PORTFOLIO RISK AND RETURN: PART II Flashcards
(124 cards)
When combining a risk-free asset with a risky portfolio, the expected return of the combined portfolio is:
A. Always equal to the risk-free rate regardless of weights
B. A weighted average of the risk-free rate and the risky portfolio’s expected return
C. Always higher than the risky portfolio’s expected return
Correct Answer: B
Explanation:
The expected return formula E(Rp) = WA E(RA) + WB E(RB) shows that when combining assets, the portfolio return is the weighted average of the component returns, including when one asset is risk-free.
Choice A is incorrect because the portfolio return varies with the weights allocated to each asset.
Choice C is incorrect because if more weight is allocated to the risk-free asset (which typically has lower returns), the portfolio return will be lower than the risky portfolio alone.
The standard deviation of a portfolio combining a risk-free asset (Asset B) with a risky asset (Asset A) is calculated as:
A. σP = √(WA²σA² + WB²σB²)
B. σP = WA σA
C. σP = WA σA + WB σB
Correct Answer: B
Explanation:
Since the risk-free asset has zero standard deviation (σB = 0) and zero correlation with the risky asset, the portfolio standard deviation simplifies to σP = WA σA.
Choice A represents the general two-asset formula but doesn’t account for the risk-free asset having zero standard deviation.
Choice C incorrectly adds standard deviations linearly rather than using the proper portfolio risk formula.
In the capital allocation line (CAL) framework, the line connecting the risk-free asset to a risky portfolio represents:
A. All possible combinations of the two assets with varying weights
B. Only efficient portfolios that minimize risk for a given return
C. The maximum return available for any level of risk
Correct Answer: A
Explanation:
The CAL shows all possible risk-return combinations when mixing a risk-free asset with a risky portfolio by varying the weights between them.
Choice B describes the efficient frontier concept, not specifically the CAL.
Choice C is incorrect as the CAL represents one specific set of combinations, not necessarily the maximum return for each risk level.
According to the reading, when Asset B is risk-free and Asset A is risky, the correlation coefficient ρAB equals:
A. +1.0
B. 0
C. -1.0
Correct Answer: B
Explanation:
A risk-free asset has zero correlation with any risky asset because its returns are constant and don’t vary with market conditions.
Choice A would indicate perfect positive correlation, which is impossible between a risk-free and risky asset.
Choice C would indicate perfect negative correlation, which would require the risk-free asset’s returns to move opposite to the risky asset, but risk-free returns are constant.
If an investor allocates 70% to a risky portfolio and 30% to a risk-free asset, the portfolio’s risk level will be:
A. 70% of the risky portfolio’s standard deviation
B. 30% of the risky portfolio’s standard deviation
C. The weighted average of both assets’ standard deviations
Correct Answer: A
Explanation:
With the formula σP = WA σA, where WA = 0.70, the portfolio risk is 70% of the risky asset’s standard deviation.
Choice B incorrectly uses the weight of the risk-free asset.
Choice C is incorrect because the risk-free asset contributes zero to portfolio risk, so there’s no meaningful weighted average.
The primary advantage of combining a risk-free asset with a risky portfolio is:
A. Elimination of all investment risk
B. Ability to achieve any desired risk level along the capital allocation line
C. Guaranteed positive returns under all market conditions
Correct Answer: B
Explanation:
By varying the weights between risk-free and risky assets, investors can achieve any risk level from zero (100% risk-free) to the full risk of the risky portfolio (100% risky asset).
Choice A is incorrect because risk is only eliminated if 100% is allocated to the risk-free asset.
Choice C is wrong because if weight is allocated to the risky asset, returns are not guaranteed to be positive.
In the context of modern portfolio theory, a risk-free asset is characterized by:
A. Low but positive correlation with market returns
B. Zero standard deviation and zero correlation with risky assets
C. Negative correlation with all risky assets
Correct Answer: B
Explanation:
A risk-free asset, by definition, has no variability in returns (zero standard deviation) and no systematic relationship with risky assets (zero correlation).
Choice A describes a low-risk asset, not a risk-free asset.
Choice C would describe an asset that moves opposite to risky assets, which is not characteristic of typical risk-free assets like government bonds.
