1. 1 The Simugram: A Holistic Paradigm for Risk Analysis, James R. Thompson, Noah Harding Professor of Statistics Rice University Copyright 2003, Simugram Systems, Inc. Patent Pending

2. 2 Horatio: You will lose this wager, my lord. Hamlet: I do not think so. Since he went into France, I have been in continual practice. I shall win at the odds.... ************************************************* Hamlet: O, I die, Horatio; The potent poison quite o'er-crows my spirit. Copyright 2003, Simugram Systems, Inc. Patent Pending

3. 3 Will Rodgers It’s not the things we don’t know that hurt us; it’s the things we know that just ain’t so. Copyright 2003, Simugram Systems, Inc. Patent Pending

4. 4 John Maynard Keynes The market can remain irrational longer than you can remain solvent Copyright 2003, Simugram Systems, Inc. Patent Pending

5. 5 Copyright 2003, Simugram Systems, Inc. Patent Pending

6. 6 Copyright 2003, Simugram Systems, Inc. Patent Pending

7. 7 Cover of Models for Investors in Real World Markets  =–.317 Copyright 2003, Simugram Systems, Inc. Patent Pending

8. 8 Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise. John W. Tukey Copyright 2003, Simugram Systems, Inc. Patent Pending

9. 9 There are dangers with maximizing the expectation of growth. St. Petersburg Paradox Copyright 2003, Simugram Systems, Inc. Patent Pending

10. 10 The modern computer enables us to use historical data to simulate many possible values of a stock at a desired time horizon. Copyright 2003, Simugram Systems, Inc. Patent Pending

11. 11 Look at a simugram for an Ibbotson Index Portfolio of initial value $100,00 over a 3 year period, using data using data from 1926-2000. The Simugram Using Ibbotson Index Data Copyright 2003, Simugram Systems, Inc. Patent Pending

12. 12 From this diagram we can note that the value of the portfolio is less than $142,000 50% of the time and that it is less than $86,000 10 % of the time. Easier to use is the cumulative simugram shown below Copyright 2003, Simugram Systems, Inc. Patent Pending

13. 13 The mean value of a $100,000 portfolio after five years is $192,676. The median value is $175,530 (growth rate of.1125). However, the lower ten percentile is $92,747 (growth rate of -.015). Copyright 2003, Simugram Systems, Inc. Patent Pending

14. 14 Next, we consider the same scenario except looking 20 years into the future. The median value is $873,100, an annual increase of 10.8%. Even the lower ten percentile value of $285,590 represents a growth rate of 5.2%. Copyright 2003, Simugram Systems, Inc. Patent Pending

15. 15 Mean = $4,850,000 Median = $2,725,000 Lower Ten Percentile = $695,000 Copyright 2003, Simugram Systems, Inc. Patent Pending

16. 16 Lower 10 Percentile = $269,000 Median = $993,000 Mean = $1,745,000 45 Year Copyright 2003, Simugram Systems, Inc. Patent Pending

17. 17 The Bear Bites All Bear Market OccurredDuration of Bear MarketAmount of DeclineRecovery Period 08/25/56 - 10/22/5614.7 months21.60%11.1 months 12/12/61 - 06/26/626.4 months28.00%14.3 months 02/09/66 - 10/07/667.9 months22.20%6.9 months 11/29/68 - 05/26/7017.9 months36.10%21.3 months 01/11/73 - 10/03/7420.7 months48.20%69.4 months 09/21/76 - 03/06/7817.5 months19.40%17.3 months 01/06/81 - 08/12/8219.2 months25.80%2.3 months 08/25/87 - 12/04/873.3 months33.50%19.7 months 07/16/90 - 10/11/902.9 months19.90%4.3 months Bear Markets 1950-2000 Copyright 2003, Simugram Systems, Inc. Patent Pending

18. 18 Resampling vs Modeled Three Years Out Copyright 2003, Simugram Systems, Inc. Patent Pending

19. 19 Resampling Versus Model 1 Year Out Copyright 2003, Simugram Systems, Inc. Patent Pending

20. 20 Ways of Dealing with Bears Go to Levy Stable Distributions Stay with Resampling Patch the Geometric Brownian Model Every Year the Market Has a 10% Bear Every Five Years the Market Has a 20% Bear Copyright 2003, Simugram Systems, Inc. Patent Pending

21. 21 Black-Scholes-Merton and Their Amazing Money Machine Definition: A Call Option is the right (but not the obligation) to buy a security of current price S(0) for strike price X at a future time T. What is the “fair price” C of such a call option? Answer: There ain’t no such thing. Copyright 2003, Simugram Systems, Inc. Patent Pending

22. 22 Wrong Answer! How about C = exp(–µt) E { Max(0,S(T) –X) } Copyright 2003, Simugram Systems, Inc. Patent Pending

23. 23 No. What is wanted is: Transforms a noisy game into a sure thing. Copyright 2003, Simugram Systems, Inc. Patent Pending

24. 24 Some Problems With Black- Scholes Transaction costs are not really free. The closer the hedge gets to being riskless, the more frequently one must rebalance (and this results in material transaction costs). The realistic value of r will be significantly higher than that of a Treasury bill. Copyright 2003, Simugram Systems, Inc. Patent Pending

25. 25 Historical records show that the Black-Scholes formula, generally does not give the actual market price of a call option. To correct this imperfection in nature, it is customary for some traders to plug in whatever value is necessary for  to give the market price for the option. Copyright 2003, Simugram Systems, Inc. Patent Pending

26. 26 In the case of horse betting, there is an arbitrary mechanism which sets payoffs at the instant the race starts. The bookmaker is allowed to set payoffs with his profit margin locked into the payoff. Suppose that the bet is placed a week before the instant the race starts. What costs must the bookmaker incur in the intervening time period to rebalance the payoffs for the bets he has covered? The answer is ``zero.'' And this is a reason the analogy between bookmaking and selling options is flawed. Copyright 2003, Simugram Systems, Inc. Patent Pending

27. 27 Looking at expectations and variances does not tell the story.We need to look at the distribution function of the payoffs. Copyright 2003, Simugram Systems, Inc. Patent Pending

28. 28 µ=.15; T=0.5;  X=$108; S(0) = $100 C=$3.54 55%of the time V=0. E= $7.23 Copyright 2003, Simugram Systems, Inc. Patent Pending

29. 29  r Copyright 2003, Simugram Systems, Inc. Patent Pending

30. 30 A Portfolio Case Study Next we take the 90 stocks in the S&P 100 that were in business prior to 1991. Optimal investment allocation maximizing the one year lower 20 percentile. Constraining each stock to no more than 5% of the portfolio share Copyright 2003, Simugram Systems, Inc. Patent Pending

31. 31 Copyright 2003, Simugram Systems, Inc. Patent Pending

32. 32 Copyright 2003, Simugram Systems, Inc. Patent Pending

33. 33 Copyright 2003, Simugram Systems, Inc. Patent Pending

34. 34 1. The main weapons of the investor are diversification and time. 2. Looking at the mean and variance Is not enough. 3.We have created a computer intensive forecasting paradigm which enables us readily and intuitively to consider questions of risk and growth simultaneously. 4. The set of algorithms can be readily learned by the financial professional. In connection with other information, it provides valuable information for advising modifications to portfolios. Conclusions Copyright 2003, Simugram Systems, Inc. Patent Pending