When implementing the
Poor Man's Hedge Fund as a small portfolio of companies that, from
statistical analysis of prior returns, appear to generate their profits by
exposure to the Dynamic
Trading Risk Factor, I arbitarily decided to choose an equally
weighted portfolio of just five companies. This choice was made without deep
thought other than the idea that managing a large, weighted, portfolio is
difficult for a small investor, and the whole point of the idea was to provide
a vehicle suitable for a small investor.
Not all financial stocks have returns that are explained by this risk factor and
in fact, some members of the
XLF are very poorly explained by it. So a legitimate question to ask is
how the tracking of a composite portfolio behaves as a function of the number
of assets included within it?
The chart shows the result of ranking individual regressions of all current
XLF member companies onto the dynamic trading risk factor. We rank the 80 index
members by their individual regression R²'s and then build a
portfolio including an equal weighted combination of the first stock; the first
two stocks; the first three stocks; etc., all the way to the entire index
membership. We then regress all of those portfolios onto the same risk factor
and plot the portfolio regression R² for all of these possible
portfolios.
There are two competing forces that describe these portfolio's relative
performance. The first is the fact that the larger the portfolio we build the
less idiosyncratic risk it will contain and the more systematic risk,
in proportion, will be left. This is basic factor theory at work, and it drives
us to build as large a portfolio as possible, as that will produce the purest
expression of the risk factors. The second is the fact that the lesser ranked
stocks have proportionately less exposure to the dynamic trading risk factor,
and more to other factors such as general market risk. Thus the more of these
stocks we include in the portfolio the more we dilute its tracking of the risk
factor we seek exposure to and replace it with general market performance.
Between these two extremes should lie an optimum, which seems to be at about
eight stocks — although, our arbitary choice of five is not so bad.