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Title: Description: The course will cover the theory and application of corporate risk management.


1
Risk Management
Identifying, Measuring, and Managing Corporate
Risk
Professor Dr. Gunter Meissner Web
www.dersoft.com E-mail gmeissne_at_aol.com
Office First Hawaiian Tower, 5th floor, Tel 544
0807
Description The course will cover the theory and
application of corporate risk management.
The course will analyze the
analytical derivation of risk as well as focus on
the practical application
of corporate risk management.
Course Objective To educate the student so
she/he will make millions in the corporate risk
management area
2
Risk Management
Identifying, Measuring, and Managing Corporate
Risk
Literature 1) Slides on www.dersoft.com/rmhpu.ppt
2) Gunter Meissner Trading Financial
Derivatives - Futures, Swaps and Options in
Theory and Application (to study the basics
derivative instruments used in RM) 3) Gunter
Meissner Credit Derivatives Application,
Pricing, and Risk Management 4) RISK
Magazine (available at Library desk)
Voluntary 5) Gunter Meissner Outperform the
Dow Using Options, Futures, and Portfolio
Strategies to Beat the Market
6) John Hull Options, Futures and other
Derivative Securities 7) Phillip Jorion
Value at Risk
Cool Websites www.garp.com (has the FRM
exam!!!), www.prmia.org, www.rmahq.com,
www.bis.org, www.gloriamundi.org,
www.defaultrisk.com, www.riskglossary.com,
www.numa.com
3
Risk Management
Identifying, Measuring, and Managing Corporate
Risk
Grading Participation/Homework 10 Paper
30 Presentation of the Paper 10 Mid
term 25 Final 25
Point System for Undergraduate Students
Point System for Graduate Students
90.00 lt A lt 100
95.00 lt A lt 100
86.66 lt A- lt 90.00
90.00 lt A- lt 95.00
83.33 lt B lt 86.66
86.66 lt B lt 90.00
80.00 lt B lt 83.33
83.33 lt B lt 86.66
76.66 lt B- lt 80.00
80.00 lt B- lt 83.33
73.33 lt C lt 76.66
76.66 lt C lt 80.00
70.00 lt C lt 73.33
73.33 lt C lt 76.66
66.66 lt C- lt 70.00
70.00 lt C- lt 73.33
63.33 lt D lt 66.66
F lt 70.00
60.00 lt D- lt 63.33
F lt 60.00
4
Risk Management
Contents Overview
Identifying Risks Market Risk Credit Risk
Operational Risk
Measuring and Managing Individual Risks with
Modern Financial Instruments Market Risk
Credit Risk Operational Risk
Managing Portfolio Risk The VAR concept for
Stocks, Bonds, Options, and Swaps The CAR
concept OpVAR concept
5
Risk Management
Contents in Detail
1. Class Intro to Corporate Risk Business Risk,
non-Business Risk CAPM Risk Concept,
Diversification
Section I Identifying, Measuring and Managing
Individual Risks with Modern Financial
Instruments
2. Class Identifying the basic types of Risk
Market Risk, Credit Risk, Operational Risk How
are they related?
3. Class Hedging Market risk with standard
Instruments and Derivatives
4. Class Hedging Credit Risk with standard
Instruments and Credit Derivatives
5. Class Hedging Operational Risk with standard
Instruments and Derivatives
6. Class The Regulatory environment Basel II
7. Class Midterm
6
Risk Management
Contents in Detail
Section II Managing Portfolio Risk
8. Class The VAR concept Assumptions,
Functionality, Criticism
9. Class The VAR concept for non-linear Assets
(Bonds, Swaps, Options)
10. Class Incremental VAR concept Brutal Force
versus partial Differentiation
11. Class Credit VAR How can we derive a and
s?
12. Class Operational VAR A realistic concept?
13. New Developments in RM Coherent Risk measures
14. Class Presentations of research project
15. Class Final
7
Risk Management
Topics for the Risk Management Projects
1) New Developments in the VAR concept 2) New
Developments in Non-VAR methods of Risk
Management 3) New Developments in Market Risk
Management 4) New Developments in Credit Risk
Management 5) New Developments in Operational
Risk Management 6) Combining Market Risk, Credit
Risk and OP Risk 7) Choose a specific OP risk
Disaster risk, Terrorism, Accounting risk,
Criminal risk, Knowledge risk, Tech risk,
Strategic risk, Political risk, Legal risk 8)
Coherent Risk Measure Approaches ETL (Expected
Tail Loss) 9) SRM (Spectral Risk Measures) 10)
Distortion Risk Measures 11) New Developments in
Basel II 12) Forecasting Risk and
Correlations 13) Backtesting 14)
Stresstesting 15) Survey of Risk Management
vendors 16) Programming a VAR, CAR or OPVAR
model 17) The FRM degree of GARP How to get it
8
Risk Management
18) Field Study How do Hawaiian Banks manage
their risks? Where do they stand with the
compliance of Basel II? 19) The next wave
Enterprise Risk Management 20) Liquidity risk
Systematic, Endogenous, Exogenous 21) Copulas
Whats so great? Programming a model 22)
Systemic Risk (Risk that a catastrophe spreads)
How to quantify? 22) Choose your own topic!
9
Risk Management
Permanent homework Read, listen to financial
news!! Bring questions to class!
Financial paper Each student will write a 10
page paper and present it leading a 30 minute
discussion on his/her findings. The paper has to
be handed in one week before presentation.
APA style, have a Table of Contents, have a
Conclusion!
The paper has to show your own thought process !
Dont cite too much, but analyze !
