In this chapter we will consider aspects of the risks to which participants in the capital markets are exposed, and the risk management function to which banks and securities houses now devote a significant part of their resources. The profile of the risk management function and risk measurement tools such as Value-at-Risk was raised during the 1990s, following bank collapses such as that of Baring’s and other trading losses suffered by banks such as Daiwa and Sumitomo. It was widely rumoured that one of the driving forces behind the merger of the old UBS with Swiss Bank (in reality, a takeover of UBS by Swiss Bank; the merged entity was named UBS) was the discovery of a multi-million loss on UBS’s currency options trading book, which senior management had been unaware of right up until its discovery. In any case, shareholders of banks now demand greater comfort that senior executives are aware of the trading risks that their bank is exposed to, and that robust procedures exist to deal with these risks. For this reason it is now essential for all staff to be familiar with the risk management function in a bank.

The types of risk that a bank or securities house is exposed to as part of its operations in the bond and capital markets are broadly characterised as follows:

We can look at some of these risk types in more detail:

The risk management function has grown steadily in size and importance within commercial and investment banks in the last decade. The development of the risk management function and risk management departments was not instituted from a desire to eliminate the possibility of all unexpected losses - should such an outcome indeed be feasible - rather from a wish to control the frequency, extent and size of trading losses in such a way as to provide the minimum surprise to senior management and shareholders.

Risk exists in all competitive business although the balance between financial risks of the types described above and general and management risk varies with the type of business engaged in. The key objective of the risk management function within a financial institution is to allow for a clear understanding of the risks and exposures the firm is engaged in, such that any monetary loss is deemed acceptable by the firm. The acceptability of any loss should be on the basis that such (occasional) loss is to be expected as a result of the firm being engaged in a particular business activity. If the bank’s risk management function is effective, there will be no overreaction to any unexpected losses, which may increase eventual costs to many times the original loss amount.

While there is no one agreed organisation structure for the risk management function, the following may be taken as being reflective of the typical bank set-up:

The risk management function is more likely to deliver effective results when there are clear lines of responsibility and accountability. It is also imperative that the department interacts closely with other areas of the front and back office. In addition to the above, the following are often accepted as ingredients of a risk management framework in an institution engaged in investment banking and trading activity:

A bank’s trading book will have an interest-rate exposure arising from its net position. For example, an interest-rate swap desk will have exposure for each point of the term structure, out to the longest dated swap that it holds on the book. A first-order measure of risk would be to calculate the effect of a 1-basis-point (1 b.p. = 0.01%) change in interest rates, along the entire yield curve, on the value of the net swaps position. This measures the effect of a parallel shift in interest rates. For large moves in interest rates, a bank’s risk management department will also monitor the effect of a large parallel shift in interest rates - say, 1% or 5%. This is known as the bank’s jump risk.

Derivatives desks often produce reports for trading books showing the effect on portfolio value of a 1-basis-point move, along each part of the term structure of interest rates. For example, such a report would show that a change of 1 basis point in 3-month rates would result in a change in value of £x - this measure is often referred to as a price variation per basis point, or sometimes as present value of a basis point (PVBP).

Jump risk refers to the effect on value of an upward move of 100 basis points for all interest rates - that is, for all points of the term structure. Each selected point on the term structure is called an interest-rate bucket or grid point. The jump risk figure is therefore the change in the value of the portfolio for a 1% parallel shift in the yield curve.

Table 14.1 shows an extract from the swap book risk report of a UK bank with the PVBP for selected points along the term structure. The jump risk report will show the effect of a 1% interest-rate move across all grid points; the sum of all the value changes is the jump risk.

As banks deal in a large number of currencies their jump risk reports will amalgamate the risk exposures from all parts of the bank. Table 14.2 shows an extract from the risk report for a currency options book of a major investment bank, dated before the introduction of the euro. It lists both Value-at-Risk exposure and jump risk exposure.

