VRM 2 Flashcards
What are linear derivatives?
Derivatives that have a linear relationship between the change in the value of the derivative and the change in the price of the underlying asset
What is the formula for calculating VaR for linear derivatives?
VaRLinear Derivative = Δ × VaRUnderlying Risk Factor
What does delta represent in the context of derivatives?
The change in price of the derivative to a change in the price of the underlying asset
What is the Delta Normal method used for?
Calculating VaR for linear assets
What assumptions does the Delta Normal method make?
Assumes that the variables are normally distributed
What is the full revaluation method for computing VaR?
A method that involves recalculating the entire portfolio value under different scenarios
What is the historical simulation approach for computing VaR?
A method that uses past data to simulate future scenarios and calculate potential losses
What is the difference between linear and non-linear derivatives?
Linear derivatives have a constant delta, while non-linear derivatives have a delta that changes with the underlying asset
What is expected shortfall (ES)?
The average loss that occurs beyond the VaR level
What is the implication of correlation breakdown for scenario analysis?
It affects the reliability of the scenarios generated as correlations may not hold in stressed market conditions
What is worst-case scenario (WCS) analysis?
An analysis that identifies the most extreme loss scenario for a portfolio
True or False: The Delta Normal method can be used for non-linear derivatives.
False
What are the two categories of risk factors in historical simulation?
- Percentage change risk factors (e.g., stock prices, exchange rates)
- Actual change risk factors (e.g., credit spreads, interest rates)
What does the symbol δ represent in portfolio valuation?
Delta, the rate of change in the value of the portfolio with respect to the rate of change in the risk factor
Fill in the blank: The calculation for a non-linear portfolio can be made more accurate by using another Greek letter called _______.
Gamma
What is the formula for the change in portfolio value that includes gamma?
ΔP = δΔS + (1/2)γ(ΔS)²
What are stressed measures in the context of VaR?
VaR and expected shortfall measures based on data from a particularly stressful one-year period
What is the key disadvantage of using the Delta Normal method?
It may be less accurate for portfolios with non-linear derivatives
What does a linear portfolio depend on?
The changes in the values of its underlying variables
What is the significance of a 95% confidence level in VaR calculations?
It indicates the level of confidence that the potential loss will not exceed the calculated VaR.
What is Monte Carlo simulation in the context of VaR?
A method that uses random sampling to simulate a range of potential outcomes for a portfolio
What is the purpose of scenario analysis in risk management?
To evaluate the impact of different risk factors on the portfolio under various hypothetical situations
What are stressed measures in the context of bank capital requirements?
Measures based on data from a one-year period that would be particularly stressful for a bank’s current portfolio
For example, using data from March 2008 to February 2009 during the financial crisis.
How many scenarios are typically used in stressed measures calculations?
250 scenarios
This is produced from one year of data.
What is the formula for the change in portfolio value in the delta-normal model?
Δ𝑃 = Σ𝛿iΔ𝑆i
This is exact for linear portfolios and approximate for non-linear portfolios.
In the delta-normal model, what does 𝑎i represent?
𝑎i = 𝛿i𝑆i
This applies when percentage changes are considered.
What does the mean (𝜇p) of Δ𝑃 represent in the delta-normal model?
𝜇P = Σ𝑎i𝑥i
This is the sum of the products of the weights and the changes.
What is the simplified expression for VaR when the mean change in each risk factor is assumed to be zero?
𝜎P𝑈
This simplifies calculations for short time periods.
What is the main advantage of using Monte Carlo simulations for calculating VaR?
It generates an infinite number of scenarios and tests many possible future outcomes
Unlike Historical VaR.
What is the key difference between Monte Carlo simulations and historical simulations?
Monte Carlo simulations generate scenarios by taking random samples from the distributions assumed for the risk factors
Historical simulations use past data.
What does the term ‘correlation breakdown’ refer to?
The phenomenon where correlations increase during stressed market conditions
For example, during the 2007 - 2008 crisis.
What is a limitation of the delta-normal model?
It only gives an approximation for non-linear portfolios
It works well for linear portfolios with approximately normal distributions.
What is the expected shortfall formula in the delta-normal model under normal distribution assumptions?
𝜇 + 𝜎 * (U2 / (1 - 𝑋) * 2𝜋)
Where 𝑋 is the confidence level.
Fill in the blank: The Monte Carlo approach assumes that there is a known probability distribution for the _______.
[risk factors]
True or False: The Monte Carlo simulation can take significantly longer to calculate VaR compared to Parametric VaR.
True
It can take 1,000 times longer due to the need for multiple price calculations.
What does the term ‘worst-case analysis’ entail?
