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Risk Management: New Approaches

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Risk Management:New Approaches

Prof Ian Giddy

New York University

- Position limits vs. “money at risk”
- Sensitivity of positions to factors
- How volatile are the factors? What is the 90% range (1.65 std dev.)?
- “How much could I lose on my overnight/monthly position?”

Potential loss (X% probability)

= Amount at risk * price volatility

=Amount at risk * Sensitivity * Adverse price move per period

May further take into account time-to-close: in JP Morgan jargon, Dear vs VaR

Var = DeaR * p(unwind period)

The variance of a 2-asset portfolio, :

where wAand wBare the weights of A and B in the portfolio.

To evaluate the gains and structure of a portfolio, we need a variance-covariance matrix:

$ AT RISKVOL.AUD BEF

AUD$85,085 2.9091

BEF$2,607,892 4.573-0.2731

Portfolio return:

where wi are the weights of each asset in the portfolio. (Expected return is simply the weighted sum of the individual asset returns.)

Portfolio variance:

When i = j, the term wiwjFiFjDijbecomes wi2Fi2.

- Defining and measuring foreign exchange risk exposure
- Corporate treasury managers often have a bogey to beat: the forward rate
- Spot risk and interest-differential risk
- Exchange rate shocks and exchange rate volatility. Can abrupt devaluations and government intervention be handled in the value-at-risk framework?
- Crossrate volatilities and correlations: can be derived from direct volatilities and correlations

The Idea of Risk: A Corporate Viewpoint

Exposure

Volatility in the market

Deviation from expectations

RISK

TRANSACTIONS

FORECASTS FROM

BUSINESS UNITS

NET POSITIONS,

BY CURRENCY

AND MATURITY

VALUE

AT

RISK

CONSOLIDATION

VOLATILITY AND

CORRELATION

FORECASTS

FARMCO CORPORATION, CASH FLOW PROJECTIONS

1st Quarter

2nd Quarter

CURRENCY

In

Out

In

Out

AUD

$0

$0

$0

$0

BEF

$4,659

$2,341

$4,854

$2,556

CAD

$76,083

$23,001

$80,237

$24,665

$477

DKK

$1,280

$546

$1,456

$11005

FFR

$33,788

$10,980

$41,578

$29,890

DEM

$2,300

$34,567

$1,207

$5561

ITL

$29,800

$4,587

$32,459

JPY

($1523)

NLG

$405

ESB

$5,623

SEK

$6789

CHF

$1,522

GBP

($10,200)

...Consolidate the Data to a Managable Set

Get Volatility and Correlation Data from the RiskMetrics Web Site...

On the World Wide Web, RiskMetrics data may be found at:

http://www.riskmetrics.reuters.com

...Find Corporate Value at Risk for Farmco

Corporate Value at Risk: Farmco

WITH DIVERSIFICATION

A Graphic Interpretation

LESS THAN 5%

CHANCE LOSS

EXCEEDS $10M

- Farmco is one of the world's largest agricultural equipment manufacturers, with $6 billion in sales in 1994. In December 1994 the Treasury department at Farmco's Atlanta headquarters was concerned about a report from the audit department that showed an exposure to potential foreign exchange losses. The positions were reported to be as on the next page.
- Treasury argued that the net exposure was trivial and that it would be too costly to hedge everything. Although the net amount as reported looked small, management was concerned with knowing how much could be lost on these positions before the end-of-December reporting date, and what could be done to reduce losses to a level that would be considered "not material" by the company's external auditors.
- Use the Value at Risk demo software to provide Farmco with a report on their exposure to the risk of market rate and price movements, and a proposed hedging strategy. (No “overhedging,” and no forward contracts in krone or pesetas.)

“At close of business each day tell me what the market risks are across all businesses and locations.”

Dennis Weatherstone, JP Morgan

Logical steps:

- Economic-value accounting (need market prices or models)
- Market-price based performance measurement
- Volatilities and correlations of market prices
- Management of risk
- Optimization of hedging

Value at Risk and RiskMetrics:

- A method for quantifying risk in dynamic, uncertain environments
- Based on the observation that volatilities and correlations are somewhat persistent
- The RiskMetrics estimates are in the ballpark of other, more sophisticated, methods

- A single number, like VaR, cannot replace a complete description of possibilities
- The method is backward-looking, and ignores qualitative factors to which markets react
- The probability and magnitude of large moves may be understated
- Estimated correlations may not tell us how markets will interact during extreme conditions
- Nonlinear derivatives may have
- changing sensitivity to factors.