Market risk and VaR

The original purpose of the 1988 BIS Accord was to impose minimum capital requirements for credit risk. More recently, the 1996 Amendment (BIS 1998) extended the Accord to incorporate market risk arising from the trading book of financial institutions. This chapter discusses what is meant by the term market risk, and then describes the most widely accepted methodology for modeling this risk: the value-at-risk (VaR) approach. As mentioned before market risk is the risk that changes in financial market prices and rates will reduce the values of a securities or portfolios. Within trading activities risk arises both from open (unhedged) positions and from imperfect correlations between market positions that are intended to offset one another. Market risk is given many different names in different contexts. For example, in the case of a fund, the market risk is often measured relative to a benchmark index or a portfolio, and is therefore referred to as "risk of tracking error." There are four major types of market risk:

Interest rate risk — The simplest form of interest rate risk is the risk that the value of a fixed-income security will fall as a result of a change in market interest rates. Open positions arise most often from differences in the maturities, nominal values, and reset dates of instruments and cash flows that are assetlike (i.e., "longs") and those that are liabilitylike (i.e., "shorts").

The exposure that such differences, or "mismatches," generates depends not only on the amount held and each position's sensitivity to interest rate changes, but also on the degree to which these sensitivities are correlated within portfolios and, more broadly, across trading desks and business lines. Imperfect correlation between offsetting instruments, both across the yield curve and within the same maturity for different issuers, can generate significant interest rate exposures. Although they may be intended to produce a hedged portfolio, offsetting positions that have different maturities may leave the portfolio holder exposed to imperfect correlations in the underlying reference rates. Such "curve" risk can arise in portfolios in which long and short positions of different maturities are effectively hedged against a parallel shift in yields but not against a change in the shape of the yield curve. Parallel shifts occur when a shock in the market has an equal effect on yields with different maturity dates; the yield curve is said to change shape when a shock in the market has a stronger effect on, say, the returns of shorter-dated instruments than it has on the returns of longer-dated instruments. Alternatively, even where offsetting positions have the same maturity, "basis" risk can arise if the rates of the positions are imperfectly correlated. For example, three-month Eurodollar instruments and three-month Treasury bills both naturally pay three-month interest rates. However, these rates are not perfectly correlated with each other, and spreads between their yields may vary over time. As a result, a three-month Treasury bill funded by three-month Eurodollar deposits represents an imperfect offset or hedged position.

Price risk for fixed-income products can be decomposed into a "general market" risk component and a "specific" risk component. Specific risk is the idiosyncratic component of the financial transaction, and in this sense it is akin to the credit risk that is analyzed in Chapters 8 to 10.

Equity price risk—The price risk associated with equities also has two components. "General market risk" refers to the sensitivity of an instrument or portfolio value to a change in the level of broad stock market indices. "Specific" or "idiosyncratic" risk refers to that portion of a stock's price volatility that is determined by characteristics specific to the firm, such as its line of business, the quality of its management, or a breakdown in its production process. A well-known result of portfolio theory is that general market risk cannot be eliminated through portfolio diversification, while specific risk can be diversified away.

Foreign exchange risk—The major sources of foreign exchange risk are imperfect correlations in the movement of currency prices and fluctuations in international interest rates. As with all other market risks, foreign exchange risk arises from open or imperfectly hedged positions. Although it is important to acknowledge exchange rates as a distinct market risk factor, the valuation of foreign exchange transactions requires knowledge of the behavior of domestic and foreign interest rates, 1 as well as of spot exchange rates. Foreign exchange risk is one of the major risks faced by large multinational corporations. Foreign exchange volatility can sweep away the return from expensive investments, and at the same time place a firm at a competitive disadvantage vis-_-vis its foreign competitors.2 It may also generate huge operating losses and inhibit investment.

Commodity price risk—The price risk of commodities are different from interest rate and foreign exchange risk because the majority of commodities are traded in markets in which the focus of supply can increase price volatility. In addition, fluctuations in the depth of trading in the market often come with and intensify high levels of price volatility. Thus, commodity prices commonly have higher volatilities and larger price discontinuities than most traded financial securities.

Measuring Risk:

A Historical Perspective

The measurement of risk has changed over time. It has evolved from simple indicators, such as the face value or "notional" amount for an individual security, through more complex measures of price sensitivities such as the duration and convexity of a bond, to the latest methodologies for computing VaR numbers (Figure 5.1). Each measure has tended at first to be applied to individual securities, and then to be adapted to measure the risk of complex portfolios such as those that contain derivatives. The quest for better and more accurate measures of market risk is ongoing; each new market turmoil reveals the limitations of even the most sophisticated measures of market risk. This said, VaR is proving to be a very powerful way of assessing the overall risk of trading positions over a short horizon, such as a 10-day period, and under "normal" market conditions. In effect, the methodology allows us to capture in a single number the multiple components of market risk we introduced in the previous section (curve risk, basis risk, volatility risk, etc.). For example, bond prices fall when interest rates rise according to a nonlinear relationship. Given a measure of the volatility of market yields, and their correlations, the market risk of a bond portfolio can be represented as a VaR number.

VaR is less reliable as a measure over longer time periods. The danger posed by exceptional market shocks, 4 which are often accompanied by a drying up of market liquidity, can only be captured by means of supplemental methodologies such as stress testing and scenario analysis.

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