The quality of the argument is important, not the
argument itself !
10
Risk Management
The Philosophy of Risk
What is Risk?
Synonyms for Risk are
In finance
A definition
Is risk subjective or objective???
Lets look at flying in an airplane
The probability of dying in a plane crash is not
Do people consider the risk of flying in an
airplane the same???
11
Risk Management
The Philosophy of Risk
Everyone has an intuitive sense what Financial
Risk is
Financial Risk is the risk of which can lead
to personal or corporate bankruptcy with many
implications (loss of housing, standard of
living, loss of respect)
While temperature is measured in degrees of
Celsius, eyesight is measured in
dioptries, Financial loss is measured in units of
However, measuring financial risk is more complex
than measuring temperatures since
a) There are different types of risk (Market
Risk, Credit Risk, Operational Risk)
b) There are many different assets in a portfolio
that have to be considered (Stocks, Bonds,
Currencies, Commodities, Real Estate, etc) and
that are exposed to the 3 types of risk.
c) Most importantly, within and between these
types of risk, has to be
considered!!!
12
Basics of Risk Management
What is Corporate Risk???
Broadly, corporate risk is the risk that stems
from events and processes that deteriorate the
corporates performance.
A simple corporate risk categorization is
Business risk e.g.
Strategic decisions as MA, Expansions in new
markets and sectors, Technological risk
Non-Business risk e.g.
(Geo)political events, Macro-economic events,
Legal changes
13
Basics of Risk Management
Another risk categorization stems from the CAPM
CAPM is multi-Nobel prize rewarded (Markowitz,
Sharpe, and Miller 1990 Modigliani (who got the
Nobel-Prize in 1985 laid CAPM ground work with
Miller)
Short Review of CAPM
CAPM states that there is a positive relation
between
and
E(Ri) Rf Ăźi E(Rm) -Rf)
E(Ri) Expected Return (sometimes called
required return) of asset i
Rf Risk free return (that of a Treasury bond)
Expected Risk is measured by
Ăźi
Ăźi is also the Covariance of asset i with the SP
E(Rm) Expected Return of the market (SP )
E(Rm) - Rf) is the market risk premium
14
Basics of Risk Management
CAPM know 2 types of risk
CAPM RISK
Systematic Risk also called Market Risk or Common
Risk
Unsystematic Risk also called Company specific
or Idiosyncratic risk
Unsystematic Risk can reduced by
Systematic Risk not!!!
Ăźi Volatility of asset i / Volatility of the
market 0ltĂźlt? is often worded as
Systematic Risk of an Asset i
Keep in mind that
Risk is often measured in terms of
15
Basics of Risk Management
What about liquidity risk???
16
Overview of Liquidity Risk
Type of Market Risk
Liquidity Risk Asset Funding f (size,
complexity, convertibility)
Uncertainty of Asset Return (Conventional VAR
or ETL, SRM, ERM approaches)
Endogenous liquidity risk
Exogenous liquidity risk
17
Hedging Liquidity Risk
Several products are possible
a) Withdrawal Option
b) Hedge Fund Return Put Option, Bermuda Style
c) Hedge Fund Return Swap
d) Liquidity Option
18
Hedging Liquidity Risk
a) Withdrawal Option
Def A withdrawal option allows the investor to
withdraw his locked-up investment at the market
price
Withdrawal Option Premium
Market Value of Investment
Hedge Fund Investor
Option Seller
Hedge Fund Investment
Return of Hedge Fund
1 mio
Hedge Fund with 2 year lock up
Pricing
Gains its value from being able to
Requires modeling investor
Derman 2006 derives the lock-up premium as 3 pa
19
Hedging Liquidity Risk
b) Hedge Fund Return Put Option, Bermuda Style
Def A hedge fund return option allows the buyer
to sell the hedge fund return at a strike
Put Option Premium
Strike1) x 1 mio
Option Seller
Hedge Fund Investor
Return of Hedge Fund
Return of Hedge Fund
1 mio
1) Strike is expressed as a percentage e.g. 90,
100 or 110
Hedge Fund with 2 year lock up
Pricing
Gains its value from being able to
Standard option valuation techniques can be
applied
If we use Black 76, the hedge fund return follows
a GBM process, possibly with Poisson jumps
see www.dersoft.com/geometricwithjumps.xls
20
Hedging Liquidity Risk
c) Hedge Fund Return Swap
Def In a Hedge Fund Return Swap, the investor
swaps the Hedge Fund Return into Libor
Libor
Hedge Fund Investor
Swap Counterpart
Return of Hedge Fund
Return of Hedge Fund
1 mio
Hedge Fund with 2 year lock up
Cons
Liquidity problem not solved
Pricing
Standard swap valuation techniques can be applied
Input requires a
Structure can be made
21
Hedging Liquidity Risk
d) Liquidity Option
Def In a liquidity option the investor can
withdraw his investment on a publicly traded
asset at the market price if the liquidity of the
asset is low.
Liquidity Option Premium
Market Value of Mexican Bond if Liquidity is low
Option Seller
Investor
Mexican Bond
Return of Mexican Bond
1 mio
Mexico
Loss for Option Seller if he sells Mexican bond
BOS can be modeled with
Pricing
22
Identifying Risk
Market Risk
An example of Interest Rate risk is
Does a fixed rate loan mean no interest rate
risk???
Interest rate risk is typically hedged with
Futures, Swaps, and Options!
What about Interest rate arbitrage?? An example
is
Borrowing in Yen, converting into and lending
in !
What is the risk??

