1.
VaR
What is VaR and describe how VaR values are estimated using the monte carlo simulation
VaR is a systematic methodology to quantify potential financial loss based on statistical
estimates of probability. An estimate of the probability of a loss being greater than (or less than)
a particular ringgit/dollar amount as a result of market fluctuations, value at risk is commonly
used to measure risk in a portfolio of assets or exposures.
In order to estimate VaR using the monte carlo simulation approach, a few steps are taken, which
include:
(1) Specify all the relevant risk factors. As in the other approaches, we need to
select all the relevant risk factors. In addition, we have to specify the dynamics of
these factors i.e. their stochastic processes, and estimate their parameters
(volatilities, correlations, mean reversion factors for interest-rate processes, and so
on)
(2) Construct price paths. Price paths are constructed using random numbers
produced by a random number generator. When several correlated risk factors are
involved, we need to simulate multivariate distributions. Only in the case where the
distributions are independent can the randomization be performed independently for
each variable.
(3) Value the portfolio for each path (scenario). Each path generates a set of values
for the risk factors for each security in the portfolio that are used as inputs into the
pricing models. The process is repeated a large number of times to generate the
distribution.
(4) Evaluate the results using the specified confidence interval.
2. Limitations of VaR and what are other methods that could help overcome this—maybe risk
budgeting, stress testing
Limitations of VaR include that the calculation could be demanding depending on the method
used. Also, the simplicity of VaR of providing only a single risk number is a limitation since it
does not consider all risk factors, nor does it perform well as risk measures for non traded
exposures. It also does not consider how market correlations might change/disintegrate under
extreme conditions in a financial crisis.
For stress testing, refer to presentation on Stress testing by Madaa (pasted below)
STRESS TESTING
It is described as the evaluation of the financial position of a financial institution
under a severe but plausible scenario to assist in decision making within the financial
institution.
In some sense, stress testing can be viewed as an extension of the historical
simulation method at increasingly higher confidence levels.
Stress tests may be performed at varying degrees of aggregation, from the level of
an individual instrument up to the institutional level. Stress tests are performed for
different risk types.
Why Should We Conduct Stress Testing?
VAR measures based on recent historical data can fail to identify extreme unusual
situations that could cause severe losses.
Thus, it complements standard VAR methods because it allows users to include
scenarios that did not occur over the VAR window but nonetheless are likely.
Types of Stress Testing
Scenario Analysis: Stress testing can be done through scenario analysis, and
scenario analysis is divided into two main types.
Type 1: Involves scenarios that apply shocks to a single parameter or risk
factor, holding constant all other risk factors. (Sensitivity Test).
Type 2: Involves more sophisticated scenarios that apply shocks to many
parameters or risk factors simultaneously. Such scenarios can be either
(Historical Scenarios) or (Hypothetical Scenarios).
Sensitivity Tests ignore multiple risk factors. Thus, their main benefit is that
they can provide a fast initial assessment of portfolio sensitivity to a given risk
factor. ex. parallel yield curve shift.
Historical Scenarios are implemented based on a significant market event
experienced in the past. This is done by examining historical data to provide
examples of joint movements in financial variables. ex. Asian currency crisis, or
9/11 attack.
 Hypothetical Scenarios represent hypothetical one-off surprises that are
analyzed in terms of their repercussions on financial markets. ex. Korean
reunification.
Generating Stress Testing Scenarios
Event-driven: The scenario is formulated from an event that generates movements
in the risk factors, or in other words an event that causes changes in the financial
market. And then figure out how much change will happen to the risk factors if such an
event takes place.
Portfolio driven: The risk vulnerabilities in the current portfolio that may lead to
adverse movements in risk factors are identified, and then we generate the kind of event
that may bring about such vulnerabilities.
Benefits of Stress Testing
Stress testing alerts financial institutions to adverse unexpected outcomes related to
a variety of risks and provides an indication of how much capital might be needed to
absorb losses should large shocks occur.
Stress testing is a tool that supplements other risk management approaches and
measures.
Stress testing facilitates the development of risk mitigation or contingency plans
across a range of stressed conditions.
Limitations of Stress Testing
The method is subjective. Bad scenarios will lead to irrelevant potential losses.
Stress test results are presented without an attached probability, which makes them
difficult to interpret.
There may be a temptation for the risk manager to produce large numbers of
scenarios just to be sure that any likely scenario is covered. This will make it harder for
top management to decide what to do.
Policy Recommendations
Stress testing should form an integral part of the overall governance and risk
management culture of the financial institution.
Stress testing should be actionable, with the results from stress testing analysis
impacting decision making.
Financial institutions should operate a stress testing programme that: promotes risk
identification and control; and provides a complementary risk perspective to other risk
management tools.
A financial institution should have written policies and procedures governing the
stress testing programme.
A financial institution should regularly maintain and update its stress testing
framework.
Stress tests should be geared towards the events capable of generating most damage
whether through size of loss or through loss of reputation.
For risk budgeting, refer to Hansang’s presentation
3.
Intergrated VaR—definition, application
Integrated VaR is a transformation of VaR methods from measuring individual risk towards a
tool for strategic decisions at the highest level of institution. The approximation of integrated
VaR cannot just simply be done by adding individual VaRs or by assuming a normal distribution
because both these methods will over or underestimate the true value of VaR. Therefore, the
closest we can get to the true VaR is through the hybrid—which is the combination of VaR for
each risk source with correlations embedded. This, still overestimates the true VaR by 13
percent, but the closest among all others.
Integrated VaR analysis, like VaR analysis also have different approaches. In this case, the
historical simulation (non parametric) and the monte carlo simulation (parametric) approaches.
In the historical simulation approach, the VaR is calculated based on intergrated indicators—past
historical information and integrated losses record. For the monte carlo simulation, it uses the
random sets for different holding periods which are used to shock both the integrated risk
indicator returns and integrated losses. Some assumptions are made for the parametric approach
which includes:
(1) The risk factors are approximately ~lognormal
(2) The relationship between the portfolio price and the risk factors is linear
(3) The time value of the contracts may be neglected
Important features to define are the strength of the shocked values and also the
bandwidth or value zones. Integrated VAR can be estimated by shocking the decomposed
matrix AT with vectors of historical or random values.
Historical or random values can be used to shock the integrated risks returns or
integrated losses. These values can be obtained by getting their rates within the same
distribution bandwidth, or by getting their rates from a variable distribution bandwidth. The
variation is derived from the degree of significance referring to each set of the integrated
risk indicators returns or to the values of the integrated risk exposure for each of the losses.
Monte-Carlo dynamic simulation method to estimate integrated VAR is notoriously
difficult to apply but it is recommended to be implemented in the financial industry. This is
because it gives more realistic results on potential values for the unexpected integrated risks
or losses that may occur.