Monte Carlo Simulation and Personal Finance

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Monte Carlo Simulation and Personal Finance

• Jacob Foley

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Background on myself

• I work at Stephens Financial Partners as a
  Financial Advisor
• Monte Carlo simulations are the most popular
  simulations used by advisors
• These simulations failed after the 2008 market
  collapse

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Where did it come from?

• John von Neumann and Stanislaw Ulam
• Los Alamos Scientific Laboratory
• Studying radiation shielding

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Why call it Monte Carlo?

• Neuman and Ulams work had to be kept a secret
  because it was part of the Manhattan Project
• Von Neuman chose the name "Monte Carlo".

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What is it?

• Class of computational algorithms
• Used to solve large systems
• Used when it is unfeasible or impossible to
  compute an exact result

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Basic Principle of the Monte Carlo Method.

• The Task Calculate a number I (one number only.
  Not an entire functional dependence)
• Example Calculate pi
• Numerically look for an appropriate convergent
  series and evaluate this approximately
• Monte Carlo look for a stochastic model
  probability space with random variable

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What makes a method a Monte Carlo Method?

• Define a domain of possible inputs.
• Generate inputs randomly from the domain using a
  certain specified probability distribution.
• Perform a deterministic computation using the
  inputs.
• Aggregate the results of the individual
  computations into the final result

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Random Numbers

• Uniform Distribution
• The random variable X is uniformly distributed on
  the interval a, b

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How many of you have played battleship?
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Dull Monte Carlo

• hit or miss
• Take a sample point
• The point has two outcomes
• True (hit)
• False (miss)
• Total number of hits and divide it by the total
  trials

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Hit or Miss
I unknown area
f(x)
I ? f(x) dx
X
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Crude Monte Carlo

• Write the integral such that I becomes the mean
  value of a random variable.
• Purposes we generate B numbers
• Uniformly distributed from (0,1)
• Then take their average

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Take Numerical Analysis

• Professor Robert Lewis
• Math 413 and 414

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Applications in the Real World

• Physical sciences
• Design and visuals
• Telecommunications
• Games
• Finance and business

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Monte Carlo in Finance

• First Introduced in 1964
• Risk Analysis in Capital Investment
• David B Hertz
• Harvard Business Review Article

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So how does Monte Carlo apply to Finance?

• Used to value and analyze
• Instruments
• Options
• Portfolios
• Investments

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How does it predict values?

• For each Simulation
• The behavior of the factors impacting the
  component instrument is simulated over time
• The values of the instrument are calculated
• The value is then observed
• The various values are then combined in a
  histogram (i.e. the probability distribution)
• The statistical characteristics are then observed

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How is it used in financial planning?

• Simulates the overall market
• Predicts the probability of reaching a target
  number
• Changes are made to reach the target number

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An Example

• http//www.flexibleretirementplanner.com/

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What works with Monte Carlo?

• Forecasting Earnings
• Modeling portfolio losses
• Provides flexibility

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What is wrong with Monte Carlo?

• Assumes normal return distributions
• We know from history that extreme returns occur
  more frequently than expected
• Cant predict every outcome
• Most clients see the simulation run through
  thousands of iterations and believe that they
  have seen all possible outcomes

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What is wrong with Monte Carlo?

• Does not measure bear markets well
• Does not include the human factor

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What is wrong with Monte Carlo?

• Does not recognize that portfolio performance
  depends at least as much on the sequence of the
  rate of return that it does on the average of
  those returns

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What can we do better?

• Lets look at an example
• Assumptions
• 20 year period
• Individual that has just retired in 1988
• Has 1,000,000 invested in DJIA
• Withdraws 50,000 each year that increases by 3
  to compensate for inflation

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Have multiple buckets of money

• Dont just have your money in the stock market
• Have money growing outside of the stock market

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Homework

• Estimate Pi using Monte Carlo

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Thank You!

• Any Questions?