# LIB Market Risk Analysis Prof Ian Giddy Stern

LIB Market Risk Analysis Prof Ian Giddy Stern School of Business New York University

Risk Management is a Process Risk Management Define Copyright © 1998 Ian H. Giddy Measure Manage Monitor Risk Analysis 5

Market Risk Measurement Where are we now? Where do we need to be? Volumetric Duration/ PVof 01 • Notional Amounts Copyright © 1998 Ian H. Giddy Option Sensitivity Measures Simulations Value at Risk • Distribution of • Non-linear risk • Limited market • Linear risk market moves and measures scenarios that measures portfolio values could include • Swap/ bond • Delta, gamma, vega, theta, rho market correlations • Includes market equivalents correlations • No aggregation of • Reprice portfolio risk measures • Parallel and non- • Reprice portfolio • Aggregate risk across asset parallel curve measures within classes or shifts instruments • Aggregate portfolio confidence interval risk per scenario Risk Analysis 6

An Overview of Corporate VAR Business 1 Business 2 Business 3 Transactional Database Portfolio Database Projected Revenues Projected Operating Costs Base rates/ Currency market conditions • • Volatilities Correlations Historical rates/ Discrete scenarios Estimates of Cash Flow Distribution Model 1 Interest Rates Model 2 Mean Equities Model 3 Commodities Model 4 Impact on Earnings Currencies Copyright © 1998 Ian H. Giddy Risk Analysis 7

Summary of “Value at Risk” Reporting “At close of business each day tell me what the market risks are across all businesses and locations. ” Dennis Weatherstone, JP Morgan Logical steps: u. Economic-value accounting (need market prices or models) u. Volatilities and correlations of market prices u. Measurement of Risk Exposure u. Management of risk u. Market-price based performance measurement Copyright © 1998 Ian H. Giddy Risk Analysis 8

Portfolio Diversification DM position l A$ position l S$ position l FIM position l Net effect? Copyright © 1998 Ian H. Giddy Risk Analysis 9

Currency Volatility: Start with the Data Copyright © 1998 Ian H. Giddy Risk Analysis 10

Calculate Daily % Changes Copyright © 1998 Ian H. Giddy Risk Analysis 11

Predict Volatilities Risk. Metrics (exponential smoothing) BIS (rolling historicals) Copyright © 1998 Ian H. Giddy Risk Analysis 12

Risk. Metrics Method Compared Copyright © 1998 Ian H. Giddy Risk Analysis 13

Risk. Metrics Method Compared Other methods include: Implied volatility from option prices l Structured volatility models (ARCH, GARCH, EGARCH) l Stochastic volatility l The task of most models is to find some historical pattern of volatility and to use this to forecast volatility, which seems to “cluster Copyright © 1998 Ian H. Giddy Risk Analysis 14

Get Volatility and Correlation Estimates. . . eg from Risk. Metrics On the World Wide Web, Risk. Metrics publications and data may be found at: http: //www. jpmorgan. com and http: //www. riskmetrics. reuters. com Copyright © 1998 Ian H. Giddy Risk Analysis 15

Risk. Metrics Coverage . . . plus about a dozen commodities, term structure of yields, more exotics. . . each day, about 450 volatilities and 100, 000 correlations. Copyright © 1998 Ian H. Giddy Risk Analysis 16

Now More. . . (and Later, Customizable) Copyright © 1998 Ian H. Giddy Risk Analysis 17

Estimated Volatilities Copyright © 1998 Ian H. Giddy Risk Analysis 18

Single-Asset Value-at-Risk Potential loss (5% probability) =Amount at risk * Adverse price/rate move period (1. 65 SD) Probability 68% 95% > 99% – 3 – 2 – 1 0 +1 +2 +3 Percentage change in exchange rate Copyright © 1998 Ian H. Giddy Risk Analysis 19

Single-Asset Value-at-Risk: Example A Single Position (Example: $100, 000 AUD) Copyright © 1998 Ian H. Giddy Volatility Risk Analysis 20

