it says in the text book that optimization requires preidoic trading to keep the risk charactersitcs of the porfolio lined up with those of the index being tracked…(can someobdy explain what they mean by risk characteristics?) AND
and why then the predicted tracking risk typically understates actual tracking risk?
THANK YOU
risk characteristics are some aspect of returns which can be attributable to a factor , such as growth style or volatility or market sensitivity . This should be unbiased , measurable , unambiguous etc.
Optimization requires modeling the risk characteristics (the characteristics of the B/m that most likely cause the largest movements in value - i.e. capitalization, liquidity, P/E valuation to name afew possibilities)
This modeling is an approximation based on past correlations between a particular security and the B/m. These are derived using some factor model such as:
R = B1*F1 + B2*F2 + … + Bn*Fn
where each F is a different factor and each B is the correlation coefficient.
Since this factor model is using historical data we cannot assume it holds in the future. In fact, quite often it does not - at least not as precisely as it had in the past. incorporating the new return information as time passes the correlation coefficients are bound to change which indicates that the previous information did not model the portfolio as acurately as the model had predicted.
since the model had originally predicted that the securities in the portfolio optimally tracked the B/m, it had a low predeicted tracking error. However, measuring the ex-ante tracking error would show that the tracking was worse than predicted (predicted tracking risk understates actual tracking risk).
Does this help to answer your question?