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2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada.

2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada. Ranjan Bhaduri , BSc (Hons), MBA, MMath, PhD. Overview. The Mathematics of Risk Portfolio Risk Elements of Risk Aftermath. The Mathematics of Risk. How do we define risk?

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2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada.

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  1. 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada. Ranjan Bhaduri , BSc (Hons), MBA, MMath, PhD.

  2. Overview • The Mathematics of Risk • Portfolio Risk • Elements of Risk • Aftermath

  3. The Mathematics of Risk How do we define risk? Entanglement between randomness, probability, and risk Mathematical tools to measure risk & performance, and improve security (cryptography)

  4. Portfolio Risk • Tail Analysis (extreme risk) • Can NOT just sweep non-normality under the rug • Must look at higher moments & journey to the tail • Omega function very useful as risk tool

  5. What is the Omega function? • Invented by mathematicians (Shadwick & Keating) in 2002 • Can be thought of as the quality of an investment on a return above a certain level (threshold) • A rankings function that encodes return, variance, skew, kurtosis, and all of the higher moments - without penalizing for upside volatility

  6. Mathematical Definition of Omega • Where F is the cumulative distribution of returns, and r is the threshold chosen by the investor.

  7. Omega - the Finance Intuition R is the threshold value (and the strike) C(R) and P(R) are prices of one period European call and put prices; the underlying is the security’s RETURN, not the security’s price. numerator = E [ max (x – R, 0)] denominator = E [ max (R – x, 0)] Can be thought of as the quality of an investment on a return above a given level (threshold); “quality” is upside versus downside

  8. Omega Graphs Omega analysis

  9. How can Omega be used in Risk Management? • Portfolio construction • Risk monitoring • Leverage setting tool • Performance review • Comparative Studies • Robustness of portfolio • Fine-tuning the tail

  10. Elements of Risk • Market Risk • Credit Risk”Credit Risk arises from the simple fact that there are an infinite number of people who wish to borrow money, but only a finite number of people capable of paying it back.” - Nobel Laureate Joseph Stiglitz • Operational Risk

  11. Elements of Risk • Liquidity Risk • Geo-Political Risk • Model Risk • Leverage - upping the stakes

  12. Aftermath • Quantitative tools to be used qualitatively(not auto-pilot) • Derivatives to hedge specific exposures • Be on top of the capital markets

  13. Aftermath • Don’t fall for the pretty pictures! Lots of phonystuff out there. Don’t follow the flock! • Be tough! (how has it helped in actual investmentactions? has the tool been vetted?) • Integrity • Act in the light of intelligence, guided by experience.

  14. Good Risk Managementis Alpha A good offence is better with a strong defence ... Every good trading strategy is better with proper risk management! Guy Lafleur!!

  15. Acknowledgments • Denis Taillefer, Mx • Christiane Lavallée, Mx • James Vandenberg, apostrophe.ca • Gunter Meissner, Derivatives Software / HPU • Oliver King, Harvard University • Nipa Banerjee, CIDA

  16. References • “The Jungles of Randomness - A Mathematical Safari”- Ivars Peterson, (Wiley, 1998) • “MFA’s 2005 Sound Practices for Hedge Fund Managers”- Managed Funds Association, August 2nd 2005 (www.mfainfo.org) • Managing Financial Risk - Guide to Derivative Products, Financial Engineering, and Value Maximization - Charles Smithson (McGraw-Hill, 1998) • “Credit Derivatives”- Gunter Meissner (Blackwell, 2005) • “Inconsistency and Interest Rate Model Risk”- Anthony Di Silvestro (McMaster, 2004)

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