WorksheetsFinancial Risk Management MCQs
Total questions: 100
Worksheet time: 50mins
What is the fundamental trade-off in finance?
Liquidity vs. Profitability
Risk vs. Return
Debt vs. Equity
Short-term vs. Long-term investment
In the Capital Asset Pricing Model (CAPM), what does beta (β) measure?
The total risk of an investment.
The non-systematic risk of an investment.
The systematic risk of an investment.
The expected return of an investment.
Non-systematic risk can be eliminated through:
Hedging with derivatives.
Increasing leverage.
Diversification.
Investing only in government bonds.
According to CAPM, what is the expected return of an asset with a beta of 0?
Zero.
The market return.
The risk-free rate.
Negative.
What does a positive "alpha" indicate?
The investment performed as predicted by CAPM.
The investment underperformed the market.
The investment generated a return higher than what CAPM predicted for its level of risk.
The investment has a high level of systematic risk.
Which of the following credit ratings from S&P is considered "non-investment grade"?
AAA
BBB-
BB+
A
An investment has an expected return of 15% and a standard deviation of 20%. The risk-free rate is 5%. What is the Sharpe Ratio?
0.50
0.75
1.00
0.25
The efficient frontier represents a set of portfolios that:
Have the highest possible risk for any given level of return.
Have zero risk.
Offer the highest expected return for a defined level of risk.
Are composed entirely of risk-free assets.
Why might company managers be concerned with total risk, not just systematic risk?
CAPM is always incorrect.
Bankruptcy costs are related to total risk.
Shareholders only care about total risk.
Regulators are only interested in systematic risk.
The Security Market Line (SML) is a graphical representation of:
The efficient frontier.
The Capital Asset Pricing Model (CAPM).
The relationship between risk and time.
The trade-off between systematic and non-systematic risk.
What does the 'delta' of an options portfolio measure?
The portfolio's sensitivity to changes in volatility.
The portfolio's sensitivity to the passage of time.
The portfolio's sensitivity to changes in the underlying asset's price.
The portfolio's sensitivity to changes in interest rates.
A portfolio has a delta of -5,000 with respect to the price of gold. To make the portfolio delta-neutral, a trader should:
Sell 5,000 ounces of gold.
Buy 5,000 ounces of gold.
Buy a call option with a delta of 5,000.
Sell a put option with a delta of -5,000.
What does 'gamma' (Γ) of an option represent?
The rate of change of vega.
The rate of change of delta.
The rate of change of theta.
The rate of change of the option price.
A delta-neutral portfolio has a large negative gamma. What is the expected outcome if the underlying asset price makes a large move, either up or down?
The portfolio will make a large profit.
The portfolio's value will remain unchanged.
The portfolio will incur a loss.
The portfolio's delta will become positive.
'Vega' (v) measures the sensitivity of a derivative's price to:
The underlying asset price.
The risk-free interest rate.
The passage of time.
The volatility of the underlying asset.
For a long position in a standard call or put option, theta (Θ) is usually:
Positive.
Negative.
Zero.
Equal to delta.
A trader wants to hedge both delta and gamma risk. Besides trading the underlying asset, what must they trade?
A risk-free bond.
Another share of the same stock.
A non-linear instrument, like another option.
A forward contract.
The practice of periodically adjusting a hedge to maintain delta neutrality is known as:
Static hedging.
Dynamic hedging.
Gamma hedging.
Vega hedging.
What does 'rho' (ρ) measure?
Sensitivity to dividend yield.
Sensitivity to a parallel shift in the yield curve.
Sensitivity to credit spreads.
Sensitivity to the stock's beta.
Why is delta hedging a short option position often described as a "buy high, sell low" strategy?
It guarantees a profit for the trader.
It involves buying the underlying asset when its price rises and selling it when its price falls.
It is a costless hedging strategy.
It involves selling the underlying asset when its price rises and buying when it falls.
What is duration of a bond?
The bond's time to maturity.
A measure of the bond's price sensitivity to changes in interest rates.
The weighted average of the coupon payments.
The time it takes for the bond's price to double.
