the oxford guide to financial modeling by ho & lee chapter 15. risk management the oxford guide...
TRANSCRIPT
![Page 1: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/1.jpg)
The Oxford Guide to Financial Modeling by Ho & Lee
Chapter 15. Risk Management
The Oxford Guide to Financial Modeling
Thomas S. Y. Ho and Sang Bin Lee
Copyright © 2004 by Thomas Ho and Sang Bin Lee. All rights reserved.
![Page 2: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/2.jpg)
Chapter 15. Risk Management 2
The Oxford Guide to Financial Modeling by Ho & Lee
15.1 Risk Measurement -Value at Risk (VaR) • Definition: a measure of potential loss at a level (99% or
95% confidence level) over a time horizon
53.473 67.1029 100Portfolio Value : $million
0
0.005
0.01
0.015
0.02
lamroNytilibaborP
ytisneD
53.473 67.1029 100
53.473 67.1029 100Portfolio Value : $million
0
0.005
0.01
0.015
0.02
lamroNytilibaborP
ytisneD
53.473 67.1029 100
![Page 3: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/3.jpg)
Chapter 15. Risk Management 3
The Oxford Guide to Financial Modeling by Ho & Lee
15.2 Market Risk
• Market risk is the losses that arise from the mark to market of the trading securities
• “Prices” for tradable securities of a portfolio are marked to market that are often derived from the fair values of the valuation models
![Page 4: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/4.jpg)
Chapter 15. Risk Management 4
The Oxford Guide to Financial Modeling by Ho & Lee
15.3 VaR for single securities
Definition: VaR time factor volatility • is called the critical value which determines the one-
tail confidence level of standard normal distribution.
• Time factor is defined as where t is the time horizon in measuring the VaR.
• Volatility is the standard deviation of the stock measured in $ over one year.
t
![Page 5: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/5.jpg)
Chapter 15. Risk Management 5
The Oxford Guide to Financial Modeling by Ho & Lee
15.3 VaR for single securities
[ ] ( [ ] )P f P M fE R r E R r
$P Duration r
( ) $
.
VaR bond time factor Duration r
rStd
r
- portfolio return distribution
- the price of the bond
- the critical value for a particular interval of a normal distribution
![Page 6: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/6.jpg)
Chapter 15. Risk Management 6
The Oxford Guide to Financial Modeling by Ho & Lee
1
$n
i
P KRD i r i
0.5
1 1
( ) ( $ $ )n n
iji j
VaR bond time factor KRD i KRD j
OAS OASVaR time factor P Duration
- the VaR of the bond
- the bond price uncertain value is a multivariate normal distribution
15.3 VaR for single securities
![Page 7: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/7.jpg)
Chapter 15. Risk Management 7
The Oxford Guide to Financial Modeling by Ho & Lee
15.3 Delta Normal Methodology (2)• VaR for a Portfolio (I)
- The portfolio value
- The portfolio uncertain value
- The VaR of the portfolio
1
n
i ii
P x P
1
$n
ii
P Duration i
0.5
1 1
( )
( $ $ )n n
iji j
VaR portfolio time factor
Duration i Duration j
![Page 8: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/8.jpg)
Chapter 15. Risk Management 8
The Oxford Guide to Financial Modeling by Ho & Lee
15.3 Portfolio VaR • VaR for a Portfolio (II)
- Component VaR
1
0.5
1 1
( ) $ $
( $ $ )
n
i ijj
n n
iji j
VaR portfolio time factor Duration i Duration j
Duration i Duration j
1
n
ii
VaR VaR
![Page 9: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/9.jpg)
Chapter 15. Risk Management 9
The Oxford Guide to Financial Modeling by Ho & Lee
15.3 Three Stocks Case
• A Numerical Example
- Calculating the VaR of a portfolio of three different
stocks (GM, WMT, and IBM)
- Calculating the daily rates of return and the variance-covariance matrix
, , 1,
, 1
22,
1
, , ,1
GM, WMT, and IBM
0
1
1
i t i ti t
i t
i
m
i i t it
m
i j i t i j t it
S Sr i
S
r
r rm
r r r rm
where m is the number of days in the estimation period.
