Constraints of Post-Modern Portfolio Theory - Outline Example

Post Modern Portfolio Theory: Breaking free of the constraints of the Modern Portfolio Theory Modern portfolio theory (MPT) established a formal risk-return structure that evaluated how rational investors make decisions through quantifying investment risk. The theory initially developed by Harry Markowitz (1959) proposed that investors expect to be compensated in terms of return for the risk they bear when investing. The pith of the argument of the MPT and its extended variant, known as the Capital Asset Pricing Model (CAPM) was that a set of portfolios with maximum returns for given risks minimum risk for given returns (thus identified as being efficient) exist to create what was called the efficient frontier. The decision making process was in essence an optimization exercise in the mean-variance plane with mean representing the expected returns and variance of return representing the associated risk of the portfolio (Rom & Ferguson, 1993). However, it is pertinent to note that these models were developed in essence as equilibrium models and the objective was to identify the optimal investment simultaneously for all participants in the market for investment. Thus, when applied to address the question of asset allocation, as the present practices are, the MPT and CAPM are likely to have significant shortfalls (Swisher & Kasten, 2005). In fact, the following shortfalls were identified by the founders themselves: “Under certain conditions, the mean-variance approach can be shown to lead to unsatisfactory predictions of behavior. Markowitz suggests that a model based on the semi-variance would be preferable; in light of the formidable computational problems, however, he bases his analysis on the variance and standard deviation.” (Sharpe, 1964) The MPT is based on the assumption that the variance or alternatively standard deviation of the returns from the portfolio can serve as an effective proxy of the associated risk of investing in the portfolio and further it assumes that the returns from all assets and portfolios to be normally distributed implying thereby that the normal distribution can adequately capture the movements of the returns. Thus, the approach is constrained by adopted measures of risk as well as return which are not always likely to represent the market realities (Rom & Ferguson, 1993). While on one hand, using variance or standard deviation of the returns as a measure of risk can only be justified provided the investor feels the same way about returns exceeding expectations as she does about returns failing to meet them, assuming returns to be normally distributed leads to overestimation of risk for returns that are majorly above expectations and underestimation of risk for returns predominantly below expectations on the other. Investors prefer above expected returns or upside returns compared to below expected returns or downside returns. But the MPT fails to reflect this due to the symmetry inbuilt due to using standard deviation and normal distribution to map risk and returns (Swisher & Kasten, 2005). Thus, standard MPT modeling for portfolio selection and asset pricing leads to distortions of reality. Thus, it is understood that often portfolio choice based on the MPT can lead to inefficiencies. In fact Sharpe’s comment pointing out Markowitz suggestion to generate further realistic results by using semi-variance reflects this understanding. However, progress in this direction was not forthcoming at that stage due to the computational difficulties associated. However, present day access to advanced computational techniques along with the ensuing advancements in portfolio theory particularly regarding the realistic representation of risk combined have expanded the fundamental ideas of the MPT into what is known as the Post-Modern Portfolio Theory (PMPT). The most important feature of PMPT is the relaxation of the assumptions that generated the symmetries which made the MPT predictions deviate from market realities. The PMPT incorporated investors’ preferences for upside variability, i.e., variations of returns above expected or target returns over downside fluctuations in returns as well as assumed that the investment returns followed a triple parameter log-normal distribution which was a significantly improved approximation of reality. Since only downside volatility is likely to be an investors; primary concern when considering risk of any investment, the PMPT since its inception has pursued the objective of generating measures that capture downside risk. And the objective is to optimize the identified downside risk through portfolio selection. Downside risk is identified based on three parameters related to the exhibited movement of the returns. The first step is to recognize that risk is a subjective notion and essentially is the possibility of the returns falling short of some minimum acceptable return or targeted return for the investor. The Downside Frequency is the first parameter and it captures how frequently returns fall short of the minimum acceptable return. Next, the mean of the downside deviations are measured from observations. In essence this measures the average magnitude of the below minimum acceptable return deviations. Finally the downside magnitude is calculated. This represents the possible maximally worst outcome with the return being located below the minimum acceptable return at the 99th percentile (Swisher & Kasten, 2005). A formula that incorporates all three of these statistics is then used finally to capture the downside risk of the investment. Although the final outcome would be a percentage that possibly maybe similar to the standard deviation the fore mentioned fundamental differences make the downside risk parameter a much more realistic measure of risk that investors find to be relevant. The PMPT provides alternatives to the alpha, beta and the Sharpe ratio statistics that serve as decision making parameters for the over-benchmark performance, relative risk compared to bench mark risk and finally the excess return per unit of risk, respectively in the MPT. Alpha is replaced by Omega excess which is essentially the measure of expected returns above the benchmark (minimum acceptable return), Beta is replaced by a ratio of actual downside risk to benchmark downside risk and the Sharpe ratio is replaced by the Sortino Ratio which measures excess returns per unit of downside risks. Thus what emerges is that the PMPT has expanded the initial MPT framework so that the earlier unrealistic assumptions which led to inefficient and unrealistic results have now been relaxed and improved measures of risk have been incorporated to make the model’s resemblance of reality of the investment market enhanced to considerable degrees. The previous constraints have thus been broken free of and a tool box that facilitates much greater approximation of the asset pricing market as well as investors behavior has now been developed in the form of the continuously expanding PMPT. References: Rom, B. M. and K. Ferguson. "Post-Modern Portfolio Theory Comes of Age." Journal of Investing, Winter 1993 Sharpe, W.F., (1964) Capital Asset Prices: A Theory of Market Equilibrium under Considerations of Risk, The Journal of Finance, XIX, 425 Sortino, F. and H. Forsey "On the Use and Misuse of Downside Risk." The Journal of Portfolio Management, Winter 1996. Sortino, F. and L. Price. "Performance Measurement in a Downside Risk Framework." Journal of Investing, Fall 1994. Swisher, P. and Kasten, G.W., (2005) Postmodern Portfolio Theory, FPA Journal, September 2005 Read More