Risk Management

Jan Röman

OM Technology

Securities Systems AB

Why Risk Management?

Types of Risk

Credit risk Market risk Liquidity risk

Settlement risk Operation risk Legal risk

The risk that the counterpart will fail to fulfill his

obligation.

The risk that movement in prices will result in loss.

One part may not be able to transfer a position quick

enough at a reasonable price. Unable to hedge.

The risk that the counterpart can´t deliver the

instruments at the expected time.

The risk for losses due to human or system errors.

The risk for losses due to the contracts are not

legally enforceable or documented correctly.

Technology Risk Credit Risk Regulatory Risk

Basis Risk Market Risk Tax Risk

Political Risk Accounting Risk Interest Rate Risk

Suitability Risk Prepayment Risk Legal Risk

Optional Risk Volatility Risk Capital Risk

Personnel Risk Reinvestment Risk Daylight Risk

Concentration Risk Netting Risk Liquidity Risk

Contract Risk Currency FX Risk Bankruptcy Risk

Systems Risk Commodity Risk Collateral Risk

Limit Risk Equity Risk Modelling Risk

Rollover Risk Call Risk Cross-market Risk

Hedging Risk Yield Curve Risk Systemic Risk

Interpolation Risk Curve Fitting Risk Time Lag Risk

Extrapolation Risk Raw Data Risk Knowledge Risk

Derivatives and Risk

Derivatives = Financial instruments/contracts with values derived from the price of the underlying instrument. Designed to transfer and isolate risk. They play a valuable rule for users at the marketplace.

Sources of Financial Risk

Unexpected Underlying price changes Unexpected Exchange rate changes Unexpected Interest rate changes Unexpected Share value changes

In all cases the changes are unexpected!

Techniques for Managing Risk

On-balance-sheet transactions

loans, bonds, stocks and deposits.

Forecasting

Diversification

holding many non-correlated instruments.

Hedging with derivatives

Hedging with derivatives

Call option = C(S, K, T, r, ) Models

Put option = P(S, K, T, r, ) Binomial or Black-Scholes

SC

2

2

S

C

TC

rC

C

Hedge parameters:

Formal Analysis

-1 = number of units of the derivative product x = number of units of the underlying S = today´s stock price T = today’s time to mature

Value of the portfolio: SxTSCV ),(1

A delta hedge is characterized by: 0SV

1

0 dNSCxx

SC

The delta hedge must be rebalanced over time.

Formal Analysis

n = number of units of the derivative product n m = number of units of the derivative product m x = number of units of the underlying S = today´s stock price T = today’s time

Value of the portfolio: SxTSmCmTS

nCnV ),(),(

A delta gamma hedge is characterized by: 0,02

2

S

VSV

0

0

mn

mn

mn

xmn Gives n and m with known x.

VaR: Value at Risk

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

GainsLosses

•Portfolio measure of risk

•Potential loss in a portfolio over a specified period of time

•Based on historyvolatilitycorrelation

change in value

Three Key Questions

ExposureWhat risk?How much?

Volatility &Correlation

How much couldprices change?

SensitivityHow much will P&L

change per unit?¨

How much can Ilose?

What is VaR

VaR is the maximum loss a portfolio can incur over aspecified time period, with a specified probability.

VaR is a vital component of current “best” practices inrisk measurement

VaR is used by practitioners and academics

VaR is valuable as a probabilistic measure of potentiallosses

What VaR is NOT

VaR is NOT the worst case scenario

VaR does NOT measure losses under any particular market condition

VaR -- by itself -- is NOT sufficient for riskmeasurement

Typical Uses of VaR

Translate portfolio exposures into potential P&L

Aggregate and reports multi-product, multi-marketexposure into one number

Uses risk factors and correlations to create a riskweighted index e.g. what is my equivalent risk position

How VaR is calculated

Sensitivity Estimate Model -- use sensitivity factors such as duration to estimate the change in value of the portfolio to changes in market rates and prices.

Full Revaluation Models -- use pricing algorithms such as bond formulae or option pricing models to estimate the the change in value of the portfolio to changes in market rates and prices.

Sensitivity vs. Revaluation

10 YearRate

SensitivityEstimated

P&L

Revaluation(Actual)

P&LDifference

8.0% -1 900 000 -1 698 493 201 507 12%

6.0% -380 500 -371 864 8 636 2%

5.5% 0 0 0 0

5.0% 380 500 389 684 9 184 2%

3.0% 1 900 000 2 145 584 245 584 11%

Why is the VaR Different?

The sensitivity VaR assumed that the bond’s value would change by some basis point.

But, as interest rates changes, bond price become more sensitive to changes in interest rates.

The change in sensitivity at different interest rate levels is nonlinear.

VaR Sensitivity vs. Revaluation

Sensitivity Models

Fast

Don’t require model library

Easy to understand

Implemented in less time

Revaluation models

Gives more accurate P&L results

Are price-based

Can handle complex products

VaR Inputs

Position Size -- the size of the instruments in the portfolio

Price/Yield Volatility -- The magnitude of the underlying prices and yield changes

Price/Yield Correlation -- Degree to which price and yield changes move together

VaR Estimation Period -- The time over which P/L in estimated

Confidence Level -- The frequency which actual losses

Monte Carlo Simulation

Scenario Generation -- produce a large number offuture price scenarios

Portfolio valuation -- for each scenario, compute aportfolio value

Summary -- report the result of the simulation, eitheras a portfolio distribution or as a risk measure

Monte Carlo is most helpful when some or all asserts in aportfolio are not amenable to analytical treatment