Is it likely that the will decrease against the
yen???
23
Identifying Risk
Market Risk
Every exporting or importing company has Currency
Risk
An example of currency risk of an exporter is..
Dell, which exports to Europe has currency risk,
since
Another example of currency risk of an importer
are European Airlines, since they purchase
gasoline, which is paid in
US .
The risk for the European Airlines is that the US

If an importer or exporter hedges the currency
risk with currency forwards, is currency risk
eliminated???
Currency risk is typically hedged with Futures,
Swaps and Options!!!
24
Identifying Risk
Market Risk
As a foreign student in the US, you have Currency
Risk
You have currency risk that the US dollar
You can hedge your currency risk by
25
Identifying Risk
Market Risk
Every exchange traded company or a company with
stocks on their balance sheet has
Naturally, if the equity price decreases, the
corporate value will decrease
Equity risk is typically reduced by Futures,
Swaps, and Options
26
Identifying Risk
Market Risk
A further type of market risk is commodity risk.
An example of commodity risk of an importer is..
Naturally, GM and Delta have the risk of
increasing steel or oil prices.
If GM and Delta hedge the commodity risk with
commodity forwards, is commodity risk
eliminated???
(see tfc-charts.com)
27
Identifying Risk
Credit Risk
What is Credit Risk??
Read G. Meissners best-seller Credit
Derivatives p. 1 - 250
Credit risk is the risk
There are principally two types of credit risk
Default risk is the risk
Credit Deterioration risk is the risk
Is Credit Deterioration risk a problem?
How are Default risk and Credit Deterioration
risk related??
28
Identifying Risk
Operational Risk
What is Operational Risk??
BIS Definition
Residual Definition
Types of Operational Risk
external damage of a companys property
Disaster Risk defined as
Examples
Technology Risk defined as
problems in a companys technology lead to a
deterioration of the companys operation
Examples
29
Identifying Risk
Operational Risk
Types of Operational Risk cont.
Knowledge Risk defined as
Examples
Accounting Risk defined as
Examples
Regulatory action against Accounting risk
30
Identifying Risk
Operational Risk
Types of Operational Risk cont.
Criminal Risk defined as
Examples
Political Risk defined as
Examples
Legal Risk defined as
Examples
31
A quick look at Credit Risk
Recall Is Credit Risk normally distributed???
Lets look at the historical Transition Matrix of
the year 2002
(Table 5.5 Numbers in )
From this matrix, if we extract the initial
rating A, we get
32
A quick look at Credit Risk
Conclusion
(see www.dersoft.com/lnd.xls)
33
A quick look at Credit Risk
For investment grade bonds that have not been
downgraded, we can assume that the credit risk
function is roughly inversely lognormally
distributed.
Later we will find how to determine a s and
consequently CAR
34
A quick look at Credit Risk
Can we forecast default probabilities???
35
The historical Yield-Spread
What does this mean???
Example Yield of Junk Bond (10) Yield of
Treasury bond (5) at end of recession
Yield of Junk Bond (9) Yield of Treasury bond
(7) at the end of expansion!
How can we exploit this???
36
Comparing Market Risk and Credit Risk
How are Market Risk and Credit Risk Distributed???
Loss 0 Profit
Loss 0 Profit
(Compare slides around 150, 175 Book p. 139f,
200f)
Conclusion
37
Identifying Risk
Are market risk, credit risk, and operational
risk related???
Yes, How?
Impact of Credit risk on Market risk
If credit quality decreases ?
Impact of Market risk on Credit risk
38
Identifying Risk
Are market risk, credit risk, and operational
risk related cont.
Is there an Impact of Operational risk on Credit
risk??
Is there an Impact of Credit risk on Operational
risk??
Is there an Impact of Operational risk on Market
risk??
Is there an Impact of Market risk on Operational
risk??
So far little research has been done that relates
the risks in a consistent manner..
39
Are market risk, credit risk, and operational
risk related cont.
Market risk, credit risk, and OP risk are not
only correlated but also
Overlap! and are driven by the same factors!
Examples
a) Interest rate risk is a type of market risk,
but also increases risk
Eliminating or reducing interest rate risk with a
cap or a swap will reduce market risk, and also
credit risk! It might also reduce certain types
of OR risk (technology risk)
b) Similarly, currency risk is a type of market
risk, but also increases risk
Eliminating or reducing currency risk with a
future, option, or a swap will reduce market
risk, and also credit risk! It might also reduce
certain types of OR risk (technology risk)
c) Eliminating or reducing credit risk with a
default swap or default swap option will
probably also reduce risk due to
lower funding costs
40
Are market risk, credit risk, and operational
risk related cont.
In practice, Market risk, credit risk, and OP
risk are calculated and then simply added!
Does this lead to an overstating or understating
of the total risk???
1) Simply adding the risks, and considering that
market risk, credit risk, and OP are positively
correlated leads to an
2) Simply adding the risks, and considering that
market risk, credit risk, and OP overlap, leads
to an
So which effect dominates in reality???
It is commonly assumed that just adding the risks
the total risk!
41
How are market risk, credit risk, and
operational risk correlated?
As discussed, the correlation of market risk and
credit (and OP risk) is typically
Empirical studies confirm this, (see Das, Duffie
et al, JF 2004 Li, Meissner, JFE 2006)
The most popular approach for measuring risk
correlation is the
COPULA
approach
Copula comes for copulare
More on Copulas when we discuss credit risk
42
Managing Single Asset Risk
1) One management strategy is
Single Asset Risk (e.g. owning a junk bond) can
be reduced by
2) Eliminating the risk via a
Cons
3) Entering into a cash position
Cons
4) Reducing the risk by entering into a derivate
position (buying a option on a stock to
hedge stock price risk, or buying a
to hedge default risk)
43
Managing Single Asset Risk
Hedging Single Asset Risk with Derivatives
Remember Derivatives??
An Option is
An Future (or Forward) is
A Swap is
44
Derivatives graphically
A long Call
Trade date t Call price
C2, Strike K60 and maturity T are agreed
Maturity date T
ST80
A long Future position
Trade date t Future price F60 is
given by the market and T is given by the
exchange
Maturity date T
ST 55
No Future premium is paid at t!!!
An Oil Swap
Trade date t Cash flows are agreed
(e.g. paying 60 per gallon and receiving market
price)
All cash flows are
80
70
60
No Swap premium is paid at t if executed at
mid-market!!!
45
Managing Single Asset Risk
When to hedge Interest Rate Risk with which
Derivative???
Example A Floating Rate Loan
Borrower A
Hedge Provider
1mio
Loan provider
When to hedge with a Cap, when to hedge with a
Swap????
46
Managing Single Asset Risk
Is borrower A happier if 6ML goes up or down???
1) If 6ML goes to 15, borrowers A total cost pa
if he hedges with a cap is
2) If 6ML decreases to 1, borrowers A total
cost is
So???
On an absolute basis (i.e. only looking at
borrower A), he is happier if 6ML
However
On a relative basis (i.e. considering also other
borrowers,) A might be happier if 6ML
since
47
Managing Single Asset Risk
Managing Interest Rate Risk
1mio
Borrower A
Borrower B
1mio
Loan provider
How else can the Borrower hedge his Interest Rate
Risk???
Potential Problems/Opportunities
48
Managing Single Asset Risk
Managing Currency Risk
Same logic applies
42 mio Baht
Thai Consumers
Dell investing in Thailand
Assumption 10 mio Baht pa
6 ML US
1mio
US Loan provider
What is the risk of Dell???
How can Dell hedge the currency risk?
49
Managing Single Asset Risk
0.24 mio US pa
10 mio Baht pa
Managing Currency Risk
How can Dell hedge the currency risk?
Currency Counter part
With Currency Forwards or Currency Options
42 mio Baht in t0
Thai Consumers
Assumption 10 mio Baht pa
Dell investing in Thailand
6 ML US
1mio
Should Dell hedge with currency forwards or
currency options???
US Loan provider
What are the 2 problems with a currency forward?
What are the drawbacks with currency options?
50
Managing Single Asset Risk
Managing Commodity Risk
How can Delta Airlines hedge the oil price risk?
With Oil Forwards or Oil Options
1 if Option
Hedge Provider e.g. CME, NYMEX
Delta Airlines
Should Delta hedge with oil forwards or oil
options???
What are the 2 problems with an oil forward?
What is the drawback of oil options?
51
Managing Single Asset Risk
Managing Credit Risk
Credit Risk
Default Risk
Credit Deterioration Risk (Migration Risk if
asset is rated)
Recall Is credit deterioration risk a problem?
52
Derivatives Market
53
Credit Derivatives Market
54
Managing Single Asset Risk
Managing Credit Risk
The products to hedge credit risk
Credit Derivatives
Credit Spread Products -Options -Forwards -Swaps
  • Default Swaps
  • Basket Swaps
  • Binary Swaps
  • Contingent Swaps
  • -Cancelable Swaps

