©2003 Algorithmics Inc. 1 Risk Measurement Risk Architecture and the Bank of the Future Ron Dembo Founding Chairman Algorithmics Incorporated May, 2004

©2003 Algorithmics Inc.1

Risk Measurement

Risk Architecture

and the

Bank of the Future

Ron Dembo Founding Chairman

Algorithmics Incorporated

May, 2004Know Your Risk


Overview

1. Measuring Risk: The scale of the problem

2. State of the Market

3. Risk Architecture

4. Simulation, Static and Dynamic (Mark-to-Future)

5. Optimization

6. Potential topics for research


Open Research

1. Scenario Generation

2. Portfolio Compression

3. Pricing in Illiquid Markets

4. Near-Time Risk for a Large Institution


Measuring Risk


A Portfolio in the Future

Fre

qu

ency

Value

t n

Timet o

+

0

Distribution (tn) = F {price, yields ( many currencies), correlations,

growth rates, exchange rates, volatility surfaces, etc.}


Derivatives“Weapons of mass destruction”

“The only thing we understand is that we don’t understand how much risk the institution is running.”

Warren BuffetFortune, March 17, 2003


Know your Risk

….we have a liability of 350 million due April…..

….drop 2 notches is credit rating and this becomes

9 Billion!

“…..we have a liability of 350 million due April……”

or………

Enron


Know your Risk

JP Morgan (Enron)

Day 1: Exposure = $500 Million

Day 5: Exposure = $1 Billion

Day 12: Exposure = $1.9 Billion

What is the real exposure?


Know your Risk

NortelLargest company in Canada by Market Cap (= Mutual Funds)

30% drop in a day!

> 10 Billion Market Loss

Compensation Risk!


Know your Risk

HSBCOne of the largest banks in the world

> 60 trading floors

> 90 countries

> 4000 traders

> 300 “Enron” sized counterparties

Each with many subsidiaries, trading with any part of the bank


Branch

Division

Subsidiary

Corporate group

Counterparty

SIC

Country

All

TypeAll

Group

Maturity

Risk Taker

Risk On

ProductSet

What is my regulatory capital

on retail mortgages for UK division ?


on retail mortgages for UK division ?

What is my total Capital requirement

for the bank ?

What is my total Capital requirement

for the bank ?

What is my exposure, expected loss and regulatory capital

for United Airlines ?

What is my exposure, expected loss and regulatory capital

for United Airlines ?


against tech sectorfor our Asian sub ?


against tech sectorfor our Asian sub ?

What is my economic capital

for North Americansubsidiary ?

What is my economic capital

for North Americansubsidiary ?

What is my exposure and

regulatory capital tonon-investment grade products ?

What is my exposure and

regulatory capital tonon-investment grade products ?

What is my exposure And regulatory capital associated with Brazil ?

What is my exposure And regulatory capital associated with Brazil ?

“Simple” Questions


Coherent Measures & Credit RiskSingle Corporate 8% zero bond, 1 year maturity

Payoff (1 year): $108 99.89% (no default) $ 54 .. 0.11% (default)

VaR (99%) = $ 0.00


Coherent Measures & Credit RiskPortfolio of 10 independent bonds same characteristics

Payoff (1 year): $108 / 10 98.9% (no default)

$ 54 / 10 .. 1.1% (default)

VaR (99%) = $ 5.40 More diversified ====> More

Risk ???


Risk and Return


At the end of the day….

Mark-to-Market

Mark-to-Future

Downside

Upside

+

+

+

-

-


Simulation (the Upside)

+

+

The Upside has the payoff of a Call option on net exposure !

+ +

The Horizon

Max{0, (Mx - eq´x)}


-

Simulation (the Downside)

-

-

The Downside is a Put option on net exposure !

-

Max{0, -(Mx - eq´x)}The Horizon


Decomposing a Risky Decision

Put

Call

Inherently forward-looking !

