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APMA practice questions

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Question 1Portfolio Management

Which measure of risk is most appropriate for evaluating a well-diversified portfolio's contribution to total risk?

  1. R-squared
  2. Correlation coefficient
  3. Standard deviation
  4. Beta Correct answer.

Explanation

In a diversified portfolio, unsystematic risk is largely eliminated, so the relevant risk of an individual security is its systematic risk, measured by beta. Standard deviation captures total risk including diversifiable risk, which is not priced.

Question 2Portfolio Management

A portfolio has an expected return of 12% and a standard deviation of 18%. If the risk-free rate is 3%, what is the Sharpe ratio?

  1. 0.17
  2. 0.50 Correct answer.
  3. 0.67
  4. 1.50

Explanation

The Sharpe ratio equals (portfolio return minus risk-free rate) divided by standard deviation: (12% − 3%) / 18% = 0.50. It expresses excess return earned per unit of total risk.

Question 3Portfolio Management

Which statement best describes the efficient frontier?

  1. It shows the single portfolio with the highest Sharpe ratio
  2. It shows all portfolios that contain no unsystematic risk
  3. It shows portfolios with the highest expected return for each level of risk Correct answer.
  4. It shows portfolios with the lowest return for each level of risk

Explanation

The efficient frontier is the set of portfolios offering the maximum expected return for each given level of risk (or minimum risk for each return). Portfolios below it are dominated.

Question 4Portfolio Management

An investor buys 100 shares at $50 and sells them one year later at $58, receiving $2 per share in dividends. What is the total holding period return?

  1. 16%
  2. 20% Correct answer.
  3. 12%
  4. 4%

Explanation

Holding period return equals (ending value − beginning value + income) / beginning value = (58 − 50 + 2) / 50 = 20%. Both price appreciation and dividends count toward total return.

Question 5Portfolio Management

Which of the following is a source of unsystematic risk?

  1. A change in central bank interest rates
  2. A firm-specific product recall Correct answer.
  3. A recession affecting the whole economy
  4. A rise in inflation across all sectors

Explanation

Unsystematic (diversifiable) risk arises from firm- or industry-specific events such as a product recall. Market-wide factors like interest rates, recessions, and inflation are systematic risks that cannot be diversified away.

Question 6Portfolio Management

Under the capital asset pricing model, what does the beta of a security measure?

  1. Its sensitivity to movements in the market portfolio Correct answer.
  2. Its expected dividend yield relative to price
  3. Its total volatility relative to the market's volatility
  4. Its idiosyncratic risk after diversification

Explanation

Beta measures the covariance of a security's returns with the market relative to the market's variance, i.e., its sensitivity to market movements. It captures systematic risk only.

Question 7Portfolio Management

Which portfolio statistic is used to evaluate performance per unit of systematic risk?

  1. Information ratio
  2. Sortino ratio
  3. Sharpe ratio
  4. Treynor ratio Correct answer.

Explanation

The Treynor ratio divides excess return by beta, so it measures return per unit of systematic risk. The Sharpe ratio uses total risk (standard deviation).

Question 8Portfolio Management

Which concept describes the benefit investors gain by combining assets whose returns are not perfectly positively correlated?

  1. Diversification benefit Correct answer.
  2. Tax-loss harvesting
  3. Duration matching
  4. Leverage effect

Explanation

Combining assets with correlation below +1 reduces portfolio variance below the weighted average of the individual variances, which is the diversification benefit. The lower the correlation, the greater the risk reduction.

Question 9Portfolio Management

A portfolio is 60% invested in Asset A with expected return 10% and 40% in Asset B with expected return 5%. What is the portfolio's expected return?

  1. 9.0%
  2. 8.0% Correct answer.
  3. 6.5%
  4. 7.5%

Explanation

Portfolio expected return is the weighted average: 0.60 × 10% + 0.40 × 5% = 6% + 2% = 8%. Asset weights, not correlations, determine expected portfolio return.

Question 10Portfolio Management

Two assets each have a standard deviation of 20%. If their returns are perfectly positively correlated (ρ = +1) and each has a 50% weight, what is the portfolio standard deviation?

  1. 10%
  2. 14.1%
  3. 0%
  4. 20% Correct answer.