Synthetic Structures -CDOs -CLNs -TPDs
Total Rate of Return Swaps
Synthetic Structures are not really a credit
product by themselves, but are simply bonds or
loans with an imbedded credit derivative
55
Managing Single Asset Risk
Managing Credit Risk
The main reason for the dominance of default
swaps are their
56
Managing Single Asset Risk
Managing Credit Risk
Default Swaps (also called Credit Default Swaps)
The Default Swap Buyer has a
position in the credit quality of the reference
obligation. This means
Hence, if the default swap buyer does not
own the reference asset, he has a
position in the credit quality of the
reference asset.
The Default Swap Seller has a
position in the credit quality of the reference
obligation. This means
57
Managing Single Asset Risk
Managing Credit Risk
Default Swaps cont.
Typically the default swap buyer owns the
reference asset
Thus, in this case, the default swap buyer does
not have a speculative position in the credit
quality of the reference obligation. The default
swap is now an
58
Managing Single Asset Risk
Features of Default Swaps
What correlation risk does the Investor have ???
Which default is worse for the default swap
buyer???
Should we include the default risk of the
Investor???
59
Credit Swaps cont.
Does the Investor still have credit deterioration
risk???
Does the Investor still have market price (
interest rate) risk???
Does the Investor still have operational risk???
What other risk does the Insurance buyer have??
60
Pricing Default Swaps
What determines the Price of a Default Swap??????
See www.dersoft.com/ dslmmkkm.xls
61
Managing Credit Risk
TRORs (Total Rate of Return Swaps)
A TROR can be viewed as a non-funded position in
an asset
- A TROR receiver is the underlying asset
- A TROR payer is the underlying asset
- Why doesnt the TROR receiver just buy the
underlying asset???
- Why doesnt the TROR payer just short the
underlying asst???
62
Managing Credit Risk
TRORs (Total Rate of Return Swaps)
Who has the credit risk of the underlying???
What determines the Libor /- spread???
If the default probability is high, the spread
will be
63
TRORs cont.
Does the Investor still have credit deterioration
risk???
Does the Investor still have market price (
interest rate) risk???
Does the Investor still have operational risk???
What other risk does the Insurance buyer have??
64
Managing Credit Risk
Credit Spread Products
As discussed earlier, credit derivatives can be
categorized in Default Swaps, TRORs and credit
spread products.
Credit spread products consist of
Credit spread options Credit spread
forwards Credit spread swaps
65
Managing Credit Risk
Credit Spread Products
Credit Spread Options
A credit spread is defined as
What determines the credit spread in an
economy???
The reader should be careful with the
terminology. In the field of exotic options,
where spread options are standard instruments, a
call on a spread has a payoff of max (spread (T)
strike spread, 0), where T is the option
maturity. However in the field of credit
derivatives, the payoff max (spread(T) strike
spread, 0) is referred to as a credit-spread put.
Thus, a credit-spread put buyer profits if the
spread widens, which means he profits if the
yield of the risky bond increases or the price of
the risky bond decreases. Lets list the payoffs
to make things clear. Including a duration term,
which is usually added to the payoff, and the
notional amount N, we get
Payoff Credit-spread Put
(T) Duration x N x max credit-spread (T)
strike spread, 0 (2.5)
Payoff Credit-spread Call (T) Duration x N x
max strike spread credit-spread (T), 0
(2.6)  
66
Managing Credit Risk
Credit Spread Products
Credit Spread Options
Example of a credit spread put payoff
A credit-spread put option has a notional amount
of 1 million. At option maturity the yield of a
bond is 10, the Treasury bond yield is 5 and
the strike spread is 2. The duration of the bond
at option start was 3.5. What is the payoff of a
credit-spread put option?
67
Managing Credit Risk
Credit Spread Products
Credit Spread Forwards
A forward is a contract between two parties to
trade a certain asset at a future date, at a
price, which is determined today. In a
credit-spread forward contract the underlying
asset is a credit-spread, defined as in equation
2.4. The structure of a credit-spread forward
contract on the credit-spread of a bond can be
seen in figure 2.12
The payoff of a long (short) credit-spread
forward is similar to the payoff of a
credit-spread call (put) option The payoff at
time t1 for a long forward is

Duration x N x K
S (t1)
(2.9)   where Duration is defined as in
equation (2.8), N is the notional amount, K is
the agreed spread at t0 (expressed in ) and
S(t1) is the actual spread at t1 (also expressed
in ).
68
Managing Credit Risk
Credit Spread Products
Credit Spread Forwards
Example 2.6a An investor believes the credit
quality of a bond will decrease and hence the
relative price of a bond will decrease. He sells
a credit-spread forward contract with an agreed
spread K of 2. The notional amount N is
1,000,000 and the duration of the bond at trade
date is 3.5. The credit quality of the bond
price, however, increases so that the yield
spread decreases to 1. What is the loss of the
credit-spread forward seller?
69
Managing Credit Risk
Credit Spread Products
Credit Spread Swaps
To begin with, the reader should not confuse
default swaps (DS) also termed credit default
swaps (CDS) with credit-spread swaps. As
mentioned above, a default swap is the most
popular credit derivatives product and can be
viewed as an insurance against default of the
underlying asset, if the underlying asset in
owned.
A swap is