![Page 10: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/10.jpg)
Chapter 15. Risk Management 10
The Oxford Guide to Financial Modeling by Ho & Lee
15.3 Correlations of the Stock Returns• Calculating the daily rates of return and the variance-
covariance matrix
0.00050827 0.000154099 0.000179167
0.000154099 0.00373365 0.00013894
0.000179167 0.00013894 0.00054746
Ω1 0.353741 0.339255
0.353741 1 0.306955
0.339255 0.306955 1
Σ
1 1 1, ,
3 3 3
Tw
2
0.00050827 0.000154099 0.000179167 1/ 3
1/ 3 1/ 3 1/ 3 0.000154099 0.00373365 0.00013894 1/ 3
0.000179167 0.00013894 0.00054746 1/ 3
0.000263866
Portfolio
Tw Ω w
![Page 11: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/11.jpg)
Chapter 15. Risk Management 11
The Oxford Guide to Financial Modeling by Ho & Lee
15.3 VaR Derivations• The detailed derivation of the individual VaR as well
as the portfolio VaR is given as follows.
Where,
i i i
P P
VaR total invest w days
VaR total invest days
,
2 2,
{ , , }
2
P
i j i ji j
i i i j i ji i j i
i GM WMT IBM
Tw Ω w
![Page 12: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/12.jpg)
Chapter 15. Risk Management 12
The Oxford Guide to Financial Modeling by Ho & Lee
15.3 VaR Derivation
100 0.00050827 2.32635 5 3.9091
3100
0.00373365 2.32635 5 3.35053
100 0.00054746 2.32635 5 4.
3
GM GM GM
WMT WMT WMT
IBM IBM IBM
VaR total invest w days
VaR total invest w days
VaR total invest w days
0619
100 0.000263866 2.32635 5 8.44989P PVaR total invest days
![Page 13: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/13.jpg)
Chapter 15. Risk Management 13
The Oxford Guide to Financial Modeling by Ho & Lee
15.3 Component VaR
1/ 3
1/ 3
1/ 3
1/ 3
1/ 3 1/ 3 1/ 3 1/ 3
1/ 3
1.0631
0.8418
1.0951
GM
Delta Normal Method WMT
IBM
Beta
T
Ω
Ω w
w Ω w
Ω
, , i i i PortfolioComponent VaR VaR i GM WMT and IBM
1 = 1.0630 8.4498 2.9943
3GM GM GM PortfolioComponent VaR VaR
![Page 14: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/14.jpg)
Chapter 15. Risk Management 14
The Oxford Guide to Financial Modeling by Ho & Lee
5-day VaR GM WMT IBM Total
Weight 1/3 1/3 1/3 1
Individual stock
VaR 3.9091 3.3505 4.0619 11.3215
Portfolio VaR - - - 8.4499
Beta 1.0631 0.8418 1.0951 -
Beta*Weight 0.3544 0.2806 0.3650 1
Component VaR 2.9943 2.3711 3.0844 8.4499
Portfolio Effects 0.9148 0.9793 0.9775 2.8716
15.3 VaR Calculation
VaR calculation output by Delta-Normal Method
![Page 15: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/15.jpg)
Chapter 15. Risk Management 15
The Oxford Guide to Financial Modeling by Ho & Lee
15.4 Historical Simulation Methodology
…
return return return return return return … return return return return
sorting the data and finding x% percentile
Today
The Historical Simulation methodology
![Page 16: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/16.jpg)
Chapter 15. Risk Management 16
The Oxford Guide to Financial Modeling by Ho & Lee
15.4 Historical Returns
Historical Return data set
8.1626[1]4.03623.22644.32921% VaR
-8.1626-4.0362-3.2264-4.32921% percentile
0.1094-0.1740-0.08800.37142002,05,02
1.48250.21490.56090.70672002,05,01
0.2531-0.0517-0.20170.50642002,04,30
-0.0720-0.17840.5217-0.41522001,10,31