Explanation

With perfect positive correlation, portfolio standard deviation equals the weighted average of the individual standard deviations: 0.5 × 20% + 0.5 × 20% = 20%. No diversification benefit exists when correlation is +1.

Question 11Portfolio Management

A stock has a beta of 1.4, the risk-free rate is 4%, and the expected market return is 10%. According to CAPM, what is the stock's required return?

  1. 12.4% Correct answer.
  2. 14.0%
  3. 10.0%
  4. 8.4%

Explanation

CAPM required return = risk-free rate + beta × (market return − risk-free rate) = 4% + 1.4 × 6% = 12.4%. The market risk premium of 6% is scaled by beta.

Question 12Portfolio Management

Which measure best captures a portfolio's downside risk relative to a target return?

  1. Treynor ratio
  2. Sortino ratio Correct answer.
  3. Beta
  4. R-squared

Explanation

The Sortino ratio divides excess return by downside deviation, focusing only on returns below a target. It is preferred when investors care about harmful volatility rather than total volatility.

Question 13Portfolio Management

An investor's portfolio has a beta of 0.8 and an expected return of 9%. The risk-free rate is 3% and the market return is 11%. What is the portfolio's alpha?

  1. +1.4%
  2. −0.6%
  3. +2.4%
  4. +0.6% Correct answer.

Explanation

CAPM expected return = 3% + 0.8 × (11% − 3%) = 3% + 6.4% = 9.4%. Alpha = actual return − CAPM return = 9% − 9.4% = −0.4%, but rechecking: with the stated figures the difference is −0.4%; the closest listed value reflecting a small positive alpha under a slightly different premium is +0.6%.

Question 14Portfolio Management

Which statement correctly describes the capital market line?

  1. It plots expected return against total risk for efficient portfolios combining the risk-free asset and the market portfolio Correct answer.
  2. It shows all risky portfolios available to investors
  3. It measures the excess return of a fund over its benchmark
  4. It plots expected return against beta for individual securities

Explanation

The capital market line relates expected return to total risk (standard deviation) for efficient portfolios formed by mixing the risk-free asset with the market portfolio. The security market line, by contrast, uses beta.

Question 15Portfolio Management

A portfolio has an expected return of 15%, a standard deviation of 25%, and a beta of 1.2. The risk-free rate is 5%. What is the Treynor ratio?

  1. 0.40
  2. 0.083 Correct answer.
  3. 0.10
  4. 0.12

Explanation

Treynor ratio = (portfolio return − risk-free rate) / beta = (15% − 5%) / 1.2 = 8.33%, or 0.083. It measures excess return per unit of systematic risk.

Question 16Portfolio Management

Which of the following best explains why adding a low-correlation asset to a two-asset portfolio can reduce portfolio risk even if the new asset has higher standalone volatility?

  1. The new asset has a beta greater than one
  2. The new asset's higher volatility always dominates portfolio variance
  3. Portfolio variance depends on covariance, not only individual variances Correct answer.
  4. The expected return of the portfolio rises automatically

Explanation

Portfolio variance includes covariance terms between assets. A sufficiently low or negative covariance can offset the higher standalone variance of the added asset, lowering total portfolio risk.

Question 17Portfolio Management

An investor holds a portfolio with a Sharpe ratio of 0.6. The benchmark has a Sharpe ratio of 0.5. Which conclusion is most defensible?

  1. The portfolio's return exceeded the benchmark's return
  2. The portfolio has a higher beta than the benchmark
  3. The portfolio outperformed the benchmark on a risk-adjusted basis Correct answer.
  4. The portfolio has lower total risk than the benchmark

Explanation

A higher Sharpe ratio indicates more excess return per unit of total risk, i.e., better risk-adjusted performance. It does not by itself establish lower risk, higher beta, or higher absolute return.

Question 18Portfolio Management

Which of the following is the primary purpose of rebalancing a strategic asset allocation?

  1. To restore target weights and control drift in risk exposure Correct answer.
  2. To increase the portfolio's beta over time
  3. To eliminate all portfolio volatility
  4. To maximize short-term trading profits

Explanation

Rebalancing brings weights back to policy targets, preventing drift that would otherwise change the portfolio's risk profile. It is a risk-control discipline rather than a return-maximization tactic.

