7.1 The coordinated max-median rule for portfolio selection

Motivation

The max-median rule for portfolio selection

Previous research suggests that there exist strategies that, when implemented over a long period of time, might provide higher returns than overall market performance (see, e.g. [1]). One of these strategies, namely the “ Max-Median Rule ”, was investigated by Thompson and Baggett (see [2]), and served as a general motivation for this research. By selecting a handful of stocks, according to some robust criterion (e.g. the median) and rebalancing consistently without straying away from the strategy, virtually any investor could easily manage his or her portfolio quite reasonably. Over the long-haul, this strategy would provide decent returns when compared to a benchmark index (e.g. the S&P 500 Index). It is worthwhile noting that in strategies such as these, time is a major consideration (and one which investors can control, e.g. when investing retirement funds such as a $401K$ ), and that these methods do not constitute day-trading strategies, and should be adhered-to consistently over a given period.

Several salient points of this motivating investment strategy are:

1. It is accessible to any individual investor.
2. Over an extensive time-period for which it was examined (i.e. 37 years - 1970 through 2006) it outperformed the S&P 500 Index by about 50%.
3. It was slightly more volatile on a yearly-basis. An effect that can, to a reasonable extent, be used to an investor's advantage in “longer”-term investment strategies.

These points clearly serve us as a motivation for further investigation and potential improvements. In particular, through recognizing that the existing strategy, albeit well-performing, is inherently a “one-at-a-time” strategy and therefore does not capture any correlation-related dynamics through its selection criteria.

Lastly, we were also motivated to investigate (at least initially) equally-weighted portfolios. An interesting finding (see, e.g. Wojciechowski, Baggett, and Thompson [3]), is that “for the 33 years from 1970 through 2002, not simply a flukish few, but a staggering 65 percent of the portfolios selected randomly from the 1,000 largest market cap stocks lie above the Capital Market Line (CML).” Also, it has been shown (see [2]) that any individual who invested equally in the S&P 500 Constituents (time period of 1970 through 2006) would have made, on a yearly average, 13.7%, as opposed to 8.9% with a competing market-cap weighted strategy. Both of these empirical realities make, at least preliminarily, a case against considering long-term market-cap weighted strategies.