For this paper, you are going to expand on one of the discussion forums that you have already written. You will choose one of the topics from discussion forums 1-4 and elaborate on the current trend in this area.

Your paper should include an introduction of the topic that includes a historical definition based on literature, a discussion of the current research in the field (last 5 years only), and a section that addresses future questions that will need to be addressed and/or explored in research.

This paper should draw on a minimum of ten substantial journal article resources and will be 10 to 12 pages in length (not including the title page, abstract, or reference pages) observing all APA style conventions.

You may use any articles or writings that you wrote about in your previous discussion forums in this.

I selected to do my functional paper on portfolio optimization. Below is my previous discussion post. You can expound upon

Portfolio Optimization attempts to answer the question:How should an investor allocate funds among the possible investment choices?  Economist Harry Markowitz first developed the theory of portfolio optimization in 1952.  Markowitz’s theory emphasized the importance of portfolios, risk, the correlations between securities, and diversification. First, Markowitz quantified return and risk of a security, using the statistical measures of its expected return and standard deviation. Then, Markowitz suggested that investors should consider return and risk together and determine the allocation of funds among investment alternatives on the basis of their return-risk trade-off. Markowitzs theory, that sound financial decision-making is a quantitative trade-off between return and risk was revolutionary. First, it posited that one could make a quantitative evaluation of portfolio return and risk jointly by considering security returns and their co-movements (Kolm, Ttnc, & Fabozzi, 2014). It is based on the idea that a portfolios riskiness depends on the correlations of its constituents, not only on the average riskiness of its separate holdings (Kolm, Ttnc, & Fabozzi, 2014). Second, it formulated the financial decision-making process as an optimization problem. In particular, the so-called meanvariance optimization (MVO) problem formulated by Markowitz suggests that among the infinite number of portfolios that achieve a particular return objective, the investor should choose the portfolio that has the smallest variance (Kolm, Ttnc, & Fabozzi, 2014).

Although Markowitzs modern portfolio theory revolutionized portfolio construction it took many years for portfolio managers to start applying it to manage real money. In real world applications there are many concerns associated with its use, and portfolio optimization is still considered by many practitioners to be impractical to apply. The portfolio optimization model has limited impact in practice because of estimation issues when applied to real data. Numerous studies have been conducted subsequently to address these limitations. Transaction costs make the portfolio optimization problem difficult to solve when the number of assets is greater than two, especially in a dynamic setting. Brown and Smith (2011) calculated portfolio optimization with transact cost using several easy-to-compute heuristic trading strategies that are based on optimizing simpler models. Using a dual approach for examining the quality of these Brown and Smith (2011), found that performance of the heuristic strategy is very close to the upper bound, indicating that the heuristic strategies are very nearly optimal (Brown & Smith, 2011).  Over estimation is also a problem with portfolio optimization.  Although, Bai et al. (2009), proposed a bootstrap-corrected estimator to correct the overestimation, there is no closed form for their estimator.  Ban, Kaouri, & Lim (2016), conducted a study to circumvent this limitation using explicit formulas for the estimate of the optimal portfolio. In the study they were able to prove their proposed closed-form return estimator is consistent and outperforms traditional estimators and the bootstrap-corrected estimators (Ban, Kaouri, & Lim, 2016). They were able to obtain an explicit formula for the variance of the improved return estimate.

In summary Markowitzs modern portfolio theory was groundbreaking for its day.  It is a seminal piece of work in finance but does have limitations in practical application.  These  limitations can be overcome to get optimal results.

References

Ban, Gah-Yi., El Karoui, Noureddine., Lim, Andrew. (2016). Machine Learning and Portfolio Optimization. Management Science. 64(3), 983-1476. https://doiorg.ezproxy.liberty.edu/10.1287/mnsc.2016.2644

Brown, D. B., & Smith, J. E. (2011). Dynamic Portfolio Optimization with Transaction Costs: Heuristics and Dual Bounds. Management Science, 57(10), 17521770. doi: 10.1287/mnsc.1110.1377

Kolm, P. N., Ttnc, R., & Fabozzi, F. J. (2014). 60 Years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234(2), 356371. doi: 10.1016/j.ejor.2013.10.060