Finance.ppt

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  • The name is a reference to the Monte Carlo Casino in Monaco where Ulam's uncle would borrow money to gamble.
  • In finance , the Monte Carlo method is used to simulate the various sources of uncertainty that affect the value of the instrument , portfolio or investment in question, and to then calculate a representative value given these possible values of the underlying inputs
  • Finance.ppt

    1. 1. Monte Carlo Simulation and Personal Finance Jacob Foley
    2. 2. Background on myself <ul><li>I work at Stephens Financial Partners as a Financial Advisor </li></ul><ul><li>Monte Carlo simulations are the most popular simulations used by advisors </li></ul><ul><li>These simulations failed after the 2008 market collapse </li></ul>
    3. 3. Where did it come from? <ul><li>John von Neumann and Stanislaw Ulam </li></ul><ul><li>Los Alamos Scientific Laboratory </li></ul><ul><li>Studying radiation shielding </li></ul>
    4. 4. Why call it Monte Carlo? <ul><li>Neuman and Ulam’s work had to be kept a secret because it was part of the Manhattan Project </li></ul><ul><li>Von Neuman chose the name &quot;Monte Carlo&quot;. </li></ul>
    5. 5. What is it? <ul><li>Class of computational algorithms </li></ul><ul><li>Used to solve large systems </li></ul><ul><li>Used when it is unfeasible or impossible to compute an exact result </li></ul>
    6. 6. Basic Principle of the Monte Carlo Method. <ul><li>The Task: Calculate a number I (one number only. Not an entire functional dependence) </li></ul><ul><li>Example: Calculate pi </li></ul><ul><ul><li>Numerically: look for an appropriate convergent series and evaluate this approximately </li></ul></ul><ul><ul><li>Monte Carlo: look for a stochastic model: probability space with random variable </li></ul></ul>
    7. 7. What makes a method a Monte Carlo Method? <ul><li>Define a domain of possible inputs. </li></ul><ul><li>Generate inputs randomly from the domain using a certain specified probability distribution. </li></ul><ul><li>Perform a deterministic computation using the inputs. </li></ul><ul><li>Aggregate the results of the individual computations into the final result </li></ul>
    8. 8. Random Numbers <ul><li>Uniform Distribution </li></ul><ul><ul><li>The random variable X is uniformly distributed on the interval [a, b] </li></ul></ul>
    9. 9. How many of you have played battleship?
    10. 11. Dull Monte Carlo <ul><li>“ hit or miss” </li></ul><ul><ul><li>Take a sample point </li></ul></ul><ul><ul><li>The point has two outcomes </li></ul></ul><ul><ul><ul><li>True (“hit”) </li></ul></ul></ul><ul><ul><ul><li>False (“miss”) </li></ul></ul></ul><ul><ul><li>Total number of hits and divide it by the total trials </li></ul></ul>
    11. 12. X f(x) I = ∫ f(x) dx I: unknown area Hit or Miss known area x 1 , uniform x 2 uniform miss hit
    12. 13. Crude Monte Carlo <ul><li>Write the integral such that I becomes the mean value of a random variable. </li></ul><ul><ul><li>Purposes we generate B numbers </li></ul></ul><ul><ul><li>Uniformly distributed from (0,1) </li></ul></ul><ul><ul><li>Then take their average </li></ul></ul>
    13. 14. Take Numerical Analysis <ul><li>Professor Robert Lewis </li></ul><ul><li>Math 413 and 414 </li></ul>
    14. 15. Applications in the Real World <ul><li>Physical sciences </li></ul><ul><li>Design and visuals </li></ul><ul><li>Telecommunications </li></ul><ul><li>Games </li></ul><ul><li>Finance and business </li></ul>
