A brief introduction to Uncertainty

1. Introduction to Risk
VIKRAM SINGH SANKHALA

2. What is Risk
CAN YOU
PREDICT A
HEART ATTACK

3. Immediate Symptoms
Sudden Chest Pain
Sweating Anxiety
YOU
SEEK
Palpitations HELP Shortness of Breath
Nausea and Vomiting

4. 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

5. Modeling and Predicting a Heart Attack
Why does
it arise
Can we make it an outcome of a Mathematical
function of Factors (Independent Variables)

6. Where is the Problem
Unpredictability Given the Same set of Risk
factors, one person may
have a heart attack and
another may not.
33%
67%
Risk
Uncertainty

7. Can we measure Risk
Uncertainty – A State of Having Limited Knowledge
40%
Probabilities are assigned to 30%
each possible state or outcome
20%
10%
Measurable Factors Uncertainty

8. 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

9. What is Predictability
Is it possible to predict the Dependent Variable
state of the system S (t+k) at
time= t+k
Independent Variable x 1%
Independent Variable y 4%
Independent variable z
15%
Independent Variable a
80%
Consider a system
whose state at the
initial state S(t) at time
t.

10. Financial Risk

11. Illustration
Can we predict the movement of Stock Markets

12. 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.

13. When do we call events random
Statistical Properties
- Is there a Correlation
- Are the Events Independent

14. How do we study Randomness
Probability theory is the branch of mathematics concerned
with analysis of random phenomena
RAIN MAYBE NO RAIN
2% Decrease
3% Increase
Statistics is used to infer the underlying probability
distribution of a collection of empirical observations.

15. Random Walk Hypothesis - No
What is a Random Walk ?
A random walk, sometimes denoted RW, is a
mathematical formalization of a trajectory that
consists of taking successive random steps.
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

16. Against the Hypothesis - Yes
Professors Andrew W. Lo and Archie Craig MacKinlay
Professors of Finance at the MIT Sloan School of
Management and the University of Pennsylvania
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
Random │ Walk │ Hypothesis

17. Some Concepts
Failure of key businesses
Declines in consumer wealth
Substantial financial commitments incurred by governments
Significant decline in economic activity
Markov Process
Stochastic Monte Carlo
Processes Methods
Simulation

18. Stochastic Process
Counterpart to a deterministic process
Stock Markets
Even if the initial condition is
known, there are many possibilities
the process might go to, but some Exchange Rate
paths are more probable and others Fluctuations
less.
Brownian
Motion

19. Markov Process
Mathematical model for the random evolution of a
Memory-less system
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
Andrei Markov │ Russian Mathematician │

20. Simulation
A model in science is a physical, mathematical, or logical
representation of a complex reality.
A simulation brings a model to life and shows how a particular object
or phenomenon will behave.

21. Some Methods of Simulation
Historical Use of
Parametric
Information Random
Distribution
Numbers
PAST DATA ASSUMPTION GENERATION
Historical Parametric Monte Carlo
Simulation Simulation Simulation

22. Monte Carlo Simulation
Use Random Numbers
to Generate Data
Make your Stochastic
Model
Plot Distribution
Analyze Distribution

23. Financial Crisis Components
Failure of key businesses
Declines in consumer wealth
Substantial financial commitments incurred by governments
Significant decline in economic activity
Business
Failure
Economic Consumer
Activity Wealth
Government
Commitments

24. 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

25. Objective of Risk Management
Take Care of Uncertainty

26. Result
BETTER PLANNING
LESS LOSSES
SECURE FUTURE

27. Warren Buffet
Risk comes from not knowing
what you're doing.