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Seems pretty simple to me. If it is wealth management, it is to make sure that others (stock brokers, private wealth management specialists etc.) do not extract my wealth in return for providing either bad or no advice.
Explore the costs of mean variance optimization when following a strict adherence to modern portfolio theory (MPT). For example, mean-variance optimization in MPT assumes a normal return distribution, even though many asset classes exhibit positive excess kurtosis (i.e. fat tails problem). Thus, a mean-variance optimization techniques under a normality assumption may cause investors to allocate too much to risky asset classes. Perhaps, you could look at the costs of assuming normality in the return distribution and improve about MPT by using model that better quantify down-side risk.
I appreciate both of your responses. I am very interested in researching how to improve about MPT by trying to better quantify down-side risk. However, I am not that familiar with the subject (I'm a USC Honors College freshman with a strong background in calculus/statistics so I could probably wrap my head around the any math involved, and I've been actively learning from a few bankers/professors and use Aswath's website a few times a week and auditing an upper level finance class here and already read 2 corp. finance books) but I would like to learn more about MPT to have a decent background prior to researching. I'll spend at least 300 hours during the process so don't worry overloading me. How's this for a book to learn about MPT first, its called Modern Portfolio Theory & Investment Analysis- heres a link to verify which one it is http://www.amazon.com/gp/product/0470050829/sr=8-1/qid=1301975132/ref=olp_product_details?ie=UTF8&me=&qid=1301975132&sr=8-1&seller= Does this look like a user friendly book that i'll will help give me the background necessary to peform the research you suggested? Any other thoughts? -Thanks for the interesting idea!
If you are strong in statistics, I really don't see any textbook on MPT not being "user friendly." The core of MPT really doesn't extend much further than correlation and standard deviation. That books seems to touch on most of the core topics of MPT. You should probably search for some articles on the topic at your school's library.