    15. 16. Monte Carlo in Finance <ul><li>First Introduced in 1964 </li></ul><ul><li>“ Risk Analysis in Capital Investment” </li></ul><ul><ul><li>David B Hertz </li></ul></ul><ul><ul><li>Harvard Business Review Article </li></ul></ul>
    16. 17. So how does Monte Carlo apply to Finance? <ul><li>Used to value and analyze </li></ul><ul><ul><li>Instruments </li></ul></ul><ul><ul><li>Options </li></ul></ul><ul><ul><li>Portfolios </li></ul></ul><ul><ul><li>Investments </li></ul></ul>
    17. 18. How does it predict values? <ul><li>For each Simulation </li></ul><ul><ul><li>The behavior of the factors impacting the component instrument is simulated over time </li></ul></ul><ul><ul><li>The values of the instrument are calculated </li></ul></ul><ul><ul><li>The value is then observed </li></ul></ul><ul><ul><li>The various values are then combined in a histogram (i.e. the probability distribution) </li></ul></ul><ul><ul><li>The statistical characteristics are then observed </li></ul></ul>
    18. 19. How is it used in financial planning? <ul><li>Simulates the overall market </li></ul><ul><li>Predicts the probability of reaching a target number </li></ul><ul><li>Changes are made to reach the target number </li></ul>
    19. 20. An Example <ul><li>http://www.flexibleretirementplanner.com/ </li></ul>
    20. 21. What works with Monte Carlo? <ul><li>Forecasting Earnings </li></ul><ul><li>Modeling portfolio losses </li></ul><ul><li>Provides flexibility </li></ul>
    21. 22. What is wrong with Monte Carlo? <ul><li>Assumes normal return distributions </li></ul><ul><ul><li>We know from history that extreme returns occur more frequently than expected </li></ul></ul><ul><li>Can’t predict every outcome </li></ul><ul><ul><li>Most clients see the simulation run through thousands of iterations and believe that they have seen all possible outcomes </li></ul></ul>
    22. 23. What is wrong with Monte Carlo? <ul><li>Does not measure bear markets well </li></ul><ul><li>Does not include the human factor </li></ul>
    23. 24. What is wrong with Monte Carlo? <ul><li>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 </li></ul>
    24. 25. What can we do better? <ul><li>Let’s look at an example </li></ul><ul><li>Assumptions </li></ul><ul><ul><li>20 year period </li></ul></ul><ul><ul><li>Individual that has just retired in 1988 </li></ul></ul><ul><ul><li>Has $1,000,000 invested in DJIA </li></ul></ul><ul><ul><li>Withdraws $50,000 each year that increases by 3% to compensate for inflation </li></ul></ul>
    25. 26. 1988 11.80% $1,118,000.00 $1,068,000.00 $50,000.00 1989 27.00% $1,356,360.00 $1,304,860.00 $51,500.00 1990 -4.30% $1,248,751.02 $1,195,706.02 $53,045.00 1991 20.30% $1,438,434.34 $1,383,797.99 $54,636.35 1992 4.20% $1,441,917.51 $1,385,642.07 $56,275.44 1993 13.70% $1,575,475.03 $1,517,511.33 $57,963.70 1994 2.10% $1,549,379.06 $1,489,676.45 $59,702.61 1995 33.50% $1,988,718.06 $1,927,224.37 $61,493.69 1996 26.00% $2,428,302.70 $2,364,964.20 $63,338.50 1997 22.60% $2,899,446.11 $2,834,207.45 $65,238.66 1998 16.10% $3,290,514.85 $3,223,319.03 $67,195.82 1999 25.20% $4,035,595.42 $3,966,383.73 $69,211.69 2000 -6.20% $3,720,467.94 $3,649,179.89 $71,288.04 2001 -7.10% $3,390,088.12 $3,316,661.44 $73,426.69 2002 -16.80% $2,759,462.31 $2,683,832.83 $75,629.49 2003 25.30% $3,362,842.53 $3,284,944.16 $77,898.37 2004 3.10% $3,386,777.43 $3,306,542.11 $80,235.32 2005 -0.60% $3,286,702.86 $3,204,060.48 $82,642.38 2006 16.30% $3,726,322.33 $3,641,200.68 $85,121.65 2007 6.80% $3,888,802.33 $3,801,127.02 $87,675.30 2008 -49.80% $1,908,165.77 $1,817,860.20 $90,305.56
