1. STABLE NON-GAUSSIAN ASSET ALLOCATION:A COMPARISON WITH THE CLASSICAL GAUSSIAN APPROACH Yesim Tokat, Svetlozar Rachev, and Eduardo Schwartz

2. I. Introduction zStrategic investment planning zStochastic programming with and without decision rules zCharacteristics of financial and macro data: heavy tails, time varying volatility and long-range dependence

3. I. Introduction zGenerate economic scenarios under Gaussian and stable Paretian non- Gaussian assumptions zDifferent allocations depending on the utility function and the risk aversion level of the agent yvery low or high risk aversion y‘typical’ risk aversion

4. II. Multistage Stochastic Programming with Decision Rules zDiscretize time into n stages, and use a decision rule at each time period zBoender et al. (1998):ALM model for pension funds zrandomly generate initial asset mixes zsimulate against generated scenarios zevaluate downside risk and contribution rate

5. III. Scenario Generation: Discrete Time Series Approach (Wilkie 1986, 1995)

6. Continuous Time Approach (Mulvey 1996, Mulvey and Thorlacius 1998)

7. IV. Stable Distribution zFinancial returns: Excess kurtosis found by Fama (1965) and Mandelbrot (1963,1967), Balke and Fomby (1994) zWhy stable Paretian distribution? yFat tails and high peak compared to Gaussian yGeneralized Central Limit Theorem zParameters: index of stability, skewness parameter, location parameter, scale parameter,

8. V. Model Setup zAsset allocation ygenerate initial asset allocations (a fixed mix) ysimulate future economic scenarios yupdate asset allocation every month using fixed mix rule ycalculate the risk and reward ychoose initial mix that gives the best risk- reward combination

9. Problem Formulation

10. Reward measure zmean final compound return where is the compound return of initial allocation i in periods 1 though T under scenario s.

11. Risk measures zmean absolute deviation of final compound return zmean deviation of final compound return

12. Utility functions z where c is the coefficient of risk aversion zpower utility where  is the coefficient of relative risk aversion

13. Scenario Generation

14. ycascade structure similar to Mulvey (1996) ymonthly data (1965-1999) yBox-Jenkins methodology yfit ARMA models to the financial variables ymodel the residuals as Gaussian and stable Paretian

15. Scenario Generation zSimulation of future scenarios yGenerate normal and stable distributions for the residuals of each model ygenerate T-bill, T-bond, inflation, stock dividend growth rate and stock dividend yield scenarios yeach variable has an innovation every month (T-bill and T-bond are dependent, others are independent)

16. Normal and Stable Fit for Treasury Bill

17. Normal and Stable Fit for Inflation

18. Normal and Stable Fit for Dividend Growth

19. Normal and Stable Fit for Dividend Yield

20. Estimated Normal and Stable Parameters for the Innovations

21. Simulation zGenerate 512 possible economic scenarios for the next 3 quarters zRepeat the scenario tree 99 times zCompare simulated scenarios with historical averages zNo back-testing yet

22. The Historical vs. Simulation Averages of Economic Variables

23. Optimal Allocations under Normal and Stable Scenarios, T= 3 quarters,

24. Optimal Allocations under Normal and Stable Scenarios, T= 3 quarters

26. VII. Conclusion zOptimal asset allocation may be sensitive to the distributional assumption zWe need to model heavy tails more realistically zFuture work: stochastic programming without decision rules