In a credit-spread swap,
party A pays a fixed credit-spread rate, and
party B pays the 6 months Libor, as seen in
figure.
What is the difference between a forward and a
swap???
What view on the credit spread does the fixed
rate payer have???
70
Speculating with Credit Spread Products
When we slide into a recession, the
Credit-spread Yield of risky bond - Yield of
risk-free bond will
When we come out of a recession and enter into an
economic expansion, the Credit-spread Yield of
risky bond - Yield of risk-free bond will
When we come out of a recession and enter into an
economic expansion, we can profit if we
Go a credit spread forward or
a credit spread call
When should we enter into the forward, when buy
the call????
71
Managing Credit Risk
Hedging with Credit Spread Products
Spread Optional of Fixed??
Investor
Hedge Counterpart
payoff
1 mio
Mexican Bond
Mexican Bond Seller
We should hedge with a future or swap if
We should hedge with an option if
72
Managing Operational Risk (OP risk)
is under construction
Currently there are very few products exist, that
hedge OP risk..
To measure OP risk, corporations often use a
Scorecard Approach
  • The scorecard is a matrix of
  • Potential Loss Severity and
  • b) Potential Frequency of Occurrence

Lets look at a scorecard
73
Managing Operational Risk (OP risk)
T
Terrorism

High
Nature Catastrophes (Flood, Earthquake, Storm)

NC
C
Criminal Activities

Medium
Loss Severity
A
Accounting Irregularities

S
Settlement Errors

Low
IT Problems (Hackers, Viruses)
I1

Low
Medium
High
IT Problems (outdated IT system)

I2
Frequency of Occurrence
L
Legal Actions

So what is the problem with OP risk????
St
Strategic Errors

74
Managing Operational Risk
The future expected OP loss, E(OP loss) for a
certain time period can now be estimated as
E(OP loss)
Example OP risk managers at Company X have
estimated the probability of a terrorist attack
of 0.001 per year and with an impact of
100,000,000. Also, they believe that the
probability of accounting fraud is 0.01 and the
impact is 10,000,000. What is the combined
terrorism - accounting risk per year?
75
Managing Operational Risk
Critical Thoughts on the Scorecard Approach
76
Managing Operational Risk
As discussed, there are very few products that
directly hedge OP risk
So what can we do to protect against OP risk???
What about an indirect hedge??
Can OP risk be hedged with credit risk
derivatives and other derivatives???
That depends
77
Managing Operational Risk
Default Swaps and Operational Risk
Does a Default Swap hedge OP risk??
Can be evaluated by equation
ROC ?B/B / ?Eo/Eo
ROC specific operational credit risk, i.e.
impact of operational event, measured by ?Eo/Eo,
on credit quality, measured by ?B/B, all other
variables constant ?B discrete change in the
bond price ?Eo discrete change in the
companys outstanding equity as a result of the
operational event
If ROC 0, it follows that
The default swap
hedges at least part of the OP risk, since
78
Managing Operational Risk
Default Swaps and Operational Risk
An Example
An investor owns bonds of company X and has
hedged the bonds with a default swap with a
notional amount of 10,000,000. Accounting errors
are found at company X, which lead to a downgrade
of the company and to a decrease of the
outstanding equity value, ?Eo, of 1 billion. The
bond falls from 100 to 80.
If equation Return on risk-free bond Return on
risky bond - Default swap premium (pa)
(2.1b) holds and we assume no change in the
risk-free bond, it follows that the
default swap present value increases by
approximately
Consequently the operational impact on the bond is
79
Managing Operational Risk
Stock Options and Operational Risk
Using stock options, how can we also hedge OP
risk???
Simply buying a
Is buying a put on the stock a more reasonable
strategy than entering into a default swap on a
bond of the company to hedge OP risk??
80
Managing Operational Risk
TRORs and Operational Risk
Does a TROR hedge OP risk??
Since a DS Market risk TROR, similar logic as
for a DS applies
Hence, a TROR will protect against OP risk, if
the bond price changes due to credit quality
changes, as displayed in equation
ROC ?B/B / ?Eo/Eo
An example
81
Managing Operational Risk
TRORs and Operational Risk
An investor is long 10,000 bonds of company X
with a par value and current price of 100. Thus
the investment is 1,000,000. To partially hedge
his bond price exposure, the investor has entered
into a TROR, where he pays the TROR on half his
investment amount of 500,000. External auditors
have found that traders of company X have
overstated their profits. The company is
downgraded and the bond falls from 100 to 80.
Consequently the TROR receiver will pay
(plus the coupon
minus Libor /- spread) to the investor at the
next payment date. Thus, the investor is partly
compensated for his losses in the amount of
82
Managing Operational Risk
Credit Spread Products and Operational Risk
Recall There are 3 types of credit spread
products Credit-spread options, credit-spread
forwards, and credit-spread swaps.
Do credit spread products hedge OP risk??
Same logic as for DSs and TRORs applies
Hence,
83
Managing Operational Risk
Conclusion
Once again When should we hedge OP risk with an
option, when with a forward or swap??
We should hedge with an option, if we are not so
sure the OP event will occur!
Are OP events ever fairly certain to occur?
Hence
Currently, it is best to hedge OP risk indirectly
with
84
Managing Operational Risk
The Regulatory Environment for Op risk (Basel II)
Basel II (as of April 2003) allows banks to use 1
of 3 methods for calculating the OP risk charge
  • Basic Indicator Approach
  • Standardized Approach
  • (iii) Advanced Measurement Approach

