Intelligent Finance Component III – Dynamic Portfolio Management

1. Second International Workshop on Intelligent Finance (IWIF-II) 6.-8. July 2007, Chengdu, China Intelligent FinanceComponent III – Dynamic Portfolio Management Prof Dr PAN Heping, Director of PRC, IIFP, SIIF & SSFI Prediction Research Centre (PRC) University of Electronic Science &Technology of China （UESTC） International Institute for Financial Prediction (IIFP), Finance Research Centre of ChinaSouthwestern University of Finance & Economics (SWUFE) Swingtum Institute of Intelligent Finance (SIIF)Swingtum School of Financial Investment (SSFI) Room 340/306 Yifu Building, Chengdu 610054, China Phone：+8628-83208728, Mobile：13908085966 Email: panhp@uestc.edu.cn, h.pan@iifp.net URL Chinese：www.swingtum.com.cn URL English： www.swingtum.com

2. Second International Workshop on Intelligent Finance (IWIF-II) 6.-8. July 2007, Chengdu, China Intelligent FinanceComponent III – Dynamic Portfolio Management 潘和平 （博士、教授、长江学者） 电子科技大学预测研究中心主任 西南财经大学中国金融研究中心国际金融预测研究所所长 形势冲智能金融研究院院长 & 形势冲金融投资学校校长 成都市建设北路二段四号逸夫楼340/306 电话：028-83208728, 手机：13908085966 电子邮件: panhp@uestc.edu.cn, h.pan@iifp.net 中文网站：www.形势冲.com, www.swingtum.com.cn 英文网站：www.swingtum.com

3. Contents • Mean-Variance Portfolio Theory (Markowitz 1950’s) • Capital Asset Pricing Model (S-M-L-T 1960’s) • Abitrage Pricing Theory (Ross 1970’s) • Multiperiod Dynamic Portfolio Theory (1990’s – 2007) • Direct Dynamic Portfolio Theory (2004 – 2007) • Naturally Dynamic Portfolio Theory (2007 onwards)- A Natural Framework for Integrated Active and Reactive Portfolio Management • Conclusions www.swingtum.com/institute/IWIF

4. 1. Mean-Varance Portfolio Theory (Markowitz 1952) www.swingtum.com/institute/IWIF

5. Portfolio Optimization for Any Given Rate of Return www.swingtum.com/institute/IWIF

6. Criticisms to Markowitz’s Mean-Variance Portfolio Theory • The biggest criticism to Markowitz’s original Mean-Variance Portfolio Theory is the use of variance as the risk measure as it considers volatility above the mean just as harmful as volatility below the mean(after 40 years of his initial paper, Markowitz (1991, 1993) recognized the potential of semivariance as a suitable risk measure for investment portfolios.) • The solution to the problem of portfolio variance minimization requires quadratic programming techniques – the least squares, which assumes the individual investment returns are normally distributed. • The theory is static, implying a single time period. Only statistical moments of the distributions of historical return data; the very nature of the time aspect of the return history is lost. www.swingtum.com/institute/IWIF

7. 2. Capital Asset Pricing Model (CAPM) (Sharpe 1963, Lintner 1965, Mossin 1966, Treynor 1961) www.swingtum.com/institute/IWIF

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9. Optimization of a Portfolio Constructed under CAPM www.swingtum.com/institute/IWIF

10. Comments to S-L-M-T’s CAPM Theory and Portfolios • The CAPM is consistent with the EMT. It provides the most simple model on the behavior of investments. With only one risk factor in the economy, the market index, all that an investor needed to know was the betas of the securities and portfolios. • While the beta of an individual stock tells an investor how much the stock should move with respect to the market, we must bear in mind that there is also stock-specific risk that could alter that relationship drastically. • The most remarkable catch came in here: the combination of the single-index model of CAPM with the diversification principle of Mean-Variance Portfolio Theory led to a powerful solution for minimizing the company-specific risk, leaving only the market-related risk, by holding a group of securities in a portfolio. Thus an investor could have a portfolio of a higher return-to-risk ratio than that of any individual stock with the desired risk level with respect to the market. • The single-index system of equations for portfolio optimization under CAPM is still a quadratic programming problem, as is the original Markowitz mean-variance problem. But the single-index problem has few variables, only requires 3N+2 inputs while the Markowitz mean-variance model requires N(N+3)/2 inputs. • The solution to the single-index model obtains a mean-variance efficient frontier with very similar values to the original Markowitz formulation when the investments are strongly related to the market index. It would not work as well if the portfolio covered a wide range of asset classes, resulting in poor relationships with a single index. www.swingtum.com/institute/IWIF

