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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 site)

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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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