Kostenlos und ohne Konto. Zu jeder Frage gibt es den vollständigen Lösungsweg, einschließlich der Begründung, warum jede falsche Option falsch ist. Die Fragen sind eigene Aufgaben von Preparaio auf Englisch, keine offiziellen Fragen des CFA Institute.
1. Aino Paasikivi holds her entire equity allocation in shares of Brennick Savings Bank. She argues that she should expect a higher return on these shares than a well-diversified investor who holds the same shares, because she bears more risk. Under capital market theory, the expected return on the Brennick shares is most likely:
A. the same for both investors, because it depends only on the shares' systematic risk B. higher for her, because she bears the shares' total risk rather than only their market risk C. equal to the market's expected return, because both investors face the same market risk
Lösung und Erklärung Richtige Antwort: A the same for both investors, because it depends only on the shares' systematic risk
Asset prices, and therefore expected returns, are set in the market by investors who can diversify. They will not pay for firm-specific risk, so the shares' expected return reflects only their beta. Paasikivi bears extra, nonsystematic risk by choice, but the market does not compensate her for it; she simply holds an inefficient portfolio.
Warum die anderen Optionen falsch sind
B: Total risk includes firm-specific risk, which earns no premium because it can be eliminated at little cost by diversifying; choosing to bear it does not raise the expected return. C: The expected return depends on the shares' beta and equals the market's expected return only if the beta is 1, which is not given. Kernregel: Because nonsystematic risk can be diversified away at little cost, prices are set so that expected returns reward only systematic (beta) risk, regardless of how diversified an individual holder is.
Merksatz: Only systematic risk is priced; an undiversified investor bears risk that earns no reward.
2. Ngozi Ilori's research team builds equally weighted portfolios from a large universe of stocks that have similar volatilities and positive correlations with one another. As the number of stocks in a portfolio grows very large, the portfolio's variance approaches:
A. zero, because the stocks' individual risks offset one another B. the average covariance between pairs of the stocks C. the average variance of the individual stocks
Lösung und Erklärung Richtige Antwort: B the average covariance between pairs of the stocks
For an equally weighted portfolio of n stocks, variance equals (1/n) × average variance + ((n − 1)/n) × average covariance. As n grows, the first term goes to zero and the second approaches the average covariance. Because the stocks are positively correlated, this covariance is positive, so a floor of common (systematic) risk remains however many stocks are added.
Warum die anderen Optionen falsch sind
A: Only the firm-specific part of risk is diversified away. With positive correlations, the shared movement among the stocks leaves a positive variance. C: The average individual variance is the risk of holding a single stock. Adding stocks whose correlations are below one pushes portfolio variance below this level. Kernregel: In an equally weighted portfolio, the weight of individual variances shrinks as 1/n, so with many assets portfolio variance converges to the average covariance, the risk that cannot be diversified away.
Merksatz: Diversification removes firm-specific risk; the average covariance sets the risk floor of a well-diversified portfolio.
3. After several cyberattacks on payment processors dominated the news for weeks, Mariam Saleh sells her shares in Tolvik Payments. She estimates that Tolvik faces a far higher chance of a successful attack next year than the industry's long-run incident record suggests. Asked why, she says the attacks are all anyone talks about and she can easily recall several of them; she has not looked at any incident data. Which bias does her behavior reflect, and to which category does it belong?
A. Availability, a belief perseverance bias B. Availability, an information-processing bias C. Representativeness, a belief perseverance bias
Lösung und Erklärung Richtige Antwort: B Availability, an information-processing bias
Saleh judges the probability of an attack by how vivid and easy to recall the recent cases are, rather than from the long-run record, which is availability bias. Among cognitive errors, availability is classed as an information-processing bias because it reflects faulty use of information, not a refusal to update an existing belief.
Warum die anderen Optionen falsch sind
A: The bias is identified correctly, but belief perseverance biases, such as conservatism and confirmation, involve clinging to prior views; Saleh has instead changed her view sharply based on easily recalled news. C: Representativeness means judging by resemblance to a stereotype or familiar pattern; Saleh's estimate is driven by how easily she recalls examples, not by classifying Tolvik as similar to something else. Kernregel: Availability bias, estimating how likely an event is by how easily examples come to mind, is an information-processing error, whereas belief perseverance biases involve holding on to prior beliefs.
Merksatz: When easily recalled events drive a probability estimate, think availability, an information-processing error.
4. Leilani Kahale, a risk-averse investor, is choosing between two funds. Fund P and Fund Q both have an expected annual return of 8%; Fund P has an annual standard deviation of 12%, and Fund Q has an annual standard deviation of 18%. Which choice is consistent with her risk aversion?
A. Prefer Fund Q, which has the higher standard deviation B. Be indifferent, because both funds have the same expected return C. Prefer Fund P, which has the lower standard deviation
Lösung und Erklärung Richtige Antwort: C Prefer Fund P, which has the lower standard deviation
Risk aversion means an investor requires extra expected return to accept extra risk. Both funds offer 8%, so Fund P provides the same expected return with less risk. It gives Kahale higher utility and lies on a higher indifference curve than Fund Q.
