,
A) the portfolio standard deviation will be greater than the weighted average of the individual security standard deviations.
B) the portfolio standard deviation will be less than the weighted average of the individual security standard deviations.
C) the portfolio standard deviation will be equal to the weighted average of the individual security standard deviations.
D) the portfolio standard deviation will always be equal to the securities' covariance.

Accepted Answer

When two risky securities that are positively correlated but not perfectly correlated are combined in a portfolio, diversification benefits lead to a portfolio standard deviation that is less than the weighted average of the individual security standard deviations. This is because the imperfect correlation allows for the offsetting of some risks.

Question 9

In words, the covariance considers the probability of each scenario happening and the interaction between
A) securities' returns relative to their variances.
B) securities' returns relative to their mean returns.
C) securities' returns relative to other securities' returns.
D) the level of return a security has in that scenario and the overall portfolio return.
E) the variance of the security's return in that scenario and the overall portfolio variance.

Accepted Answer

The answer of In words, the covariance considers the probability...

Question 10

For a two-stock portfolio, what would be the preferred correlation coefficient between the two stocks?
A) +1.00
B) +0.50
C) 0.00
D) −1.00
E) None of the options are correct.

Accepted Answer

A correlation coefficient of -1.00 between two stocks in a portfolio is preferred for diversification purposes because it means the stocks move in exactly opposite directions, reducing the portfolio's overall risk.

Question 11

The line representing all combinations of portfolio expected returns and standard deviations that can be constructed from two available assets is called the
A) risk/reward tradeoff line.
B) capital allocation line.
C) efficient frontier.
D) portfolio opportunity set.
E) Security Market Line.

Accepted Answer

The line representing all combinations of portfolio expected returns and standard deviations that can be constructed from two available assets is called the portfolio opportunity set. This set includes all possible portfolios that can be formed with a given pair of assets, showing the trade-off between risk (standard deviation) and expected return for those portfolios.

Question 12

Given an optimal risky portfolio with expected return of 20%, standard deviation of 24%, and a risk free rate of 7%, what is the slope of the best feasible CAL?
A) 0.64
B) 0.14
C) 0.62
D) 0.33
E) 0.54

Accepted Answer

The answer of Given an optimal risky portfolio with expected...

Question 13

Given an optimal risky portfolio with expected return of 13%, standard deviation of 26%, and a risk free rate of 5%, what is the slope of the best feasible CAL?
A) 0.60
B) 0.14
C) 0.08
D) 0.36
E) 0.31

Accepted Answer

The answer of Given an optimal risky portfolio with expected...

Question 14

The risk that can be diversified away in a portfolio is referred to as ___________. I) diversifiable riskII) unique riskIII) systematic riskIV) firm-specific risk
A) I, III, and IV
B) II, III, and IV
C) III and IV
D) I, II, and IV
E) I, II, III, and IV

Accepted Answer

Diversifiable risk, unique risk, and firm-specific risk are all terms used to describe the type of risk that can be mitigated through diversification in a portfolio. Systematic risk, on the other hand, affects the entire market and cannot be diversified away.

Question 15

Security X has expected return of 12% and standard deviation of 18%. Security Y has expected return of 15% and standard deviation of 26%. If the two securities have a correlation coefficient of 0.7, what is their covariance?
A) 0.038
B) 0.070
C) 0.018
D) 0.033
E) 0.054

Accepted Answer

Covariance is calculated using the formula: Cov(X,Y) = ρ(X,Y) * σX * σY, where ρ(X,Y) is the correlation coefficient between X and Y, σX is the standard deviation of X, and σY is the standard deviation of Y. Substituting the given values: Cov(X,Y) = 0.7 * 0.18 * 0.26 = 0.03276, which rounds to 0.033.

Question 16

Given an optimal risky portfolio with expected return of 12%, standard deviation of 26%, and a risk free rate of 5%, what is the slope of the best feasible CAL?
A) 0.64
B) 0.27
C) 0.08
D) 0.33
E) 0.36

Accepted Answer

The answer of Given an optimal risky portfolio with expected...

Question 17

Which of the following is not a source of systematic risk?
A) The business cycle
B) Interest rates
C) Personnel changes
D) The inflation rate
E) Exchange rates

Accepted Answer

Systematic risk refers to the overall risk that affects the entire market or a segment of the market. It is not specific to a particular company or industry. Factors such as the business cycle, interest rates, the inflation rate, and exchange rates are external and affect the entire market. In contrast, personnel changes are specific to a company and represent unsystematic risk, which can be diversified away.