-1.53840.0092-0.8306-0.71702001,10,30
-3.6504-0.7636-0.9508-1.93612001,10,29
-1.0441-0.15700.0000-0.88712001,01,08
-2.86460.2915-1.3321-1.82402001,01,05
-0.3901-0.5069-1.28651.40322001,01,04
8.35943.85572.82191.68172001,01,03
(1)+(2)+(3)Portfolio
(3)IBM
(2)WMT
(1)GM
Date
8.1626[1]4.03623.22644.32921% VaR
-8.1626-4.0362-3.2264-4.32921% percentile
0.1094-0.1740-0.08800.37142002,05,02
1.48250.21490.56090.70672002,05,01
0.2531-0.0517-0.20170.50642002,04,30
-0.0720-0.17840.5217-0.41522001,10,31
-1.53840.0092-0.8306-0.71702001,10,30
-3.6504-0.7636-0.9508-1.93612001,10,29
-1.0441-0.15700.0000-0.88712001,01,08
-2.86460.2915-1.3321-1.82402001,01,05
-0.3901-0.5069-1.28651.40322001,01,04
8.35943.85572.82191.68172001,01,03
(1)+(2)+(3)Portfolio
(3)IBM
(2)WMT
(1)GM
Date
![Page 17: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/17.jpg)
Chapter 15. Risk Management 17
The Oxford Guide to Financial Modeling by Ho & Lee
15.4 VaR Calculation
5-day VaR GM WMT IBM Total
Weight 1/3 1/3 1/3 1
Individual stock VaR
4.3292 3.2264 4.0362 11.5917
Portfolio VaR - - - 8.1626
Beta 1.0631 0.8418 1.0950 -
Beta*Weight 0.3544 0.2806 0.3650 1
Component VaR 2.8925 2.2906 2.9795 8.1626
Portfolio Effects 1.4367 0.9358 1.0567 3.4291
VaR calculation output by Historical Simulation Method
![Page 18: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/18.jpg)
Chapter 15. Risk Management 18
The Oxford Guide to Financial Modeling by Ho & Lee
15.5 Monte Carlo Simulation Methodology
• Random numbers generated from Multi Normal Distribution
-3.7629**-2.0318-1.5446-1.72111% percentile
-0.0832/3-0.0279-0.0108-0.0445Scenario 5
0.0078/30.0073-0.00340.0039Scenario 4
0.0047/3-0.00810.00220.0106Scenario 3
-0.0544/3-0.0017-0.0148-0.0379Scenario 2
-0.0149/3-0.0165-0.00740.0090Scenario 1
Portfolio((1)+(2)+(3))/3
IBM (3)WMT (2)GM (1)
Random Number = Return data
Scenario
-3.7629**-2.0318-1.5446-1.72111% percentile
-0.0832/3-0.0279-0.0108-0.0445Scenario 5
0.0078/30.0073-0.00340.0039Scenario 4
0.0047/3-0.00810.00220.0106Scenario 3
-0.0544/3-0.0017-0.0148-0.0379Scenario 2
-0.0149/3-0.0165-0.00740.0090Scenario 1
Portfolio((1)+(2)+(3))/3
IBM (3)WMT (2)GM (1)
Random Number = Return data
Scenario
![Page 19: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/19.jpg)
Chapter 15. Risk Management 19
The Oxford Guide to Financial Modeling by Ho & Lee
15.5 Simulations based on the Correlation Matrix• The variance-covariance matrix of stock returns generated by Monte Carlo
simulation
Monte-Carlo
0.00050792 0.00015374 0.00017815
0.00015374 0.00037336 0.00013749
0.00017815 0.00013749 0.00054419
Ω
0.01
100 0.052593 5 3.9200
3
0.01
GM GM GM
WMT WMT WMT
MonteCarlo VaR Percentile of Scenario total invest w day
MonteCarlo VaR Percentile of Scenario total invest w day
100 0.044945 5 3.3504
3
0.01
100 0.054149 5 4.0361
3
0.01
IBM IBM IBM
P
MonteCarlo VaR Percentile of Scenario total invest w day
MonteCarlo VaR Percent
0.037629 100 5 8.4141
Pile of Scenario total invest day
![Page 20: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/20.jpg)
Chapter 15. Risk Management 20
The Oxford Guide to Financial Modeling by Ho & Lee
15.5 VaR Calculation
