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

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2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Qubec, 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? - PowerPoint PPT Presentation

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<ul><li><p>2005 Canadian Annual Derivatives ConferenceAugust 17 - 20, 2005 Qubec, Canada.</p><p>Ranjan Bhaduri , BSc (Hons), MBA, MMath, PhD.</p></li><li><p>OverviewThe Mathematics of Risk Portfolio RiskElements of RiskAftermath</p></li><li><p>The Mathematics of RiskHow do we define risk?</p><p>Entanglement between randomness, probability, and risk</p><p>Mathematical tools to measure risk &amp; performance, and improve security (cryptography)</p></li><li><p>Portfolio RiskTail Analysis (extreme risk)Can NOT just sweep non-normality under the rugMust look at higher moments &amp; journey to the tailOmega function very useful as risk tool</p></li><li><p>What is the Omega function?Invented by mathematicians (Shadwick &amp; Keating) in 2002Can 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</p></li><li><p>Mathematical Definition of OmegaWhere F is the cumulative distribution of returns, and r is the threshold chosen by the investor.</p></li><li><p>Omega - the Finance IntuitionR is the threshold value (and the strike)</p><p>C(R) and P(R) are prices of one period European call and put prices; the underlying is the securitys RETURN, not the securitys price. </p><p>numerator = E [ max (x R, 0)]</p><p>denominator = E [ max (R x, 0)]</p><p>Can be thought of as the quality of an investment on a return above a given level (threshold); quality is upside versus downside</p></li><li><p>Omega GraphsOmega analysis</p></li><li><p>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</p></li><li><p>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</p></li><li><p>Elements of Risk Liquidity Risk Geo-Political Risk Model Risk Leverage - upping the stakes</p></li><li><p>Aftermath</p><p> Quantitative tools to be used qualitatively (not auto-pilot) Derivatives to hedge specific exposures Be on top of the capital markets</p></li><li><p>Aftermath Dont fall for the pretty pictures! Lots of phony stuff out there. Dont follow the flock! Be tough! (how has it helped in actual investment actions? has the tool been vetted?) Integrity Act in the light of intelligence, guided by experience.</p></li><li><p>Good Risk Managementis AlphaA good offence is better with a strong defence ... Every good trading strategy is better with proper risk management!Guy Lafleur!! </p></li><li><p>AcknowledgmentsDenis Taillefer, MxChristiane Lavalle, MxJames Vandenberg, apostrophe.caGunter Meissner, Derivatives Software / HPUOliver King, Harvard UniversityNipa Banerjee, CIDA</p></li><li><p>ReferencesThe Jungles of Randomness - A Mathematical Safari - Ivars Peterson, (Wiley, 1998)MFAs 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)</p></li></ul>

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