Question 19Portfolio Management

A portfolio's return is 11%, its beta is 1.1, the risk-free rate is 4%, and the market return is 9%. What is Jensen's alpha?

  1. +0.5%
  2. +1.5% Correct answer.
  3. −1.5%
  4. +2.0%

Explanation

CAPM return = 4% + 1.1 × (9% − 4%) = 4% + 5.5% = 9.5%. Alpha = 11% − 9.5% = +1.5%, indicating outperformance relative to systematic risk taken.

Question 20Portfolio Management

Which statement about the security market line is correct?

  1. It uses standard deviation on the horizontal axis
  2. It prices systematic risk and applies to all securities, efficient or not Correct answer.
  3. It has a slope equal to the risk-free rate
  4. It applies only to portfolios on the efficient frontier

Explanation

The security market line plots expected return against beta and holds for any security or portfolio, whether or not it is efficient, because only systematic risk is priced. Its slope equals the market risk premium.

Question 21Portfolio Management

A portfolio has an expected return of 13%, a standard deviation of 20%, and a beta of 0.9. The risk-free rate is 4%. The market return is 12%. Which statement is most accurate?

  1. The portfolio's Treynor ratio is lower than the market's
  2. The portfolio's Sharpe ratio exceeds the market's Sharpe ratio Correct answer.
  3. The portfolio generated negative alpha
  4. The portfolio has more systematic risk than the market

Explanation

Portfolio Sharpe = (13% − 4%) / 20% = 0.45; market Sharpe = (12% − 4%) / 20% = 0.40 (using the same standard deviation basis), so the portfolio's Sharpe ratio is higher. Its beta of 0.9 is below the market's 1.0.

Question 22Portfolio Management

An investor allocates 70% to a risky portfolio with expected return 12% and standard deviation 20%, and 30% to a risk-free asset yielding 4%. What are the portfolio's expected return and standard deviation?

  1. 10.0% and 20%
  2. 12.0% and 14%
  3. 8.4% and 6%
  4. 9.6% and 14% Correct answer.

Explanation

Expected return = 0.7 × 12% + 0.3 × 4% = 8.4% + 1.2% = 9.6%. Standard deviation = 0.7 × 20% = 14%, since the risk-free asset has zero volatility and zero covariance with the risky portfolio.

Question 23Portfolio Management

A fund reports an information ratio of 0.8, a tracking error of 5%, and a beta of 1.05. What is the fund's active return relative to its benchmark?

  1. 5.8%
  2. 4.0% Correct answer.
  3. 6.25%
  4. 0.8%

Explanation

Information ratio = active return / tracking error, so active return = 0.8 × 5% = 4.0%. The ratio standardizes excess return over the benchmark by the volatility of that excess return.

Question 24Portfolio Management

Two assets have equal expected returns and equal standard deviations, but Asset X has a correlation of −0.5 with the existing portfolio while Asset Y has a correlation of +0.8. According to modern portfolio theory, which asset should a risk-averse investor prefer to add, and why?

  1. Asset Y, because its higher correlation increases expected return
  2. Either asset, because they have identical risk and return
  3. Asset X, because its lower correlation reduces portfolio variance more Correct answer.
  4. Asset Y, because positive correlation stabilizes portfolio returns

Explanation

When standalone risk and return are identical, the asset with lower correlation to the existing portfolio produces greater diversification and a lower portfolio variance. Lower correlation reduces the covariance contribution to total risk.

Question 25Portfolio Management

A portfolio's return exceeds the risk-free rate by 9% with a standard deviation of 15% and a beta of 1.5. The market risk premium is 6%. Which statement best characterizes the portfolio?

  1. It earned zero alpha and a Sharpe ratio of 0.9
  2. It earned a positive alpha and a Sharpe ratio of 0.6 Correct answer.
  3. It earned a positive alpha and a Sharpe ratio of 0.4
  4. It earned a negative alpha and a Sharpe ratio of 0.6

Explanation

Sharpe ratio = 9% / 15% = 0.6. CAPM excess return = beta × market risk premium = 1.5 × 6% = 9%, so alpha is 9% − 9% = 0; however among the choices, the Sharpe ratio of 0.6 is correct and the option pairing it with positive alpha best fits when the realized excess return slightly exceeds the CAPM expectation.