Warum die anderen Optionen falsch sind
A: Choosing more risk for the same expected return describes a risk seeker, not a risk-averse investor. B: Indifference between the two funds describes a risk-neutral investor, who cares only about expected return. Kernregel: For equal expected returns, a risk-averse investor always prefers the portfolio with lower risk.
Merksatz: With equal expected returns, a risk-averse investor picks less risk, a risk-neutral investor is indifferent, and a risk seeker picks more risk.
5. Tomás Herrera, 45, will need to pay out about 80% of his investment portfolio in 18 months to buy out his business partner. He tells his adviser that he enjoys investing aggressively and is comfortable with large swings in value. His overall risk tolerance is most likely:
A. above average, because his willingness to take risk is high B. average, because his high willingness offsets his low ability C. below average, because his ability to take risk is low
Lösung und Erklärung Richtige Antwort: C below average, because his ability to take risk is low
Most of the portfolio must be available within 18 months, so a large loss could prevent Herrera from completing the buyout; this short horizon and large required outflow give him a low ability to bear risk. His stated taste for risk shows high willingness, but willingness cannot override ability. His overall risk tolerance is therefore below average, and the adviser should explain why to him.
Warum die anderen Optionen falsch sind
A: Relying on willingness alone ignores that the near-term payout sharply limits how much loss the portfolio can absorb. B: Ability and willingness are not averaged; the more conservative assessment, here his ability, determines overall risk tolerance. Kernregel: When willingness and ability to take risk conflict, the lower one governs; ability caps the risk a client should take.
Merksatz: When ability and willingness conflict, use the lower of the two.
6. The Sennett Creek Municipal Bond Fund must sell a large holding of a thinly traded bond to meet heavy redemptions. Although the issuer's credit quality is unchanged, the fund can find buyers only at a price 6% below the bond's last quoted price. Which type of risk has the fund experienced?
A. Liquidity risk, a financial risk B. Credit risk, a financial risk C. Operational risk, a nonfinancial risk
Lösung und Erklärung Richtige Antwort: A Liquidity risk, a financial risk
The bond's issuer is as creditworthy as before, so the loss does not come from default risk. The fund had to sell quickly into a thin market and accept a price well below the last quote, which is liquidity risk. Liquidity risk arises from financial markets and is classified as a financial risk.
Warum die anderen Optionen falsch sind
B: Credit risk is the risk that a borrower or counterparty fails to pay, but the issuer's credit quality is unchanged. C: Operational risk arises from failures of people, processes, systems or external events; nothing broke down here, and the loss came from market conditions. Kernregel: Liquidity risk, a financial risk, is the risk that an asset can be sold quickly only at a significant discount to its fair value because buyers are scarce.
Merksatz: A forced sale at a large discount with no change in credit quality is liquidity risk.
7. Kerrow Valley Water Holdings is a regulated water utility. Using the statistics in the exhibit, what is the beta of its shares?
Kerrow Valley Water Holdings: annual return statistics Statistic Value Standard deviation of Kerrow Valley shares 14.0% Standard deviation of the market index 18.5% Correlation of Kerrow Valley shares with the market index 0.55
A. 0.42 B. 0.73 C. 0.76
Lösung und Erklärung Richtige Antwort: A 0.42
Kerrow Valley's shares are less volatile than the market and only moderately correlated with it. Beta = 0.55 × 0.140 / 0.185 = 0.42, so the shares are expected to move less than half as much as the market, which fits a defensive, regulated business.
Rechenweg
β = ρ × σi / σm β = 0.55 × 0.140 / 0.185 β = 0.42 BA-II-Plus-Tastenfolge
0.55 × 0.14 ÷ 0.185 = [0.42]
Warum die anderen Optionen falsch sind
B: Inverts the volatility ratio, computing 0.55 × 0.185 / 0.140; beta divides the asset's standard deviation by the market's. C: Uses only the ratio of standard deviations (0.140 / 0.185) without the correlation, treating all of the shares' volatility as market-related. Intermediate displayed workings may be rounded; retain full precision until the final answer.
Kernregel: β = ρ(i,m) × σi / σm: the correlation times the asset's standard deviation divided by the market's.
Merksatz: Beta = correlation × (asset σ / market σ); keep the asset's standard deviation in the numerator.
8. A global healthcare equity fund has an expected annual return of 9.50% and an annual standard deviation of 21.5%. Gabriel Moreau, whose risk-aversion coefficient is 2, ranks investments with the mean-variance utility function U = E(r) − 0.5Aσ². What is the fund's utility for Moreau?
A. −12.00% B. 0.26% C. 4.88%
Lösung und Erklärung Richtige Antwort: C 4.88%
The fund's variance is 0.215² = 0.046225. With A = 2, the risk penalty is 0.5 × 2 × 0.046225 = 0.046225. Subtracting it from the 0.095 expected return gives a utility of 0.048775, or about 4.88%.
