Financial Risk Management – Final Exam, 2026 – Study Material and
Practice Questions
VAR with the confidence level of 1% means - ANS✔✔ •the worst possible loss such that there is
less than 1% chance of losing more than that in a single trading day.
This worst possible loss determines - ANS✔✔ the minimum capital requirement for financial
institutions, scaled by an (arbitrary) multiplier to compensate for model errors and imperfect
risk assessment. The multiplier can be increased by regulators.
Value at Risk DOES ATTEMPT to answer the question - ANS✔✔ •What is the maximum loss over
a given time period such that there is only a 1 percent probability that the actual loss over the
given period will be larger?
•In other words, what is the loss such that there is only a 1% chance of losing more than that
over a given period of time?
VaR equation variables - ANS✔✔ •V Current marked-to-market value of the position
•E(V) Expected value of the position at the end of the holding horizon
•H Holding horizon (1 day, 1 week, 1 month, etc)
•R Return over the holding horizon (this is a random variable)
•μ Expected return
•c Confidence level, say 99%
•R* Return corresponding to the worst-case loss at c
•V* "Worst-case-loss-at-c" value of the position after 1 day
In a normal distribution if c = 99% then α = - ANS✔✔ -2.33
,In a Student-T distribution if c = 99% then α = - ANS✔✔ 3.365
VaR: Benefits - ANS✔✔ •VaR provides a common, consistent, and integrated measure of risk
across risk factors, instruments, and asset classes
•VaR provides a single number that can be easily translated into a capital requirement
•VaR allows for risk monitoring across businesses in a consistent way
•VaR is easy to communicate and understand
•VaR allows the firm to assess the benefits of diversification
VaRhas become an internal and external reporting tool
Estimating μ and σ - ANS✔✔ 1) select the risk factors.
2) assume that the distribution of the changes in the portfolio values is normal and can be
completely characterized by mean and variance.
3) derive the mean and variance of the portfolio under the normality assumption
4) using the mean and variance, calculate the VaR
Historical Simulation - ANS✔✔ •No assumptions are made regarding any distributions.
Instead:
•For each combination of changes, calculate the corresponding change in the value of your
portfolio
•This way, you have the empirical distribution of your portfolio value
•Find the expected value and the 1st percentile of this distribution and the difference is your
VaR.
Advantages and Disadvantages of historical simulation - ANS✔✔ •The biggest advantage is no
need to assume any distribution.
, •The biggest disadvantage is that the method relies heavily on the sample period.
Monte Carlo Approach - ANS✔✔ •Identify the risk factors (as with the previous approaches)
•Specify the stochastic processes that describe their dynamics (have to assume). Could be an
AR(1) process or some other type.
•Using historical data, estimate the parameters of the specified stochastic processes
•Using these stochastic processes and the parameter estimates, simulate about 10,000 possible
price paths for your portfolio value
•From the simulated distribution, derive VaR as the difference between expected change and
the 1st percentile change in the value of your portfolio.
VaR: Disadvantages - ANS✔✔ •Does not tell which components contribute most to total risk
•Based on distributions derived under normal market conditions and does not incorporate
crises characterized by large price changes, high volatility and a breakdown in correlations
among the risk factors
•Does not account for liquidity risk: the risk that trading will be too costly
•Some methodologies provide no or poor statistical estimation of error term (VaR is not exact
due to measurement error in estimating means and variances)
•VaR may take too much computational resources
Delta-VaR measures - ANS✔✔ The change in VaR if you had one more unit of asset A
Stress Testing; Scenario Analysis - ANS✔✔ •The purpose of stress testing and scenario analysis
is to determine the size of potential losses related to specific scenarios.
•A scenario is usually modeled after extreme historical events, such as
- October 1987 stock market crash
- Asian flu 1997
Practice Questions
VAR with the confidence level of 1% means - ANS✔✔ •the worst possible loss such that there is
less than 1% chance of losing more than that in a single trading day.
This worst possible loss determines - ANS✔✔ the minimum capital requirement for financial
institutions, scaled by an (arbitrary) multiplier to compensate for model errors and imperfect
risk assessment. The multiplier can be increased by regulators.
Value at Risk DOES ATTEMPT to answer the question - ANS✔✔ •What is the maximum loss over
a given time period such that there is only a 1 percent probability that the actual loss over the
given period will be larger?
•In other words, what is the loss such that there is only a 1% chance of losing more than that
over a given period of time?
VaR equation variables - ANS✔✔ •V Current marked-to-market value of the position
•E(V) Expected value of the position at the end of the holding horizon
•H Holding horizon (1 day, 1 week, 1 month, etc)
•R Return over the holding horizon (this is a random variable)
•μ Expected return
•c Confidence level, say 99%
•R* Return corresponding to the worst-case loss at c
•V* "Worst-case-loss-at-c" value of the position after 1 day
In a normal distribution if c = 99% then α = - ANS✔✔ -2.33
,In a Student-T distribution if c = 99% then α = - ANS✔✔ 3.365
VaR: Benefits - ANS✔✔ •VaR provides a common, consistent, and integrated measure of risk
across risk factors, instruments, and asset classes
•VaR provides a single number that can be easily translated into a capital requirement
•VaR allows for risk monitoring across businesses in a consistent way
•VaR is easy to communicate and understand
•VaR allows the firm to assess the benefits of diversification
VaRhas become an internal and external reporting tool
Estimating μ and σ - ANS✔✔ 1) select the risk factors.
2) assume that the distribution of the changes in the portfolio values is normal and can be
completely characterized by mean and variance.
3) derive the mean and variance of the portfolio under the normality assumption
4) using the mean and variance, calculate the VaR
Historical Simulation - ANS✔✔ •No assumptions are made regarding any distributions.
Instead:
•For each combination of changes, calculate the corresponding change in the value of your
portfolio
•This way, you have the empirical distribution of your portfolio value
•Find the expected value and the 1st percentile of this distribution and the difference is your
VaR.
Advantages and Disadvantages of historical simulation - ANS✔✔ •The biggest advantage is no
need to assume any distribution.
, •The biggest disadvantage is that the method relies heavily on the sample period.
Monte Carlo Approach - ANS✔✔ •Identify the risk factors (as with the previous approaches)
•Specify the stochastic processes that describe their dynamics (have to assume). Could be an
AR(1) process or some other type.
•Using historical data, estimate the parameters of the specified stochastic processes
•Using these stochastic processes and the parameter estimates, simulate about 10,000 possible
price paths for your portfolio value
•From the simulated distribution, derive VaR as the difference between expected change and
the 1st percentile change in the value of your portfolio.
VaR: Disadvantages - ANS✔✔ •Does not tell which components contribute most to total risk
•Based on distributions derived under normal market conditions and does not incorporate
crises characterized by large price changes, high volatility and a breakdown in correlations
among the risk factors
•Does not account for liquidity risk: the risk that trading will be too costly
•Some methodologies provide no or poor statistical estimation of error term (VaR is not exact
due to measurement error in estimating means and variances)
•VaR may take too much computational resources
Delta-VaR measures - ANS✔✔ The change in VaR if you had one more unit of asset A
Stress Testing; Scenario Analysis - ANS✔✔ •The purpose of stress testing and scenario analysis
is to determine the size of potential losses related to specific scenarios.
•A scenario is usually modeled after extreme historical events, such as
- October 1987 stock market crash
- Asian flu 1997