VaR calculation output by Monte Carlo Simulation Method
5-day VaR GM WMT IBM Total
Weight 1/3 1/3 1/3 1
Individual stock
VaR 3.9200 3.3504 4.0361 11.3065
Portfolio VaR - - - 8.4141
Beta 1.0656 0.8433 1.0910 -
Beta*Weight 0.3552 0.2811 0.3637 1
Component VaR 2.9888 2.3652 3.0601 8.4141
Portfolio Effects 0.9312 0.9851 0.9760 2.8923
![Page 21: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/21.jpg)
Chapter 15. Risk Management 21
The Oxford Guide to Financial Modeling by Ho & Lee
15.6 Extreme Value Theory
• multiply historical returns by –1 to convert them into positive values.
• choose a threshold (): a parametric distribution of the tail beyond the threshold.
• The ratio: count how many observations are beyond the threshold in the actual data and divide it by the total observation.
• Parameters () estimation • VaR calculation
![Page 22: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/22.jpg)
Chapter 15. Risk Management 22
The Oxford Guide to Financial Modeling by Ho & Lee
-0.1 -0.05 0 0.05GM daily stock return
0
5
10
15
20ytisned
15.6 Extreme Value Theory - Historical return data vs. Standard Normal Distribution
1/1 (1 ) 0( )
1 exp( ) 0
u
u
Ny when
NF yN
y whenN
- cumulative distribution functions
![Page 23: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/23.jpg)
Chapter 15. Risk Management 23
The Oxford Guide to Financial Modeling by Ho & Lee
15.6 calculate the VaR by the extreme value theory
0.2086
0.20860.6509 12.5 (1 0.9995) 1 5 9.600
170.2086332
EVTVaR
0.2086, 0.6509, 0.9995confidence level
ˆ(1 ) 1EVT
u
NVaR u c day
N
1
11
( ) 1uNf x x u
N
- The formula to calculate the VaR based on the Extreme Value Theory
- probability density function
![Page 24: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/24.jpg)
Chapter 15. Risk Management 24
The Oxford Guide to Financial Modeling by Ho & Lee
15.7 Credit Risk
• Definition
the loss of principal or interest or any promised payments from the borrow for bonds or loans of any securities
![Page 25: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/25.jpg)
Chapter 15. Risk Management 25
The Oxford Guide to Financial Modeling by Ho & Lee
15.7 Credit Risk and Market Risk Model
• VaR of a Bond - Firm value process (Merton)
• Integrating Credit Risk and Market Risk in a Portfolio Context (I)
- Firm value process (Merton, Longstaff and Schwarzt)
- interest rate model (Hull and White)
( )dV V C dt dz
( )dV rV C dt Vdz
( ( ) )dr t ar dt dz
![Page 26: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/26.jpg)
Chapter 15. Risk Management 26
The Oxford Guide to Financial Modeling by Ho & Lee
15.7 Portfolio Credit and Market Risk
• Integrating Credit Risk and Market Risk in a Portfolio Context
- The stock risk
( ( ) )i f i M fk r E R r z
![Page 27: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/27.jpg)
Chapter 15. Risk Management 27
The Oxford Guide to Financial Modeling by Ho & Lee
15.7 Portfolio Credit Risk • Specify a set of macro-economic factors that would
affect the credit risk of the firms. • Define the default index by measuring default rate. The
macro economic factors are used as the independent variables to explain the default rate.
