Risk Measurement Risk Architecture and the Bank of the Future

1. Know Your Risk Risk Measurement Risk Architecture and the Bank of the Future Ron Dembo Founding Chairman Algorithmics Incorporated May, 2004

2. Overview • Measuring Risk: The scale of the problem • State of the Market • Risk Architecture • Simulation, Static and Dynamic (Mark-to-Future) • Optimization • Potential topics for research

3. Open Research • Scenario Generation • Portfolio Compression • Pricing in Illiquid Markets • Near-Time Risk for a Large Institution

4. Measuring Risk

5. t n A Portfolio in the Future Distribution (tn) = F {price, yields ( many currencies), correlations, growth rates, exchange rates, volatility surfaces, etc.} Frequency 0 Value Time t o +

6. Derivatives“Weapons of mass destruction” “The only thing we understand is that we don’t understand how much risk the institution is running.” Warren Buffet Fortune, March 17, 2003

7. Know your Risk Enron “…..we have a liability of 350 million due April……” or……… ….we have a liability of 350 million due April….. ….drop 2 notches is credit rating and this becomes 9 Billion!

8. 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?

9. Know your Risk Nortel Largest company in Canada by Market Cap (= Mutual Funds) 30% drop in a day! > 10 Billion Market Loss Compensation Risk!

10. Know your Risk HSBC One 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

11. Corporate group Division Risk Taker Subsidiary Branch Maturity Group Type Counterparty SIC Country All All Product Set Risk On “Simple” Questions What is my exposure, expected loss and regulatory capital for United Airlines ? What is my exposure And regulatory capital associated with Brazil ? What is my total Capital requirement for the bank ? What is my exposure and regulatory capital to non-investment grade products ? What is my regulatory capital against tech sector for our Asian sub ? What is my regulatory capital on retail mortgages for UK division ? What is my economic capital for North American subsidiary ?

12. Coherent Measures & Credit Risk • Single Corporate 8% zero bond, 1 year maturity • Payoff (1 year): $108 99.89% (no default) $ 54 .. 0.11% (default) • VaR (99%) = $ 0.00

13. Coherent Measures & Credit Risk • Portfolio 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???

14. Risk and Return

15. + + + - - At the end of the day…. Mark-to-Future Upside Mark-to-Market Downside

16. The Horizon + + The Upside has the payoff of a Call option on net exposure ! Simulation (the Upside) + + Max{0, (Mx - eq´x)}

17. The Horizon - - - - The Downside is a Put option on net exposure ! Simulation (the Downside) Max{0, -(Mx - eq´x)}

18. Decomposing a Risky Decision Call (Mx - eq´x)+ Put (Mx - eq´x)- Inherently forward-looking !

19. Regret + Upside l Downside - + - (Call) (Put) (Equity) (Debt) Risk-Adjusted Performance

20. The “Put / Call” Efficient Frontier Maximize: Upside Subject to: Limited Downside Call Put

21. + + - Risk-Adjusted Performance Call- l Put l > 1 Concave function of net exposure Exposure

22. The “Put / Call” Efficient Frontier Max: p´u Subject to:p´d k() where: u - d - (Mx -rq´x) = 0 ( ) u  0; d  0 u´d = 0

23. Dual of “Put / Call” Trade-off Max: p´u Subject to:p´d k() where: u - d - (M - rq´)x = 0 () u  0; d  0 Min: kµ Subject to: (M - rq´)´ = 0 (x) p  - µp  0 (u,d) µ  0

24. + + + - (/) - Dual of “Put / Call” Trade-off Min: kµ Subject to: (M - rq´)´ = 0 (x) p   - µp  0 (u,d) µ  0 Dual feasibility (r = 1) implies: M´(/)= q

25. Complementarity Max: p´u Subject to: p´d  k () where: u - d - (M - rq´)x = 0 ( ) u  0; d  0 Min: kµ Subject to: (M - rq´)´ = 0 (x) p   - µp  0 (u,d) µ  0 ´{u - d - (M - rq´)x} = 0

26. Complementarity ´{u - d - (M - rq´)x} = 0 (/)´u - (/)´d = (/)´(Mx - q´x) Call - Put = Future Gain/Loss Complementarity iff Put / Call parity !

27. Modelling Liquidity Price vs. Quantity is piecewise linear x = x1 + x2 + x3 (x1)L x1 (x1 )U Price 0 x2  (x2)U 0 x3 (x3)U “fill” (x1) before (x2) before (x3) Quantity

28. km ( m > 1; infinite liquidity ) km - (wU) xU + (wL) xL Adjustment for liquidity The Put/Call Efficient Frontier Call(k) k (Put)

29. Prices in an Illiquid Market Different tolerances for downside lead to different risk neutral discount factors Call r3 r2 Put

30. ? + 0 Value Target t + Time 0 Value Portfolio Replication

31. benchmark portfolio Single Period, Multi State m11 m21 t1 m31 Probabilities p1 Security Prices q1 q2 c q3 p2 m12 m22 t2 m32 State Values p3 m13 m23 t3 m33

32. target gain portfolio gain - “Regret” Based Efficient Frontier MR(K) = Minimize x..... E ( ||(MTx - t)||- ) Regret Subject to : [E {MTx} -qTx] - [ E {t} - c] >K

33. 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)

34. p1 p2 ? p3 t + Time 0 Value Portfolio Images of a Portfolio Inverse problems • Implied Views • Stability of Optimal solutions • No-arbitrage (risk-neutral) parameters (implied discount factors, distributions)

35. Govt. Book Scenario Opt. Hedge PV01 Hedge Immunization US Govt. Bond Portfolio Ranges

36. Immunization • 99% Confidence VaR • US Govt Book $6,480,000 .. With PV01 Hedge $2,275,344 .. With Scenario-Optimal Hedge $353,634

37. 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

38. 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

39. Compression Results • VaR Original (95%) 14,963,188 • VaR Compressed (95%) 14,981,115 • Error < 5 basis points! • TIME ( Compressed ) • TIME ( Original) < 1 / 1000

40. Risk Architecture

41. Real-time Intraday Overnight Risk Computation Needs A single risk architecture must be able to handle business needs ranging from overnight batch to real-time

42. Real-time Intraday Overnight Risk Computation Needse.g. Counterparty credit exposures Baseline exposure profile Pre-deal checking “Round robin” 24x7 updating

43. Risk Architecture Monolithic vs Distributed Intraday possible Inherently slow

44. Distributed Architecture Multiple data sources communicating with multiple risk engines producing output in multiple locations all interconnected ! Data Risk Engines Output

45. Mark-to-Future An Architectural Vision

46. Mark-to Future Scenario based Links all risk types Full forward valuation, no shortcuts Separates simulation and reporting

47. value date now Bond age age Bond An example of the complexities The floating leg of a swap:

48. present value reset rate value date now indexing Monte-Carlo generation … reset date An example of the complexities The floating leg of a swap:

49. The “Cube” The Mark-to-Future “Cube” Scenario Security Time

50. 3 16 5 45 Any Portfolio MtF sort statistics MtF of a Portfolio All Instruments (MtF) Scenarios