Due to their level of sophistication, a bank can
choose an approach
Lets have a look at the (i) Basic Indicator
Approach
85
Managing Operational Risk
The Regulatory Environment for OP risk (Basel II)
The (i) Basic Indicator Approach requires banks
to calculate the OP risk charge by equation
KBIA GI x a
KBIA Capital charge under the Basic Indicator
Approach GI1-8 the average annual level of
gross income over the past 3 years a a fixed
percentage, set by the committee as 15
Simple example of the the Basic Indicator
Approach
The average annual gross income of Company X for
the last 3 years was 50 million. What is the
capital charge, KBIA, of company X following the
Basic Indicator Approach?
86
Managing Operational Risk
The Regulatory Environment for OP risk (Basel II)
(ii) The Standardized Approach
The (ii) Standardized Approach requires banks to
calculate the OP risk charge by equation
KTSA S (GI1-8 x Ăź1-8)
KTSA Capital charge under the Standardized
Approach GI1-8 the average annual level of
gross income over the past 3 years, for each of
the 8 business lines Ăź1-8 a
fixed percentage, set by the committee as
Ăź-Factor
Business Lines
Corporate Finance (Ăź1)
18
Trading and Sales (Ăź2)
18
Retail Banking (Ăź3)
12
Commercial Banking (Ăź4)
15
Payment and Settlement (Ăź5)
18
Agency Services (Ăź6)
15
Asset Management (Ăź7)
12
Retail Brokerage (Ăź8)
12
87
Managing Operational Risk
The Regulatory Environment OP risk (Basel II)
(ii) The Standardized Approach cont.
Example of the (ii) Standardized Approach
The average annual gross income of Company X for
the last 3 years was 1 million in Trading and
Sales, 2 million in Commercial Banking and 2.5
million in Retail Brokerage. All other business
lines produced no income. What is the capital
charge, KTSA, of company X following the Basic
Indicator Approach?
88
The Regulatory Environment for combined risk
(Basel II)
By the beginning of 2007, the BIS requires every
internationally active bank to report a combined
VAR number
Tier 1 capital in equation (4.6) is defined as
core capital, including permanent shareholders
equity and disclosed reserves. Tier 2 is capital
of lesser quality and includes for example
(long) subordinated debt and is limited to 100
of Tier 1.
Example 4.26 Bank X has combined Tier 1 and Tier
2 capital of 3 billion. Bank X also has
risk-weighted assets compiled for credit risk of
10 billion, a market risk charge of 1 billion and
an operational risk charge of 2 billion.
Following equation (4.6), we derive
Result
89
Section 2 Managing Portfolio Risk
Value at Risk (VAR)
What is VAR???
In very simple terms what question does VAR
answer?
more precisely
The amount we can lose is the VAR number
Naturally the VAR calculation should take into
account the of the risky positions
90
Market Value at Risk
1. Assumption Single asset (stocks, bonds,
currencies, commodities) returns are normally
distributed as in figure 6.1


Stock Return
0.45
0.4
0.35
0.3
0.25
Unexpected
0.2
Loss
0.15
0.1
s
VAR1.65
0.05
0
a -1.65
-
3.5
-
3
-
2.5
-
2
-
1.5
-
1
-
0.5
0
0.5
1
1.5
2
2.5
3
3.5
Loss Profit
2. Assumption The mean and volatility of the
underlying is constant during the time of
observation
Are the assumptions realistic??? What about fat
tails (called kurtosis)???
91
Market Value at Risk
What about fat tails (called kurtosis)???
Conclusion
92
Market Value at Risk
Market VAR is the difference between the mean
return µ of an asset S and a maximum loss return
m.
VAR(S) µ m (6.1)
If we assume that the return of S,
(Si-Si-1)/Si-1, is normally distributed, we can
express the maximum loss return m via a
confidence interval expressed by a, the mean µ,
and the standard deviation s (the third and
fourth moment of a normal distribution, skewness
and kurtosis are 0)
m - a s µ (6.2)
Combining equations (6.1) and (6.2), we derive
(6.3)
For a standardized normal distribution, the
standard deviation s is
1.
Hence in this case, VAR (S)
93
Market Value at Risk
Understanding the standardized normal
distribution
N(a -1.65)5
Since the units on the x-axis are , it
follows that VAR is the distance from 0 to a,
times the real s, VAR a s , where the real
s is derived from historical data!!
What about the area on the right side of 0???
94
Market Value at Risk
Understanding a and s
a x
-
axis value of a cumulative distribution e.g. for
a cumulative normal distribution N, we have
formal N(-2.33)
1
5
as shown in previous graph!
N(-1.65)
50
N(0)
N(1.65)
99
N(2.33)
(see Table A at the end of the book)
95
Market Value at Risk
Understanding a and s
s (S) standard deviation, Std, of returns
((Si-Si-1)/Si-1) s (S) can be more conveniently
interpreted as the volatility of asset price S,
calculated as

