Systemic Effects of Market Risk Management Systems. Philippe Jorion. Systemic Effects of Risk Management Systems: PLAN

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1 Systemic Effects of Market Risk Management Systems VAR Philippe Jorion University of California at Irvine July P.Jorion Please do not reproduce without author s permission \varmrc\fallacies03.ppt Systemic Effects of Risk Management Systems: PLAN! The age of financial instability! Financial engineering increases market volatility! The events of 1998 can be attributed to VAR systems! Risk-sensitive capital requirements create herding in financial markets (See also article in Journal of Risk, Fall 2002) Philippe Jorion 1

2 Herding and Market-Sensitive Risk Management Practices (1) There is growing instability in the financial system (crises in EMS, Mexico, Asia ) (2) Banks and investors tend to herd, i.e. buy what others are also buying (3) Rising risk will increase VAR, and with binding constraints, lead to reduction in exposures (4) This leads to a vicious circle of greater volatility and more selling The VAR Vicious Circle Rise in market volatility VAR limits of some banks are hit limits of more The VAR banks are hit Several banks sell same asset at the same time Market volatility volatility and and correlations rise rise Source: Avinash Persaud Philippe Jorion 2

3 Fallacy #1: The Age of Financial Instability Arguments: (1) Risk management methods have been developed recently (2) Financial markets have become recently more unstable Conclusion: risk management methods increase risk Problem: financial markets are no more unstable than over the past century 40 Returns on U.S. Equities: Philippe Jorion 3

4 Financial Instability in a Century Losses Moves Moves >10% >10% >10% S&P Gold DM/$ Total Financial Instability in a Century Losses Moves Moves >5% >5% >5% S&P Gold DM/$ Total Philippe Jorion 4

5 40 Frequency of Financial Crises Number per decade Banking Crises Currency Crises Source: Bordo et al. (2001) Fallacy #2: The Role of Financial Engineering Arguments: (1) Automatic trading rules such as portfolio insurance (long option positions) lead to automatic sales when markets fall (2) Large price drops lead to further sales, creating excess volatility Conclusion: risk management tools increase risk Philippe Jorion 5

6 Dynamic Hedging and Option Replication! A position in an option is equivalent to in the asset plus borrowing: p = S + B! Example:» assume that S=$100, a 1-year at-the-money put option is worth p=$10 with delta= -0.5» then buying the put is equivalent to (1) buying *S (selling $50 worth of stock) + (2) investing $60 (net outflow is $10, price of put)! As the stock price falls, the delta decreases, going to -1.0, and we sell more Call value now A Call and its Delta-Equivalent Positions in the Asset Slope = c/ S Spot price now Philippe Jorion 6

7 Put price Replicating a Put with Dynamic Hedging Option Delta 1 1 S S, current spot price Fallacy #2: Problems (1) Exogenous increase in volatility often reflects fundamental news, e.g. increased probability of default by sovereigns, or major banks: confounding effect (2) Price drops could be due to market microstructure effects, e.g. inability of NYSE to handle large trading volumes (3) Price drops could be also due to increase in risk aversion common across markets (4) Even so, many other rules also contribute to selling in a falling market Philippe Jorion 7

8 Other Potential Destabilizers (1)! Technical analysis: trend-following system buy as the price increases! Margin calls: create claims on liquidity and may force to sell after price drop! Rebalancing with leverage: creates sales after price drop due to falling portfolio value! Stop-losses: sell after incurs a loss All of these can be blamed for increasing risk (e.g. margin-setting authority transferred to Fed after 1929 stock market crash) Other Potential Destabilizers (2)! Investment rules: only hold investment-grade bonds--sell after a downgrade! Contingent requirements: create claims on liquidity at worst possible times» e.g. credit triggers, or bonds w/ put options Provide fallacious protection Do not create systemic risk, however because company-specific Philippe Jorion 8