11. 3. Arbitrage Pricing Theory (Ross 1976) www.swingtum.com/institute/IWIF

12. APT is consistent with the EMT: true factor surprises Assumptions: • fk(t) is the surprise component of the factor (i.e. factor shock). Its mean is equal to 0. fk(t) are not allowed to be predictable from their own past – no autocorrelation is allowed; they must be unanticipated shocks. • fk(t) are not required to be independent of each other. • Asset-specific shocks εi(t) do not affect the expected asset return. • The factor realizations and asset-specific shocks are uncorrelated. • ri(t), fk(t), andεi(t) are not required to be normally distributed or follow any other distribution. • The number of assets N is much greater than the number of factors K. • All the loading factors βik are unknown constants to be determined. www.swingtum.com/institute/IWIF

13. Second Postulate: No Pure Arbitrage Opportunities www.swingtum.com/institute/IWIF

14. The Full APT Model www.swingtum.com/institute/IWIF

15. Comments to the APT • The APT is consistent with the EMT. It contained brilliant and novel ideas that brought modern portfolio theory another large leap. • Most of the follow-up developments on (linear) dynamic portfolio theory were extensions of the APT through testing various risk factors. • One of the drawbacks of the APT is that it is a financial mathematical theory, and unfortunately, the theory does not tell us which factors should be included in the multifactor model. • The biggest limitation of the APT is that the factor risk premiums are supposed to be constant. Investigators such as Connor and Korajczyk (1988) and Ferson and Harvey (1991), soon considered that the risk premiums might not be constant over time. This means that either the βik or the Pk or both may need to change with time in response to a set of exogeneous variables (endogeneous variables as well such as the concept of “situation”– Pan). www.swingtum.com/institute/IWIF

16. 4. Multi-Period Dynamic Portfolio Theory Multi-Period Portfolio Theory (MPPT) refers to a body of knowledge concerning conditional multi-period portfolio optimization under two assumptions: • Asset returns at each period of the horizon are not constant but vary conditionally with a set of exogeneous factors in accordance with some model; • There may be budget constraints between one time period and the next. Changes in wealth involve both the periodic rate of return on the underlying investments and the periodic capital consumption of a portion of the portfolio. Still, the way of modeling is in line with the APT: when investment returns are not independent and identically distributed over the investment horizon, the asset allocations at each time period (or each point in time) can be calculated as a linear function of macroeconomic factors in order to maximize the resulting terminal wealth. But new problems have arisen when MPPT is concerned, such as hedging demand – the difference in asset allocation between a dynamic and myopic portfolio policy. www.swingtum.com/institute/IWIF

17. Methodologies and Solution Tools for MPPT Problems • Most of the techniques for MPPT employ discrete-time formulations while there are several continuous-time approaches.References:- Merton (1969, 1971, 1973) - Samuelson (1969)- Klemkosky and Bharati (1995)- Brennen, Schwartz, and Lagnado (1997)- Brandt (1999), Aït-Sahalia and Brandt (2001), Brandt, Goyal and Santa-Clara (2001)- Barberis (2000)- Lynch and Balduzzi (2000)- Xia Yihong (2001)- Campbell, Chan and Viceira (2003)- Ziemba (2000-2007) • Solution tools include- Dynamic Programming- Stochastic Processes- Monte Carlo Simulation www.swingtum.com/institute/IWIF

18. 5. Direct Dynamic Portfolio Theory (DDPT) Further Significant Developments after MVPT, CAPM & APT, leading to DDPT: • Mean Absolute Deviation (MAD) Portfolio Optimization Model of Konno & Yamazaki (1991), and revised by Feinstein & Thapa (1993): • Downside-Risk Models- Downside risk is defined as a norm (L2 or L1) of the performance deviations below a target or benchmark value.- Semi-variance is L2 downside risk measure (Markowitz 1991, 1993; Markowitz, Todd, Xu & Yamane 1993)- Semi-MAD is L1 downside risk measure (Feinstein & Thapa 1993, Zenios & Kang 1993, Oberuc 2004)- Fitting of skewed distribution (Sortino & Price 1994, Sortino & Fosey 1996) www.swingtum.com/institute/IWIF