When constructing a portfolio with both risk-free and risky assets, an investor who wants to achieve a return higher than the risky portfolio alone must:
A. Allocate more than 100% to the risky asset through borrowing
B. Find assets with negative correlation to the risky portfolio
C. Diversify across multiple risky assets
Correct Answer: A
Explanation:
To achieve returns higher than the risky portfolio alone, an investor must leverage by borrowing at the risk-free rate and investing more than 100% in the risky asset.
Choice B describes a different diversification strategy that doesn’t necessarily lead to higher expected returns.
Choice C involves diversification among risky assets but doesn’t address achieving returns higher than a single risky portfolio.
The slope of the capital allocation line (CAL) connecting a risk-free asset to a risky portfolio represents:
A. The correlation coefficient between the two assets
B. The risk premium per unit of risk (Sharpe ratio)
C. The total return of the risky portfolio
Correct Answer: B
Explanation:
The slope of the CAL is calculated as [E(RA) - Rf]/σA, which is the excess return per unit of risk, also known as the Sharpe ratio.
Choice A is incorrect because the correlation between a risk-free asset and risky asset is always zero.
Choice C is wrong because the slope measures the risk-return trade-off, not the absolute return level.
The capital allocation line (CAL) represents:
A. The line of possible portfolio risk and return combinations given the risk-free rate and the risk and return of a portfolio of risky assets
B. The optimal risky portfolio for all investors assuming homogeneous expectations
C. The relationship between systematic risk and expected return for individual securities
Correct Answer: A
Explanation:
The CAL represents all possible combinations of risk and return that an investor can achieve by combining a risk-free asset with a risky portfolio
Option B describes the Capital Market Line (CML), which is a specific CAL that applies when all investors have homogeneous expectations
Option C describes the Security Market Line (SML), not the CAL
The slope of the capital allocation line represents:
A. The correlation coefficient between the risk-free asset and risky portfolio
B. The reward-to-risk ratio of the risky portfolio
C. The beta of the risky portfolio
Correct Answer: B
Explanation:
The slope of the CAL equals (E(Rp) - Rf)/σp, which is the reward-to-risk ratio or Sharpe ratio of the risky portfolio
Option A is incorrect because the risk-free asset has zero correlation with risky assets by definition
Option C is incorrect as beta measures systematic risk relative to the market, not the slope of the CAL
Which statement best describes the optimal risky portfolio for an individual investor?
A. It is always the market portfolio regardless of investor preferences
B. It is the risky portfolio that results in the most preferred set of possible portfolios in terms of risk and return
C. It is the portfolio with the highest expected return
Correct Answer: B
Explanation:
The optimal risky portfolio is the one that offers the greatest expected utility to the investor, creating the most preferred set of possible portfolios when combined with the risk-free asset
Option A is incorrect because individual investors may have different optimal risky portfolios based on their expectations and preferences
Option C is incorrect because the highest return portfolio may not be optimal due to excessive risk
The capital market line (CML) is defined as:
A. Any capital allocation line for an individual investor
B. The capital allocation line using the market portfolio as the optimal risky portfolio
C. The line connecting all efficient portfolios of risky assets
Correct Answer: B
Explanation:
The CML is the specific CAL that uses the market portfolio as the optimal risky portfolio, applicable when all investors have homogeneous expectations
Option A is incorrect because individual CALs may use different risky portfolios
Option C describes the efficient frontier, not the CML
The y-intercept of the capital market line equals:
A. The expected return of the market portfolio
B. The risk-free rate
C. The market risk premium
Correct Answer: B
Explanation:
The y-intercept of the CML occurs when portfolio risk (σp) equals zero, which corresponds to investing entirely in the risk-free asset, yielding the risk-free rate
Option A is incorrect as the market portfolio return is a point on the CML, not the y-intercept
Option C is incorrect as the market risk premium is the difference between market return and risk-free rate
Under the assumption of homogeneous expectations, all investors will:
A. Choose the same portfolio weights for the risk-free asset and risky portfolio
B. Face the same efficient frontier of risky portfolios and have the same optimal risky portfolio
C. Have the same risk tolerance and indifference curves
Correct Answer: B
Explanation:
Homogeneous expectations means all investors have identical estimates of expected returns, standard deviations, and correlations, leading to the same efficient frontier and optimal risky portfolio
Option A is incorrect because investors will choose different weights based on their individual risk preferences