9 Rebalancing with No Leverage (Schinasi and Smith-2000) Stock Stock Cash Portfolio Value Position Position Value $100 $50 $50 $100 allocation: 50% 50% 100% Price falls by 20% $80 $40 $50 $90 allocation: 44% 56% Rebalancing $90 $45 $45 $90 new allocation: 50% 50% Conclusion: buy after the price falls to rebalance Rebalancing with Leverage (Schinasi and Smith-2000) Stock Stock Cash Portfolio Value Position Position Value $100 $200 -$100 $100 allocation: 200% -100% 100% Price falls by 20% $80 $160 -$100 $60 allocation: 267% -167% Rebalancing $90 $120 -$60 $60 new allocation: 200% -100% Conclusion: sell after the price falls to rebalance Philippe Jorion 9

10 Fallacy #3: The Role of VAR Arguments: (1) Traders are now given VAR limits, in addition to notional limits, due to Basel Market Risk Charges (2) Exogenous increases in volatility and binding constraints on VAR lead to forced liquidation, with further price drops Conclusion: VAR-based risk management methods increase volatility Fallacy #3: Problems (1) Argument assumes that all VAR-constrained traders have similar positions--otherwise liquidation has no effect (2) VAR limits only applied at the top level of commercial banks, not hedge funds nor investment banks (3) Regulatory VARs were not binding, nor sufficiently volatile to induce position cutting in 1998 Philippe Jorion 10

11 Similarity of Positions? Correlations of Profit and Loss Across Individual Banks Bank Bank Bank Bank Bank Bank Bank Average correlation of daily P&L is 0.17 Source: Berkowitz, J. and J. O'Brien (BO), How Accurate are the Value-at-Risk Models at Commercial Banks, Journal of Finance (June 2002) Regulatory VAR (1)! Regulatory Market Risk Charge based on: MRC = Max [k (1/60)Σ i=1 60 VAR t-i, VAR t-1 ]! Parameters for VAR should be based on at least a year of data, and an average life of at least six months» this rules out GARCH/EWMA, unless λ>0.992! The multiplier k is 3, to which is added a plus factor, that reflects number of exceptions observed by the model Philippe Jorion 11

12 Regulatory VAR (2)! VAR should be a 10-day VAR but is typically obtained from 1-day VAR multiplied by 10! Second factor is nearly never binding; with EWMA starting from stationary state, need h t-1 > 3 (1/60)[ h t h 0 ], or VAR t-1 >3.11 VAR 0 Decay (λ) Required scaled return for last VAR be binding 10.4σ 12.0σ 14.7σ 20.8σ 3.5 Comparison of VAR Models: $/DM Rate Historical simulation-250 days Normal model-250-day SD EWMA-decay= Philippe Jorion 12

13 10 Market Risk Charge: $/DM Rate Historical simulation-250 days Normal model-250-day SD EWMA-decay= Market Risk Charge for US Equities Historical simulation-250 days Student-t model-250-day SD Normal model-250-day SD EWMA-decay=0.94 Aug Philippe Jorion 13

14 Market Risk Charge for US Equities: 1998 Aug 31, Historical simulation-250 days Student-t model-250-day SD Normal model-250-day SD EWMA-decay= Market Risk Charge for Credit Position Historical simulation-250 days Student-t model-250-day SD Normal model-250-day SD EWMA-decay= Philippe Jorion 14

15 Regulatory VAR in 1998: Summary! Examine VAR and MRC for various models» Historical simulation-250 days (minimum)» Student-t model with σ estimated over 250 days» Normal-model with σ estimated over 250 days» EWMA-normal with decay=0.94 (not allowed)! For $/DM, S&P, credit position (Baa-T note) (1) Increase in VAR not out of line with longer history (2) Actual MRC changed very slowly and are unlikely to have caused VAR-related selling The Puzzle of Conservatiness of VAR Measures Comparison of P&L Percentile and VAR P&L VAR Excess Exceptions 99th Pc Mean of VAR Obs Exp Nb Mean Bank % Bank % Bank % Bank % NA Bank % Bank % ! BO found that reported VARs are too large :» possibly because capital adequacy requirements are not binding, or to avoid regulatory intrusion Philippe Jorion 15