• Measure the rating migrations against the speculative default rates: change of the speculative default rate determines the change in the rating migrations.
• The simulations can then be used to simulate the change in value of a bond portfolio.
![Page 28: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/28.jpg)
Chapter 15. Risk Management 28
The Oxford Guide to Financial Modeling by Ho & Lee
15.7 Credit VaR - a Numerical Example by
CreditMetrics
Initial
rating
Rating at year-end (%)
AAA AA A BBB BB B CCC Default
AAA 90.81 8.33 0.68 0.06 0.12 0.00 0.00 0.00
AA 0.70 90.65 7.79 0.64 0.06 0.14 0.02 0.00
A 0.09 2.27 91.05 5.52 0.74 0.26 0.01 0.06
BBB 0.02 0.33 5.95 86.93 5.30 1.17 1.12 0.18
BB 0.03 0.14 0.67 7.73 80.53 8.84 1.00 1.06
B 0.00 0.11 0.24 0.43 6.48 83.46 4.07 5.20
CCC 0.22 0.00 0.22 1.30 2.38 11.24 64.86 19.79
- One-year Transition Matrix
![Page 29: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/29.jpg)
Chapter 15. Risk Management 29
The Oxford Guide to Financial Modeling by Ho & Lee
Category 1 2 3 4
AAA 3.60 4.17 4.73 5.12
AA 3.65 4.22 4.78 5.17
A 3.72 4.32 4.93 5.32
BBB 4.10 4.67 5.25 5.63
BB 5.55 6.02 6.78 7.27
B 6.05 7.02 8.03 8.52
CCC 15.05 15.02 14.03 13.52
Bond number Credit Grade Face value Maturity Coupon RateRecovery
Rate
1 A 100 5 zero 0.60
2 BBB 100 5 0.06 0.55
3 BB 100 5 0.03 0.40
- Bond Data set
15.7 cont.. - Example one -year forward zero curves by crediting rating category
![Page 30: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/30.jpg)
Chapter 15. Risk Management 30
The Oxford Guide to Financial Modeling by Ho & Lee
Grade AAA AA A BBB BB B CCC Default
Price 95.6241 95.456 94.959 93.928 88.7654 85.0951 71.9208 40
Profit/Loss 6.8587 6.6909 6.1936 5.1626 0 -3.6703 -16.8446 -48.7654
Probability 0.03 0.14 0.67 7.73 80.53 8.84 1.00 1.06
Cumulative Probab
ility100.00 99.97 99.83 98.16 91.43 10.90 2.06 1.06
15.7 cont..