(Mx - eq´x)+

(Mx - eq´x)-


Risk-Adjusted Performance

++ -

Upside Downside -

Regret

(Call)

(Equity)

(Put)

(Debt)


The “Put / Call” Efficient Frontier

Put

Call

Maximize: Upside Subject to: Limited Downside


Risk-Adjusted Performance

Exposure

Call - Put

Concave function of net exposure

++ -


The “Put / Call” Efficient Frontier

Max: pú

Subject to: p´d k ()

where: u - d - (Mx -rq´x) = 0 ( )

u 0; d 0

u´d = 0


Dual of “Put / Call” Trade-off

Min: kµ

Subject to: (M - rq´)´ = 0 (x)

p - µp 0 (u,d)

µ 0

Max: pú


where: u - d - (M - rq´)x = 0 ()

u 0; d 0


Dual of “Put / Call” Trade-off

Min: kµ


p - µp 0 (u,d)

µ 0

Dual feasibility (r = 1) implies:

M´(/) = q

+

+

+

-

-

(/)


Complementarity

Min: kµ


p - µp 0 (u,d)

µ 0

Max: pú


where: u - d - (M - rq´)x = 0 ( )

u 0; d 0

´{u - d - (M - rq´)x} = 0


Complementarity

´{u - d - (M - rq´)x} = 0

(/)ú - (/)´d = (/)´(Mx - q´x)

Call - Put = Future Gain/Loss

Complementarity iff Put / Call parity !


Modelling Liquidity

Price

Quantity

Price vs. Quantity is piecewise linear

(x1)L x1

(x1 )U

x = x1 + x2 + x3

0 x2 (x2)U

“fill” (x1)

before (x2)

before (x3)

0 x3 (x3)U


The Put/Call Efficient Frontier

Call(k)

k

k - (U) xU + (L) xL

(Put)

kinfinite liquidity )

Adjustment for liquidity


Prices in an Illiquid Market

Put

Call

Different tolerances for downside lead to different risk neutral discount factors

3

2


Replication

Value

+

0

Value

t

Time

+

0

?

Target

Portfolio


Single Period, Multi State

Security Prices

q1

q2 c

q3

m11

m21 1

m31

m12

m22 2

m32

m13

m23 3

m33

State Values 2

3

1

Probabilities

benchmarkportfolio


“Regret” Based Efficient Frontier

MR(K) = Minimize x ..... E ( ||(MTx - )||- )

Subject to : [E {MTx} -qTx] - [ E {} - c] > K

portfolio gain - target gain

Regret


A “Nobel” Quote

“…I should have computed the historical covariance of the asset

classes and drawn an efficient frontier….Instead I visualized my

grief if the stock market went way up and I wasn’t in it…or if it

went way down and I was completely in it. My intention was to

minimize my future regret, so I split my contributions 50/50

between bonds and equities..”

Harry Markowitz

(Money Magazine 1997)


Images of a Portfolio Inverse problems

Value

t

Time+

0

Portfolio

?

p1

p2

p3

Implied Views

Stability of Optimal solutions

No-arbitrage (risk-neutral) parameters (implied discount factors, distributions)


Immunization US Govt. Bond Portfolio

RangesGovt. Book

PV01 Hedge

Scenario Opt. Hedge


Immunization

99% Confidence VaR

US Govt Book $6,480,000

.. With PV01 Hedge $2,275,344

.. With Scenario-Optimal Hedge $353,634


Portfolio Compression

Portfolio: 1,025 Positions

Composition: Options on Bond Futures 4.9%

Callable Bonds 4.8%

Caps/Floors 32.3%

Bond Futures 1.6%

Interest Rate Swaps 15.5%

Treasury Bills, Bonds, Strips 40.9%

Replication with hypothetical Treasury Strips, European Options on long-dated Treasury Bonds, spanning monthly periods from January 1995 to December 2025


Compressed Portfolio

Compressed Portfolio: 51 Positions (simple)

Scenario Set: 50 randomly generated

Composition: 17 puts on long-dated Treasury Bonds

32 calls on long-dated Treasury Bonds

2 Treasury Strips

Replication with hypothetical Treasury Strips, European Options on long-dated Treasury Bonds, spanning monthly periods from January 1995 to December 2025


VaR Original (95%) 14,963,188

VaR Compressed (95%) 14,981,115

Error < 5 basis points!