19. 5. Direct Dynamic Portfolio Theory (DDPT)[Brandt 1999; Campbell, Chan & Viceira 2003; Oberuc 2004] The key idea of DDPT is to formulate the asset allocations directly as linear functions of the exogeneous risk factors (we are considering discrete-time periods). This approach has several advantages: • It avoids the two-stage process of determining the performance expectations from the influential factors and then using these expectations to generate the asset allocations. • It also avoids the problem of building a consistent set of expectations based on the factors as required in the consistency of covariance terms of a correlation matrix in which each covariance term is independently developed based on a factor model. www.swingtum.com/institute/IWIF

20. An Integrated Formulation of DDPT Based on the concepts and approaches of MAD and Downside Risk Modeling of Konno & Yamazaki (1991), Feinstein & Thepa (1993), and Zenios and Kang (1993), Oberuc (2004) provides an integrated formulation of the objective function of DDPT, which he termed DynaPorte Model: Let the rate of return of the portfolio Rt less the threshold value Tt during one time period be broken into two components: a positive component above the threshold Vt and a negative component below the threshold Zt Rt – Tt = + Vt – Zt The Semi-MAD Objective Function (SMAD) can be expressed as The complete formulation can include leverage, lower and upper bounds of asset allocation, lower and upper bounds of leverage, the cost of borrowing plus purchase and sales transaction costs. The solution is a linear programming for minimizing the SMAD subject to all the constraints. www.swingtum.com/institute/IWIF

21. 6. Naturally Dynamic Portfolio Theory (NDPT) The key ideas of NDPT: • As a departure from the DDPT, we make the asset returns a general nonlinear function of the economical, fundamental and technical factors. The reaction of the asset returns to the factor surprises will not only depend on the magnitude of the factor surprises, but also be conditioned on the “situation” of the asset prices. • The concept of “situation” has its structure consisting of - Trends on multiple levels- Cycles of different periodicity- Seasonalities of multiple horizon- Possible surprising events of different types • A natural blending of active and reactive management: We keep unambiguous distinction between prediction, decision and action in the sense that even a portfolio change is suggested and decided by the theoretical model computation, the decision should be executed into an action until the market price signal has confirmed the validity of this decision.--- No Signal, No Trading! www.swingtum.com/institute/IWIF

22. Evidence for Why Factor Influences Must Be Conditioned on the “Situation” of the Asset Prices www.swingtum.com/institute/IWIF

23. Naturally Dynamic Portfolio Theory (NDPT) A possible method for this kind of active and reactive management can be imagined as • model the asset returns directly as nonlinear functions of all the risk factors; • solve for the optimal asset allocations for the next time period from the nonlinear model under the Semi-MAD objective function; • prepare for the changes of asset allocation together with scenario analysis; • use trend following mechanisms to trigger the action of asset allocation changes. www.swingtum.com/institute/IWIF

24. Log-Periodic Power Laws as a kind of Trend and Cycle for Naturally Dynamic Portfolio Management Discontinuation of LPPL www.swingtum.com/institute/IWIF

25. Intraday Patterns Must Be Conditioned on Daily Situation www.swingtum.com/institute/IWIF

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27. Golden Section of Day Session1:42pm www.swingtum.com/institute/IWIF

28. Golden Section of Day Session1:42pm www.swingtum.com/institute/IWIF

29. Volatility Breakout as a Signal for Trend Resumption or Reversal Stop Buy for going long Stop loss of long Stop loss of short Stop Sell for shorting www.swingtum.com/institute/IWIF

30. Trend Following with Stop Loss Trailed Stop loss of short Stop loss of short Stop loss of short www.swingtum.com/institute/IWIF

31. A Top-Down Algorithm for Multilevel Fractal Decomposition www.swingtum.com/institute/IWIF

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36. Trend Reversal and Trend Following with Stop Loss Trailed Enter Stop Loss www.swingtum.com/institute/IWIF

37. Enter Stop Loss www.swingtum.com/institute/IWIF

38. Stop Loss Entry Initial Stop Loss www.swingtum.com/institute/IWIF

39. Target Stop Loss Stop Loss Entry www.swingtum.com/institute/IWIF

40. Target Stop Loss Stop Loss Entry www.swingtum.com/institute/IWIF

41. The End of Intelligent Finance Component III – Dynamic Portfolio Management Thank you for your attention! www.swingtum.com/institute/IWIF