an introduction to risk - by vikram sankhala
DESCRIPTION
A brief introduction to UncertaintyTRANSCRIPT
Introduction to Risk
VIKRAM SINGH SANKHALA
What is Risk
CAN YOU PREDICT A HEART ATTACK
Immediate Symptoms
Sudden Chest Pain
Anxiety
Shortness of Breath
Sweating
Palpitations
Nausea and Vomiting
YOUSEEKHELP
Risk Factors
• Previous cardiovascular disease• Older age• Tobacco smoking• High levels of certain lipids and
low levels of high density lipoprotein
• Excessive alcohol consumption and drug abuse
• Diabetes• High blood pressure• Obesity• Chronic kidney disease• Heart failure• Chronic high stress levels
Modeling and Predicting a Heart Attack
Can we make it an outcome of a Mathematical function of Factors (Independent Variables)
Why does it arise
Where is the Problem
Uncertainty
33%
Unpredictability Given the Same set of Risk factors, one person may have a heart attack and
another may not.
67%Risk
Can we measure Risk
Uncertainty – A State of Having Limited Knowledge
Probabilities are assigned to each possible state or outcome
10%
20%
30%
40%
UncertaintyMeasurable Factors
What is Risk
– A set of measured uncertainties – Where some possible outcomes have
an undesired effect or significant loss– There is also scope for the upside i.e.
profit
What is Predictability
Is it possible to predict the state of the system S (t+k) at
time= t+k
Dependent Variable
Independent Variable a
Independent variable z
Independent Variable y
Independent Variable x
80%
15%
4%
1%
Consider a system whose state at the
initial state S(t) at time t.
Financial Risk
Illustration
Can we predict the movement of Stock Markets
What is Randomness
Random Process
1. A random process is a repeating process
2. whose outcomes follow no describable deterministic pattern,
3. but follow a probability distribution,
4. Such that the relative probability of the occurrence of each outcome can be approximated or calculated.
When do we call events random
- Is there a Correlation
- Are the Events Independent
Statistical Properties
How do we study Randomness
Statistics is used to infer the underlying probability distribution of a collection of empirical observations.
2% Decrease
RAIN
3% Increase
MAYBE NO RAIN
Probability theory is the branch of mathematics concerned with analysis of random phenomena
Random │ Walk │ Hypothesis
Random Walk Hypothesis - No
A random walk, sometimes denoted RW, is a mathematical formalization of a trajectory that consists of taking successive random steps.
What is a Random Walk ?
What does the Random Walk Hypothesis say ?
The random walk hypothesis is a financial theory stating that stock market prices evolve according to a random walk and thus the prices
Random │ Walk │ Hypothesis
Against the Hypothesis - Yes
Professors of Finance at the MIT Sloan School of Management and the University of Pennsylvania
Professors Andrew W. Lo and Archie Craig MacKinlay
Volatility Besed Equation
• Xt is the price of the stock at time t• μ is an arbitrary drift parameter• εt is a random disturbance term
Some Concepts
Failure of key businesses
Declines in consumer wealth
Substantial financial commitments incurred by governments
Significant decline in economic activity
Simulation
Stochastic Processes
Monte Carlo Methods
Markov Process
Stochastic Process
Even if the initial condition is known, there are many possibilities the process might go to, but some paths are more probable and others less.
Stock Markets
Exchange Rate Fluctuations
Brownian Motion
Counterpart to a deterministic process
Andrei Markov │ Russian Mathematician │
Markov Process
Process for which the likelihood of a given future state, at any given moment, depends only on its present state, and not on any past states
Mathematical model for the random evolution of a Memory-less system
Simulation
A simulation brings a model to life and shows how a particular object or phenomenon will behave.
A model in science is a physical, mathematical, or logical
representation of a complex reality.
Some Methods of Simulation
Historical Simulation
Parametric Simulation
Monte Carlo Simulation
ASSUMPTION
Parametric Distribution
GENERATION
Use of Random Numbers
PAST DATA
Historical Information
Monte Carlo Simulation
Use Random Numbers to Generate Data
Make your Stochastic Model
Analyze Distribution
Plot Distribution
Financial Crisis Components
Failure of key businesses
Declines in consumer wealth
Substantial financial commitments incurred by governments
Significant decline in economic activity
Government Commitments
Economic Activity
Consumer Wealth
Business Failure
US Mortgage Crisis
Between 1997 and 2006, the price of the typical American house increased by 124%
124% INCREASE
Housing Prices: • peaked in early 2005
• started to decline in 2006• Led to US Mortgage Crisis
At Least Possible Cost
Objective of Risk Management
Take Care of Uncertainty
Provide B
est Risk C
over
Result
BETTER PLANNING
LESS LOSSES
SECURE FUTURE
Warren Buffet
Risk comes from not knowing what you're doing.