How Many Independent Bets Are There?

We discuss a robust alternative to the ex-post decomposition of a portfolio into the fundamental law co-efficients using statistically estimated breadth. The breadth of a market provides a measure of the number of independent bets available to the investor. We use the Keiser-Gutman stopping criterion to select the integer valued effective dimension eigenvalues greater-than or equal to 1. Such a method for the estimation of breadth relies critically on the appropriate estimation of the covariance matrix of price fluctuations (returns). In a emerging market such as South African it is not surprising to find that the breadth is low because of market concentration, exposure to the global commodity cycle and currency volatility. The implications of refocussing investment objectives on effective dimensionality are further discussed.