    26. 27. 1988 -49.80% $502,000.00 $452,000.00 $50,000.00 1989 6.80% $482,736.00 $431,236.00 $51,500.00 1990 16.30% $501,527.47 $448,482.47 $53,045.00 1991 -0.60% $445,791.57 $391,155.22 $54,636.35 1992 3.10% $403,281.04 $347,005.59 $56,275.44 1993 25.30% $434,798.01 $376,834.31 $57,963.70 1994 -16.80% $313,526.14 $253,823.53 $59,702.61 1995 -7.10% $235,802.06 $174,308.36 $61,493.69 1996 -6.20% $163,501.25 $100,162.74 $63,338.50 1997 25.20% $125,403.75 $60,165.09 $65,238.66 1998 16.10% $69,851.67 $2,655.85 $67,195.82 1999 22.60% $3,256.08 $65,955.62 $69,211.69 2000 26.00% $83,104.08 $154,392.12 $71,288.04 2001 33.50% $206,113.48 $279,540.17 $73,426.69 2002 2.10% $285,410.51 $361,040.00 $75,629.49 2003 13.70% $410,502.48 $488,400.85 $77,898.37 2004 4.20% $508,913.68 $589,149.00 $80,235.32 2005 20.30% $708,746.25 $791,388.63 $82,642.38 2006 -4.30% $757,358.92 $842,480.58 $85,121.65 2007 27.00% $1,069,950.33 $1,157,625.63 $87,675.30 2008 11.80% $1,294,225.46 $1,384,531.02 $90,305.56
    27. 28. 1988 11.80% $1,118,000.00 $1,068,000.00 $50,000.00 1989 27.00% $1,356,360.00 $1,304,860.00 $51,500.00 1990 -4.30% $1,248,751.02 $1,195,706.02 $53,045.00 1991 20.30% $1,438,434.34 $1,438,434.34 $0.00 1992 4.20% $1,498,848.58 $1,423,219.09 $75,629.49 1993 13.70% $1,618,200.11 $1,540,301.74 $77,898.37 1994 2.10% $1,572,648.07 $1,492,412.75 $80,235.33 1995 33.50% $1,992,371.02 $1,909,728.63 $82,642.39 1996 26.00% $2,406,258.07 $2,321,136.42 $85,121.66 1997 22.60% $2,845,713.25 $2,758,037.94 $87,675.31 1998 16.10% $3,202,082.05 $3,111,776.48 $90,305.57 1999 25.20% $3,895,944.16 $3,802,929.42 $93,014.73 2000 -6.20% $3,567,147.80 $3,471,342.62 $95,805.18 2001 -7.10% $3,224,877.30 $3,224,877.30 $0.00 2002 -16.80% $2,683,097.91 $2,683,097.91 $0.00 2003 25.30% $3,361,921.68 $3,361,921.68 $0.00 2004 3.10% $3,466,141.25 $3,358,311.65 $107,829.60 2005 -0.60% $3,338,161.78 $3,227,097.30 $111,064.49 2006 16.30% $3,753,114.16 $3,753,114.16 $0.00 2007 6.80% $4,008,325.92 $3,890,497.62 $117,828.30 2008 -49.80% $1,953,029.80 $1,831,666.66 $121,363.15
    28. 29. 1988 -49.80% $502,000.00 $452,000.00 $50,000.00 1989 6.80% $482,736.00 $482,736.00 $0.00 1990 16.30% $561,421.97 $508,376.97 $53,045.00 1991 -0.60% $505,326.71 $450,690.36 $54,636.35 1992 3.10% $464,661.76 $464,661.76 $0.00 1993 25.30% $582,221.18 $524,257.48 $57,963.70 1994 -16.80% $436,182.22 $376,479.61 $59,702.61 1995 -7.10% $349,749.56 $349,749.56 $0.00 1996 -6.20% $328,065.08 $328,065.08 $0.00 1997 25.20% $410,737.48 $410,737.48 $0.00 1998 16.10% $476,866.22 $386,851.49 $90,014.73 1999 22.60% $474,279.93 $381,564.75 $92,715.17 2000 26.00% $480,771.59 $385,274.96 $95,496.63 2001 33.50% $514,342.08 $415,980.55 $98,361.53 2002 2.10% $424,716.14 $349,086.65 $75,629.49 2003 13.70% $396,911.52 $319,013.15 $77,898.37 2004 4.20% $332,411.70 $252,176.37 $80,235.33 2005 20.30% $303,368.18 $220,725.79 $82,642.39 2006 -4.30% $211,234.58 $126,112.93 $85,121.66 2007 27.00% $160,163.42 $160,163.42 $0.00 2008 11.80% $179,062.70 $57,699.55 $121,363.15
    29. 30. Have multiple buckets of money <ul><li>Don’t just have your money in the stock market </li></ul><ul><li>Have money growing outside of the stock market </li></ul>
    30. 31. Homework <ul><li>Estimate Pi using Monte Carlo </li></ul>
    31. 32. Thank You! Any Questions?

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