The advent of Value-at-Risk (VaR) as an accepted methodology for quantifying market risk and its adoption by bank regulators is part of the evolution of risk management. The application of VaR has been extended from its initial use in securities houses to commercial banks and corporates, following its introduction in October 1994 when JP Morgan launched RiskMetrics™ free over the Internet.

VaR is a measure of market risk. It is the maximum loss which can occur with X% confidence over a holding period of t days.

VaR is the expected loss of a portfolio over a specified time period for a set level of probability. For example, if a daily VaR is stated as £100,000 to a 95% level of confidence, this means that during the day there is a only a 5% chance that the loss will be greater than £100,000. VaR measures the potential loss in market value of a portfolio using estimated volatility and correlation. The ‘correlation’ referred to is the correlation that exists between the market prices of different instruments in a bank’s portfolio. VaR is calculated within a given confidence interval, typically 95% or 99%; it seeks to measure the possible losses from a position or portfolio under ‘normal’ circumstances. The definition of normality is critical and is essentially a statistical concept that varies by firm and by risk management system. Put simply, however, the most commonly used VaR models assume that the prices of assets in the financial markets follow a normal distribution. To implement VaR, all of a firm’s positions data must be gathered into one centralised database. Once this is complete, the overall risk has to be calculated by aggregating the risks from individual instruments across the entire portfolio. The potential move in each instrument (i.e., each risk factor) has to be inferred from past daily price movements over a given observation period. For regulatory purposes this period is at least 1 year. Hence, the data on which VaR estimates are based should capture all relevant daily market moves over the previous year.

The main assumption underpinning VaR - and which in turn may be seen as its major weakness - is that the distribution of future price and rate changes will follow past variations. Therefore, the potential portfolio loss calculations for VaR are worked out using distributions from historic price data in the observation period.

For a discussion of the normal distribution, refer to the author’s book An Introduction to Value-at-Risk, part of this series.

There are three main methods for calculating VaR. As with all statistical models, they depend on certain assumptions. The methods are:

(also known as the variance/covariance method)

This method assumes the returns on risk factors are normally distributed, the correlations between risk factors are constant and the delta (or price sensitivity to changes in a risk factor) of each portfolio constituent is constant. Using the correlation method, the volatility of each risk factor is extracted from the historical observation period. Historical data on investment returns are therefore required. The potential effect of each component of the portfolio on the overall portfolio value is then worked out from the component’s delta (with respect to a particular risk factor) and that risk factor’s volatility.

There are different methods of calculating the relevant risk factor volatilities and correlations. We consider two alternatives below:

The historic simulation method for calculating VaR is the simplest and avoids some of the pitfalls of the correlation method. Specifically, the three main assumptions behind correlation (normally distributed returns, constant correlations, constant deltas) are not needed in this case. For historic simulation the model calculates potential losses using actual historic returns in the risk factors and so captures the non-normal distribution of risk factor returns. This means rare events and crashes can be included in the results. As the risk factor returns used for revaluing the portfolio are actual past movements, the correlations in the calculation are also actual past correlations. They capture the dynamic nature of correlation as well as scenarios when the usual correlation relationships break down.

The third method, Monte Carlo simulation, is more flexible than the previous two. As with historic simulation, Monte Carlo simulation allows the risk manager to use actual historic distributions for risk factor returns rather than having to assume normal returns. A large number of randomly generated simulations are run forward in time using volatility and correlation estimates chosen by the risk manager. Each simulation will be different, but in total the simulations will aggregate to the chosen statistical parameters (i.e., historic distributions and volatility and correlation estimates). This method is more realistic than the previous two models and therefore is more likely to estimate VaR more accurately. However, its implementation requires powerful computers and there is also a trade-off in that the time to perform calculations is longer.

