FRM 一级练习题

The board of directors approves the firm's risk appetite, oversees the risk management framework, and reviews significant exposures. Day-to-day execution belongs to front office and risk management staff, while capital calculations are typically prepared by finance or risk functions. Board responsibility is oversight rather than direct model ownership.

The CRO is responsible for the firm-wide risk profile, including identifying, measuring, monitoring, and reporting risks to the board and senior management. Compensation design, trading execution, and external financial audit are separate functions. The CRO role provides independent oversight of risk-taking activities.

The risk appetite statement sets out the aggregate level and types of risk the firm is willing to accept in pursuit of its strategic objectives. It is implemented through risk limits such as VaR, earnings-at-risk, and capital thresholds. It is a governance document, not a guarantee against losses or a uniform regulatory requirement.

The COSO ERM framework has five components: governance and culture, strategy and objective-setting, performance, review and revision, and information, communication, and reporting. Governance and culture establish board oversight, organizational values, and accountability for risk. The other components support execution, learning, and reporting rather than the overall governance structure.

Pillar 1 sets minimum capital requirements, Pillar 2 provides for supervisory review of risks not fully captured in Pillar 1, and Pillar 3 promotes market discipline through disclosure. The Basel standards also include specific risk-type charges and liquidity measures, but these are not the three pillars. Governance functions such as internal and external audit support the framework rather than define it.

The Sharpe ratio equals the excess return divided by volatility, or (9% - 3%) / 12% = 0.50. Option (b) divides the total return by volatility, option (c) divides the volatility minus the risk-free rate by the return, and option (d) divides volatility by total return. Only option (a) correctly uses the excess return over the risk-free rate.

ERM considers the firm's full portfolio of risks and how they interact, allowing diversification and netting effects to be recognized. It does not eliminate risk, and firms still need capital allocation and risk limits to implement the framework. ERM is used by banks, insurers, and other organizations across industries.

For independent events, the joint probability equals the product of the individual probabilities: 0.3 times 0.4 = 0.12. Option (c) is the sum of the probabilities, which would apply only to mutually exclusive events. The other options are arithmetic errors.

The multiplication rule states that P(A and B) = P(A) times P(B | A), so 0.5 times 0.6 = 0.30. Option (a) uses the conditional probability incorrectly, and options (c) and (d) treat the probabilities as additive or divide instead of multiply. Only option (b) follows the multiplication rule.

For a normal distribution, roughly 68% of observations lie within one standard deviation, 95% within two, and 99.7% within three. The 95% figure reflects the well-known two-standard-deviation rule. The other choices correspond to other intervals or common approximations.

The slope b gives the expected change in the dependent variable per one-unit change in the independent variable. The correlation coefficient is bounded between -1 and 1, but the slope is not, and the slope depends on the units of X. Changing the units of X rescales b rather than leaving it unchanged.

Pearson correlation captures linear association, so two variables can have zero correlation yet be strongly dependent in a nonlinear way. Rank-based measures are invariant to monotonic transformations, but Pearson correlation is not. Correlation can be negative, zero, or positive.

Because the p-value of 0.03 is below the 5% significance level, the test result provides sufficient evidence to reject the null hypothesis. Rejection is a statistical decision, not proof that the alternative is certainly true. Failing to reject would be the correct action only if the p-value exceeded 5%.

Monte Carlo simulation draws a large number of random paths or scenarios from assumed probability distributions and uses the resulting payoff distribution to estimate statistics such as VaR or option prices. The estimates contain sampling error that decreases as the number of simulations increases. Distributional assumptions are essential to the method.

VaR is a quantile of the loss distribution, so a 99% one-day VaR of USD 10 million means only a 1% probability that the loss exceeds USD 10 million on any given day. The expected loss conditional on the tail can differ from the VaR amount. VaR does not set a hard maximum loss.

When a bond trades below par, it is a discount bond, and the yield to maturity must be higher than the coupon rate to compensate investors for the capital gain to par at maturity. A bond at par has yield equal to the coupon, and a premium bond has yield below the coupon. Therefore only option (b) is consistent with a price below par.

Common stockholders own the firm and have a residual claim on assets and earnings after all debt holders and preferred shareholders are satisfied. Bonds and commercial paper are debt claims with priority, while preferred stock has priority over common stock. Therefore common stock is the ownership security described.

A call option confers the right, but not the obligation, to buy the underlying asset at the strike price. A put option confers the right to sell. Options do not convert into forwards, and the call writer is obligated to sell the underlying if the holder exercises.

Exchange-traded futures have standardized terms and are cleared through a central clearinghouse with daily marking to market and margin requirements. OTC forwards are bilateral agreements with customized terms and are typically settled at maturity. These differences affect liquidity, counterparty risk, and flexibility.

