This chapter discusses market risk and its measurement. It provides examples of how major trading losses at banks like Barings and Sumitomo occurred due to poor risk management. It then outlines approaches to measuring market risk exposure, including dollar value exposure, RiskMetrics, historical simulation, and Monte Carlo simulation. Regulators set capital requirements based on measures of market risk to ensure banks hold sufficient capital to cover potential losses.

1. Market Risk
Chapter 10
© 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.
K. R. Stanton

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Overview
 This chapter discusses the nature of
market risk and appropriate measures
 Dollar exposure
 RiskMetrics
 Historic or back simulation
 Monte Carlo simulation
 Links between market risk and capital
requirements

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Trading Risks
 Trading exposes banks to risks
 1995 Barings Bank
 1996 Sumitomo Corp. lost $2.6 billion in
commodity futures trading
 1997 market volatility in Eastern Europe and
Asia
 1998 continuation with Russian bonds
 AllFirst/ Allied Irish $691 million loss
 Partly preventable with software
 Rusnak currently serving 7 ½ year sentence for fraud
 Allfirst sold to Buffalo based M&T Bank

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Implications
 Emphasizes importance of:
 Measurement of exposure
 Control mechanisms for direct market risk—and
employee created risks
 Hedging mechanisms

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Market Risk
 Market risk is the uncertainty resulting from
changes in market prices .
 Affected by other risks such as interest rate risk
and FX risk
 It can be measured over periods as short as
one day.
 Usually measured in terms of dollar exposure
amount or as a relative amount against some
benchmark.

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Market Risk Measurement
 Important in terms of:
 Management information
 Setting limits
 Resource allocation (risk/return tradeoff)
 Performance evaluation
 Regulation
 BIS and Fed regulate market risk via capital
requirements leading to potential for overpricing of
risks
 Allowances for use of internal models to calculate
capital requirements

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Calculating Market Risk Exposure
 Generally concerned with estimated
potential loss under adverse circumstances.
 Three major approaches of measurement
 JPM RiskMetrics (or variance/covariance
approach)
 Historic or Back Simulation
 Monte Carlo Simulation

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JP Morgan RiskMetrics Model
 Idea is to determine the daily earnings at risk =
dollar value of position × price sensitivity ×
potential adverse move in yield or,
DEAR = Dollar market value of position × Price
volatility.
 Can be stated as (-MD) × adverse daily yield
move where,
MD = D/(1+R)
Modified duration = MacAulay duration/(1+R)

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Confidence Intervals
 If we assume that changes in the yield are
normally distributed, we can construct
confidence intervals around the projected
DEAR. (Other distributions can be
accommodated but normal is generally
sufficient).
 Assuming normality, 90% of the time the
disturbance will be within 1.65 standard
deviations of the mean.

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Confidence Intervals: Example
 Suppose that we are long in 7-year zero-coupon
bonds and we define “bad” yield changes such
that there is only 5% chance of the yield change
being exceeded in either direction. Assuming
normality, 90% of the time yield changes will be
within 1.65 standard deviations of the mean. If the
standard deviation is 10 basis points, this
corresponds to 16.5 basis points. Concern is that
yields will rise. Probability of yield increases
greater than 16.5 basis points is 5%.

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Confidence Intervals: Example
 Price volatility = (-MD)  (Potential adverse
change in yield)
= (-6.527)  (0.00165) = -1.077%
DEAR = Market value of position  (Price
volatility)
= ($1,000,000)  (.01077) = $10,770

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Confidence Intervals: Example
 To calculate the potential loss for more than
one day:
Market value at risk (VARN) = DEAR × N
 Example:
For a five-day period,
VAR5 = $10,770 × 5 = $24,082

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Foreign Exchange & Equities
 In the case of Foreign Exchange, DEAR is
computed in the same fashion we employed
for interest rate risk.
 For equities, if the portfolio is well diversified
then
DEAR = dollar value of position × stock
market return volatility where the market
return volatility is taken as 1.65 sM.

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Aggregating DEAR Estimates
 Cannot simply sum up individual DEARs.
 In order to aggregate the DEARs from
individual exposures we require the
correlation matrix.
 Three-asset case:
DEAR portfolio = [DEARa
2 + DEARb
2 +
DEARc
2 + 2rab × DEARa × DEARb + 2rac ×
DEARa × DEARc + 2rbc × DEARb × DEARc]1/2

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Historic or Back Simulation
 Advantages:
 Simplicity
 Does not require normal distribution of
returns (which is a critical assumption for
RiskMetrics)
 Does not need correlations or standard
deviations of individual asset returns.

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Historic or Back Simulation
 Basic idea: Revalue portfolio based on
actual prices (returns) on the assets that
existed yesterday, the day before, etc.
(usually previous 500 days).
 Then calculate 5% worst-case (25th lowest
value of 500 days) outcomes.
 Only 5% of the outcomes were lower.

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Estimation of VAR: Example
 Convert today’s FX positions into dollar
equivalents at today’s FX rates.
 Measure sensitivity of each position
 Calculate its delta.
 Measure risk
 Actual percentage changes in FX rates for each
of past 500 days.
 Rank days by risk from worst to best.

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Weaknesses
 Disadvantage: 500 observations is not very
many from statistical standpoint.
 Increasing number of observations by going
back further in time is not desirable.
 Could weight recent observations more
heavily and go further back.

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Monte Carlo Simulation
 To overcome problem of limited number of
observations, synthesize additional
observations.
 Perhaps 10,000 real and synthetic
observations.
 Employ historic covariance matrix and
random number generator to synthesize
observations.
 Objective is to replicate the distribution of
observed outcomes with synthetic data.

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Regulatory Models
 BIS (including Federal Reserve) approach:
 Market risk may be calculated using standard
BIS model.
 Specific risk charge.
 General market risk charge.
 Offsets.
 Subject to regulatory permission, large banks
may be allowed to use their internal models as
the basis for determining capital requirements.

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BIS Model
 Specific risk charge:
 Risk weights × absolute dollar values of long and
short positions
 General market risk charge:
 reflect modified durations  expected interest rate
shocks for each maturity
 Vertical offsets:
 Adjust for basis risk
 Horizontal offsets within/between time zones

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Web Resources
 For information on the BIS framework, visit:
Bank for International Settlement www.bis.org
Federal Reserve Bank
www.federalreserve.gov

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Large Banks: BIS versus
RiskMetrics
 In calculating DEAR, adverse change in rates
defined as 99th percentile (rather than 95th
under RiskMetrics)
 Minimum holding period is 10 days (means that
RiskMetrics’ daily DEAR multiplied by 10)*.
 Capital charge will be higher of:
 Previous day’s VAR (or DEAR  10)
 Average Daily VAR over previous 60 days times a
multiplication factor  3.
*Proposal to change to minimum period of 5 days
under Basel II, end of 2006.

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Pertinent Websites
American Banker www.americanbanker.com
Bank of America www.bankofamerica.com
Bank for International Settlements
www.bis.org
Federal Reserve www.federalreserve.gov
J.P.Morgan/Chase www.jpmorganchase.com
RiskMetrics www.riskmetrics.com