The level of confidence in the VaR estimation process is selected by the number of standard deviations of variance applied to the probability distribution. Figure 14.1 shows a 98% confidence level interval for the normal distribution. A standard deviation selection of 1.645 provides a 95% confidence level (in a one-tailed test) that the potential, estimated price movement will not be more than a given amount based on the correlation of market factors to the position’s price sensitivity. This confidence level is used by the RiskMetrics™ version of correlation VaR.

Figure 14.1 Measuring value-at-risk; a 98% confidence interval (1.41 standard deviations).

Although the methodology behind VaR is based on well-established statistical techniques, it is a more complex exercise to apply VaR in practice. Applying VaR to the whole firm can result in problems hindering the calculation, including unstable market data, issues in synchronising trading book positions across the bank and across global trading books, and issues presented by the differing characteristics of different instruments. As one might expect, a VaR calculation can be undertaken more easily (and is likely to be proved inaccurate on fewer occasions) for an FX trading book than an exotic option trading book, due to the different behaviour of the prices of those two instruments in practice. Often banks will use a correlation method VaR model for some of their trading books and a Monte Carlo simulation approach for books holding exotic option instruments.

It is important to remember that VaR is a tool that attempts to quantify the size of a firm’s risk exposure to the market. It can be viewed as a management information tool, useful for managing the business. It is conceptually straightforward to grasp because it encompasses the market risk of a firm into one single number; however, it is based on a statistical model of that firm’s risks and it does not capture - nor does it attempt to capture - all the risks that the firm is faced with. In the real world, the statistical assumptions used in VaR calculation will sometimes not apply - for example, in times of extreme market movements, such as market crashes or periods of high volatility, as experienced recently with the turmoil in Asian currency markets. For example, VaR makes no allowance for liquidity risk. In times of market correction and/or high market volatility, the inability of a bank to trade out of its positions (possibly because all of the other market participants have the same positions and wish to trade out of them at the same time) will result in higher losses than normal, losses that a VaR model is unlikely to have catered for. In such a case, it would have been a combination of market and liquidity risk that the bank was exposed to and which resulted in trading losses. In addition, it has been argued that the normal distribution underestimates the risks of large market movements (as experienced in market crashes) and, therefore, is not an accurate representation of real market conditions. Banks may need to allow for this when calculating their VaR estimate - for example, by building a compensating factor into their model.

Our discussion needs to be borne in mind at senior management level, so that it is clearly understood what the VaR figure means to a bank. It is important not to be over-reliant on VaR as the only measure of a firm’s risk exposure, but rather as a tool forming part of an integrated and independent risk management function operating within the firm.

Credit risk emerged as a significant risk management issue in the 1990s. As returns and interest spreads in developed markets have been reducing over time, in increasingly competitive markets banks and securities houses are taking on more forms of credit risk, in a bid to boost returns. This has led to both retail and investment banks being exposed to higher levels of credit risk. There are two main types of credit risk:

Credit spread is the excess premium required by the market for taking on a certain assumed credit exposure. Credit spread risk is the risk of financial loss resulting from changes in the level of credit spreads used in the marking-to-market of a product. It is exhibited by a portfolio for which the credit spread is traded and marked. Changes in observed credit spreads affect the value of the portfolio. Credit default risk is the risk that an issuer of debt (obligor) is unable to meet its financial obligations. Where an obligor defaults a firm generally incurs a loss equal to the amount owed by the obligor less any recovery amount which the firm receives as a result of foreclosure, liquidation or restructuring of the defaulted obligor. By definition, all portfolios of exposures, except those of developed country government bonds, exhibit an element of credit default risk.

After its initial introduction as a measurement tool for market risk, practitioners have recently begun to apply VaR methodology in the estimation of credit risk exposure. For example, JP Morgan’s CreditMetrics™ applies the same methodology that is used in its RiskMetrics™ VaR model. CreditMetrics™ calculates probabilities of loss on a portfolio due both to default of any issuer or due to any change in credit rating of an issuer. The investment bank CSFB has introduced its own credit risk VaR model that calculates the probability of loss due solely to instances of default of any issuer; their system is known as CreditRisk+. The main credit risk VaR methodologies take a portfolio approach to credit risk analysis. This means that:

This allows portfolio effects - the benefits of diversification and risks of concentration - to be quantified.