16 The Puzzle of Bunching VAR Measures (1)! B&O found that reported VARs can be easily beaten by GARCH model applied to P&L! This is surprising since GARCH models have no information on changing positions One interpretation is that these results may reflect substantial computational difficulties in constructing large-scale structural models of trading risks for large, complex portfolios Philippe Jorion 16

17 The Puzzle of Bunching VAR Measures (2) Another interpretation is that the banks' structural models are simply hamstrung by the Basel requirements! But this may be a rational outcome since the purpose of these VAR models is to produce a smooth capital requirement and not necessarily to measure next day's risk with utmost accuracy Objective Functions for VAR Models (1)! Most literature on VAR focuses exclusively on statistical properties:» low bias, using percentage of exceptions» low bunching, using patterns in exceptions (EWMA and GARCH lowers bunching)! This ignores economic properties, patterns of capital charges:» lower VAR is better as it leads to lower risk charges» stable VAR is better as it leads to less variable charges (raise capital/change positions quickly?) Philippe Jorion 17

18 Objective Functions for VAR Models (2)! Low bias vs. low VAR: controlled by exception tests and penalties for failures! Less bunching vs. more stable VAR: bunching not controlled but not important» rapidly moving models that lead to less bunching (e.g. EWMA, GARCH) also lead to more variable capital charges» square root of time rule exacerbates swings in 10- day risk forecasts! Empirically, best model is Student, with low bias, low average capital, stable capital charge Philippe Jorion 18

19 3% EWMA+HS Bias-Stability Tradeoff Equities Bonds Currencies Instability (std.dev. of MRC) 2% 1% EWMA+HS Hist.Sim. EWMA+HS Student Hist.Sim. Hist.Sim. Student Student Normal Normal EWMA+N Normal EWMA+N EWMA+N 0% Bias (absolute value of t-test on exceptions) \varmrc\table3new.xls Fallacy #3: Additional Issues (4) Risk management systems vary widely in sophistication and structure, which makes herding less likely (5) Risk models are just one part of the formal risk-management process and are never likely to be the dominant driver of actions Also, formal risk modeling is an improvement over previous practices See also: Vice Chairman Roger W. Ferguson, Financial Engineering and Financial Stability, Remarks at the Annual Conference on the Securities Industry, November 20, 2002 Philippe Jorion 19

20 RISK MANAGEMENT FALLACIES: CONCLUSIONS! There is no evidence of recent increase in volatility in financial markets! It is difficult to differentiate between the effect of news/microstructure and dynamic trading! There is no evidence that VAR limits contributed to the volatility of Summer 1998! However:» all dynamic strategies that involve selling after price fell can potentially increase volatility» regulatory VAR should be relatively smooth Bibliography! Jorion, P., 2002, Fallacies about the Effects of Market Risk Management Systems, Journal of Risk 5, 1: 75 96, and Bank of England's Financial Stability Review 13 (December: ! Persaud, Avinash, 2000, Sending the Herd Off the Cliff Edge: The Disturbing Interaction between Herding and Market-Sensitive Risk Management Practices, Journal of Risk Finance 2, ! Schinasi, Garry and R. Todd Smith, 2000, Portfolio Diversification, Leverage, and Financial Contagion, IMF Staff Papers 47 (December), Philippe Jorion 20

21 References! Philippe Jorion is Professor of Finance at the Graduate School of Management at the University of California at Irvine! Author of Value at Risk, published by McGraw-Hill in 1997, which has become an industry standard, translated into 7 other languages; revised in 2000! Author of the Financial Risk Manager Handbook, published by Wiley and exclusive text for the FRM exam; revised in 2003! Editor of the Journal of Risk Phone: (949) FAX: (949) pjorion@uci.edu Web: Philippe Jorion 21