**“S****cience progresses funeral by funeral”
**

*–*

*Paul Samuelson*

**“****History is not a random walk it is mean-reverting”
**

*–*

*C. Kenneth Jones*

*Digital Portfolio Theory* introduces a new age of portfolio analysis and selection. The *Digital Portfolio Theory* model allows us to use memory to make timely portfolio decisions. *Modern Portfolio Theory* generated inappropriate decisions because it assumes that investors and financial markets have no time dependent memory. In *Modern Portfolio Theory* memory is not based on any time dimension. We estimate mean, variance and covariance and suppose that these will be the same regardless of time. In *Digital Portfolio Theory* risk and relationship are quantified based on time intervals. To satisfy our desire to profit we can adjust our risk exposures based on memory to find diversified portfolios that will benefit from forecast scenarios. Profitable portfolios are found using memory to adjust risk exposure. *Digital Portfolio Theory* represents a conceptual shift from the world of risk and return to the world of risk, return and time.

*Digital Portfolio Theory*** Adds a Time Dimension to the Theory of Risk.**

*Digital Portfolio Theory* (*DPT*) measures a security’s return with a 48 month digital signal. Each security’s variance is broken into 24 components, 8 are calendar related and 16 are non-calendar related. These describe the memory of the return process. Long term financial risk is broken into monthly, quarterly, 6-month, annual, 2-year and 4-year calendar related variance components. *Digital Portfolio Theory* uses linear constraints to control these portfolio variance components. Each portfolio calendar and non-calendar risk component is further separated into systematic and unsystematic parts. The *PSS* optimization package simultaneously performs optimal fundamental analysis.

**The Rise of Digital Portfolio Theory**

The modern portfolio theorist has been doing it the wrong way and that is the reason why *Modern Portfolio Theory* has not worked. *Digital Portfolio Theory* will massively change the process of portfolio construction and security analysis. The rise of *Digital Portfolio Theory* will bring about significant realignment in the investment business causing the emergence of new organizations and the decline of old ones. While *Modern Portfolio Theory* (*MPT*) examined portfolio risk and return, *Digital Portfolio Theory* is a scientific method of quantifying the relationship between return, risk and time. In *Digital Portfolio Theory* the definition of risk and return remain the same as in *Modern Portfolio Theory* but risk now appears in multiple time interval related dimensions.

*Digital Portfolio Theory* is a More Intuitive Linear Model

*Digital Portfolio Theory* while using digital signal processing is a more intuitive model than *Modern Portfolio Theory*. We all know that risk and the calendar are related. While *Modern Portfolio Theory* was trying to sell us a world of random walks *Digital Portfolio Theory* tell us that risks in Oct and Jan are higher and quantifies how much higher for each security. Additionally *DPT* measures risk based on 4-year Presidential periods as well as 2-year periods that with our short term memories we may have totally forgotten about. In fact *Digital Portfolio Theory* is much easier to use than *MPT*, just as the new digital electronic technology is easier to use than the analog counterparts. *Digital Portfolio Theory* is a completely linear optimization model. The cumbersome and confusing non-linear quadratic algorithm used in *Modern Portfolio Theory* is no longer necessary.

Using *Digital Portfolio Theory* the financial analyst rather than being left out of the loop is put squarely in charge with the ability to control the risk characteristics of his or her portfolio recommendations with great accuracy and with correspondingly great profits for the client. Now the analyst can construct a portfolio that is high or low in unsystematic risk while diversifying systematic risk completely to zero if required to take a market neutral position. Now the investor who prefers long term gains can eliminate short term calendar related risk. Now non-calendar risk can be eliminated or increased to suit the preferences of the investor. *Modern Portfolio Theory* simply allows us to restrain or limit total portfolio risk by diversification. *Digital Portfolio Theory* finds diversified portfolios with multiple controls for restraining portfolio risk. *Digital Portfolio Theory* allows us to conserve capital by avoiding one kind of risk and accumulate capital by taking on only that risk which we believe is appropriate.