Calculating statistics for worst-case results over a defined period
For instance, determining the worst return over 52 weeks.
In a Monte Carlo simulation, how is the VaR with a 99% confidence level determined?
It is the tenth worst loss from 1000 simulation trials
Expected shortfall is the average of the nine losses worse than this.
What is the common assumption about the mean change in each risk factor in the delta-normal model?
The mean change is assumed to be zero
This simplifies the expression for VaR.
What are linear derivatives?
Derivatives that have a linear dependence on changes in the values of their underlying variables.
Provide an example of a linear portfolio.
A portfolio consisting of 100 shares worth USD 50 each.
What is the Delta of a derivative?
The change in price of the derivative relative to the change in the price of the underlying asset.
How is VaR for linear assets calculated?
Using the Delta Normal method.
What assumption does the Delta Normal method make?
That the variables are normally distributed.
Fill in the blank: VaR for Linear Derivative = _______ × VaR Underlying Risk Factor.
Delta
What is the historical simulation approach for computing VaR?
It involves identifying market variables, collecting daily data, and sorting it to create scenarios.
What does the delta-normal method assume for non-linear derivatives?
It assumes linear payoffs, which is not applicable for non-linear derivatives.
What is the full revaluation method for computing VaR?
It involves fully revaluating the portfolio using methods like Monte Carlo or Historical Simulation.
What are the strengths of the Monte Carlo method for computing VaR?
It can model complex portfolios and non-linear relationships.
What is a worst-case scenario (WCS) analysis?
An analysis that examines the worst possible outcomes for a portfolio.
True or False: The delta of non-linear derivatives is constant.
False
What are the two categories of risk factors in historical simulation?
- Percentage change for stock prices and exchange rates
- Actual change for credit spreads and interest rates.
How is Expected Shortfall typically calculated?
As the average of the losses that are worse than the VaR level.
What is the role of Greek letters in portfolio valuation?
They help to calculate changes in portfolio value with respect to risk factors.
What is delta in the context of portfolio valuation?
The rate of change in the value of the portfolio with respect to the change in the risk factor.
How is the change in portfolio value calculated when multiple risk factors are involved?
Using the formula ΔP = ΣδiΔSi.
What is gamma in portfolio valuation?
A Greek letter that measures the curvature in the relationship between portfolio value and risk factors.
What is stressed VaR?
A measure based on data from a one-year period that would be particularly stressful for market conditions.
What does the delta-normal method fail to account for in non-linear derivatives?
The changing delta and non-linear relationships.
What is the formula for approximating the change in portfolio value with gamma?
ΔP = δΔS + (1/2)γΔS².
How many days are assumed in a year for VaR calculation?
250 days.
What is necessary for situations where portfolio components are dependent on several risk factors?
A more complicated expression involving cross gammas.
What are stressed measures used for in banking?
Determining bank capital requirements based on stressed VaR and stressed expected shortfall.
What time period is typically used to develop stressed measures for banks?
A one-year period that would be particularly stressful for a bank’s current portfolio.
How many scenarios are typically used in stressed measures calculations?
250 scenarios.
What is the delta-normal model used for?
Calculating portfolio value changes based on risk factors.
What does Δ𝑃 represent in the delta-normal model?
The change in portfolio value.
In the delta-normal model, what is the formula to calculate the mean change in portfolio value?
𝜇P = Σ𝑎i𝑥i.
What is the formula for calculating VaR in the delta-normal model?
𝑉𝑎𝑅 = 𝜇p + 𝜎p𝑈.
What is the assumption made about the mean change in each risk factor in the delta-normal model?
The mean change is assumed to be zero.
What is a limitation of the delta-normal model?
It only provides an approximation for non-linear portfolios.
What is the Monte Carlo simulation used for?
Calculating VaR and expected shortfall.
How does Monte Carlo simulation differ from historical simulations?
Monte Carlo generates scenarios by taking random samples from assumed distributions for risk factors.
What is the typical number of trials conducted in a Monte Carlo simulation?
1000 trials.
What is a common assumption made in Monte Carlo simulations regarding risk factors?
Risk factors have a multivariate normal distribution.
What are some advantages of Monte Carlo simulation?
- Captures effects of nonlinearities
- Can generate infinite scenarios
What is a disadvantage of Monte Carlo simulation?
It can take 1,000 times longer than Parametric VaR.
What phenomenon occurs during stressed market conditions regarding correlations?
Correlations generally increase.
What is correlation breakdown?
The phenomenon where correlations can differ significantly in periods of heightened volatility.
What is worst-case analysis used for in portfolio management?
Calculating statistics for worst-case results over a period.
True or False: Worst-case statistics can be regarded as an alternative to VaR and ES.
False.
