Quantitative Finance

Modern Portfolio Theory has become pervasive due to its effectiveness, simplicity and formal foundation. However, with time, its assumptions have become less valid and its primary purpose, risk reduction, has become more difficult to acheive. Our goal here is to determine if one can make a slight change to the theory and still acheive:

Hellmut D Scholtz's paper takes a step in this direction by slightly changing Modern Portfolio Theory to better model "up" and "down" markets. He starts with the Single-index model (German) of Asset Pricing:
where: then includes the assumptions of Elton/Gruber's market model (6th Ed p152: cov(ei, ej) <> 0) and develops the "Multifactor" equation below:

The Multifactor approach shows promise especially when compared to Rouwenhorst's Momentum Model and several models in Chapter 9 of Elton/Gruber. In particular, a Multifactor portfolio gained 9.75% while the Dow Jones Industrial Average lost 9.2% during the August-September 2015 correction.

Demonstration of the multifactor model during the August-September 2015 correction

However, the standard questions plaguing all portfolio modeling approaches still remain: These are questions that we would be interested in discussing and hearing feedback on. The model is discussed in more detail in English and German. Another useful paper (German) discusses how to maximize Return while ensuring solvency. Readers with sound input on these topics are welcome to submit their comments here.