The dismal market conditions of the past few years and the difficulty of preserving capital, let alone achieve superior performance has caused a growing inclination by portfolio managers to seek out new investment technologies with the power of the *Digital Portfolio Theory* model. Managers these days need to cover their ass and the best way is to benchmark themselves to a market index. Active portfolio managers are dying breeds as “closest indexers” hold on to their jobs whiles the hot stock pickers of the 1990s find themselves out on the street. Clients who thought they were paying for diversified performance are increasingly paying only for diversification. Many funds are moving to the multiple manager concept to diversify managerial skill, objective strategies, and technologies. The result is equivalent to an index fund with high manager fees and high turnover. Diversification and performance are increasingly viewed as distinct and separate investment services. The performance manager needs an innovative solution to be able to make a case for having skill that is worth the extra fee. To achieve higher performance a manager must be able to intelligently take on non-market risk. *Modern Portfolio Theory* does not allow you to independently control non-market risk so that positive alphas that may have been possible will be diversified away by high levels of systematic risk. *Digital Portfolio Theory* not only allows you to use a market neutral strategy by eliminating market risk but also allows calendar and non-calendar related risk to be controlled as well.

If a manager has identified an area where high positive alphas may be available, *Digital Portfolio Theory* allows the manager to construct an efficient portfolio to take advantage of that area. While many organizations are moving towards indexing there will always remain a market for active management to arbitrage market conditions to outperform an index strategy. Thus superior alpha gains need to be based on a rational analytic framework and *Digital Portfolio Theory* gives the portfolio manager the ability to eliminate or increase systematic risk, bet on calendar phenomenon, and adjust exposure to multiple fundamental variables.

*Digital Portfolio Theory* Benefits both Active and Passive Managers

*Digital Portfolio Theory* gives a more concise framework for both active and passive strategies. Active managers will still require correct judgment about future market conditions and areas of possible superior performance to set constraints to maximize profits in a diversified portfolio. Passive managers will require more access to broad diversification to allow the portfolio to weather any kind of storm and still match the performance benchmark. *Digital Portfolio Theory* is the best framework for performing both tasks because it quantifies risk in more dimensions than other models. One reason that today’s active managers achieve only mediocre performance is not from lack of ideas capable of outperforming the market. Instead it is the result of an inadequate mechanism by which they attempt to capitalize on their ideas. *Digital Portfolio Theory* provides the means to obtain the maximum profit from good ideas. Managers have been using inadequate tools. They don’t quantify the risks they are taking particularly with respect to time. *Modern Portfolio Theory*, for example, assumes all securities generate financial return processes that are random walks. Monte Carlo simulation and resampling techniques also assume a random walk world. Only *Digital Portfolio Theory* utilizes calendar based risk to take advantage of memory characteristics in return processes. Additionally *MPT* cannot distinguish the level of systematic versus unsystematic risk in the portfolio and therefore cannot control the level of market risk in the optimal portfolio.

*Modern Portfolio Theory* because it relies on random walks to define risk is like throwing darts at a collection of targets averaged over all past conditions. *DPT* because it utilized time dependent information allows us to aim our darts at a future target. The portfolio analyst provides the hunch or projection of the future and *DPT* provides the pattern recognition based on the maximum amount of information available and supplies the optimal diversified portfolio given the analysts insights. The *DPT* model makes the decision allowing the portfolio manager to utilize his or her expectations while relieving the portfolio manager of the task of remembering all past risks and relationships in time. Thus portfolio managers can make decisions based on judgment that will add value to their portfolios. You need the best technology available to be able to profit from weak forecasting ability and the *DPT* portfolio optimization engine is the first new investment technology to offer a framework and a solution.

