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Trading and
Capital-Markets Activities Manual
Trading
Activities: Market Risk (Continue)
Source: Federal Reserve System
(The complete Activities
Manual (pdf format) can be downloaded from the Federal Reserve's web
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MARKET-RISK MEASUREMENT
There are a number of methods for measuring
the various market risks encountered in trading operations. All require
adequate information on current positions, market conditions, and instrument
characteristics. Regardless of the methods used, the scope and sophistication
of an institution's measurement systems should be commensurate with the
scale, complexity, and nature of its trading activities and positions
held.
Adequate controls should be imposed on all elements of the process for
market-risk measurement and monitoring, including the gathering and transmission
of data on positions, market factors and market conditions, key assumptions
and parameters, the calculation of the risk measures, and the reporting
of risk exposures through appropriate chains of authority and responsibility.
Moreover, all of these elements should be subject to internal validation
and independent review.
In most institutions, computer models are used to measure market risk.
Even within a single organization, a large number of models may be used,
often serving different purposes. For example, individual traders or desks
may use ''quick and dirty'' models that allow speedy evaluation of opportunities
and risks, while more sophisticated and precise models are needed for
daily portfolio revaluation and for systematically evaluating the overall
risk of the institution and its performance against risk limits. Models
used in the risk-measurement and front- and back-office control functions
should be independently validated by risk-management staff or by internal
or outside auditors.
Examiners should ensure that institutions have internal controls to check
the adequacy of the valuation parameters, algorithms, and assumptions
used in market-risk models. Specific considerations with regard to the
oversight of models used in trading operations and the adequacy of reporting
systems are discussed in sections 2100 and 2110, ''Financial Performance''
and ''Capital Adequacy of Trading Activities,'' respectively.
Basic Measures of Market Risk
Nominal Measures
Nominal or notional measurements are the most basic methodologies used
in market-risk management. They represent risk positions based on the
nominal amount of transactions and holdings. Typical nominal measurement
methods may summarize net risk positions or gross risk positions. Nominal
measurements may also be used in conjunction with other risk-measurement
methodologies. For example, an institution may use nominal measurements
to control market risks arising from foreign-exchange trading while using
duration measurements to control interest rate risks.
For certain institutions with limited, noncomplex risk profiles, nominal
measures and controls based on them may be sufficient to adequately control
risk. In addition, the ease of computation in a nominal measurement system
may provide more timely results. However, nominal measures have several
limitations. Often, the nominal size of an exposure is an inaccurate measure
of risk since it does not reflect price sensitivity or price volatility.
This is especially the case with derivative instruments. Also, for sophisticated
institutions, nominal measures often do not allow an accurate aggregation
of risks across instruments and trading desks.
Factor-Sensitivity Measures
Basic factor-sensitivity measures offer a somewhat higher level of measurement
sophistication than nominal measures. As the name implies, these measures
gauge the sensitivity of the value of an instrument or portfolio to changes
in a primary risk factor. For example, the price value of a basis point
change in yield and the concept of duration are often used as factor-sensitivity
measures in assessing the interest-rate risk of fixed-income instruments
and portfolios. Beta, or the measure of the systematic risk of equities,
is often considered a first-order sensitivity measure of the change in
an equity-related instrument or portfolio to changes in broad equity indexes.
Duration provides a useful illustration of a factor-sensitivity measure.
Duration measures the sensitivity of the present value or price of a financial
instrument with respect to a change in interest rates. By calculating
the weighted average duration of the instruments held in a portfolio,
the price sensitivity of different instruments can be aggregated using
a single basis that converts nominal positions into an overall price sensitivity
for that portfolio. These portfolio durations can then be used as the
primary measure of interest-rate risk exposure.
Alternatively, institutions can express the basic price sensitivities
of their holdings in terms of one representative instrument. Continuing
the example using duration, an institution may convert its positions into
the duration equivalents of one reference instrument such as a four-year
U.S. Treasury, three-month Eurodollar, or some other common financial
instrument. For example, all interest-rate risk exposures might be converted
into a dollar amount of a ''two-year'' U.S. Treasury security. The institution
can then aggregate the instruments and evaluate the risk as if the instruments
were a single position in the common base.