If a bond has a duration of 7 years, and interest rates increase by 0.5% (50 basis points), the bond's price will approximately:
Increase by 3.5%
Decrease by 3.5%
Increase by 7%
Decrease by 7%
Convexity is a measure that improves the price change estimate provided by duration because it accounts for:
The linear relationship between bond prices and yields.
The credit risk of the bond.
The curvature in the relationship between bond prices and yields.
The liquidity risk of the bond.
What does DV01 (Dollar Value of a 01) measure?
The change in portfolio value for a 1% change in yield.
The change in portfolio value for a one-basis-point (0.01%) parallel shift in the yield curve.
The portfolio's duration in dollars.
The portfolio's convexity.
The OIS (Overnight Indexed Swap) rate is often used as a proxy for the risk-free rate because:
It is based on long-term government bonds.
It reflects the credit risk of AAA-rated banks.
It is based on overnight borrowing rates which have minimal credit risk.
It is always higher than the LIBOR rate.
What is a "partial duration"?
The duration of a zero-coupon bond.
The duration of only the coupon payments.
A measure of portfolio sensitivity to a change in just one point on the yield curve.
A simplified duration calculation.
Principal Component Analysis (PCA) applied to yield curve movements typically shows that the most significant factor (the first principal component) is:
Twist in the yield curve (short rates move opposite to long rates).
Bowing or curvature change.
Parallel shift in the yield curve.
Random movement.
If a bank funds long-term fixed-rate loans with short-term deposits, it is exposed to the risk that:
Long-term rates will fall.
Short-term rates will rise.
The yield curve will invert.
The yield curve will flatten.
The duration of a zero-coupon bond is:
Equal to its time to maturity.
Half of its time to maturity.
Zero.
Dependent on its coupon rate.
A portfolio has a positive convexity. Compared to the estimate using duration alone, the actual price of the portfolio when interest rates fall will be:
Lower.
The same.
Higher.
Impossible to determine.
Implied volatility is the volatility that, when used in an option pricing model, yields:
The historical price of the option.
The current market price of the option.
A zero value for the option.
The future volatility of the underlying asset.
The distribution of daily returns for many market variables is observed to have "heavy tails," which means:
Small changes are less frequent than in a normal distribution.
The distribution is skewed to the right.
Extreme outcomes (large gains or losses) are more likely than predicted by a normal distribution.
The mean of the distribution is not zero.
In the EWMA (Exponentially Weighted Moving Average) model for estimating volatility, what happens to the weights assigned to past observations?
All observations are weighted equally.
Weights increase as observations get older.
Weights decline exponentially as observations get older.
Only the most recent observation is given any weight.
What is the primary difference between the GARCH(1,1) model and the EWMA model?
GARCH(1,1) is simpler to calculate.
EWMA assumes volatility is constant.
GARCH(1,1) incorporates a long-run average variance level.
EWMA uses more parameters.
In the GARCH(1,1) model, σt2=ω+αut−12+βσt−12 , the term ω represents:
The weight on the previous period's volatility.
The weight on the previous period's squared return.
A term related to the long-run variance (γV_L).
The current volatility.
The power law, Prob(r>x)=Kx−r , is used to model:
The mean of asset returns.
The tails of the distribution of asset returns.
The correlation between asset returns.
The risk-free interest rate.
If the daily volatility of an asset is 1%, what is its approximate annual volatility (assuming 252 trading days)?
1%
15.87%
25.2%
12.6%
Maximum Likelihood Estimation is a method used to:
Choose model parameters that maximize the probability of the observed data occurring.
Minimize the volatility of a portfolio.
Forecast the price of an asset.
Calculate the correlation between two assets.
In the GARCH(1,1) model, the condition α + β < 1 ensures that:
Volatility is always positive.
The model is stable and volatility reverts to a long-run average.
The model is easy to compute.
The volatility forecast is always increasing.
The VIX index is a measure of:
The historical volatility of the S&P 500 index.
The implied volatility of the S&P 500 index over the next 30 days.
The current level of the S&P 500 index.
The correlation between stocks in the S&P 500 index.
The covariance between two variables measures:
The strength of the linear relationship between them.
The direction of the linear relationship between them.
Both the strength and direction of the linear relationship.