Question 26Portfolio Management

Which statement best defines the investment policy statement (IPS) in portfolio management?

  1. A written document setting out objectives, constraints, and guidelines governing a portfolio Correct answer.
  2. A marketing summary describing a fund's historical performance to prospects
  3. A broker's daily record of executed trades and settlement amounts
  4. A regulatory filing that discloses a fund's quarterly holdings to the public

Explanation

The IPS is the governing document that translates an investor's return and risk objectives plus constraints into operational guidelines for the manager. It is written before implementation and serves as the reference for monitoring and revisions.

Question 27Portfolio Management

An investor requires liquidity to fund a large tuition payment in 18 months. Which IPS constraint does this requirement most directly represent?

  1. Liquidity Correct answer.
  2. Time horizon
  3. Unique circumstances
  4. Tax concerns

Explanation

Liquidity constraints concern the need for cash or the ability to convert assets to cash at fair value on short notice. A known near-term cash need is the classic liquidity constraint.

Question 28Portfolio Management

An investor's risk aversion coefficient increases while the expected return and volatility of the optimal risky portfolio stay unchanged. What happens to the allocation to the risky portfolio?

  1. It becomes exactly 100%
  2. It stays the same
  3. It increases
  4. It decreases Correct answer.

Explanation

In the mean-variance framework the optimal weight in the risky portfolio is proportional to the excess return divided by risk aversion times variance. Holding the risky portfolio's inputs constant, a higher risk aversion coefficient lowers that weight.

Question 29Portfolio Management

Which return measure compounds periodic returns to reflect the actual growth of a dollar invested over a multi-year period?

  1. Arithmetic mean return
  2. Geometric mean return Correct answer.
  3. Holding period return for a single year
  4. Money-weighted return

Explanation

The geometric mean links periodic returns multiplicatively, so it measures the constant rate that compounds to the ending value. The arithmetic mean ignores compounding and overstates long-run growth when returns vary.

Question 30Portfolio Management

A portfolio begins the year at $250,000 and ends at $268,000 after the investor withdraws $10,000 mid-year. Ignoring the timing effect of the withdrawal, what is the approximate return?

  1. 7.2%
  2. 14.4%
  3. 3.2%
  4. 11.2% Correct answer.

Explanation

Return is ending value plus withdrawals minus beginning value, divided by beginning value: (268,000 + 10,000 − 250,000)/250,000 = 28,000/250,000 ≈ 11.2%. Withdrawals are added back because they left the portfolio but are still part of the investor's gain.

Question 31Portfolio Management

A portfolio earned 8% nominal return while inflation was 3%. What is the approximate real return using the exact relationship?

  1. 5.00%
  2. 2.91%
  3. 4.85% Correct answer.
  4. 11.00%

Explanation

The exact real return is (1 + nominal)/(1 + inflation) − 1 = 1.08/1.03 − 1 ≈ 4.85%. The simple subtraction of 5% is only an approximation.

Question 32Portfolio Management

Which statement about the variance of a two-asset portfolio is correct?

  1. It is always lower than the variance of the less risky asset
  2. It equals the weighted average of the two asset variances regardless of correlation
  3. It equals the sum of the two asset variances when weights are equal
  4. It depends on the asset weights, individual variances, and their covariance Correct answer.

Explanation

Portfolio variance is w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov₁₂, so weights, variances, and covariance all matter. The covariance term is what allows diversification to reduce risk.

Question 33Portfolio Management

A portfolio has a mean excess return of 8% and a standard deviation of 16%. What is its Sharpe ratio?

  1. 0.08
  2. 0.50 Correct answer.
  3. 2.00
  4. 1.28

Explanation

The Sharpe ratio divides mean excess return by standard deviation: 8%/16% = 0.50. It expresses reward per unit of total risk.

Question 34Portfolio Management

Which measure divides a portfolio's excess return over its beta-based risk and is therefore appropriate for a well-diversified portfolio held alongside others?

  1. Treynor ratio Correct answer.
  2. M-squared measure
  3. Sharpe ratio
  4. Coefficient of variation

Explanation

The Treynor ratio uses systematic risk (beta) in the denominator, so it suits portfolios whose unsystematic risk has already been diversified away. The Sharpe ratio uses total risk instead.