In a plain vanilla interest rate swap, one party pays a fixed rate and receives a floating rate, while the counterparty does the opposite. The notional principal is generally not exchanged at initiation; it is used only to calculate payments. Both parties face interest rate risk because the value of their payment streams changes with rates.

The quote USD/EUR = 1.10 means one euro costs 1.10 U.S. dollars. Dividing USD 1 million by 1.10 gives approximately EUR 0.909 million. Option (b) reverses the conversion, and the other choices reflect arithmetic errors.

A certificate of deposit is an unsecured time deposit issued by a bank, often in negotiable form, and is a common money market instrument. Commercial paper is typically issued by corporations, Treasury bills by the government, and repurchase agreements are collateralized loans. Therefore the certificate of deposit matches the description.

The intrinsic value of a call equals the maximum of the underlying price minus the strike price and zero, or max(60 - 50, 0) = 10. Option (a) would apply if the underlying were at or below the strike. Options (c) and (d) use the strike or underlying price directly instead of the difference.

The price is the face value discounted over three years: 100 / (1.05)^3 = approximately 86.38. Option (a) uses continuous compounding, option (c) discounts over only two years, and option (d) discounts over one year. Only option (b) matches annual compounding over the full three-year horizon.

Duration increases with time to maturity and decreases with coupon size. The 10-year 2% coupon bond dominates the 5-year bonds in maturity and has a lower coupon than the 10-year 8% bond. Therefore it has the highest modified duration.

Positive convexity means the price-yield curve bends upward, so actual price gains from falling yields exceed duration-based estimates and actual price losses from rising yields are smaller than duration-based estimates. As a result, duration alone overstates declines and understates gains. A convexity adjustment improves the approximation for larger yield changes.

Higher volatility increases the probability of large favorable price moves while the call's downside is limited to the premium paid, so the option value rises. This is a core insight of option pricing theory. Options never have negative value because the holder has the right, not the obligation, to exercise.

If R is outside the range spanned by u and d, an arbitrage can be constructed by borrowing or lending against the stock's possible payoffs. The condition d < R < u ensures that a replicating portfolio with positive state prices exists. The up probability does not need to equal 0.5, and the risk-free rate need not be zero.

Expected shortfall is the probability-weighted average of losses beyond the VaR quantile, so it captures tail severity that VaR ignores. Because it averages losses in the tail, expected shortfall is at least as large as the corresponding VaR. It is a coherent risk measure and provides more information about extreme outcomes.

The approximate percentage price change equals the negative of modified duration times the yield change, or -6 times 0.005 = -0.03, which is -3.0%. Option (a) treats 50 basis points as 0.5 instead of 0.005, and option (d) uses a 100 basis point change. Option (c) has the wrong sign.

Risk limits should be established within the risk appetite approved by the board and monitored by independent risk management. Allowing traders to set their own limits creates a conflict of interest and weakens control. The statement is false.

A valid probability distribution assigns nonnegative probabilities to every possible outcome, and the sum of those probabilities must equal 1. This requirement follows from the axioms of probability. The statement is true.

Futures positions are settled daily through variation margin, and initial margin is posted by both sides. Daily marking to market substantially reduces counterparty credit risk relative to OTC forwards. The statement is true.

Higher coupons return a larger share of cash flows earlier, which reduces a bond's duration. All else equal, a low-coupon bond has a longer duration than a high-coupon bond of the same maturity. The statement is false.

The board approves the risk appetite, oversees management's execution of the framework, and reviews material exposures and framework effectiveness. Trade execution belongs to the front office, and tax preparation belongs to finance or compliance. Together, options (a), (b), and (d) reflect the board's oversight responsibilities.

A Type I error is rejecting a true null, and a Type II error is failing to reject a false null. Power equals one minus the Type II error probability and generally decreases when the significance level is lowered. The p-value is the smallest significance level at which the null can be rejected, so options (a), (b), (d), and (e) are correct.

Futures are standardized, centrally cleared, and marked to market daily, which reduces counterparty risk. OTC forwards are customized bilateral contracts with settlement at maturity. The clearinghouse reduces credit risk but does not make default impossible.

A call's value increases with volatility, the risk-free rate, time to expiration, and the underlying price relative to the strike. A lower strike price makes the call more in the money, while higher volatility expands the range of favorable outcomes. Lower volatility reduces option value, so option (e) is incorrect.

Risk appetite defines the aggregate risk the firm is willing to accept, and risk limits translate that appetite into binding constraints. ERM coordinates risk management across the whole firm, while residual risk is what remains after controls are applied.

Macaulay duration is the present-value-weighted average time to cash flows, and modified duration converts that into price sensitivity to yield changes. Convexity captures the curvature of the price-yield relationship, while expected shortfall measures average tail losses beyond VaR.