While basic factor-sensitivity measures can provide useful insights, they
do have certain limitations-especially in measuring the exposure of complex
instruments and portfolios. For example, they do not assess an instrument's
convexity or volatility and can be difficult to understand outside of
the context of market events. Examiners should ensure that factor sensitivity
measures are used appropriately and, where necessary, supported with more
sophisticated measures of market-risk exposure.
Basic Measures of Optionality
At its most basic level, the value of an option can generally be viewed
as a function of the price of the underlying instrument or reference rate
relative to the exercise price of the option, the volatility of the underlying
instrument or reference rate, the option contract's time to expiration,
and the level of market interest rates. Institutions may use simple measures
of each of these elements to identify and manage the market risks of their
option positions, including the following:
• ''Delta'' measures the degree to which the option's value will
be affected by a (small) change in the price of the underlying instrument.
• ''Gamma'' measures the degree to which the option's delta will
change as the instrument's price changes; a higher gamma typically implies
that the option has greater value to its holder.
• ''Vega'' measures the sensitivity of the option value to changes
in the market's expectations for the volatility of the underlying instrument;
a higher vega typically increases the value of the option to its holder.
• ''Theta'' measures how much an option's value changes as the
option moves closer to its expiration date; a higher theta is typically
associated with a higher option value to its holder.
• ''Rho'' measures how an option's value changes in response to
a change in short-term interest rates; a higher rho typically is associated
with a lower option value to its holder.
Measurement issues arising from the presence of options are addressed
more fully in the instrument profile on options (section 4330.1).
Scenario Simulations
Another level of risk-exposure measurement is the direct estimation of
the potential change in the value of instruments and portfolios under
specified scenarios of changes in risk factors. On a simple basis, changes
in risk factors can be applied to factor-sensitivity measures such as
duration or the present value of a basis point to derive a change in value
under the selected scenario. These scenarios can be arbitrarily determined
or statistically inferred either from analyzing historical data on changes
in the appropriate risk factor or from running multiple forecasts using
a modelled or assumed stochastic process that describes how a risk factor
may behave under certain circumstances. In statistical inference, a scenario
is selected based on the probability that it will occur over a selected
time horizon. A simple statistical measure used to infer such probabilities
is the standard deviation.
Standard deviation is a summary measure of the dispersion or variability
of a random variable such as the change in price of a financial instrument.
The size of the standard deviation, combined with some knowledge of the
type of probability distribution governing the behaviour of a random variable,
allows an analyst to quantify risk by inferring the probability that a
certain scenario may occur. For a random variable with a normal distribution,
68 percent of the observed outcomes will fall within plus or minus one
(±1) standard deviation of the average change, 90 percent within 1.65
standard deviations, 95 percent within 1.96 standard deviations, and 99
percent within 2.58 standard deviations. Assuming that changes in risk
factors are normally distributed, calculated standard deviations of these
changes can be used to specify a scenario that has a statistically inferred
probability of occurrence (for example, a scenario that would be as severe
as 95 percent or 99 percent of all possible outcomes). An alternative
to such statistical inference is to use directly observed historical scenarios
and assume that their future probability of occurrence is the same as
their historical frequency of occurrence.
However, some technicians contend that short-term movements in the prices
of many financial instruments are not normally distributed, in particular,
that the probability of extreme movements is considerably higher than
would be predicted by an application of the normal distribution. Accordingly,
more sophisticated institutions use more complex volatility-measurement
techniques to define appropriate scenarios.
A particularly important consideration in conducting scenario simulations
is the interactions and relationships between positions. These interrelationships
are often identified explicitly with the use of correlation coefficients.
A correlation coefficient is a quantitative measure of the extent to which
changes in one variable are related to another. The magnitude of the coefficient
measures the likelihood that the two variables will move together in a
linear relationship. Two variables (that is, instrument prices) whose
movements correspond closely would have a correlation coefficient close
to 1. In the case of inversely related variables, the correlation coefficient
would be close to -1.
