Chapter 10
Market Risk
http://davidmlane.com/hyperstat/z_table.html
http://www.statsoft.com/textbook/sttable.html for 50% table OR
http://www.sjsu.edu/faculty/gerstman/EpiInfo/z-table.htm for 100%
table
McGraw-Hill/Irwin
© 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
Overview

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
Bank Asset Categories

Classification of bank assets determines how they
are reported:

Trading


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Mark-to-market gains/losses flow to Income statement and on to
SE
Held For Sale

Mark-to-market gains/losses bypass income statement, but flow
directly to SE
Held For Investment


10-3
Market value is ignored
Text breaks into two categories

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Banking Book (Held for Investment)
Trading Book (Trading and Held for Sale)
Bank Asset Categories
10-4
Trading accounts are small
 Held for Sale category is usually very limited
 Vast majority of assets are Held for
Investment (Banking Book)


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Market risk is not measured
Severely limits scope of any mark-to-market
reporting
Trading Book vs “Banking Book”
10-5
Trading Risks

10-6
Trading exposes banks to risks



1995 Barings Bank
1996 Sumitomo Corp. lost $2.6 billion in
commodity futures trading
AllFirst/ Allied Irish $691 million loss


Allfirst eventually sold to Buffalo based M&T Bank
due to dissatisfaction among stockholders of Allied
Irish
Untold trading position losses at Merrill Lynch,
Lehman et al in 2008
Implications

Emphasizes importance of:
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
10-7
Measurement of exposure
Control mechanisms for direct market risk—and
employee created risks
Hedging mechanisms
Of interest to regulators
Market Risk

10-8
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 (factors)
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

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
10-9
Calculating Market Risk Exposure
10-10
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 (later)
Monte Carlo Simulation (later)
JP Morgan RiskMetrics Model

10-11
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)
JP Morgan RiskMetrics Model

10-12
Idea is to determine the daily earnings at risk
= dollar value of position × price sensitivity ×
potential adverse move in yield or,
DEAR = Dollar loss on what we define as a bad
day in the market
 A bad day of interest rate movements is
measuring interest rate risk
 A bad day in the exchange rate if measuring
currency risk
 A bad day of credit spread movements if
measuring credit risk
DEAR

10-13
Simplified:

Dollar Sensitivity of portfolio x estimated
adverse move in factor

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For fixed income securities, dollar sensitivity of
portfolio = MD% x $PV
For Treasury securities, the risk factor we measure
against is market interest rate changes
DEAR Denomination
10-14
The prices sensitivity% in the first term must
be consistent with the measure used for the
adverse move
 For fixed income, if you use MD% as the
base measure, that means you are using
1% as a base


You must use a consistent measure for the
factor. In this case, use 1.0 stated as a whole
number
An Example
10-15
$100,000 portfolio of fixed income securities
with MD% of 5%.
 Estimated adverse interest rate move for
one day is .30%
 Tail is 2% = 2.05 SD
 DEAR = $100,000 x .05 x 30/100 x 2.05 =
$3075
 DEAR is a product of how much you own,
how volatile it is and how much you think
rates might go against you on a bad day.

An Example – What is New?

You know how to find the PV of the position
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Calculate price
You know how find %MD
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
10-16
Calculate modified duration
How do you define “a bad day”?
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Riskmetrics variance/covariance approach
Historic or back simulation
Monte Carlo analysis
Riskmetrics variance/covariance approach
10-17

Steps to define “a bad period”

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Select the measurement period – we use a
period of one day for DEAR
Compile data on past “one-period” changes in
the risk factor (interest rate?)
Calculate SD and mean to create a normal
distribution


Note that SD will be a one-day SD for DEAR
Select how bad you think “bad” is

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The worst 5% of days?
The worst 1% of days
The worst .01% of days?
Confidence Intervals
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10-18
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.

(5% of the extreme values greater than +1.65
standard deviations and 5% of the extreme values
less than -1.65 standard deviations)
Adverse 7-Year Rate Move
Computed: http://davidmlane.com/hyperstat/z_table.html
Table: http://www.statsoft.com/textbook/sttable.html
10-19
Confidence Intervals: Example

10-20
p271
Suppose that we are long in 7-year zero-coupon
bonds and the market rate is 7.24682 %. 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

10-21
MD = 7/(1+.072468) = 6.527
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

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
Note that DEAR is nothing more than a
VAR with one day as the period
10-22
Foreign Exchange
10-23
In the case of Foreign Exchange, DEAR is
computed in the same fashion we employed
for interest rate risk.
 We can skip the step of converting yield
changes to price changes because we
directly measure price change.
 DEAR = dollar value of position × FX rate
volatility volatility where the FX rate volatility
is taken as 1.65 sFX

http://www.oanda.com/convert/fxhistory
Foreign Exchange Example in Text p273
10-24
Have position of E1,600,000
 Exchange rate = 1.6E per $ or 1E=$.625
 $PV of position = $1,000,000
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You find that daily SD of exchange rate= 55.5 BP
You want a “worst 5% of bad days” level, so you
choose a confidence interval of 90%
For a 90% confidence interval, Z= 1.65
1.65 x 55.5BP =1.65x.00555 = .00932
$PV x price volatility = $1,000,000 = .00932 =
$9,320
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.
10-25
Aggregating DEAR Estimates
10-26
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

This should look very familiar from FNCE 4030
Skewness
10-27
Kurtosis (Fat Tails)
Normal
Cauchy
10-28
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.
10-29
Historic or Back Simulation
10-30
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.

Estimation of VAR: Example
10-31
Convert today’s FX positions into dollar
equivalents at today’s FX rates.
 Measure sensitivity of each position
 Measure risk
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Actual percentage changes in FX rates for each
of past 500 days.
Rank days by risk from worst to best.
Weaknesses
10-32
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.

Monte Carlo Simulation

To overcome problem of limited number of
observations, synthesize additional
observations.
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
10-33
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.
Regulatory Models

10-34
BIS (including Federal Reserve) approach:

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

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 (credit)
Adjust for basis risk
Horizontal offsets within/between time zones

Gaps
10-35
10-36
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:


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.
10-37