TIME ( Compressed )TIME ( Original)

Compression Results

< 1 / 1000


Risk Architecture


Risk Computation Needs

Real-time IntradayOvernight

A single risk architecture must be able to handle business needs ranging from overnight batch to real-time


Risk Computation Needse.g. Counterparty credit exposures

Real-time IntradayOvernight

Baseline exposure profile

“Round robin” 24x7 updating Pre-deal checking


Risk Architecture

Monolithic vs Distributed

Intraday possibleInherently slow


Distributed Architecture

Data

Risk Engines

Output

Multiple data sources

communicating with multiple risk engines

producing output in multiple locations

all interconnected !


Mark-to-FutureAn Architectural Vision


Scenario based

Links all risk types

Full forward valuation, no shortcuts

Separates simulation and reporting

Mark-to Future


An example of the complexities

The floating leg of a swap:

now

value date

Bond

Bond

age

age


An example of the complexities

The floating leg of a swap:

now

value date

reset date…

reset rate

present value

indexing

Monte-C

arlo generation


TimeSecurity

Scenario

The “Cube”

The Mark-to-Future “Cube”


MtF of a Portfolio

Scenarios

Any

Portfolio MtF

sort

statistics

3 16 45 5

All Instruments

(MtF)


Mark-to-Future Values

MtFCube MappingS

cena

rios

Sce

nario

s

Mark-to-Future

Instruments

Mark-to-Future

Credit Portfolio

Netting,Netting,Credit MitigationCredit MitigationCollateral, etc.Collateral, etc.


Mapping to Basis Instruments

Risk Factor

3 month rate6 month rate1 year rate 5 year rate

Product

Bond

Basic Instrument

3M Zero 6M Zero 1Y Zero5Y Zero

e.g.


Maps for Equities

MtM

MtF

=m21

m31

m11

m21

m31

m11

m21

m31

m11

213

++ d2

d3

d1

Scenarios

Factor MtF (done once!)

f11 + f2 2 + f33

Stock or portfolio of stocks

Is mapped into

a portfolio of factors


A Swap Portfolio

Single Currency; 40,000 (Vanilla) Swaps20 points on yield curve; 1000 scenarios; 10 time periods

1020

1000 = 200,000!

Swap Portfolio = F(m1,…,m20 )

Risk in an instant!


“Real Time” Mark to Future

MtF Incremental Deal Full MtF Exposure Calc Statistics

Simulation Aggregation

Heavy Light

Counterparty portfolio:• 2000 positions

• FRAs, FX Forwards & Options, IRS, Caps/Floors, Swaptions etc… (long & short positions)

• 83 risk factors

• 1000 scenarios across 50 time steps

• netting agreements & collateral

Pre-deal ‘what-if’ for new interest rate swap with a counterparty:

Total simulation and aggregation time to derive a full montecarlo updated profile: 13 seconds!!!!


Consistency

Consistent Measurement of Earnings and Value at Risk

Scenarios

Growth and

re-investment

assumptions

Cash flow

generation

Valuation

Models

Earnings-at-Risk

Value-at-Risk

Pre-cube Post-cube


Without the “cube”, scalability to 20,000 users in real time would be prohibitive!

Mark-to Future


Only a few scenarios are relevant!

Mean of Distribution (10,000 scenarios)

11 “Bucket Scenarios” reproduce the distribution for 1/1000th the work!

Mean of a Bucket

Single scenario result


Liquidity and the true simulation of dynamic portfolio risk


Dynamic Portfolios

Time

Events

Portfolio changes

Function of the scenarios and strategy


A Regime

If( margin on the derivatives book is below s, liquidate sufficient bonds to raise it to S)

Apply to all marked nodes

A “Regime”


Funding Liquidity Risk

Cash /Collateral Account

Time

Multiperiod Simulation


The Regulators


ConvergenceRegulatory Capital and Economic Capital will converge

Asset Liability

Management

Market Risk

Management

1970 - 1979 1980 - 1989 1990 - 1999 2000+

Gap AnalysisDuration

Sensitivity

Parallel Shifts

Stress Tests

Earnings Simulation

Parametric VaR

Fair Accounting Value

Scenario Based VaR

Integrated

ERM

Basel 1 Basel 2


State of the Enterprise Risk Market(Banks) Mapped to Products

Innovators

EarlyAdopters

EarlyMajority

LateMajority

Laggards(Skeptics

)