where
This is because the standard deviation of returns
Std ((Si-Si-1)/Si-1) is equal to the volatility
of prices, s (Si), hence Std ((Si-Si-1)/Si-1)
sS.
The standard deviation of the standard normal
distribution is . It also means that the
(absolute) units on the x-axis represent standard
deviations from the zero mean. One standard
deviation from the mean represents 34.13,
(0.8413 0.5 in Table A at the end of the book),
two standard deviations from the mean is 47.72
(0.9772-0.5 in Table A).
96
Market Value at Risk
Understanding a and s
Using the results from the last 2 slides, we can
interpret an a of 2.33, hence
N(-2.33)
There is a 1 chance that we
We are 99 sure that we will
For an a of 1.65, similar logic applies.
N(-1.65)
There is a 5 chance that we
We are 95 sure that we will
97
Market Value at Risk
Market VAR for a certain time frame
The volatility s in equation (6.3) is expressed
as a daily volatility, i.e. for the time horizon
of one day. This is typically the case in reality
since end-of-day prices are used. Volatility can
easily be transformed into any time frame by
multiplying it with the square root of that time
frame. For example a daily volatility, sdaily, is
transformed into a yearly volatility, syearly, by
multiplying by , assuming there 252
trading days in a year sdaily x
syearly. A daily volatility is transformed into
a 10-day volatility by multiplying by the square
root of 10 sdaily x s10day.
Example
The daily volatility of IBM is 4. What it the
one-month volatility assuming there are 22
trading days in one month?
The one-month volatility of IBM is
Using this transformation and adding the notional
amount N to the equation (6.3), we derive the VAR
for a x-day time period as
VAR (S) N a s
98
Market Value at Risk for a single asset
Example
A company owns 3,000,000 worth of asset S. The
daily volatility of asset S is 0.5. What is the
10-day market VAR for a confidence level of 99?
We first find the value for a for the 99
confidence level from Table A at the end of the
book, or with Excel function normsinv(0.99)
Following equation
(6.4)
VAR (S) N a s
the market VAR is
Hence, the company is 99 sure that it will not
lose more than within the
next 10 days due to market price changes of asset
S.
99
Market Value at Risk for a single asset
The regulatory market VAR requirement
The number 110,522 is the 10-day VAR on a 99
confidence level. This means that on average once
in a hundred 10-day periods (so once every 1,000
days), this VAR number of 110,522 will be
exceeded.
If we have roughly 252 trading days in a year, a
company will expect to exceed the VAR roughly
once every years. The Basel committee of the
BIS considers this as too often. Hence, they
require that banks hold 3-times the 10-VAR, which
means that they will expect to exceed their VAR
approximately once every years.
4
In the previous example, a VAR capital charge of
is required by the BIS regulators.
100
Market Value at Risk for a single asset
A Numerical Example
In figure 6.2, VAR is . This can be derived by
the numerical values of N 100, a 1.65, s
for a one-day time horizon, so x 1.
Hence, from equation (6.4), VAR
. Naturally, if
the position in the asset would be N
1,000,000, the VAR would result in
Remark On the x-axis we have -changes. Assuming
we have 100 invested, the x-axis numbers
can interpreted as absolute values.
101
Market Value at Risk for a single asset
A Numerical Example cont.
From figure 6.2, we can also derive the
accumulated expected loss, AEL, within VAR. It
can be interpreted as the sum of all losses,
which will not be exceeded for a certain time
frame, for a certain probability. It is the
surface from d to the mean, where d is the value
on the x-axis corresponding to a certain a.
In figure 6.2, d . Since the mean is 1, AEL
is the area from 3 to 1. So in figure 6.2 the
accumulated expected loss AEL, for a discrete
price change is
102
Market Value at Risk for a single asset
A Numerical Example cont.
We can also derive the average expected loss,
AVEL, which is the accumulated loss per unit of
observation. It can be calculated by equation
where n total number of days, di
number of days on which the i-th price change
occurred, ?Pi price change for di.
Assuming the units on the y-axis of figure 6.2
are days, we have
observation days. Hence, in the example in
figure 6.2, the expected loss per day, AVEL, is
103
Market Value at Risk for a single asset
VAR with respect to zero
In equations (6.3) and (6.4) we have calculated
the VAR with respect to the return mean, which
may not be zero as in figure 6.2. If we choose to
disregard this positive mean and want to derive
the VAR with respect to a relative price change
of zero, which give us the absolute loss, we have
to adjust equation (6.4). We derive
VAR (zero) N sS a
-
µ x



where x time period of observation, expressed
in days µ return mean of the underlying asset
Using the same values as above, i.e. N 100, a
1.65, s 2.425, x 1 and µ 1, from figure
6.2 we derive following equation (6.8)
This result can be directly observed from figure
6.2 as the distance between
0 and 3 on the x-axis.
104
Market Value at Risk for a portfolio of linear
assets
VARP sP a
(6.9)
However, sP is now calculated as
sP
where Ăźi and Ăźj are the invested notional amounts
(price S times quantity q) of asset i and j,
respectively and ?i,j is the correlation
coefficient of the returns of i and j. Hence, the
term sP includes the notional amounts of assets i
and j via Ăźi and Ăźj. Therefore the notional
amount N does not appear in equation (6.9).
105
Market Value at Risk for a portfolio of linear
assets
VARP sa
sP
Example 6.2a What is the 10-day VAR for a
2-asset portfolio with a correlation coefficient
of 0.7, daily standard deviation of returns of
asst i of 2, asset j of 1, and 10 mio
invested in asset i and 5mio invested in asset j
on a 99 confidence interval?
sP
VAR10day
Interpretation
We are 95 sure that the portfolio will not
result in a higher loss than million in the
next 10 days due to market price changes of asset
i and j.
106
Market Value at Risk for a portfolio of linear
assets
Using equation sP
can be cumbersome
In reality sP is calculated with 2 vectors and a
Covariance matrix!
sP

(6.10a)
where Ăźh is the horizontal Ăź vector of invested
amounts Ăźv is the vertical Ăź vector
of invested amounts C is the
covariance matrix
Lets prove equation (6.10a)
107
Market Value at Risk for a portfolio of linear
assets
Lets first generate the Covariance-matrix C
C
The individual covariances sij can be derived by
equation
(6.10b)
where s12 is the covariance of assets 1 and 2
?12 is the correlation coefficient of
assets 1 and 2 s1 and s2 is the
volatility of assets 1 and asset 2
108
Market Value at Risk for a portfolio of linear
assets
For a 2-asset portfolio, we have 4 covariances
C
From equation (6.10b), and example 6.2a What is
the 10-day VAR for a 2-asset portfolio with a
correlation coefficient of 0.7, daily standard
deviation of returns of asset 1 of 2, asset 2 of
1, and 10 mio invested in asset 1 and 5mio
invested in asset 2, on a 99 confidence level?,
we derive
s11
s12
s21
s22
(see file riskmanagement.xls sheet 1)
Recall Covariances can also be calculated
directly by equation
109
Market Value at Risk for a portfolio of linear
assets
Hence, in our example, the covariance matrix is
C
From equation (6.10a),
, we get
C Ăźv

Ăźh C Ăźv
This is the same result as with equation
see 4 slides before.
(see file riskmanagement.xls sheet 1, and VAR
for linear portfolio of linear asset and VAR for
options.xls)
110
Market Value at Risk for a portfolio of linear
assets
VARP sP a
The VAR can now be calculated again with equation
(6.9)
For a 99 confidence interval, for 10 days (x
10), we get again
VAR10day
We are 95 sure that the portfolio will not
result in a higher loss than million in the next
10 days due to market price changes of asset i
and j.
Interpretation
(see file VAR for linear assets.xls in TRADE
SMART)
111
Comparison of VAR Methods
There are principally 3 VAR methods used in
practice
a) Historical Simulation
This is the one we discussed so far and it is the
most widely used in Risk Management practice.
The historical simulation method uses historical
data (prices and correlations) and projects them
into the future. Pros? Cons?
b) Variance/Covariance Approach
Uses variance and covariance matrices of market
variables e.g. inflation rate, unemployment
rate (not asset prices as in the historical
simulation) Drawback Difficult to apply to
fat-tailed distributions this drawback also
applies also to the historical distribution
c) Monte Carlo Approach
Computer program that randomly generates
outcomes. Drawback Computationally
intensive, theoretical
In practice, sometimes a combination of the
methods is applied.
112
Market Value at Risk and Diversification
What is Diversification???
Diversification is
If you have 2 assets 1 and 2 in your portfolio,
which are perfectly negatively correlated i.e.
?12 -1, what is the risk??? (assuming same
notional amount and same volatility)
What is your Profit Potential???
However, the CAPM shows that Diversification
increases the ratio
113
Market Value at Risk and Diversification
The benefits of Diversification on VAR
From diversification, it follows that
If ?12 lt 1
VARP VAR1 VAR2
For the theoretical case of extreme
diversification, we have already concluded
If ?12 -1
VARP

