Question 1

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

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 2

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

Accepted Answer

When two risky securities are positively correlated but not perfectly correlated, diversification benefits reduce the portfolio's standard deviation below the weighted average of the individual securities' standard deviations.

Question 3

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

Accepted Answer

In a two-security minimum variance portfolio, the security with the lower standard deviation will be weighted more heavily and the security with the higher standard deviation will be weighted less heavily. This is because the goal of a minimum variance portfolio is to minimize the overall variance of the portfolio, which is achieved by reducing exposure to the security with the higher standard deviation. Therefore, option B is the correct answer.

Question 4

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

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 5

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

Accepted Answer

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

Question 6

Security X has expected return of 12% and standard deviation of 20%.Security Y has expected return of 15% and standard deviation of 27%.If the two securities have a correlation coefficient of 0.7,what is their covariance?

Accepted Answer

Covariance = Correlation coefficient * Standard deviation of Security X * Standard deviation of Security Y= 0.7 * 0.20 * 0.27= 0.038

Question 7

Given an optimal risky portfolio with expected return of 18% and standard deviation of 21% and a risk free rate of 5%,what is the slope of the best feasible CAL?

Accepted Answer

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

Question 8

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

Accepted Answer

As the number of securities in a portfolio is increased, the diversification effect works to reduce the overall portfolio risk. However, this effect diminishes as more securities are added because of the law of diminishing marginal returns. Therefore, the average portfolio standard deviation decreases at a decreasing rate.

Question 9

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

-The expected rates of return of stocks A and B are _____ and _____,respectively.

Accepted Answer

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

Question 10

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

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 11

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

Accepted Answer

The portfolio opportunity set represents all possible combinations of expected returns and standard deviations (risk) that can be achieved by combining two assets in different proportions.

Question 12

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

Accepted Answer

Personnel changes are not a source of systematic risk. Systematic risk refers to risks that affect a large portion of the market or the entire market as a whole, such as changes in the economy, interest rates, inflation, and exchange rates. Personnel changes affect individual companies or industries and are therefore considered idiosyncratic risk rather than systematic risk.

Question 13

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

Accepted Answer

When the correlation coefficient between two securities is -1.0, it is possible to construct a portfolio that completely eliminates risk, making it riskless.

Question 14

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

-The standard deviations of stocks A and B are _____ and _____,respectively.

Accepted Answer

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

Question 15

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

Accepted Answer

Slope = (13 - 5)/26 = .31

Question 16

Given an optimal risky portfolio with expected return of 14% and standard deviation of 22% and a risk free rate of 6%,what is the slope of the best feasible CAL?

Accepted Answer

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

Question 17

The separation property refers to the conclusion that

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.

Question 18

The individual investor's optimal portfolio is designated by:

Accepted Answer

The optimal portfolio for an individual investor is determined where their highest indifference curve is tangent to the capital allocation line, indicating the best trade-off between risk and return according to their preferences.

Question 19

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

Accepted Answer

A correlation coefficient of -1.00 is preferred for diversification benefits, as it indicates that the stocks move in opposite directions, reducing overall portfolio risk.

Question 20

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.

Accepted Answer

The investor should choose the CAL with the highest reward-to-variability ratio, which corresponds to the steepest slope, to maximize returns for a given level of risk. This CAL will also maximize the investor's utility if it aligns with their risk preferences.

Quiz 7: Optimal Risky Portfolios