Operational Risk

Collateral

Credit risk

Market risk

Market

Matu

rity

Risk Architecture


State of the Enterprise Risk Market(Asset Managers) Mapped to Products

Innovators

EarlyAdopters

EarlyMajority

LateMajority

Laggards(Skeptics

)

Operational Risk

Collateral

Credit risk

Market risk

Market

Matu

rity

Risk Architecture


State of the Enterprise Risk MarketMapped to Regulations

Innovators

EarlyAdopters

EarlyMajority

LateMajority

Laggards(Skeptics

)

Basel II

Basel I

Market

Matu

rity

Patriot ActFSA 195Sarbanes-Oxley

FAS 133


The Regulatory Environment

Basel II is a regulatory framework for risk measurement

• Market Risk (as in previous accord)• Credit Risk (a fundamental change)• Operational Risk (new)

Just think back to the fundamental changes to risk management

practice brought about by Basel I.

Basel II will result in much bigger changes.


“institutions wishing to qualify . . . will have to prove . . .that the internal ratings system and its component parts are all used in the active day-to-day granting of credit.”

From the New Basel Accord.

• pricing of credit risk

• incorporation of credit mitigation

• setting of credit limits

• calculation of economic capital

Use test to qualify for waiver


Basel II Highlights

The biggest change will occur in the measurement and management of credit:

• credit touches all aspects of banking

• significant amount of new sophistication in credit measurement infrastructure

• usage criteria will require banks to re-engineer their IT architecture


Basel II ..some quotes

“…..Basel II is nice, but we are re-architecting our credit infrastructure because it is good for business!”

…Tim Howell, Head Group Treasury, HSBC

In the first day of operation of its new credit risk system, HSBC saved more than the cost of the software!


The Bank of the Future


A Fundamental Change

Today:

Banks do business and then compute risk

Tomorrow:

They will compute risk and then do business!


Traded Products (Non-Traded) Products

Capital Mkts

Market Risk

ERM

Capital Mkts

Credit Risk

ERM

Credit Risk

Limits

Asset

Liability

Credit

Risk

Banks Today

Limits Mgt.

Front

Middle

Limits Mgt.

Front

Middle

Back

Limits Mgt.

Front

Middle

Back

Limits Mgt.

Front

Middle

Back

Retail

Mortgages

Comm.

Lending

Credit

Cards

Back

Swaps FxCreditDerivatives

Emerging

Markets

Collateral


ConvergenceRegulatory Capital and Economic Capital will converge

Asset Liability

Management

Market Risk

Management

1970 - 1979 1980 - 1989 1990 - 1999 2000+

Gap AnalysisDuration

Sensitivity

Parallel Shifts

Stress Tests

Earnings Simulation

Parametric VaR

Fair Accounting Value

Scenario Based VaR

Integrated

ERM

Basel 1 Basel 2


Enterprise Risk Today

Banks today are a collection of Independent silos

Bank of today

Enterprise risk is an adjunct to the operation (one way)

Eq

uit

y

Sw

aps

FX

Bon

ds


A Non-Invasive Architecture


The Bank of the Future

Eq

uit

y

Sw

aps

FX

Bon

ds

Risk computation will no longer be an adjunct to the business, it will be at the core


Vision….usage scenarios

A global investment bank 8 am any day of the week

You are the CFO for the Global Credit Operation and you have just come into your

office to review the P/L statement for your global loan portfolio. You download a

report that has undertaken a full mark-to-market for your loan book on a daily

basis.

Using credit spread curves that are updated daily using the bond and credit default

swap markets along with credit migrations from the day before you are able to

analyze your loan balance sheet on the same basis as your trading book --

including assessing the embedded optionality such as prepayment and credit line

utilization.


Conclusions

Today……….. enterprise risk systems are an adjunct to a bank

Tomorrow…... they will be central

Up until today.. risk architecture has not been so important

Tomorrow…… it will separate high performing banks from under-performers


The End

Financial Intelligence

Documents

©2003 Algorithmics Inc. 1 Risk Measurement Risk Architecture and the Bank of the Future Ron Dembo Founding Chairman Algorithmics Incorporated May, 2004