The degree of non-linear dependence.
The correlation coefficient is a more useful measure of linear dependence than covariance because it is:
Always positive.
Easier to calculate.
Scaled to be between -1 and +1.
Measured in the same units as the variables.
If two variables are independent, their correlation coefficient is:
+1
-1
0
Not defined
A positive semi-definite condition for a variance-covariance matrix ensures that:
All correlations are positive.
The matrix is internally consistent and the variance of any portfolio formed from the assets is non-negative.
All variances are equal.
The matrix can be inverted.
What is the main purpose of a factor model in the context of correlation?
To ensure all correlations are positive.
To reduce the number of correlation parameters that need to be estimated.
To model non-linear relationships.
To calculate the exact future correlation.
A Gaussian copula is a tool used to:
Create a normal distribution from any data.
Define a dependence structure (correlation) between variables, regardless of their marginal distributions.
Calculate the expected return of a portfolio.
Test if a distribution is normal.
In a one-factor model U_i = a_i * F + sqrt(1 - a_i²) * Z_i, what does the term 'F' represent?
The idiosyncratic risk component for asset i.
The common factor affecting all assets.
The mean return of asset i.
The correlation between asset i and asset j.
If the correlation between U_i and U_j in a one-factor model is given by a_i * a_j, and a_i = 0.6, a_j = 0.7, what is the correlation?
1.30
0.10
0.42
0.85
What is tail dependence?
The tendency for variables to be correlated only when they are close to their mean.
The tendency for variables to become highly correlated during extreme events (in the tails of the distribution).
The dependence of a variable on its own past values.
A property of the normal distribution.
Credit default correlation measures the tendency of two companies to:
Have the same credit rating.
Default at around the same time.
Have correlated stock prices.
Be in the same industry.
Value at Risk (VaR) at 99% confidence level represents:
The maximum possible loss over the time horizon.
The expected loss over the time horizon.
The loss level that is not expected to be exceeded 99% of the time.
The expected loss, given that the loss is in the worst 1% of cases.
What is Expected Shortfall (ES)?
Another name for Value at Risk.
The expected loss given that the loss is greater than the VaR level.
The probability of a loss exceeding VaR.
The most likely loss amount.
Why is Expected Shortfall considered a "coherent risk measure" while VaR is not?
VaR is more difficult to calculate.
VaR does not satisfy the subadditivity property.
ES is always a smaller number than VaR.
ES can be used for any time horizon, but VaR cannot.
If the 1-day 99% VaR of a portfolio is $1 million, and daily returns are independent and normally distributed with a mean of zero, what is the 10-day 99% VaR?
$1 million
$10 million
$3.16 million
$0.316 million
A portfolio's gain is normally distributed with a mean of 5millionandastandarddeviationof 12 million. What is the 95% VaR? (z-score for 5% = 1.645)
$14.74 million
$24.74 million
$19.74 million
$5 million
Back-testing a VaR model involves:
Comparing the forecasted VaR with the actual profit or loss that occurred.
Using a different model to check the VaR calculation.
Increasing the confidence level of the VaR.
Calculating the VaR for a longer time horizon.
Which of the following is NOT a property of a coherent risk measure?
A. Monotonicity
B. Subadditivity
C. Positive Homogeneity
D. Normality
What is Marginal VaR?
The total VaR of the portfolio.
The change in portfolio VaR resulting from adding a new position.
The rate of change of portfolio VaR with respect to the size of a position.
The VaR of a single position in isolation.
Component VaR has the useful property that:
The sum of the Component VaRs equals the total portfolio VaR.
It is always positive for every component.
It is independent of correlations.
It is equal to the stand-alone VaR of the component.
Regulators have indicated a plan to move from using VaR to using ES for determining market risk capital primarily because:
ES is easier to calculate.
ES better captures the risk in the tail of the distribution and is a coherent risk measure.
VaR cannot be back-tested.
ES results in lower capital requirements.
In the basic historical simulation method for calculating VaR, each simulation trial is based on:
A random number drawn from a normal distribution.
The percentage change in market variables from a specific day in the past.
A forecast from a GARCH model.
The average change in market variables over the historical period.
