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# Finance.ppt

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• The name is a reference to the Monte Carlo Casino in Monaco where Ulam&apos;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?