*Digital Portfolio Theory* gives portfolio managers for the first time the ability to simultaneously examine as many as 8000 stocks. For this reason smaller less well know companies may be found along with big names in the portfolio to benefit from inefficiencies. One drawback of *DPT* is that since it quantifies long memory risk smaller companies that do not have sixteen year histories cannot be included in the alternative security universe. An advantage of *DPT* is that it is able to identify areas where long term trends may produce higher returns. The idea of measuring a 4-year beta that is independent of a 2-year beta, a one year beta, and a one quarter beta has not previously been implemented. Thus *DPT* offers significant long term benefit that can not be obtained using *Modern Portfolio Theory*, or the CAPM. Additionally, Dr. Jones’ stochastic portfolio network model carefully presented in his 1992 textbook “Portfolio Management” allows creative active managers to construct much more complex portfolio strategies that include arbitrage positions, and complex leverage and futures contract schemes.

**Imprudent Portfolio Recommendations**

Because *Digital Portfolio Theory* and the stochastic portfolio network are more quantitative models they will allow more accurate measurement of the performance of investment managers. Additionally, by adding a time interval dimension to risk, we can identify securities or portfolios that may have been recommended to an investor without regard to his or her holding period. Thus it would be imprudent to recommend to an investor with a four year holding period that he or she hold a portfolio with high 4-year risk. At the same time it might be reasonable to recommend a portfolio with high 3-month risk to this same investor provided he or she had indicated a desire for a high risk exposure. Conversely it would be a breach of professional duty to recommend a strategy that contains high levels of 3-month risk to a short term investor with a three month holding period, unless the investor was actually seeking 3-month risk exposure. On the other hand it may be prudent for this short term investor to hold a portfolio with a large amount of 2-year or 4-year risk.

*Digital Portfolio Theory* allows more carefully designed active strategies because it controls the level of market and non-market risk independently at 24 different time intervals and in addition controls fundamental factor risk. Such a high level of risk control will allow the optimal portfolio to be diversified to eliminate unwanted non-market risk while accurately exposing the portfolio to the type of non-market risk the active manager deems to be likely to achieve the highest alphas. In addition, it gives the manager the ability to generate alpha gains based on calendar or non-calendar risk.

**The Modern Portfolio Theory Struggle for Implementation**

The stock market euphoria of the 1960’s shortly after the arrival of *MPT* meant that a diversification strategy would deteriorate performance and the under experienced portfolio manager who specialized in hot stock picking were highly rewarded without regard to risk or timing. The slower market of the 1970’s brought investors back down to earth and searching for a new investment technology. The growing number of MBAs who were turned out in the late 70s and 80s were feed random walk, efficient markets, *Modern Portfolio Theory* and the Capital Asset Pricing Model (CAPM). Portfolio managers were told to turn to *MPT* as the solution to finding efficient diversified portfolios. But in the 1970s the computational intensity of the *MPT* nonlinear optimization algorithm and the slow computer processor speeds meant that *MPT* was not a practical investment technology.

It has been said that the investment profession has always been dominated by people from the right school and the right background. They are smart people but they all look and act the same. There resumes all read the same. It’s an environment where prestige and personal characteristics are very important. The investment community is made up of two groups; the computer people or quants and the investment people or analysts. There is a cultural gap between the two. In an article in Institutional Investor in 1970 Charles Ellis using the pseudonym Harold Holmes compares the two. “Computer people studied mechanical engineering at Penn, Investment people took English lit at Brown. Investment people went to graduate school at Harvard, the University of Virginia., and Stanford. Computer people went to MIT and Carnegie Tech. Investment people eat at expensive restaurants and are fat. Computer people do not eat at restaurants and are not fat.” One of the obstacles to adopting *MPT* has been fear. The investment people are afraid that the quants will actually find an investment methodology that will provide reliable superior performance. This fear is only growing as the poor financial markets of 2000 to 2002 have resulted in performance that has many investors screaming for some accountability. In fact while the quants will continue to become more quantitative they can never replace the judgment and forecasts of the good analyst.

