VAR with the confidence level of 1% means - answer-•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 - answer-the minimum capital requirement for financial institutions, scaled by an (arbitrary)...
, FINANCIAL RISK MANAGEMENT FINAL EXAM
VAR with the confidence level of 1% means - answer-•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 - answer-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 - answer-•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 - answer-•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 = - answer--2.33
In a Student-T distribution if c = 99% then α = - answer-3.365
VaR: Benefits - answer-•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 - answer-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 - answer-•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 - answer-•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 - answer-•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
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