2005 canadian annual derivatives conference august 17 - 20, 2005 québec, canada
DESCRIPTION
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? - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/1.jpg)
![Page 2: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/2.jpg)
2005 Canadian Annual Derivatives Conference
August 17 - 20, 2005 Québec, Canada.
Ranjan Bhaduri , BSc (Hons), MBA, MMath, PhD.
![Page 3: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/3.jpg)
Overview
•The Mathematics of Risk
•Portfolio Risk
•Elements of Risk
•Aftermath
![Page 4: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/4.jpg)
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)
![Page 5: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/5.jpg)
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
![Page 6: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/6.jpg)
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
![Page 7: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/7.jpg)
Mathematical Definition of Omega
Mathematical Definition of Omega
•Where F is the cumulative distribution of returns, and r is the threshold chosen by the investor.
•Where F is the cumulative distribution of returns, and r is the threshold chosen by the investor.
![Page 8: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/8.jpg)
Omega - the Finance IntuitionOmega - 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
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
![Page 9: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/9.jpg)
Omega GraphsOmega Graphs
Omega analysisOmega analysis
![Page 10: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/10.jpg)
How can Omega be used in Risk Management?
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
Portfolio construction
Risk monitoring
Leverage setting tool
Performance review
Comparative Studies
Robustness of portfolio
Fine-tuning the tail
![Page 11: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/11.jpg)
Elements of RiskElements 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
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
![Page 12: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/12.jpg)
Elements of RiskElements of Risk
Liquidity Risk
Geo-Political Risk
Model Risk
Leverage - upping the stakes
Liquidity Risk
Geo-Political Risk
Model Risk
Leverage - upping the stakes
![Page 13: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/13.jpg)
AftermathAftermath
Quantitative tools to be used qualitatively (not auto-pilot)
Derivatives to hedge specific exposures
Be on top of the capital markets
Quantitative tools to be used qualitatively (not auto-pilot)
Derivatives to hedge specific exposures
Be on top of the capital markets
![Page 14: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/14.jpg)
AftermathAftermath 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.
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.
![Page 15: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/15.jpg)
Good Risk Managementis Alpha
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!!
A good offence is better with a strong defence ...
Every good trading strategy is better with proper risk
management!Guy Lafleur!!
![Page 16: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/16.jpg)
AcknowledgmentsAcknowledgmentsDenis Taillefer, Mx
Christiane Lavallée, Mx
James Vandenberg, apostrophe.ca
Gunter Meissner, Derivatives Software / HPU
Oliver King, Harvard University
Nipa Banerjee, CIDA
![Page 17: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/17.jpg)
ReferencesReferences“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)
![Page 18: 2005 Canadian Annual Derivatives Conference August 17 - 20, 2005 Québec, Canada](https://reader036.vdocuments.net/reader036/viewer/2022070418/56815989550346895dc6cc75/html5/thumbnails/18.jpg)