**Asset Allocation as an Alternative to Modern Portfolio Theory**

In the 1980s the lack of any user friendly software to solve the *MPT* problem resulted in a shift to what Bill Sharpe called asset allocation. The solution to the *MPT* model was only possible for small universes of alternative investment (say 20). Larger solutions were not practical since *MPT* required a computationally intensive non-linear (quadratic) solution technique. The idea was to find an efficient mix of various assets classes. This problem was not difficult to solve and lead by Sharpe’s Asset Allocation Tools software package many software vendors began to market this strategy.

These conventional asset allocation packages depend on *MPT*. They cannot provide appropriate risk characteristics that reflect the judgments or forecasts of the portfolio manager. Asset allocation that uses *DPT* to quantify risk allows appropriate decisions of the portfolio manager to be programmed into the portfolio diversification optimization model. The resultant optimal portfolio will maximize return given that the manager’s outlook is correct. *DPT* will allow active managers to strategically allocate assets based on the purchase date and the time horizon of their holding periods. Because *DPT* is a long term model based on 4-year digital return signals estimated over 16 years of history, its decisions are useless to the analyst that trades daily or weekly. Using *DPT* trading cannot be carried on more frequently than monthly saving turnover costs resulting from trades based on random events. *DPT* allows rational asset allocation decisions to be made in every environment by using an exposure strategy that is appropriate to that environment.

**The CAPM is more Appealing than Portfolio Theory**

Most investment professionals who came up through the MBA education route were not quantitative enough to implement the *MPT* technology. When they were introduced to the CAPM, an equilibrium linear risk return relation it was an acceptable level of statistical sophistication. To go beyond linear regression to the nonlinear *MPT* optimization model was a stretch for their quantitative capabilities. As new levels of fiduciary responsibility and prudence were being proposed CAPM appeared to satisfy the need to clearly specify investment objectives and performance monitoring. Beta services and risk return ratios became common place. The growth of the index funds was justified by the CAPM and the efficient marketers.

One major drawback of the traditional CAPM is that Betas of individual securities are unrelated to time and therefore they are poor estimates of future Betas. In Jones’ calendar based CAPM presented in his 1992 textbook “Portfolio Management,” calendar betas can be used to get better forecasts of future betas based on the holding period of the investor. For example, it is not unusual for a security to have a high short term beta (3-month or 6-month) and at the same time have a low long term beta (2-year or 4-year) or visa versa. Older methods of trying to predict betas such as those employed by Barr Rosenberg based on trends in fundamental variables such as earnings growth or P/E may be misleading because the time horizon can not be precisely specified. Since all investors have some holding period in mind, individual stock selection without calendar betas often results in inferior performance.

**The MPT Approach was a One Size Fits All Model**

The *MPT* approach was a one size fits all model with the only variation being the investor’s total level of risk aversion. The *DPT* model offers more dimensions of risk as well as offering time dependent measures of risk while keeping the same mean-variance framework. Because investors often have different holding periods, one investor’s optimal portfolio will differ markedly from another investor with a different holding period and purchase date even when the two investors have the same risk tolerance. *MPT* because of its lack of time dimension recommends the same portfolio regardless of holding period. *DPT* offers a rigorous tool for information process recognition that when combined with the imaginative ideas of the analyst will result in continuous superior performance.

**The Tech Bubble**

In the 1990s when computer advances had finally made the practical application of *MPT* a real possibility prudent portfolio managers were again found sitting on the sidelines as the internet and tech bubble made hot stock pickers king. In fact by 1990 *Modern Portfolio Theory* was still relegated for use in the classroom as a pedagogical tool. In the 1990s less than 10% of investment managers were really utilizing the capabilities of *MPT* while 80% paid only lip service to the new portfolio management technique.