Question 18

Consider the following probability distribution for stocks A and B: $\begin{array}{cccc}
\text { State } & \text { Probability } & \text { Return on Stock A } & \text { Return on Stock B } \
1 & 0.15 & 8 \% & 8 \% \
2 & 0.20 & 13\% & 7\% \
3 & 0.15 & 12\%& 6\% \
4 & 0.30 & 14\%& 9\% \
5 & 0.20 & 16\% & 11 \%
\end{array}$
  The standard deviations of stocks A and B are _____ and _____, respectively.
A) 1.56%; 1.99%
B) 2.45%; 1.66%
C) 3.22%; 2.01%
D) 1.54%; 1.11%

Accepted Answer

To calculate the standard deviation of the returns for stocks A and B, we first need to find the expected return (mean) for each stock, then calculate the variance, and finally take the square root of the variance to get the standard deviation.**For Stock A:**- Expected Return = $0.15 \times 8\% + 0.20 \times 13\% + 0.15 \times 12\% + 0.30 \times 14\% + 0.20 \times 16\% = 12.7\%$- Variance = $0.15 \times (8\% - 12.7\%)^2 + 0.20 \times (13\% - 12.7\%)^2 + 0.15 \times (12\% - 12.7\%)^2 + 0.30 \times (14\% - 12.7\%)^2 + 0.20 \times (16\% - 12.7\%)^2 = 6.01\%$- Standard Deviation = $\sqrt{6.01\%} \approx 2.45\%$**For Stock B:**- Expected Return = $0.15 \times 8\% + 0.20 \times 7\% + 0.15 \times 6\% + 0.30 \times 9\% + 0.20 \times 11\% = 8.35\%$- Variance = $0.15 \times (8\% - 8.35\%)^2 + 0.20 \times (7\% - 8.35\%)^2 + 0.15 \times (6\% - 8.35\%)^2 + 0.30 \times (9\% - 8.35\%)^2 + 0.20 \times (11\% - 8.35\%)^2 = 2.76\%$- Standard Deviation = $\sqrt{2.76\%} \approx 1.66\%$Therefore, the correct answer is B) 2.45%; 1.66%.

Question 19

The standard deviation of a two-asset portfolio is a linear function of the assets' weights when
A) the assets have a correlation coefficient less than zero.
B) the assets have a correlation coefficient equal to zero.
C) the assets have a correlation coefficient greater than zero.
D) the assets have a correlation coefficient equal to one.
E) the assets have a correlation coefficient less than one.

Accepted Answer

The standard deviation of a two-asset portfolio becomes a linear function of the assets' weights only when the assets have a correlation coefficient equal to one. This is because, at a correlation of one, the assets move perfectly together, making the portfolio's risk (standard deviation) a simple weighted average of the individual assets' risks.

Question 20

The separation property refers to the conclusion that
A) the determination of the best risky portfolio is objective, and the choice of the best complete portfolio is subjective.
B) the choice of the best complete portfolio is objective, and the determination of the best risky portfolio is objective.
C) the choice of inputs to be used to determine the efficient frontier is objective, and the choice of the best CAL is subjective.
D) the determination of the best CAL is objective, and the choice of the inputs to be used to determine the efficient frontier is subjective.
E) investors are separate beings and will, therefore, have different preferences regarding the risk-return tradeoff.

Accepted Answer

The separation property, as described in modern portfolio theory, indicates that the process of selecting the optimal mix of risky assets (to form the best risky portfolio) is based on objective criteria (market data, expected returns, variances, and covariances). In contrast, the choice of the best complete portfolio, which involves combining the risky portfolio with a risk-free asset, is subjective and depends on the individual investor's risk tolerance.

Quiz 7: Efficient Diversification

The global minimum variance portfolio formed from two risky securities will be riskless when the correlation coefficient between the two securities is

In a two-security minimum variance portfolio where the correlation between securities is greater than −1.0,

A two-asset portfolio with a standard deviation of zero can be formed when

As the number of securities in a portfolio is increased, what happens to the average portfolio standard deviation?

When two risky securities that are positively correlated but not perfectly correlated are held in a portfolio,

In words, the covariance considers the probability of each scenario happening and the interaction between

For a two-stock portfolio, what would be the preferred correlation coefficient between the two stocks?

The line representing all combinations of portfolio expected returns and standard deviations that can be constructed from two available assets is called the

Given an optimal risky portfolio with expected return of 20%, standard deviation of 24%, and a risk free rate of 7%, what is the slope of the best feasible CAL?

Given an optimal risky portfolio with expected return of 13%, standard deviation of 26%, and a risk free rate of 5%, what is the slope of the best feasible CAL?

The risk that can be diversified away in a portfolio is referred to as ___________. I) diversifiable riskII) unique riskIII) systematic riskIV) firm-specific risk

Security X has expected return of 12% and standard deviation of 18%. Security Y has expected return of 15% and standard deviation of 26%. If the two securities have a correlation coefficient of 0.7, what is their covariance?

Given an optimal risky portfolio with expected return of 12%, standard deviation of 26%, and a risk free rate of 5%, what is the slope of the best feasible CAL?

Which of the following is not a source of systematic risk?

The standard deviation of a two-asset portfolio is a linear function of the assets' weights when

The separation property refers to the conclusion that