An Introduction to Risk - by Vikram Sankhala

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.