VaR states a loss threshold that will not be exceeded with a given confidence level over a specified horizon. At the 95% confidence level, the loss is expected to exceed the VaR figure only 5% of the time. VaR does not describe a guaranteed or exact loss amount.

Expected shortfall is the probability-weighted average loss conditional on the loss exceeding the VaR threshold. Because it uses the distribution of tail losses, ES is more sensitive than VaR to the shape of the tail. ES is generally greater than or equal to VaR at the same confidence level.

Historical stress scenarios rely on past episodes, so they may not reflect new correlations, instruments, or market structures. They are useful for assessing how a portfolio would have performed, but they cannot guarantee coverage of future tail events. Stress testing supplements rather than replaces VaR and other risk measures.

Backtesting counts exceptions, which are days when the actual loss exceeds the VaR estimate. Under the Basel framework for a 250-day sample at the 99% confidence level, 0 to 4 exceptions are in the green zone, 5 to 9 are in the yellow zone, and 10 or more are in the red zone. A high exception count signals that the model may underestimate risk.

Market risk factors are the observable variables that drive portfolio value, such as equity index returns, interest rates, exchange rates, and commodity prices. A parametric VaR model maps portfolio positions to these factors and uses their volatilities and correlations. Employee counts, complaints, and audit schedules are not market risk factors.

The trading book contains instruments held with trading intent or to hedge other trading book positions, and they are generally marked to market. Banking book positions are more typically held to maturity or for customer relationships. The trading book is associated with market risk, while the banking book is more associated with credit and interest rate risk.

Parametric VaR is calculated as portfolio value multiplied by the standard deviation and the normal deviate. The calculation is 10,000,000 x 0.012 x 2.326, which equals 279,120. This represents the loss threshold expected to be exceeded only 1% of the time over one day.

Monte Carlo simulation generates many hypothetical paths from assumed distributions, so the risk manager can set current volatility, correlation, and other parameters. Historical simulation uses past returns directly and may lag changes in market conditions. Monte Carlo is computationally intensive and does require random number generation.

The survival probability for one year is 98%, so the two-year survival probability is 0.98 x 0.98 = 96.04%. The cumulative default probability is therefore 1 - 0.9604 = 3.96%. This is slightly less than 4% because the second-year default event requires surviving the first year.

Credit ratings classify issuers into broad categories that reflect relative expected default risk. They are ordinal measures, so a rating does not imply an exact probability of default for a specific issuer. Ratings are reviewed periodically and do not guarantee against default.

CVA adjusts the risk-free valuation of a derivative to reflect the possibility that the counterparty may default. It is calculated from expected exposure, the counterparty's default probability, and loss given default. A higher counterparty credit risk leads to a larger downward CVA adjustment.

Collateral reduces credit exposure only to the extent that it covers the exposure net of thresholds and minimum transfer amounts. When collateral value falls, less protection is available against the current exposure. The bank may need to issue a margin call, but until it is met, uncollateralized exposure rises.

Current exposure reflects what the bank would lose today if the counterparty defaulted, which is the positive mark-to-market value of netted transactions. It is the starting point for measuring potential future exposure. Collateral, netting, and future changes in value are handled separately in exposure models.

Credit spreads compensate investors for default risk, liquidity risk, and other credit-related risks. When spreads widen, the market is demanding more compensation, which usually reflects higher default probability or lower recovery expectations. A rating upgrade would typically narrow the spread.

Expected loss is the product of the probability of default, the loss severity given default, and the exposure at default. This formulation allows a bank to estimate the average loss from a credit exposure. Unexpected loss and economic capital are then assessed around this expected level.

Loss given default is the percentage of exposure lost when a default occurs. It is equal to 1 minus the recovery rate, so 1 - 0.40 = 0.60. Higher recovery rates reduce LGD and therefore reduce expected loss.

Operational losses arise from inadequate or failed internal processes, people, systems, or external events. Internal loss data are collected from the bank's own operational loss events, such as settlement failures, fraud, or system outages. Market movements and borrower defaults are not operational losses.

The AMA permitted banks to quantify operational risk capital using internal loss data, scenario analysis, and business environment and internal control factors, subject to supervisory approval. The BIA and Standardised Approach rely on gross income-based formulas. The Internal Ratings-Based Approach applies to credit risk, not operational risk.

Scenario analysis combines expert judgment and plausible stress scenarios to assess losses from events such as fraud, cyber attacks, or business disruption. It supplements historical loss data, which may not contain enough severe events. The results support capital estimates, risk appetite, and contingency planning.

Compensating controls provide alternative protection when the primary control is weak, missing, or has failed. They lower residual risk and are often documented in risk assessments and audit findings. They do not eliminate risk but reduce the likelihood or impact of losses.

