Simulation as a means of portfolio performance evaluation 143
and allowing some inferences about the impact of constraints. A
second set of simulations quantiﬁes the impact of portfolio design on
the observed tracking error of an international equity portfolio, allowing
the conclusion that holding constraints designed to limit tracking error
actually increase it. A third set of simulations tests the relationship
between maximum number of stocks allowed on tracking error for a
domestic equity indexed portfolio.
Despite increasingly sophisticated techniques for portfolio return and attribu-
tion analysis, there remain limits to the inferences that can be drawn from
the results they give. A single period attribution analysis, for example, can
identify which relative imbalances contributed to return variation from bench-
mark, but cannot say with certainty whether those imbalances and the results
to which they contributed were due to deliberate portfolio construction choices
or the result, essentially, of luck. For investors choosing between investment
managers and strategies, this lack of information can pose serious problems.
A positive active return can be achieved by an investment manager through
either luck or skill. If the result is due to skill, the investor can reasonably
conclude that this skill is likely to be repeated in future, and is therefore
worth paying active management fees. If, on the other hand, the result is due
mainly to chance, then subsequent active returns are as likely to be positive as
negative and the investor will prefer either to invest in an indexed portfolio
or to engage an investment manager who has demonstrated skill. Similar
logic applies to selecting investment strategies. Observed positive returns to
a strategy can be the result of either chance or strategy design and the ability
to distinguish between the two is imperative for selecting a strategy that will
yield positive results in the future.
Other aspects of portfolio performance that are often not adequately
addressed by conventional return and attribution analysis include:
• The suitability and investability of the benchmark.
• The impact of constraints.
• The contribution of mid-period trading activity.
An important feature of a benchmark is that it should be investable. In other
words, the investment manager should be able to buy all the assets in the
benchmark in benchmark proportions without incurring excessive transactions
costs. Not all benchmarks comply with this. Many investors work around
this problem by using peer groups as benchmarks on the basis that, being