The portfolio risk of an exposure is determined by four factors:

All of these elements need to be accounted for when attempting to quantify credit risk exposure.

Credit VaR, like market risk VaR, considers (credit) risk in a mark-to-market framework. That is, it views credit risk exposure to arise because of changes in portfolio value that result from credit events, which are changes in obligor credit quality that include defaults, credit-rating upgrades and rating downgrades. Nevertheless, credit risk is different in nature from market risk. Typically, market return distributions are assumed to be relatively symmetrical and approximated by normal distributions, for the purposes of VaR calculations. (In fact, the occurrence of extreme market movements, such as stock market crashes, is more frequent than would be predicted by pure normal distributions. If we were to model the frequency of actual market returns, our resulting distribution would exhibit fatter tails than the conventional normal curve, a phenomenon referred to as leptokurtosis.) In credit portfolios, value changes will be relatively small as a result of minor credit-rating upgrades or downgrades, but can be substantial upon actual default of a firm. This remote probability of large losses produces skewed distributions with heavy downside tails that differ from the more normally distributed returns assumed for market VaR models. We illustrate the different curves in Figure 14.2.

This difference in risk profiles does not prevent us from assessing risk on a comparable basis. Analytical method market VaR models consider a time horizon and estimate Value-at-Risk across a distribution of estimated market outcomes. Credit VaR models similarly look to a horizon and construct a distribution of values given different estimated credit outcomes.

When modelling credit risk the two main measures of risk are:

To simplify modelling no assumptions are made about the causes of default. Mathematical techniques used in the insurance industry are used to model the event of an obligor default.

The choice of time horizon will not be shorter than the time frame over which ‘risk-mitigating’ actions can be taken - that is, the time to run down a book or offload the exposure. In practice, this can be a fairly time-consuming and costly process. CSFB (who introduced the CreditRisk+ model) suggests two alternatives:

Modelling credit risk requires certain data inputs - for example, CreditRisk+ uses the following:

These data requirements present some difficulties. There is a lack of comprehensive default and correlation data, and assumptions need to be made at certain times, which will affect the usefulness of any final calculation. For more liquid bond issuers there is obviously more data available. In addition, rating agencies such as Moody’s have published data on, for example, the default probabilities of bonds of each category. We illustrate the 1-year default rates for rated bonds, as quoted by Moody’s in 1997, at Table 14.3.

The annual probability of default of each obligor can be determined by its credit rating and then mapping between default rates and credit ratings. A default rate can then be assigned to each obligor.

Source: CSFB.

Default-rate volatilities can be observed from the historic volatilities of such rates.

A risk manager will often tell you that one purpose of a risk management system is to direct and prioritise actions, with a view to minimising the level of loss or expected loss. If we are looking at a firm’s credit exposure, when considering risk-mitigating actions there are various features of risk worth targeting, including obligors having:

In theory, a credit VaR methodology helps to identify these areas and allows the risk manager to prioritise risk-mitigating action. This is clearly relevant in a bond-dealing environment - for example, in times of market volatility or economic recession - when banks will seek to limit the extent of their loan book. Bond desks will seek to limit the extent of their exposure to obligors.

Another application that applies in a bond-dealing environment is in the area of exposure limits. Within bank dealing desks, credit risk limits are often based on intuitive, but arbitrary, exposure amounts. It can be argued that this is not a logical approach because resulting decisions are not risk-driven. Risk statistics used as the basis of VaR methodology can be applied to credit limit setting, in conjunction with the standard qualitative analysis that is normally used. For this reason the limit-setting departments of banks may wish to make use of a credit VaR model to assist them with their limit setting.

Butler, C. (1999). Mastering Value-at-Risk. FT Prentice Hall, London.