The 90s long bull market was dominated by market cheer leaders orchestrated by a host of new financial television networks like Bloomberg, CNN fn and CNBC, etc. Pretty faces with little or no investment education gushed smiling and winking comments. Every hour a new bull market analyst was interviewed for the hottest stock picks. Rarely was an investment Ph.D. consulted, or interviewed. The idea that investors should be advised by people versed in scientific scrutiny and quantitative testing seems completely beyond the programming capability of the financial networks. Many commentators did not even know why they thought the market would be rising. They have worked themselves up into such a bull market hype that they cannot fathom the idea of risk let alone risk with some time element involved.

In the early stages of the tech bubble, in 1992, Professor Jones’ book “Portfolio Management” was published by McGraw-Hill outlining the new digital financial technology. Even the most quantitative financial academics tuned out when they realized that they must now understand the basics of Digital Signal Processing (DSP). They knew instinctively that the revolutionary new digital technology of the 1990s was the province of engineering nerds. Financial analyst and academicians did not like to be challenged by the new digital technology and when required to comment reverted back to the efficient market rhetoric, or CAPM emanations without showing the least sign of any comprehensive. Calendar anomalies were a continuous topic in the financial economics, but how could risk have a time dimension as the new *Digital Portfolio Theory* showed? Yes, risk might change over time, but to have a time dimension that did not change with time was too much of a conceptual shift.

Researchers and security analyst often reacted to *Digital Portfolio Theory* with angry comments, insulted that such a revolutionary financial theory could have appeared without warning. In fact they had plenty of warning. Talking on their new digital mobile phones, watching digital images on their televisions and diverting there time to the new digital internet environment. They knew something had changed but how could this have any impact on the analysis of financial processes? Sure financial return time series were digital sequences but how could this be related to security analysis? In extreme cases rather than make any attempt at all to understand this new digital technology they preferred to question the character of the author and the capabilities of DSP. Digital Signal Processing was not a course taught in the economics department and was not a topic covered in econometrics. Introductory spectral analysis techniques were relegated to the last chapters of econometric textbooks. Some econometrics authors such as Hamilton for example, freely admitted that they did not understand the frequency domain. Digital Signal Processing was not even taught in engineering schools until 1987. Clive Granger who is often thought of as the expert in the field because he published many of the early spectral analysis stock market studies in the 1950s and 60s is not familiar with the new signal processing methodologies.

**Using DPT an Example Case**

The concept behind *DPT* is that there are many time dependent risks and we can control all of them simultaneously with a return optimization model given a forecast over our holding period. For example, suppose we believe there will be a strong January effect in a recovering market with falling interest rates and a high degree of uncertainty in international political and corporate governance environments. Before optimization to find the best portfolio we can adjust various levels of risk using the *Digital Portfolio Theory* constraints. First we lower our unsystematic risk to benefit from our forecast market upturn and to reduce our exposure to corporate governance problems. Next we reduce our exposure to non-calendar risk to protect ourselves from random events; environmental, political, terrorist, etc. Next we adjust levels of calendar risk to maximize exposure to the January effect. If we have a long term bull market forecast we may also increase our exposure to 4-year and 2-year risk. Finally we adjust our exposure to fundamental variable risk to focus our portfolio on small firms with high earnings growth and low P/E ratios. In each of these risk dimensions; systematic, calendar, and fundamental there are efficient frontiers. Because *DPT* is linear, the sensitively of the optimal portfolio can easily be examined in all three dimensions. Suppose our holding period is two years. After January we re-optimize the portfolio to maximize the benefit from the current situation given our current forecast.

