Transcript Saunders Cornett Chapter 10

Chapter 10
Market Risk
McGraw-Hill/Irwin
© 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Overview
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This chapter discusses the nature of
market risk and appropriate measures
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Dollar exposure
RiskMetrics
Historic or back simulation
Monte Carlo simulation
Links between market risk and capital
requirements
10-2
Trading Risks
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10-3
Trading exposes banks to risks
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1995 Barings Bank
1996 Sumitomo Corp. lost $2.6 billion in
commodity futures trading
AllFirst/ Allied Irish $691 million loss
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Allfirst eventually sold to Buffalo based M&T Bank
due to dissatisfaction among stockholders of Allied
Irish
Implications
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Emphasizes importance of:
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10-4
Measurement of exposure
Control mechanisms for direct market risk—and
employee created risks
Hedging mechanisms
Of interest to regulators
Market Risk
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10-5
Market risk is the uncertainty resulting from
changes in market prices .
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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.
Market Risk Measurement
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Important in terms of:
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Management information
Setting limits
Resource allocation (risk/return tradeoff)
Performance evaluation
Regulation
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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
10-6
Calculating Market Risk Exposure
10-7
Generally concerned with estimated
potential loss under adverse circumstances.
 Three major approaches of measurement
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JPM RiskMetrics (or variance/covariance
approach)
Historic or Back Simulation
Monte Carlo Simulation
JP Morgan RiskMetrics Model
10-8
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) × (potential adverse
daily yield move) where,
MD = D/(1+R)
Modified duration = MacAulay duration/(1+R)
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Confidence Intervals
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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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(5% of the extreme values greater than +1.65
standard deviations and 5% of the extreme values
less than -1.65 standard deviations)
10-9
Adverse 7-Year Rate Move
10-10
Confidence Intervals: Example
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10-11
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%.
Confidence Intervals: Example
10-12
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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N
Confidence Intervals: Example
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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
10-13
Foreign Exchange
10-14
In the case of Foreign Exchange, DEAR is
computed in the same fashion we employed
for interest rate risk.
 DEAR = dollar value of position × FX rate
volatility volatility where the FX rate volatility
is taken as 1.65 sFX
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Equities
For equities,
Total risk
= Systematic risk + Unsystematic risk
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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.
10-15
Aggregating DEAR Estimates
10-16
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 = [DEARa2 + DEARb2 +
DEARc2 + 2rab × DEARa × DEARb + 2rac ×
DEARa × DEARc + 2rbc × DEARb × DEARc]1/2
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Historic or Back Simulation
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Advantages:
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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.
10-17
Historic or Back Simulation
10-18
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
10-19
Convert today’s FX positions into dollar
equivalents at today’s FX rates.
 Measure sensitivity of each position
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Measure risk
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Calculate its delta.
Actual percentage changes in FX rates for each
of past 500 days.
Rank days by risk from worst to best.
Weaknesses
10-20
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
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To overcome problem of limited number of
observations, synthesize additional
observations.
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10-21
Perhaps 10,000 real and synthetic
observations.
Employ historic covariance matrix and
random number generator to synthesize
observations.
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Objective is to replicate the distribution of
observed outcomes with synthetic data.
Regulatory Models
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10-22
BIS (including Federal Reserve) approach:
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Market risk may be calculated using standard
BIS model.
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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.
BIS Model
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Specific risk charge:
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General market risk charge:
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reflect modified durations  expected interest rate
shocks for each maturity
Vertical offsets:
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Risk weights × absolute dollar values of long and
short positions
Adjust for basis risk
Horizontal offsets within/between time zones
10-23
Web Resources
10-24
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
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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:
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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.
10-25
Pertinent Websites
10-26
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