As mentioned above, we applied out of
sample testing in order to evaluate the performance of the
optimal tracking portfolio. To do so, we calculated two
tracking errors based on the data samples from the period
03/03/2004-03/03/2005. The first tracking error E1 is directly
related to the volatility of the tracking error and is based on
an estimation of standard deviation (1). It is written as where rP and rB are the arithmetic mean of the returns of
tracking portfolio and the benchmark portfolio respectively.
The second out-of-sample tracking error E2 is defined as
the average of absolute differences in the returns rP (t) of
the index portfolio and the returns rB(t) of the benchmark.
According to [29], E2 can be stated as.