Estimated Correlations Copyright © 1998 Ian H. Giddy Risk Analysis 21

A Correlation Matrix Copyright © 1998 Ian H. Giddy Risk Analysis 22

Measuring Portfolio Exposure: Two Assets The variance of a 2 -asset portfolio, : where w. A and w. B are 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 RISK AUD $50, 000 BEF $50, 000 Copyright © 1998 Ian H. Giddy VOL. 2. 909% 4. 573% AUD BEF 1 -0. 273 1 Risk Analysis 23

Two-Asset Value-at-Risk: Example Two Positions (Example: $100, 000 AUD & BEF) Copyright © 1998 Ian H. Giddy Volatility & Correlation Risk Analysis 24

Return and Risk, Generalized 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 wiwj Copyright © 1998 Ian H. Giddy becomes wi 2 Risk Analysis 25

Portfolio Value at Risk + = Value-at-Risk Mean Copyright © 1998 Ian H. Giddy Risk Analysis 26

A Management-Friendly Report An example is Four. Fifteen™, named after J. P. Morgan's market risk report produced at 4: 15 p. m. each day. l The "4: 15 Report, " a single sheet of paper, summarizes the Daily Earnings at Risk for J. P. Morgan worldwide. Gov't Bonds Zero Cashflow l AUD 1 Mo 3 Mo 6 Mo ($000) RISK Risk. Metricsª USD Base. Vols. & correls. as of May 04, 1995. Portfolio Risk Simulation CAD DKK FFR DEM BEF 15 -200 ITL 20 -30 25 12 Mo NLG ESB SEK CHF GBP JPY 22 XEU USD Total 37 160 - 50 -5 20 -105 - 105 2 Yr 0 3 Yr 0 4 Yr 0 5 Yr 0 7 Yr 0 9 Yr 0 10 Yr 0 15 Yr 0 20 Yr 0 30 Yr Equity Implied FX - 196. 1 -29 0 0 54 -145 23 22 -29 262 5 139 5, 048 4265 1383 1820 8516 -347 -6 -83 -451 4181 1383 1876 82 502 - 196. 1 22 23 Int. 59 -122 400 740 Spot Net Copyright © 1998 Ian H. Giddy Eq. Fx divers. Net -200 5, 350 400 8805 Risk Analysis 27

Exposure Report: Example Copyright © 1998 Ian H. Giddy Risk Analysis 28

The Next Step: Efficient Hedging 30% HEDGE (VAR $25 M, COST $0. 8 M) NO HEDGE (VAR $46 M, COST $0) Copyright © 1998 Ian H. Giddy Risk Analysis 29

Efficient Hedging, Constrained Copyright © 1998 Ian H. Giddy Risk Analysis 30

Efficient Hedging, Constrained Copyright © 1998 Ian H. Giddy Risk Analysis 31

The Va. R Management Cycle This process can be undertaken on a monthly cycle basis, as the institution revises its estimates of future business and as new data on volatilities and correlations are acquired. Copyright © 1998 Ian H. Giddy Risk Analysis 32

Value at Risk: Assessment Value at Risk and Risk. Metrics: l A method for quantifying risk in dynamic, uncertain environments l Based on the observation that volatilities and correlations are somewhat persistent l The Risk. Metrics estimates are in the ballpark of other, more sophisticated, methods Copyright © 1998 Ian H. Giddy Risk Analysis 33

Value at Risk: Assessment Copyright © 1998 Ian H. Giddy Risk Analysis 34

Value at Risk: Assessment Copyright © 1998 Ian H. Giddy Risk Analysis 35

Is VAR Valid? Are we measuring the right thing for our purpose? l Since we are measuring deviations from expected, do we have a good approximation of the distribution of changes? l How good are our forecasts of volatilities and correlations? l How good are our exposure measures? l How good are our valuation models? l Copyright © 1998 Ian H. Giddy Risk Analysis 36

Alternatives Worst-case analysis l Scenario analysis l Historical simulation l Monte-Carlo simulation l Sensitivity measures l Copyright © 1998 Ian H. Giddy Risk Analysis 37