(assuming same notional amount and same
volatility of asset 1 and 2)
If the returns of assets 1 and 2 are perfectly
positively correlated, i.e. ?12 1, the
portfolio VAR is
If ?12 1
VARP VAR1 VAR2
Hence, in the case of ?12 1, there is
positive effect of diversification
The principle of Subadditivity is
VARP VAR1 VAR2
VAR is not subadditive!!! Later more
114
Market Value at Risk and Diversification
Lets prove
If ?12 1
VARP VAR1 VAR2
Lets use example 6.2a and change the correlation
coefficient to 1 What is the 10-day VAR for a
2-asset portfolio with a correlation coefficient
of 1, daily standard deviation of returns of
asset 1 of 2, asset 2 of 1, and 10 mio
invested in asset 1 and 5mio invested in asset
2, on a 99 confidence level?
s11
s12
s21
s22
115
Market Value at Risk and Diversification
Hence, the covariance matrix is
C
From equation (6.10a),
, we get
C Ăźv

Ăźh C Ăźv
116
Market Value at Risk and Diversification
VARP sP a
The VAR can now be calculated again with equation
(6.9)
VARP
Lets compare this with the individual VARs
N a s
VAR1
N a s
VAR2
Hence, for ?12 1, we have
VARP VAR1 VAR2
Homework A portfolio consists of 2 assets, with
the same notional amount and volatility. Show
that
if ?12 -1
VARP 0

117
Market Value at Risk and Diversification
A Short Position
If we are long asset 1 and short asset 2, the
lowest risk occurs with a correlation coefficient
?12 of
?12
The risk will be highest if the correlation
coefficient has a value of
?12
(see file riskmanagement.xls sheet 1, and VAR
for linear options.xls)
118
Market Value at Risk Management
In order to manage market risk, we have to know
what impact a change in the position (i.e. price
or the invested amount) of an asset has on
portfolio VAR.
How can we measure the impact of a change in the
price of an asset on portfolio VAR???
a) Brutal Force Method
Just simulate an increase in the position and
calculate the entire portfolio VAR.
Advantage
Drawback
b) Marginal or Incremental VAR
Calculate the marginal VAR (which is a good
approximation for a 1-unit price change in the
asset), and approximate an incremental (bigger
than 1 unit) change
Advantage
Drawback
119
Market Value at Risk Management
a) Brutal Force Method
Lets recall example 6.2a and simulate a 1
position change of asset 1
What is the 10-day VAR for a 2-asset portfolio
with a correlation coefficient of 0.7, daily
standard deviation of returns of asset 1 of 2,
asset 2 of 1, and 10,010,000 invested in asset
1 (which is an increase of 1) and 5mio
invested in asset 2, on a 99 confidence level?
The covariance matrix is
unchanged
s11
s12
s21
s22
Hence the covariance matrix is
120
Market Value at Risk Management
a) Brutal Force Method cont.
C
From equation (6.10a),
, we get
C Ăźv

Ăźh C Ăźv
121
Market Value at Risk for a portfolio of linear
assets
a) Brutal Force Method cont.
VARP sP a
The VAR can now be calculated again with equation
(6.9)
For a 99 confidence interval, for 10 days (x
10), we get
VAR10day
If we increase the position of asset 1 by
10,000, we are then 99 sure that we will not
lose more than mio within the
next 10 days.
Interpretation
Comparing mio to the
original result of 1.7514 mio, we get an increase
in the portfolio VAR of
?VARP
(see file VAR for linear assets.xls in TRADE
SMART)
122
Market Value at Risk Management
b) Marginal or Incremental VAR
This method derives the first partial derivatives
of VAR with respect to the position of an asset
Ăźi.
VAR (S) N a sP
Since in the VAR equation N, a and x are
constants we only have to
partially differentiate s with respect to Ăźi.
123
Market Value at Risk Management
b) Marginal or Incremental VAR cont.
Equation

After more transformations, we derive
From (6.x), it follows that a VAR Ăźi, which is
equation
(6.4)
with N s x Ăźi 1
(6.x)
VAR (S) N a s
Used in my model VAR for a portfolio of linear
assets
Will be used here now
124
Market Value at Risk Management
b) Marginal or Incremental VAR cont.
and compare it to the Brutal Force result
Lets use the marginal VAR method to calculate
We use again example 6.2a
What is the 10-day VAR for a 2-asset portfolio
with a correlation coefficient of 0.7, daily
standard deviation of returns of asset 1 of 2,
asset 2 of 1, and 10,000,000 invested in asset
1 and 5mio invested in asset 2, on a 99
confidence level?
We derive again (as 14 slides before)
C
From equation (6.10a),
, we get
C Ăźv

125
Market Value at Risk Management
b) Marginal or Incremental VAR cont.
Now we calculate from equation (6.10a),
, we get
Ăźh C Ăźv
From equation (6.x)
we get
126
Market Value at Risk Management
b) Marginal or Incremental VAR cont.
Lets now increase the position in asset 1 by
10,000
Hence,
Comparing this approximation of
to the true result of 1,457 of the brutal
force method, we find that the marginal VAR
approximation works very well.
The marginal VAR approximation works the better,
the the simulated increase in the
position of an asset
(see file VAR for linear assets.xls in TRADE
SMART)
127
Market Value at Risk for an Option
Options are non-linear instruments
If the underlying S (e.g. a stock) changes by one
unit, the option price for a Call C or a put P
changes by (for standard options)
The nonlinearity of options is measured by the
delta and gamma (ignoring the third and higher
orders).
The delta d is the
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