Option C is incorrect because risk tolerance and indifference curves reflect individual preferences, not expectations
The equation of the capital market line is:
A. E(Rp) = Rf + [E(RM) - Rf] × βp
B. E(Rp) = Rf + [(E(RM) - Rf)/σM] × σp
C. E(Rp) = Rf + [E(RM) - Rf] × σp
Correct Answer: B
Explanation:
The CML equation shows expected portfolio return as a function of portfolio risk (standard deviation), with the slope being the market risk premium divided by market risk
Option A is the Security Market Line (SML) equation using beta
Option C is missing the denominator σM in the slope term
The market risk premium in the context of the capital market line represents:
A. The additional return per unit of total risk
B. The additional return per unit of systematic risk
C. The correlation between market returns and individual security returns
Correct Answer: A
Explanation:
In the CML context, the market risk premium [E(RM) - Rf] represents the additional return investors receive for bearing one unit of total risk (standard deviation)
Option B describes the market risk premium in the context of the SML, which deals with systematic risk (beta)
Option C describes correlation, not risk premium
An investor who chooses to take on no risk (σp = 0) will earn:
A. The expected return of the market portfolio
B. The risk-free rate
C. Zero return
Correct Answer: B
Explanation:
When portfolio risk equals zero, the investor is investing entirely in the risk-free asset and will earn the risk-free rate
Option A is incorrect because the market portfolio has positive risk
Option C is incorrect because the risk-free asset still provides a positive return
If investors can both lend and borrow at the risk-free rate, they can:
A. Only select portfolios on the efficient frontier
B. Select portfolios to the right of the market portfolio by borrowing
C. Eliminate all portfolio risk
Correct Answer: B
Explanation:
Borrowing at the risk-free rate allows investors to leverage their investment in the market portfolio, creating portfolios with higher risk and return than the market portfolio alone
Option A is incorrect because investors can move beyond the efficient frontier through borrowing and lending
Option C is incorrect because risk can only be eliminated by investing entirely in the risk-free asset
According to the capital market line, an investor can expect to receive one unit of market risk premium for every:
A. Unit of systematic risk accepted
B. Unit of total risk accepted
C. Percentage point of expected return
Correct Answer: B
Explanation:
The CML shows that investors receive market risk premium in proportion to total risk (standard deviation) accepted: [E(RM) - Rf]/σM per unit of σp
Option A describes the SML relationship with systematic risk (beta)
Option C incorrectly describes the relationship in reverse
Active portfolio management differs from passive investment strategy by:
A. Using market index weights for the optimal risky asset portfolio
B. Investing more than market weights in securities believed to be undervalued
C. Always achieving higher returns than passive strategies
Correct Answer: B
Explanation:
Active management involves deviating from market weights by overweighting securities believed to be undervalued and underweighting those believed to be overvalued
Option A describes passive management
Option C is incorrect as active management doesn’t guarantee higher returns
In Figure 84.4, a portfolio with WM = 125% indicates:
A. The investor has lent 25% of their wealth at the risk-free rate
B. The investor has borrowed 25% of their wealth at the risk-free rate
C. The investor holds 125% of the market portfolio and 25% risk-free assets
Correct Answer: B
Explanation:
WM = 125% means the investor has borrowed 25% of their wealth to invest 125% in the market portfolio, with the remaining -25% representing the borrowing (negative position in risk-free asset)
Option A is incorrect as lending would result in WM < 100%
Option C is incorrect as the weights must sum to 100%
Passive investment strategy involves:
A. Actively selecting undervalued securities based on fundamental analysis
B. Investing in an index that serves as a proxy for the market portfolio
C. Frequently trading to exploit market inefficiencies
Correct Answer: B
Explanation:
Passive investment strategy involves investing in a market index that serves as a proxy for the market portfolio, based on the belief that markets are informationally efficient
Option A describes active portfolio management
Option C also describes active management techniques
The efficient frontier in Figure 84.3 Determining the Optimal Risky Portfolio and Optimal CAL
Assuming Homogeneous Expectations represents:
A. All possible combinations of risk and return for individual securities
B. The set of portfolios that offer the highest expected return for each level of risk
C. The capital allocation line for a specific investor
Correct Answer: B
Explanation:
The efficient frontier shows the set of optimal risky portfolios that maximize expected return for each level of risk
Option A is incorrect as individual securities are not necessarily efficient
Option C describes the CAL, which is a straight line from the risk-free rate