  In this paper, we study the behavior of information ratio (IR) as determined
by the fundamental law of active investment management. We extend the classic
relationship between IR and its two determinants (i.e., information coefficient
and investment "breadth") by explicitly and simultaneously taking into account
the volatility of IC and the cost from portfolio turnover. Through mathematical
derivations and simulations, we show that - for both mean-variance and quintile
portfolios - a turnover-adjusted IR is always lower than an IR that ignores the
cost from turnover; more importantly, we find that, contrary to the implication
from the fundamental low but consistent with available empirical evidence,
investment managers may improve their investment performance or IR by
limiting/optimizing trade or portfolio turnover.