**Reprogramming the Portfolio Manager**

*Digital Portfolio Theory* and the model of calendar based risk require re-education not only of the client to think in terms of time dependent risk but the analyst and portfolio manager as well. In fact the last group to fully internalize the concepts of calendar based risk may be the academic researchers. The financial journals have been so focused on the options pricing model and corresponding concepts of short term time varying risk that the idea of stationary time invariant calendar and long memory risk is very hard to understand for the academic researchers. While options pricing is a very eloquent and useful model that deserves the attention it has received, the average investor and the majority of institutional investors must focus their attention on economic investment value and growth. Calendar anomalies are real economic events. But researchers have been unable to identify their corresponding risk. The overall benefits to investors and the financial markets of moving from thinking in terms of short term transient risk to longer term stationary risk make the conceptual shift worth the cost of damaging the egos of a handful of PhDs. Reeducation may take time but for those who re-educate themselves sooner there may be significant rewards in the financial markets.

Recent empirical studies indicate that the equity risk premium will never return to the elevated levels of the 60’s or 90’s and will remain for the foreseeable future at a level of about 4.5 percent. Low returns will cause a growing demand for active portfolio analysts. This can already be seen in the growth of the hedge fund industry. As the demand for actively managed money grows there will be an increase in demand for technology that can capitalize on the judgment of the superior analyst. *Digital Portfolio Theory* offers not only the risk control mechanics to capitalize but the stochastic portfolio network model offers strategy formulation methodologies that will be invaluable tools. Analysts and portfolio managers who adopt these new investment techniques will be better able to provide clients with portfolios that reflect the client’s goals, expectations and holding period. Wall Street research firms who adopt the new *DPT* will be able to generate truly innovative, dependable, and insightful research that reflects a more quantitative and scientific approach.

**Conclusion**

As passive index strategies continue to expand particularly in large investment firms. These firms will be forced to lay off staffs of conventional analyst and portfolio managers. The remaining active managers will have to adopt a more high powered investment technology to consistently outperform the indexes. The new active portfolio managers may be paid based on a performance fee. Managers effectively utilizing the new *Digital Portfolio Theory* technology will become the real stars of the profession. How rapidly the *Digital Portfolio Theory* ideas will come into the forefront may depend on the financial markets themselves. In a bull market investors will again be content with putting their money in a portfolio of growth stocks and forget the advantages of the new investment technology. On the other hand, in a prolonged flat or falling market more and more attention will be drawn to the *Digital Portfolio Theory* model. In the long run weather it takes 10 years or 50 years *Digital Portfolio Theory* will become the mainstay of all portfolio management decisions.

**References**

Bernstein, Peter L., *Capital Ideas: The improbable Origins of Modern Wall Street, New York, Free Press, Macmillan, 1992.*

Fabozzi, Frank J., Francis Gupta, and Harry M. Markowitz, *The Journal of Investing*, Fall, 2002, p. 7-22.

Jones, C. Kenneth, *Portfolio Management: New Model for Successful Investment,* London, McGraw-Hill, 1992.

Jones, C. Kenneth, “Digital Portfolio Theory” *Journal of Computational Economics*, Vol. 18, No. 3, December, 2001, p. 287-316.

Markowitz, Harry M., “The Early History of Portfolio Theory 1600-1960” *Financial Analysts Journal*, July/August, 1999, p. 5-16.

Michaud, Richard O. “The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?” *Financial Analysts Journal*, January-February, 1989, p 31-42.

Rubinstein, Mark, “Markowitz’s “Portfolio Selection”: A fifty-Year Retrospective,” *Journal of Finance*, Vol. LVII, No 3, June 2002. p. 1041-1045.

Speidell, Lawrence S., Deborah H. Miller and James R. Ullman, “Portfolio Optimization: A Primer,” *Financial Analysts Journal*, January-February, 1989, p 22-30.

Sharpe, William F., “Microcomputer Perspectives: Asset Allocation Systems” *Financial Analysts Journal*, May-June 1985 p 10-75

Wells, Chris “Modern Portfolio Theory: Reprogramming the money manager, *Institutional Investor*, April 1977.

Weston, J. Fred “Programming Investment Portfolio Construction” *The Financial Analysts Journal*, Vol. II, No 2, May 1955, p. 51-55.

© Copyright 2002 C Kenneth Jones All rights reserved.

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