Immediate Symptoms Sudden Chest Pain Sweating Anxiety YOU SEEK Palpitations HELP Shortness of Breath Nausea and Vomiting
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 Why does it arise Can we make it an outcome of a Mathematical function of Factors (Independent Variables)
Where is the ProblemUnpredictability Given the Same set of Risk factors, one person may have a heart attack and another may not. 33% 67% Risk Uncertainty
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
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 Dependent Variablestate 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.
IllustrationCan we predict the movement of Stock Markets
What is RandomnessRandom Process1. A random process is a repeatingprocess2. whose outcomes follow nodescribable deterministic pattern,3. but follow a probabilitydistribution,4. Such that the relative probabilityof the occurrence of each outcomecan be approximated or calculated.
When do we call events random Statistical Properties- Is there a Correlation- Are the Events Independent
How do we study Randomness Probability theory is the branch of mathematics concerned with analysis of random phenomena RAIN MAYBE NO RAIN2% Decrease 3% Increase Statistics is used to infer the underlying probability distribution of a collection of empirical observations.
Random Walk Hypothesis - NoWhat 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
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 PennsylvaniaVolatility 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
Some ConceptsFailure of key businessesDeclines in consumer wealthSubstantial financial commitments incurred by governmentsSignificant decline in economic activity Markov Process Stochastic Monte Carlo Processes Methods Simulation
Stochastic Process Counterpart to a deterministic process Stock MarketsEven if the initial condition isknown, there are many possibilitiesthe process might go to, but some Exchange Ratepaths are more probable and others Fluctuationsless. Brownian Motion
Markov ProcessMathematical model for the random evolution of aMemory-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 │
SimulationA model in science is a physical, mathematical, or logicalrepresentation of a complex reality. A simulation brings a model to life and shows how a particular object or phenomenon will behave.
Some Methods of Simulation Historical Use of Parametric Information Random Distribution Numbers PAST DATA ASSUMPTION GENERATION Historical Parametric Monte Carlo Simulation Simulation Simulation
Monte Carlo Simulation Use Random Numbers to Generate DataMake your StochasticModel Plot Distribution Analyze Distribution
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
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
Objective of Risk Management Take Care of Uncertainty
Result BETTER PLANNING LESS LOSSES SECURE FUTURE
Warren BuffetRisk comes from not knowingwhat youre doing.