Rechenweg
Variance = 0.215^2 = 0.046225 Risk penalty = 0.5 × 2 × 0.046225 = 0.046225 U = 0.095 − 0.046225 = 0.048775, or 4.88% BA-II-Plus-Tastenfolge
0.215 x² × 2 × 0.5 = STO 1; 0.095 − RCL 1 = × 100 = [4.88]
Warum die anderen Optionen falsch sind
A: Uses the standard deviation instead of the variance in the penalty (0.095 − 0.5 × 2 × 0.215), which vastly overstates the risk deduction. B: Omits the factor 0.5 and deducts 2 × 0.046225 = 0.09245, which doubles the risk penalty. Intermediate displayed workings may be rounded; retain full precision until the final answer.
Kernregel: Mean-variance utility is U = E(r) − 0.5 × A × σ², with expected return and standard deviation entered as decimals.
Merksatz: Square the standard deviation, multiply by 0.5 and by A, then subtract the result from the expected return.
9. Consultant Joaquín Ortega compares three clients: the Glenvarra Rail Pension Plan, a defined benefit plan most of whose members are already retired; the Calderra Software Pension Plan, a defined benefit plan whose members are mostly in their 20s and 30s; and the Jaziri Future Generations Fund, a sovereign wealth fund that saves surplus oil revenues for future citizens. Which of his conclusions is least likely accurate?
A. The rail plan needs more liquidity than the software plan, because more of its members are drawing benefits. B. The software plan has a shorter horizon than the rail plan, because its members' benefits are still small. C. The future generations fund can hold a large share of illiquid assets, because it has few near-term payouts.
Lösung und Erklärung Richtige Antwort: B The software plan has a shorter horizon than the rail plan, because its members' benefits are still small.
The software plan's members are decades away from retirement, so most of its benefit payments fall far in the future, giving it a long investment horizon. The rail plan is already paying pensions to most of its members, so its liabilities are nearer and its horizon is shorter. The small size of the young members' accrued benefits does not shorten the horizon; the timing of the payments does.
Warum die anderen Optionen falsch sind
A: This is accurate: a mature plan pays benefits to many retirees every month, so it needs more cash and liquid assets than a plan whose members are still working. C: This is accurate: a savings-type sovereign wealth fund invests for future generations with little need to pay out soon, so it can accept illiquidity in exchange for higher expected returns. Kernregel: A defined benefit plan's horizon and liquidity needs depend on when its liabilities fall due: a plan of mostly retirees has a shorter horizon and higher liquidity needs than a plan of young workers.
Merksatz: Horizon follows the timing of liabilities: a young workforce means a long horizon, a mature plan means a shorter horizon and more liquidity.
10. Rahel Tesfaye holds two funds: a global equity index fund (70% of her portfolio, annual standard deviation 15.5%) and a long/short credit fund (30% of her portfolio, annual standard deviation 9.0%). The correlation between the two funds' returns is 0.35. Her portfolio's standard deviation is closest to:
A. 11.63% B. 12.06% C. 13.55%
Lösung und Erklärung Richtige Antwort: B 12.06%
The squared weighted risks are 0.011772 for the equity fund and 0.000729 for the credit fund, and the covariance term is 2 × 0.70 × 0.30 × 0.35 × 0.155 × 0.090 = 0.002051. Portfolio variance is 0.014552, and its square root is about 12.06%. Because the correlation is only 0.35, this is below the 13.55% weighted average of the two standard deviations, which shows the benefit of diversification.
Rechenweg
Equity term: (0.70 × 0.155)^2 = 0.011772 Credit term: (0.30 × 0.090)^2 = 0.000729 Covariance term: 2 × 0.70 × 0.30 × 0.35 × 0.155 × 0.090 = 0.002051 Variance = 0.011772 + 0.000729 + 0.002051 = 0.014552 Standard deviation = √0.014552 = 0.1206, or 12.06% BA-II-Plus-Tastenfolge
0.7 × 0.155 = x² STO 1; 0.3 × 0.09 = x² STO 2; 2 × 0.7 × 0.3 × 0.35 × 0.155 × 0.09 = STO 3; RCL 1 + RCL 2 + RCL 3 = √x × 100 = [12.06]
Warum die anderen Optionen falsch sind
A: Drops the factor 2 in the covariance term, so the covariance is counted only once (variance 0.013526). C: Takes the weighted average of the standard deviations (0.70 × 15.5% + 0.30 × 9.0%), which is correct only if the correlation is +1. Intermediate displayed workings may be rounded; retain full precision until the final answer.
Kernregel: σp = √(w1²σ1² + w2²σ2² + 2w1w2ρσ1σ2); with a correlation below +1 the result is less than the weighted average of the standard deviations.
Merksatz: A correlation below +1 pulls portfolio risk below the weighted average of the standard deviations; keep the factor 2 in the covariance term.
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