What is "Stressed VaR"?
VaR calculated with a very high confidence level.
VaR calculated using a historical period of significant financial stress.
VaR calculated for a very illiquid portfolio.
The average of VaR and Expected Shortfall.
A key advantage of the historical simulation method is that it:
Assumes market variables are normally distributed.
Does not require assumptions about the statistical distribution of market variables.
Is computationally very fast.
Provides a precise estimate of tail losses.
In the weighted historical simulation approach, more recent observations are typically given:
Lower weights.
Equal weights to all other observations.
Higher weights.
Zero weight.
Volatility scaling in historical simulation involves adjusting the historical data to reflect:
Changes in interest rates.
The difference between current volatility and historical volatility.
The number of days in the historical sample.
The confidence level of the VaR.
Extreme Value Theory (EVT) is a statistical tool used to model:
The mean of a distribution.
The entire distribution of returns.
The tail of a probability distribution.
The correlation between variables.
The Generalized Pareto Distribution (GPD) is used in EVT to model:
The distribution of all losses.
The distribution of losses that exceed a certain high threshold 'u'.
The number of losses exceeding a threshold.
The average size of a loss.
When calculating 1-day 99% VaR from 500 days of historical data, the VaR is typically estimated as:
The worst loss.
The 5th worst loss.
The 10th worst loss.
The average of the 5 worst losses.
The bootstrap method can be used in historical simulation to:
Calculate the expected loss.
Determine a confidence interval for the VaR estimate.
Adjust historical data for volatility.
Choose the optimal historical period.
A limitation of the basic historical simulation approach is that:
It is too complex.
It can only be used for short time horizons.
It is limited to the events that occurred in the historical data sample.
It requires a correlation matrix.
The model-building approach (or variance-covariance approach) for VaR calculation assumes that:
A. Asset returns follow a historical pattern.
B. Asset returns are normally distributed.
C. Options are not present in the portfolio.
D. Volatility is constant.
When applying the model-building approach, for variables like interest rates or credit spreads, what is typically considered?
Their squared changes.
Their proportional changes.
Their actual changes (e.g., basis point changes).
A major limitation of the linear model in the model-building approach is that it cannot properly handle:
Portfolios with many assets.
Portfolios containing options and other non-linear derivatives.
Portfolios with negative correlations.
Portfolios with short positions.
In the context of the model-building approach, Monte Carlo simulation is used to:
Estimate historical correlations.
Overcome the limitations of the normality assumption and handle non-linearities.
Calculate the delta of options.
Determine the risk-free rate.
When using Monte Carlo simulation to calculate VaR, what is the first step?
Value the portfolio today.
Calculate the portfolio's delta.
Sort the simulated portfolio losses.
Sample from the distribution of risk factors.
The quadratic model, which includes a gamma term, is an extension of the linear model to better handle:
Interest rate risk.
Credit risk.
Non-linear portfolios (e.g., options).
Liquidity risk.
What is a key advantage of the model-building approach over historical simulation?
It does not assume normality.
It is conceptually simpler.
It can easily incorporate volatility updating schemes like GARCH.
It is not limited by historical events.
When using Principal Component Analysis (PCA) for the yield curve in VaR calculations, the goal is to:
Replace a large number of correlated interest rate movements with a few independent factors.
Forecast the future shape of the yield curve.
Calculate the duration of the portfolio.
Ensure the yield curve is always upward sloping.
The linear model within the model-building approach for calculating VaR relies on two key assumptions. What are they?
Risk factor returns are historically correlated and have heavy tails.
Risk factor returns are independent and follow a Student's t-distribution.
The portfolio's change in value is linearly related to risk factor returns, and these returns are normally distributed.
All risk factors are interest rates and have constant volatility.
In Monte Carlo simulation for VaR, if you run 5,000 trials, the 99% VaR is estimated by:
The 50th worst loss.
The 5th worst loss.
The average of the worst 50 losses.
The value of the worst loss.
What are the three pillars of the Basel II framework?
Credit Risk, Market Risk, Operational Risk.
Minimum Capital, Supervisory Review, Market Discipline.
Tier 1 Capital, Tier 2 Capital, Tier 3 Capital.