Outsourcing transfers activities but not the underlying operational risk, and the bank remains responsible to regulators and clients. The provider may fail to deliver, suffer outages, or expose data, creating concentration and continuity risk. Outsourcing requires vendor due diligence, contracts, monitoring, and exit plans.

Cyber risk falls within operational risk because it involves failures of systems and security controls that can cause financial loss or disruption. A ransomware attack can halt processing, destroy data, and create reputational harm. Interest rate moves, borrower defaults, and rate-driven withdrawals belong to market, credit, and liquidity risk respectively.

KRIs are forward-looking metrics linked to operational risk drivers, such as failed transaction rates, staff turnover, or system downtime. They alert management when risk is increasing so action can be taken before losses materialize. They complement, rather than replace, internal loss data and scenario analysis.

Funding liquidity risk is the risk that a firm lacks sufficient cash or access to funding to meet payment obligations. It can arise from deposit outflows, maturing wholesale funding, or impaired market access. Unacceptable losses may be required to liquidate assets or obtain emergency funding.

Market liquidity risk is the risk that a position cannot be unwound quickly at a price close to its fair value. Illiquid assets trade with wide bid-ask spreads and large price impacts, which is especially costly during stress. Funding liquidity risk and market liquidity risk can reinforce each other during a crisis.

The LCR compares the stock of high-quality liquid assets (HQLA) with expected net cash outflows over 30 calendar days under a severe stress scenario. A ratio of at least 100% ensures the bank can survive the stress horizon without relying on new funding. The NSFR, not the LCR, addresses the one-year structural funding horizon.

The NSFR promotes a sustainable funding structure by requiring available stable funding to cover required stable funding over one year. Assets with longer maturities and lower liquidity receive higher required stable funding factors. It complements the LCR, which focuses on the 30-day horizon.

Liquidity stress testing projects cash inflows and outflows under scenarios such as deposit runs, wholesale funding withdrawal, and market-wide crises. The results identify potential funding gaps and support contingency funding plans and early warning indicators. Stress testing cannot eliminate interest rate risk.

When liabilities come due before assets, the bank must refinance them, and funding may be unavailable or costly. This is refinancing risk, a component of funding liquidity risk. The mismatch also exposes the bank to interest rate risk when rates change before the assets mature.

Level 1 HQLA have the highest liquidity and can be included without haircuts under the LCR rules, subject to operational requirements. They include cash, central bank reserves, and certain high-quality government securities. Level 2 assets have haircuts and are subject to caps.

Expected shortfall is the average loss conditional on exceeding the VaR threshold, so it is at least as large as the VaR figure. This property holds by construction for a continuous loss distribution. ES therefore provides additional information about the severity of tail losses.

Credit ratings are ordinal categories that rank relative default risk, not precise default probabilities. Two issuers with the same rating can have different expected default rates. Ratings should therefore be used alongside quantitative credit models and market information.

The Basic Indicator Approach applies a fixed alpha factor, historically 15%, to the average of positive annual gross income over three years. It is the simplest Basel operational risk approach and does not use internal loss data. More advanced approaches use additional risk-sensitive inputs.

The LCR requires HQLA to cover projected net cash outflows over 30 calendar days under a defined stress scenario. The 30-day horizon reflects the period during which a bank should be able to take corrective actions. The NSFR uses a one-year horizon.

Backtesting evaluates model accuracy by comparing actual outcomes with VaR forecasts and counting exceptions. The Basel traffic light approach maps exception counts into green, yellow, and red zones for a 250-day sample. Zero exceptions can still indicate a conservative or poorly specified model, so it does not prove perfect calibration.

CVA rises with the counterparty's probability of default and the expected loss given default. Larger expected positive exposure also increases the amount that could be lost. Full collateralization and short maturities with no exposure reduce CVA, not increase it.

Operational risk arises from failed processes, people, systems, or external events, so system outages, internal fraud, and cyber attacks qualify. An equity market crash is market risk, and a borrower default is credit risk. These categories are separate in the risk taxonomy used by banks and regulators.

The LCR is the ratio of HQLA to net cash outflows over 30 days, so increasing HQLA or reducing outflows improves it. Stable retail deposits have lower runoff assumptions than volatile wholesale funding, which lowers net outflows. Overnight funding and unhedged maturity extension increase outflow assumptions and weaken the ratio.

Operational risk is defined by the Basel Committee as the risk of loss from inadequate or failed internal processes, people, systems, or external events. Key risk indicators monitor exposure, compensating controls reduce residual risk, and scenario analysis estimates losses from rare events. Matching these terms tests the definitions that underpin operational risk measurement.

The LCR focuses on 30-day survival using high-quality liquid assets, while the NSFR promotes stable funding over one year. Market liquidity risk concerns the ease of selling assets, and funding liquidity risk concerns the ability to meet payment obligations. The two forms of liquidity risk can interact during stress.