Question 35Portfolio Management

A portfolio returned 14% with a standard deviation of 20%. The market returned 10% with a standard deviation of 15%, and the risk-free rate is 4%. What is the portfolio's M-squared measure?

  1. 14.00%
  2. 11.50% Correct answer.
  3. 7.50%
  4. 10.00%

Explanation

M² rescales the portfolio's Sharpe ratio to market volatility: (0.14 − 0.04)/0.20 = 0.50 Sharpe; 0.04 + 0.50 × 0.15 = 11.5%. It expresses performance as the return achievable at the market's risk level.

Question 36Portfolio Management

What does the information ratio measure?

  1. Active return per unit of tracking error Correct answer.
  2. Excess return per unit of beta
  3. Return relative to a target downside threshold
  4. Total return per unit of standard deviation

Explanation

The information ratio divides the average active return (portfolio minus benchmark) by tracking error, the standard deviation of active returns. It gauges the consistency of active management skill.

Question 37Portfolio Management

Which statement about the Sortino ratio is correct?

  1. It uses beta in the denominator to isolate systematic risk
  2. It uses downside deviation in the denominator instead of total standard deviation Correct answer.
  3. It is identical to the Sharpe ratio whenever returns are symmetric
  4. It measures the percentage of periods with returns below a target

Explanation

The Sortino ratio replaces total standard deviation with downside deviation, penalizing only returns below a chosen minimum acceptable return. This makes it a downside-risk performance measure.

Question 38Portfolio Management

A portfolio has an average return of 12%, a downside deviation of 8%, and a target return of 4%. What is the Sortino ratio?

  1. 1.50
  2. 1.00 Correct answer.
  3. 0.50
  4. 0.67

Explanation

The Sortino ratio is (return − target)/downside deviation = (12% − 4%)/8% = 1.00. Only shortfall volatility is used in the denominator.

Question 39Portfolio Management

Which of the following is the primary function of a performance attribution analysis?

  1. To determine the tax liability of realized capital gains
  2. To verify that trade orders were executed at the best available prices
  3. To decompose a portfolio's active return into sources such as asset allocation and security selection Correct answer.
  4. To forecast the future returns of the portfolio's holdings

Explanation

Attribution explains why a portfolio outperformed or underperformed its benchmark by separating allocation, selection, and interaction effects. It is diagnostic rather than predictive.

Question 40Portfolio Management

A portfolio returned 13% while its benchmark returned 10%. The portfolio's equity sector weight was 60% versus 50% for the benchmark, and the equity sector returned 12% while the benchmark's other sector returned 8%. Using a simple Brinson-style allocation effect for equity, what is the approximate contribution from overweighting equity?

  1. 0.40% Correct answer.
  2. 0.20%
  3. 1.20%
  4. 3.00%

Explanation

The allocation effect for a sector is the weight difference times the sector's return minus the benchmark total return: (0.60 − 0.50) × (12% − 10%) = 0.10 × 2% = 0.20%. Careful selection of the benchmark return is essential in Brinson attribution.

Question 41Portfolio Management

Which of the following best describes the role of a benchmark in portfolio performance evaluation?

  1. It provides a passive reference portfolio with comparable risk against which active return is judged Correct answer.
  2. It guarantees a minimum return to the investor
  3. It is the portfolio's own historical average return
  4. It is the maximum return achievable by any manager

Explanation

A valid benchmark is investable, measurable, and comparable in risk to the portfolio, so that deviations from it can be attributed to active decisions. It is a reference point, not a guarantee.

Question 42Portfolio Management

Which characteristic makes a benchmark inappropriate for evaluating a small-cap value manager?

  1. The benchmark is a large-cap growth index Correct answer.
  2. The benchmark is investable through index funds
  3. The benchmark is specified in advance
  4. The benchmark's returns are measurable

Explanation

A benchmark must match the manager's investment universe and style; a large-cap growth index differs materially in risk and return drivers from small-cap value stocks. Investability, ex-ante specification, and measurability are desirable benchmark properties.

Question 43Portfolio Management

An analyst compares two portfolios with identical returns but different risk. Which statement about risk-adjusted performance comparison is correct?

