66 Optimizing Optimization
application of this enhanced functionality to stabilize optimization results. In par-
ticular, a further area of research is explicit risk budgeting via constraints.
In the context of a structured factor risk model, this can be implemented as
separate constraints on Factor Contributions to Total Factor Risk or to Total
Risk. In addition, it would be possible to separately constrain asset-specific risk
contribution to Total Risk.
Constraining Contributions to Total Risk enables the user to dictate where
exposure to risk is taken, in essence “ budgeting ” risk exposure. This is useful
in hedging risk exposure in areas where alpha expertise is not claimed, e.g., if
the manager is taking a systematic bet, the contribution to risk constraint to the
relevant risk factor can be loosened. Likewise, if the manager is making asset-
specific bets, exposure to asset-specific risk can be expanded. This is different
from the traditional factor exposure constraints in that it is constraining the
resultant (output) contribution to risk, not the input exposure. In addition, this
procedure tells the user a priori whether the goal is feasible, eliminating the need
to fiddle with inputs in vain attempts to reach an impossible solution.
Alternatively , if the risk model structure does not represent a relevant catego-
rization upon which to levy risk constraints, it is possible to use any external,
arbitrary categorization system and apply risk constraints to each category. For
example, if the risk model does not contain sector exposures, and it is impor-
tant to budget for risk at the sector level, it is possible to levy risk constraints
for each of the relevant sectors of the type in Equation (3.4). Effectively, this
means splitting the portfolio into several subsections corresponding to sec-
tor classifications and constraining the tracking error of each of those. This
would be useful in producing a more stable result by ensuring that risk is taken
evenly across the investment universe. For example, if the alphas are skewed
toward the technology sector, such an approach would prevent the optimizer
from loading up on volatile technology assets at the expense of volatile assets
in other sectors, in effect forcing the optimizer to diversify within sectors as
opposed to across sectors.
3.5 BITA GLO(TM)-Gain/Loss optimization
3.5.1 Introduction
Mean – variance investing is arguably the most popular framework to construct
optimal portfolios. However, its consistency with expected utility maximiza-
tion requires that returns are normally distributed and/or the investor’s prefer-
ences are quadratic.
First , the assumption of normality in return distributions is breached for
many asset classes. Second, an investor’s utility might rather be driven by the
impact of expected gains and losses than by expected return and variance. This
is strongly supported by experimental evidence in Kahneman and Tversky
(1979). Considering expected gains and losses (i.e., expected returns relative