Conceptually, using correlation coefficients allows an institution to
incorporate multiple risk factors into a single risk analysis. This is
important for instruments whose value is linked to more than one risk
factor, such as foreign exchange derivatives, and for measuring the risk
of a trading portfolio. The use of correlations allows the institution
to hedge positions-to partially offset long positions in a particular
currency/maturity bucket with short positions in a different currency/maturity
bucket-and to diversify price risk for the portfolio as a whole in a unitary
conceptual framework. The degree to which individual instruments and positions
are correlated determines the degree of risk offset or diversification.
By fully incorporating correlation, an institution may be able to express
all positions, across all risk factors, as a single risk figure.
Value-at-Risk
Value-at-risk (VAR) is the most common measurement technique used by trading
institutions to summarize their market-risk exposures. VAR is defined
as the estimated maximum loss on an instrument or portfolio that can be
expected over a given time interval at a specified level of probability.
Two basic approaches are generally used to forecast changes in risk factors
for a desired probability or confidence interval. One involves direct
specification of how market factors will act using a defined stochastic
process and Monte Carlo techniques to simulate multiple possible outcomes.
Statistical inference from these multiple outcomes provides expected values
at some confidence interval. An alternative approach involves the use
of historical changes in risk factors and parameters observed over some
defined sample period. Under this alternative approach, forecasts can
be derived using either variance-covariance or historical simulation methodologies.
Variance-covariance estimation uses standard deviations and correlations
of risk factors to statistically infer the probability of possible scenarios,
while the historical-simulation method uses actual distributions of historical
changes in risk factors to estimate VAR at the desired confidence interval.
Some organizations allocate capital to various divisions based on an internal
transfer-pricing process using measures of value-at-risk. Rates of return
from each business unit are measured against this capital to assess the
unit's efficiency as well as to determine future strategies and commitments
to various business lines. In addition, as explained in the section on
capital adequacy, the internal value-at-risk models are used for risk-based
capital purposes.
Assumptions about market liquidity are likely to have a critical effect
on the severity of conditions used to estimate risk. Some institutions
may estimate exposure under the assumption that dynamic hedging or other
rapid portfolio adjustments will keep risk within a given range even when
significant changes in market prices occur. Dynamic hedging depends on
the existence of sufficient market liquidity to execute the desired transactions
at reasonable costs as underlying prices change. If a market liquidity
disruption were to occur, the difficulty of executing transactions would
cause the actual market risk to be higher than anticipated.
To recognize the importance of market liquidity assumptions, measures
such as value-at-risk should be estimated over a number of different time
horizons. The use of a short time horizon, such as a day, may be useful
for day-to-day risk management. However, prudent managers will also estimate
risk over longer horizons, since the use of a short horizon relies on
an assumption that market liquidity will always be sufficient to allow
positions to be closed out at minimal losses. In a crisis, the firm's
access to markets may be so impaired that closing out or hedging positions
may be impossible except at extremely unfavourable prices, in which case
positions may be held for longer than envisioned. This unexpected lengthening
of the holding period will cause a portfolio's risk profile to be much
greater than expected because the likelihood of a large price change increases
with time (holding period), and the risk profile of some instruments,
such as options, changes substantially as their remaining time to maturity
decreases.
Stress Testing
The underlying statistical methods used in daily risk measurements summarize
exposures that reflect the most probable market conditions. Market participants
should periodically perform simulations to determine how their portfolios
will perform under exceptional conditions. The framework of this stress
testing should be detailed in the risk-management policy statement, and
senior management should be regularly apprised of the findings. Assumptions
should be critically questioned and input parameters altered to reflect
changing market conditions.
The examiner should review available simulations to determine the base
case, as well as review comparable scenarios to determine whether the
resulting ''worst case'' is sufficiently conservative. Similar analyses
should be conducted to derive worst-case credit exposures. Non-quantifiable
risks, such as operational and legal risks, constraints on market or product
liquidity, and the probability of discontinuities in various trading markets,
are important considerations in the review process. Concerns include unanticipated
political and economic events which may result in market disruptions or
distortions. This overall evaluation should include an assessment of the
institution's ability to alter hedge strategies or liquidate positions.
Additional attention should be committed to evaluating the frequency of
stress tests.
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