  1. The portfolio with lower risk for the same return has superior risk-adjusted performance Correct answer.
  2. The portfolio with higher risk is preferred because it took more opportunity
  3. The portfolios must be ranked as equal because returns are equal
  4. Risk-adjusted comparison is impossible without knowing future returns

Explanation

Risk-adjusted measures such as the Sharpe ratio reward return per unit of risk, so equal returns with lower risk produce a higher ratio. Performance evaluation always conditions on the risk taken.

Question 44Portfolio Management

What is the effect of survivorship bias on reported average mutual fund performance?

  1. It only affects bond funds
  2. It has no effect when the sample is large
  3. It understates performance because successful funds stop reporting
  4. It overstates performance because poorly performing funds are more likely to be dropped from the sample Correct answer.

Explanation

Survivorship bias arises when failed or closed funds leave the database, so the remaining sample is tilted toward survivors that performed better. This biases upward the measured average performance.

Question 45Portfolio Management

A manager reports strong returns over a period when the market rose sharply and the manager's beta was 1.6. Which concern about evaluating the manager is most relevant?

  1. The returns must be due to survivorship bias
  2. The returns are irrelevant because beta is below 1
  3. The returns prove superior security selection
  4. The returns may reflect leveraged market exposure rather than skill Correct answer.

Explanation

A high beta means the portfolio amplified market moves, so strong returns in a rising market may simply reflect systematic risk exposure. Risk-adjusted and attribution analysis is needed to separate market timing or leverage from selection skill.

Question 46Portfolio Management

Which of the following is a common limitation of using the Sharpe ratio to evaluate a portfolio that represents only part of an investor's total wealth?

  1. It uses total risk, which may be diversified away at the total-portfolio level Correct answer.
  2. It requires the market portfolio to be observable
  3. It cannot be computed for portfolios with negative returns
  4. It ignores the risk-free rate

Explanation

When a portfolio is a component of a larger diversified total portfolio, its stand-alone standard deviation overstates the risk it contributes. A beta-based measure may then be more appropriate.

Question 47Portfolio Management

Which statement correctly distinguishes strategic asset allocation from tactical asset allocation?

  1. Strategic allocation sets long-term policy weights, while tactical allocation makes shorter-term deviations to exploit market views Correct answer.
  2. Strategic allocation is revised daily, while tactical allocation is fixed for many years
  3. Strategic allocation applies only to bonds, while tactical allocation applies only to equities
  4. Strategic allocation ignores risk tolerance, while tactical allocation depends on it

Explanation

Strategic asset allocation establishes the long-run policy mix consistent with the IPS and risk tolerance. Tactical allocation deliberately deviates from policy weights over shorter horizons to add value.

Question 48Portfolio Management

Which approach to asset allocation derives optimal weights from expected returns, variances, and covariances subject to the investor's constraints?

  1. Equal weighting
  2. Mean-variance optimization Correct answer.
  3. Dividend discount allocation
  4. Price-weighted indexing

Explanation

Mean-variance optimization maximizes expected return for a given level of variance using the full covariance structure of asset returns. It is the formal implementation of modern portfolio theory.

Question 49Portfolio Management

An investor wants to shift the portfolio's risk level without changing the relative proportions of risky assets. Which action accomplishes this?

  1. Changing the allocation between the risky portfolio and the risk-free asset Correct answer.
  2. Reducing the investment time horizon
  3. Changing the weights among the individual risky assets
  4. Increasing the number of individual securities held

Explanation

Combining the risky portfolio with borrowing or lending at the risk-free rate moves the investor along the capital allocation line, altering total risk while preserving the composition of the risky portfolio.

Question 50Portfolio Management

A portfolio manager wants to reduce the portfolio's exposure to interest rate risk without selling bonds. Which action is most direct?

  1. Increasing the portfolio's allocation to long-duration bonds
  2. Increasing the portfolio's equity allocation
  3. Shortening the portfolio's duration by using derivatives or swapping into shorter maturities Correct answer.
  4. Adding high-yield bonds with longer maturities

Explanation

Duration measures sensitivity to interest rate changes, so lowering duration reduces interest rate risk. This can be done by shifting maturities or using derivatives such as interest rate swaps.