5) Validation: 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.