- 1year forward bond Price, Profit/Loss and Probability for the BB-grade bond
![Page 31: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/31.jpg)
Chapter 15. Risk Management 31
The Oxford Guide to Financial Modeling by Ho & Lee
-50 -40 -30 -20 -10 0ProfitLoss $0
0.2
0.4
0.6
0.8
1FDC
15.7 cont.. - Cumulative Probability of BB-Grade Bond’s Profit/Loss
![Page 32: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/32.jpg)
Chapter 15. Risk Management 32
The Oxford Guide to Financial Modeling by Ho & Lee
Thresholds A BBB BB
AAZ 3.12139 3.54008 3.43161
AZ 1.9845 2.69684 2.92905
BBBZ -1.50704 1.53007 2.39106
BBZ -2.30085 -1.49314 1.36772
BZ -2.71638 -2.17808 -1.23186
CCCZ -3.19465 -2.74778 -2.04151
DZ -3.23888 -2.91124 -2.30440
Covariance
Matrix A BBB BB
A 0.9 0.7 -0.3
BBB 0.7 2 0.5
BB -0.3 0.5 1
- Estimate the correlation matrix or variance-covariance matrix among the bond returns
15.7 cont.. - Z-threshold
![Page 33: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/33.jpg)
Chapter 15. Risk Management 33
The Oxford Guide to Financial Modeling by Ho & Lee
-120 -100 -80 -60 -40 -20 0Portfolio LossProfit0
2000
4000
6000
8000
10000
12000
14000
ycneuqerF
Number of Scenario 100000
15.7 cont.. - Bond Portfolio Default Risk Distribution
A-Grade
Bond
BBB-Grade
Bond
BB-Grade
Bond Portfolio
10% VaR 0.9143 5.3193 5.01155 9.1948
Portfolio effect 11.2448-9.1948=2.05
![Page 34: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/34.jpg)
Chapter 15. Risk Management 34
The Oxford Guide to Financial Modeling by Ho & Lee
15.8 Risk Reporting Aggregation of Risks to Equity ($mil.) (the VaR Table)
10.590.9810.591,078Equity
15.161.7319.851,146Long term market funding
36.890.8544.625,250Demand deposits
9.552.6411.69443Fixed rate time deposits
0.980.541.56289Prime rate time deposits
3.240.305.831,959Base rate time deposits
-28.21.1733.462,854Bonds
-22.52.5030.491,231Fixed rate loans
-4.80.875.47625Variable rate mortgages
-4.30.234.922,170Base rate loans
4.50.3411.313,286Prime rate loans
Component VaRVaR/MV (%)VaRMarket ValueItems
10.590.9810.591,078Equity
15.161.7319.851,146Long term market funding
36.890.8544.625,250Demand deposits
9.552.6411.69443Fixed rate time deposits
0.980.541.56289Prime rate time deposits
3.240.305.831,959Base rate time deposits
-28.21.1733.462,854Bonds
-22.52.5030.491,231Fixed rate loans
-4.80.875.47625Variable rate mortgages
-4.30.234.922,170Base rate loans
4.50.3411.313,286Prime rate loans
Component VaRVaR/MV (%)VaRMarket ValueItems
![Page 35: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/35.jpg)
Chapter 15. Risk Management 35
The Oxford Guide to Financial Modeling by Ho & Lee
15.9 Risk Monitoring • Back testing
600 650 700 750 800Sample Period
-20
-10
0
10
tiforP?ssoL
![Page 36: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/36.jpg)
Chapter 15. Risk Management 36
The Oxford Guide to Financial Modeling by Ho & Lee
15.10 Risk Measurement • Strategic Risk Management
– Smith and Smithson (1998) determines the economic factors affecting the equity value of a firm
– Hedging against these economic factors is strategic risk management
• Business Process – Build a model of the firm as a system of
processes– Manage the processes by monitoring and
controlling the risks in each phase
![Page 37: The Oxford Guide to Financial Modeling by Ho & Lee Chapter 15. Risk Management The Oxford Guide to Financial Modeling Thomas S. Y. Ho and Sang Bin Lee](https://reader034.vdocuments.site/reader034/viewer/2022051416/56649e665503460f94b604ea/html5/thumbnails/37.jpg)
Chapter 15. Risk Management 37
The Oxford Guide to Financial Modeling by Ho & Lee
15.10 Risk Measurement (2)• Investment Cycle
▶ Implementation Phase :
Execute trades, and reportpositions
▶ Test Phase :
PerformanceEvaluation
▶ Requirement Phase :
Monitor portfolio returns andpositions, and establish goals tomeet client's needs
▶ Design Phase :
Forcast market dynamics, adjust forconstraints, and set directions forportfolio managers
InvestmentObjective
InvestmentStrategies
Take directions from marketoutlook, evaluate portfolioposition, and set trades for traders
MarketOutLook