What Happens in the Tails? For credit and capital purposes, we want to know about the probability, size and impact of extreme events. Worst-Case Analysis: How skewed? How many? How large? Probability of extreme events? Mean Copyright © 1998 Ian H. Giddy Risk Analysis 38

EMU Scenario Analysis for Publicorp Baseline Scenario This scenario assumes that current predictions of volatilities and correlations are valid for Publicorp’s FX risk management horizon. As is shown in the table below, the monthly volatility -- defined as the standard deviation of percentage changes in the dollar value of foreign currencies -- ranges from 1. 69% for the Canadian dollar to 2. 55%% for the Swedish Krona. The correlations between the DM and the core European currencies are very high - for example, the French franc has a 98% correlation with the DM - while the other European currencies have a positive but lower correlation coefficient. In particular, the British pound’s correlation with the DM is 55%. The table shows that the Value-at-Risk (Va. R) for Publicorp’s existing, unhedged positions is $1. 222 million. EMS Crisis Scenario Under this scenario, we assume that the “inner core” European currencies, the mark, guilder and Austrian schilling, remain closely linked, but that the correlations between German mark and the Belgian franc, the French franc, Finnish markka, Spanish peseta and Portuguese escudo all fall to 65%. The result of this is to increase the Va. R to $1. 291 million -- not a dramatic increase. EMS Convergence Scenario The third scenario is one in which the correlations among all the major European Union currencies rise to 100%. This could be regarded as the “single currency in Europe” scenario. Because of Publicorp’s offsetting long and short positions in these currencies, the result is a reduction in currency exposure: the monthly Va. R drops to below $1 million. Copyright © 1998 Ian H. Giddy Risk Analysis 39

Scenario Analysis Has its Limitations, Too Copyright © 1998 Ian H. Giddy Risk Analysis 40

The Alternative: Full-Valuation Methods Prices, rates, and estimated variances and covariances Monte Carlo Simulation Generate Scenarios Delta-Gamma Valuation Estimated value changes Copyright © 1998 Ian H. Giddy MODELS Full Valuation Distribution of Values Risk Analysis 41

Using a Va. R Measure for Trading-Portfolio Performance Evaluation l The Sharpe ratio. (actual return relative to actual risk) l The risk ratio. (actual return relative to prospective risk) l The efficiency ratio. (actual risk relative to prospective risk) Use risk-return performance measures to evaluate individual trader performance. Copyright © 1998 Ian H. Giddy Risk Analysis 42

Performance Evaluation: Example Copyright © 1998 Ian H. Giddy Risk Analysis 46

Performance Measurement: Roadmap l Map exposures FINANCIAL SIDE EXPOSURES Known Anticipated OPERATIONAL SIDE l Map risks MARKET PRICES RISK MEASUREMENT Va. R Worst-case scenario, etc. MARKET VOL & CORR. l Manage risks Measure performance l Take actions to improve performance l Copyright © 1998 Ian H. Giddy RISK MANAGEMENT Hedging Investment or trading PERFORMANCE MEASUREMENT Relative return Relative risk. INCENTIVES ALLOCATION OF RESOURCES. Risk Analysis 47

Treasury Performance Measurement: Conclusion Performance evaluation: “the science of attribution” l Why did we make/lose money? l u. The market; the FX manager; my lousy instructions? How much should I tip this FX manager? l Would I use this method again? l How good is my performance measurement system? l Copyright © 1998 Ian H. Giddy Risk Analysis 48

Summary: Market Risk Management is a Process Risk Management Define Copyright © 1998 Ian H. Giddy Measure Manage Monitor Risk Analysis 49

Ian H. Giddy Professor of Finance Stern School of Business New York University 44 West 4 th Street, New York, NY 10012, USA Tel 212 -998 -0332; Fax 212 -995 -4233 Email: ian. giddy@nyu. edu World Wide Web: http: //giddy. org Copyright © 1998 Ian H. Giddy Risk Analysis 55

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