Standardized, Foundation IRB, Advanced IRB.
Under Basel I, the minimum total capital requirement was set at what percentage of risk-weighted assets (RWA)?
4%
8%
10%
12%
Which of the following is typically considered Tier 1 Capital?
Subordinated debt with a maturity of 5 years.
Common equity and retained earnings.
Revaluation reserves.
General loan-loss reserves.
In the Basel II Standardized Approach for credit risk, how are risk weights for corporate loans determined?
Based on the bank's internal models.
Based on external credit ratings (e.g., from S&P, Moody's).
All corporate loans have a 100% risk weight.
Based on the loan's maturity.
What is the main advantage of the Internal Ratings-Based (IRB) approach compared to the Standardized Approach in Basel II?
It is simpler to implement.
It results in higher capital requirements.
It allows banks to use their own internal estimates of risk parameters (like PD, LGD), making capital more risk-sensitive.
It is mandatory for all banks.
Basel II introduced a new capital charge for which type of risk that was not explicitly covered in Basel I's 8% rule?
Market Risk
Credit Risk
Liquidity Risk
Operational Risk
In the Gaussian copula model used by regulators for the IRB approach, WCDR stands for:
Worst Case Default Rate.
Weighted Corporate Default Ratio.
World Credit Default Rate.
Worst Case Duration Ratio.
Under the Advanced IRB approach, banks are allowed to estimate which of the following parameters?
Only Probability of Default (PD).
PD and Loss Given Default (LGD).
PD, LGD, and Exposure at Default (EAD).
PD, LGD, EAD, and Maturity (M).
What is the purpose of Pillar 3 (Market Discipline) in Basel II?
To set minimum capital levels.
To require banks to disclose more information about their risks and capital adequacy to the public.
To allow supervisors to intervene if a bank is undercapitalized.
To define the types of capital.
Solvency II is a regulatory framework primarily designed for which type of financial institution?
Banks.
Hedge funds.
Insurance companies.
Broker-dealers.
Altman's Z-score is a model used to:
Predict the probability of a company's default.
Estimate the volatility of a company's stock.
Calculate the value of a company's debt.
Determine a company's credit rating.
Default probabilities derived from historical data (like Moody's default rate tables) are known as:
Risk-neutral default probabilities.
Real-world default probabilities.
Implied default probabilities.
Forward default probabilities.
Default probabilities backed out from credit spreads or CDS prices are known as:
Risk-neutral default probabilities.
Real-world default probabilities.
Historical default probabilities.
Z-score probabilities.
What is a Credit Default Swap (CDS)?
A type of bond issued by a company with high credit risk.
An insurance-like contract where the buyer pays a premium to be protected against the default of a reference entity.
A swap where two parties exchange fixed and floating interest rate payments.
An option to buy a company's stock at a predetermined price.
In Merton's model, a company's equity is viewed as:
A put option on the company's assets.
A risk-free bond.
A call option on the company's assets with a strike price equal to its debt.
A forward contract on the company's assets.
The "hazard rate" or "default intensity" is the:
Unconditional probability of default over a long period.
Cumulative probability of default.
Conditional probability of default over a short period, given no earlier default.
Recovery rate in the event of default.
The recovery rate of a bond is typically defined as:
The probability that the bond will not default.
The price of the bond shortly after default, as a percentage of its face value.
The coupon rate of the bond.
The original issue price of the bond.
Which world's default probabilities (real-world or risk-neutral) should be used for valuing credit derivatives?
Real-world, because they reflect historical facts.
Risk-neutral, because valuation must be done in a no-arbitrage framework consistent with market prices.
An average of the two.
Whichever is lower.
Which world's default probabilities (real-world or risk-neutral) should be used for scenario analysis and calculating Credit VaR?
Real-world, because these analyses aim to estimate the actual probability of future losses.
Risk-neutral, because they are more conservative.
An average of the two.
Whichever is higher.
In Merton's model, a default occurs when:
The value of the company's equity falls to zero.
The value of the company's assets falls below the value of its debt at the time of maturity.
The company's Z-score is below 1.8.
The company's credit rating is downgraded.
