The optimal risky portfolio asked me to shortsell the market for -1.6081 and invest 280.1% of my investable wealth in the active portfolio. Within the active portfolio itself, among 16 different tickers that I chose, my optimal weights were to invest in Kraft, General Mills, Visa, and Walmart.
Running a regression of Risky Portfolio HPR against Market Portfolio HPR, we obtain the below line fit plot. Though the fit may not look all that bad, it is actually quite low with a R^2 of roughly 0.3. This does not come as too big of a surprise, though, as the risky portfolio utilizes active portfolio management that itself aims to break from the market. Also, the 16 tickers I used in this exercise could not possibly reflect all of the movements of the S&P market index. To extend our analysis of the relationship between the risky portfolio and market portfolio, we consult the following graph modeling their quantitative movements over roughly the past four months. As one would expect, the Risky HPR fluctuates a lot wilder than the Market HPR does. However, it does not consistently stray in any one direction away from 0%. Interestingly, looking at the dollar paths tells us a completely unexpected story. Usually we would expect an actively managed, risky portfolio to generate higher returns (barring transaction fees) than a passive, market portfolio. Yet here, we see that the dollar path of the market in fact outgrows the dollar path of the risky portfolio. In fact, by the end of four months, $1 invested in S&P grows to $1.10 whereas that same dollar invested in our risky portfolio grows only to $1.04. Of many factors that might describe the reason for this phenomenon, an appropriate one might just be that high variance and low R2 with the market caught up to this portfolio. The low dollar path return may just be the consequence of several unlucky turns