1 / 18

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?

coral
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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)

More Related