TABLE OF CONTENTS In this section we provide empirical examples of applications of optimization from ordering information using the linear, centroid, optimized linear and optimized centroid algorithm. Throughout this section we look to quantify the absolute and relative performance of the optimized centroid portfolios to portfolios constructed using the other methodologies. In particular, we would like to study the significance of incorporating covariance information into portfolio formation, especially as it pertains to improving performance relative to methods that omit this information. Since in practice many portfolio managers who use ordering information ignore covariance information, we believe that an important part of this work involves examining the extent to which using this method improves investment performance over existing methods. Put simply, we have proved the theoretical superiority of the centroid optimization method. Now we examine its practical significance.
We take two approaches to this, one based on studying an actual portfolio sort on real historical data, and the other based on simulations. In both approaches we create backtests over a period of time, and for each time within the backtest period produce portfolios using four different construction methods from a single sort. The four methods we look at are the optimized and unoptimized versions of the linear and centroid methods, as described above.
To evaluate performance we examine the information ratio that is, the annualized ratio of the sample mean and sample standard deviation of daily returns, of each time series derived from returns using the different...
