Modern Portfolio Theory and a regular guy's portfolio

I took a course at UNCC called Statistical Techniques in Finance. There was enough math to make strong men weep, but there was a gem of a section about Modern Portfolio Theory (MPT). A quick search on MPT will tell you that Harry Markowitz got a Nobel Prize for the theory. 

Here's a quote from Wikipedia about MPT:

The fundamental concept behind MPT is that the assets in an investment portfolio should not be selected individually, each on its own merits. Rather, it is important to consider how each asset changes in price relative to how every other asset in the portfolio changes in price.

So I started from a list of assets from Agora Financial (their Focus stocks for 4Q14). I normally have a dilemma in trying to figure out how to buy these stocks: Fixed dollars of each? Fixed percentage of each? Look for the best story? The lowest risk? A high dividend? 

The list, usually about a dozen, is picked by all different money managers with quite different outlooks. By design, some are high-yield stocks, some are pharmaceuticals, some are military, some are undervalued. 

Instead of picking and choosing, I let the math do the work for me. I had Google Finance create a spreadsheet that retrieve the past 520 trading days, had the market return (SPX) as one of the stocks, and then had Excel line up the prices so that they were all the same date. 

Then I ran the correlation function in Excel, which returns a number between 1.0 (perfect correlation) and -1.0 (inversely correlated). In my Focus set, the maximum correlation was 0.27 and the minimum was -0.197.

MPT says that risky, uncorrelated stocks will give you a better return with a lower proportional risk than unrisky, correlated stocks. (By the way, when I say risk, I am referring to the square of the Standard Deviation of the return.)

Then I took the correlations and their log returns and tossed the numbers into Matlab. The program I ran did some optimization of risk to return, using linear programming (a branch of operations research). 

Anyway, here is what Matlab said the optimal weighting would be.

        Ticker      Original weight     name      
        SPX         13.66%              Standard & Poor   
        SE           8.62%              Spectra Energy    
        ICON         8.61%              Iconix    
        RYAM         8.33%              Rayonier      
        AKG         10.97%              Asanko Gold   
        SNMX        11.72%              Senomyx   
        EVER-A       7.99%              Everbank      
        INFI         5.18%              Infinity Pharma   
        NLNK         8.90%              NewLink Genetics      
        SRPT         3.86%              Serepta Therapeutics      
        CRY          7.52%              Cryolife      
        CMRX         4.64%              Chimerix       

The results were surprisingly good.