VRM 3 Flashcards
What does ππ΄π represent?
Maximum potential loss in value of a portfolio of financial instruments with a given probability over a certain time horizon.
What is the implication of a 95% daily VAR of $100 million?
95% of the time, daily loss will be less than or equal to $100 million.
What is the formula for calculating Dollar πππ x%?
Dollar $πππ x% = π§x% Γ π Γ Portfolio Value.
What are the two main types of distributions discussed?
Conditional and unconditional distributions.
What does the term βfat tailsβ refer to in return distributions?
Return distributions that exhibit more extreme outcomes than a normal distribution would predict.
Which model is used to estimate long horizon volatility?
πΊπ΄π πΆπ»(1,1) model.
True or False: Conditional volatility can be calculated using both parametric and non-parametric approaches.
True.
What is the impact of mean reversion on volatility estimation?
Mean reversion affects long horizon conditional volatility estimation.
What is the Exponentially Weighted Moving Average (πΈπππ΄) approach used for?
To estimate volatility.
What is the implication of regime switching on quantifying volatility?
Regime switching presents additional challenges for risk managers due to unanticipated changes.
Fill in the blank: ππ΄π is a measure of potential loss with a certain _______.
[probability]
What are the two approaches for estimating πππ mentioned?
- Historical based approach
- Implied volatility based approach
What does the parametric approach assume about asset returns?
Asset returns are normally or lognormally distributed with time-varying volatility.
What happens to the return distribution during periods of market stress?
Volatility tends to increase.
What is a common method for estimating current volatility?
Using recent historical data.
What can lead to an unreliable estimate of current volatility?
Using data from too long ago or including outliers.
What are the two types of changes in volatility described?
- Slow changes
- Regime switching
True or False: A mixture of two normal distributions can create fat tails.
True.
What is the formula for calculating standard deviation from sample data?
π = β(1/m Ξ£ (πnβi)Β²)
What does the term βunconditional normalityβ refer to?
Probability distribution of the return each day has the same normal distribution.
What does a conditionally normal model improve upon?
Assuming returns are constantly normal.
What is the relationship between volatility and asset return distribution during high volatility?
Daily return is normal with a high standard deviation.
Fill in the blank: The historical simulation is a type of ______ approach for estimating πππ .
[Non-Parametric]
What is the significance of the correlation coefficient in a two-asset portfolio?
It affects the combined πππ calculation.
What does EWMA stand for?
Exponentially Weighted Moving Average
What is the primary purpose of using EWMA?
To overcome problems of estimating volatilities of market variables.
In EWMA, how are the weights applied to squared returns determined?
Weights are determined by a persistence factor (Ξ») multiplied by the weight applied to the previous squared return.
What is the value of Ξ» that Risk Metrics found to work well in the 1990s?
0.94
True or False: In EWMA, the weights given to all squared returns must be equal.
False
What is the effect of a higher Ξ» in EWMA?
Gives more weight to older data.
What is the weight given to the latest squared return in EWMA called?
Reactive factor
How does the new estimate of the variance rate on day n get calculated in EWMA?
It is a weighted average of the previous dayβs variance estimate and the most recent squared return.
What does the term βmean reversionβ refer to in the context of GARCH models?
The tendency of volatility to revert toward the long-run average mean.
In GARCH(1,1), what do the parameters Ξ±, Ξ², and Ξ³ represent?
- Ξ±: weight for the most recent squared return
- Ξ²: weight for the previous variance rate estimate
- Ξ³: weight for the long-run average variance rate
Fill in the blank: In the GARCH model, the unconditional variance has been normalized to _______.
one
What is the implication of having a Ξ» value much higher than 0.94 in EWMA?
It would make EWMA relatively unresponsive to new data.
What does the term βdecay factorβ refer to?
Ξ» in the context of EWMA
What happens to estimates if Ξ» is set to a low value (e.g., 0.5)?
Estimates would overreact to new data.
What is the relationship between EWMA and GARCH(1,1)?
EWMA is a particular case of GARCH(1,1) where Ξ³ = 0.
What is the significance of the weights in GARCH models?
Weights must sum to one and determine the influence of past returns and variance.
What is the expected variance rate on day t in GARCH?
ΟΒ² = VL + Ξ± + Ξ² ΟΒ²(n-t) - VL
What are the three main nonparametric methods used to estimate VaR?
- Historical simulation
- Hybrid approach
- Multivariate density estimation
True or False: Nonparametric methods require assumptions about the entire distribution of returns.
False
What is the square root rule in the context of volatility?
Assumes that the variance rate over T days is T times the variance rate over one day.
What does multivariate density estimation (MDE) focus on?
Determining weights based on periods in the past that are most similar to the current period.
In GARCH(1,1), what does the notation (1,1) signify?
Weight is given to one most recently observed squared return and one most recent variance rate estimate.
What does EWM stand for in the context of weighting historical data?
EWM stands for Exponentially Weighted Moving Average.
EWM applies decreasing weights to historical data as one moves back in time.
What is the main concept behind multivariate density estimation (MDE)?
MDE determines weights based on the similarity of historical periods to the current period.
Weights are assigned according to how similar past days are to the current day.
How does volatility of interest rates behave in relation to interest rate levels?
Volatility tends to decrease as interest rates increase.
What are conditioning variables in the context of MDE?
Conditioning variables are additional variables used to assess similarity between periods, such as GDP growth and interest rate levels.
In the formula for similarity in MDE, what does X* represent?
X* represents the value of Xi today.
What is a disadvantage of using MDE?
MDE may lead to over-fitting of data.
What is another disadvantage of MDE?
MDE requires a large amount of data.
What is Value at Risk (VaR)?
VaR is a statistical measure that estimates the potential loss in value of an asset or portfolio with a specified confidence level.
What is the expected shortfall in risk management?
Expected shortfall is the average loss given that a loss is beyond the VaR threshold.
What does implied volatility indicate?
Implied volatility indicates the average volatilities expected over the life of an option.
What is the VIX index?
The VIX is an index of the implied volatilities of 30-day options on the S&P 500.
What typical range does the VIX index fall within?
The VIX typically ranges from 10 to 20.
True or False: Correlations should be monitored alongside volatilities in risk management.
True.
What is the formula used for updating covariance in EWM?
covn = Ξ»covnβ1 + (1 - Ξ») xnβ1ynβ1.
How is the correlation between two variables calculated?
Correlation is calculated as the covariance divided by the product of their standard deviations.
What is the relationship between the coefficient of correlation and covariance?
Covariance is the coefficient of correlation multiplied by the product of the standard deviations.
Fill in the blank: The covariances can be updated using the _______ model.
EWM model.
What does GARCH stand for?
Generalized Autoregressive Conditional Heteroskedasticity.
What is one complexity involved in using GARCH for updating covariances?
Using GARCH to update multiple covariances in a consistent way is complex.
